10 Very Similar Practice Sets JEE Main PCM 9389461782, 9789389461787

Citation preview

Telegram @unacademyplusdiscounts

Join Us on Telegram for More Such Books https://telegram.me/unacademyplusdiscounts

Join us from the above link or search ''unacademyplusdiscounts'' in Telegram

Telegram @unacademyplusdiscounts

Join Us on Telegram for More Such Books https://telegram.me/unacademyplusdiscounts

Join us from the above link or search ''unacademyplusdiscounts'' in Telegram

Telegram @unacademyplusdiscounts

Join Us on Telegram for More Such Books https://telegram.me/unacademyplusdiscounts

Join us from the above link or search ''unacademyplusdiscounts'' in Telegram

Test-1

1

VERY SIMILAR

PRACTICE TEST 1 Time : 3 hrs.

1.

2.

3.

4.

PHYSICS The moment of inertia of a uniform disc about an axis passing through its centre and perpendicular to its plane is 1 kg m2. It is rotating with an angular velocity 100 rad s–1. Another identical disc is gently placed on it so that their centres coincide. Now these two discs together continue to rotate about the same axis. Then the loss in kinetic energy in kilojoules is (a) 2.5 (b) 3.0 (c) 3.5 (d) 4.0 In the given figure, the equivalent capacitance between points A and B is (a) 1.5C (b) 2C (c) 3C (d) 6C An ideal gas is taken through a cyclic thermodynamic process through four steps. The amount of heat involved in these steps are Q1 = 5960 J, Q2 = – 5585 J, Q3 = – 2980 J and Q4 = 3645 J respectively. The corresponding quantities of work involved are W1 = 2200 J, W2 = – 825 J, W3 = – 1100 J and W4 respectively. Find the value of W4. What is the efficiency of the cycle ? (a) 3.33% (b) 6.76% (c) 5.91% (d) 10.83% Three long, straight parallel wires, carrying current, are arranged as shown in figure. The force experienced by a 25 cm length of wire C is. (a) 10–3 N (b) 2.5 × 10–3 N (c) zero (d) 1.5 × 10–3 N

Max. Marks : 300

5. Of the following quantities which one has the dimensions different from the remaining three? (i) Energy density (ii) Force per unit area (iii) Product of charge per unit volume and voltage (iv) Angular momentum per unit mass (a) (i) (b) (ii) (c) (iii) (d) (iv) 6. A magnetic flux through a stationary loop with a resistance R varies during the time interval t as f = at(t – t). What is the amount of heat generated in the loop during that time ? 2 3 a 2τ 3 a 2τ 3 a2 τ3 (c) a τ (d) (a) (b) 4R 3R 2R 6R 7. A block of mass m1 lies on a smooth horizontal table and is connected to another freely hanging block of mass m2 by a light inextensible string passing over a smooth fixed pulley situated at the edge of the table as shown in the figure. Initially the system is at rest with m1 at a distance d from the pulley. The time taken for m1 to reach the pulley is m2 g 2d(m1 + m2) (a) (b) m1 + m2 m2 g 2m2d 4d(m1 + m2 ) (d) (m1 + m2) g 3 gm1 8. Two identical charged spheres suspended from a common point by two massless strings of length l are initially a distance d(d < < l) apart because of their mutual repulsion. The spheres begins to leak from both the spheres at a constant rate. As a result the charges approach each other with (c)

2

Very-Similar Practice Tests

a velocity v. Then as a function of distance x between them (a) v ∝ x–1/2 (b) v ∝ x–1 1/2 (c) v ∝ x (d) v ∝ x 9. A stone of mass 2 kg is projected upward with kinetic energy of 98 J. The height at which the kinetic energy of the stone becomes half its original value, is given by (a) 5 m (b) 2.5 m (c) 1.5 m (d) 0.5 m 10. In a series LCR circuit, different physical quantities vary with frequency u. Which of the following curves represent correct frequency variation of the corresponding quantity? y (I) (III)

14. The surface energy of a liquid drop is u. It is splitted into 1000 equal droplets. Then its surface energy becomes (a) u (b) 10u (c) 100u (d) 1000u 15. 2 kg of ice at –20°C is mixed with 5 kg of water at 20°C in an insulating vessel having a negligible heat capacity. Calculate the final mass of water remaining in the container. (Given : Specific heat capacities of water and ice are 1 cal g–1 °C–1 and 0.5 cal g–1 °C–1 respectively. Latent heat of fusion of ice = 80 cal g–1) (a) 7 kg (b) 6 kg (c) 4 kg (d) 2 kg 16. To get an output Y = 1 from circuit of figure, the inputs must be

(IV) (II) 

(a) Curve I for R and curve III for XL (b) Curve II for current I (c) Curve III for XL and curve IV for R (d) Curve IV for XC 11. The wavelengths and frequencies of photons in transitions 1, 2, and 3 for hydrogen like atom are l1, l2, l3; u1, u2 and u3 respectively. Then

(a) u3 = u1 – u2 (c) λ3 =

λ1λ2 λ1 + λ2

(b) l3 = l1 + l2 (d) υ3 =

υ1υ2 υ1 + υ2

12. A lift is tied with thick iron wire and its mass is 1000 kg. The minimum diameter of the wire if the maximum acceleration of the lift is 1.2 m s–2 and the maximum safe stress is 1.4 × 108 N m –2, is (Take g = 9.8 m s –2) (a) 0.00141 m (b) 0.00282 m (c) 0.005 m (d) 0.01 m 13. Resolving power of reflecting type telescope increases with (a) decrease in wavelength of incident light (b) increase in wavelength of incident light (c) increase in diameter of objective mirror (d) both (a) and (c).

A B C (a) 0 1 0 (b) 0 0 1 (c) 1 0 0 (d) 1 0 1 17. The escape velocity for a planet is ve. A tunnel is dug along a diameter of the planet and a small body is dropped into it at the surface. When the body reaches the centre of the planet, its speed will be v v (c) e (d) zero (a) ve (b) e 2 2 18. In a plane electromagnetic wave, the electric field oscillates sinusoidally at a frequency of 2 × 1010 Hz and amplitude 54 V m–1. (a) The amplitude of oscillating magnetic field will be 18 × 10–7 Wb m–2. (b) The amplitude of oscillating magnetic field will be 18 × 10–8 Wb m–2. (c) The wavelength of electromagnetic wave is 1.5 m. (d) The wavelength of electromagnetic wave is 1.5 cm. 19. A uniform rod of mass m and length l0 is pivoted at one end and is hanging in the vertical l0 direction. The period of small angular oscillations of the rod (if displaced slightly from its position) is

Test-1

3

(a) 3π

2l0 3g

(b) 4π

l0 g

(c) 2π

l0 3g

(d) 2π

2l0 3g

20. Two radioactive nuclei P and Q, in a given sample decay into a stable nucleus R. At time t = 0, number of P species are 4 N0 and that of Q are N0 . Half-life of P (for conversion to R) is 1 minute where as that of Q is 2 minutes. Initially no nuclei of R present in the sample. When number of nuclei of P and Q are equal, the number of nuclei of R present in the sample would be 9N 0 5N 0 (d) (a) 2 N0 (b) 3 N0 (c) 2 2 NUMERICAL VALUE TYPE 21. A particle is projected from a horizontal plane with velocity of 5 2 m s −1 at an angle. If at highest point its velocity is found to be 5 m s–1. Then its range _____ m. (Take g = 10 m s–2) 22. In the given circuit diagram, the current passing through wire CD is _____ A. 23. For a certain organ pipe, three successive resonance frequencies are observed at 425, 595 and 765 Hz respectively. Taking the speed of sound in air to be 340 m s–1, the length of the pipe will be _____ m. 24. A fish at a depth of 12 cm in water is viewed by an observer on the bank of a lake. The image of fish is raised by height _____ cm. 4 (Refractive index of lake water = ) 3 25. If the ratio of the de Broglie wavelength of a proton and an a-particle of same kinetic energy is x : 1, then the value of x is _____. CHEMISTRY 26. Among the following complexes the one which shows zero crystal field stabilization energy (CFSE) is (a) [Mn(H2O)6]3+ (b) [Fe(H2O)6]3+ 2+ (c) [Co(H2O)6] (d) [Co(H2O)6]3+

27. Li occupies higher position in the electrochemical series of metals as compared to Cu since (a) the standard reduction potential Li+/Li is lower than that of Cu2+/Cu (b) the standard reduction potential of Cu2+/Cu is lower than that of Li+/Li (c) the standard oxidation potential of Li/Li+ is lower than that of Cu/Cu2+ (d) Li is smaller in size as compared to Cu. 28. Which of the following colloids cannot be easily coagulated? (a) Multimolecular colloids (b) Irreversible colloids (c) Lyophobic colloids (d) Macromolecular colloids 29. Which of the following represents the correct order of increasing first ionization enthalpy for Ca, Ba, S, Se and Ar? (a) Ca < Ba < S < Se < Ar (b) Ca < S < Ba < Se < Ar (c) S < Se < Ca < Ba < Ar (d) Ba < Ca < Se < S < Ar 30. Hydrogen peroxide on treatment with an acid solution of titanium salt gives (a) yellow colour (b) red colour (c) blue colour (d) white colour. 31. If the rate of reaction is r = k[X]1/3[Y]2/3, what is the unit of rate constant? (a) mol1/3 L–2/3 time–1 (b) mol2/3 L1/3 time–1 (c) mol1/6 L–1/6 time–1 (d) mol0 L0 time–1 32. Arrange the carbanions, (CH3 )3 C , CCl 3 , (CH3 )2 CH , C 6 H5CH2

in order of their decreasing stability. (a) C 6 H5 CH2 > CCl 3 > (CH3 )3C > (CH3 )2CH (b) (CH3 )2CH > CCl 3 > C 6 H5 CH2 > (CH3 )3C (c) CCl 3 > C6 H5 CH2 > (CH3 )2 CH > (CH3 )3C (d) (CH3 )3C > (CH3 )2 CH > C 6 H5 CH2 > CCl 3 33. Which of the following compounds is the major product when o-chlorotoluene reacts with sodamide in presence of ammonia?

(a)

(b)

(c)

(d)

4

Very-Similar Practice Tests

34. Which of the following statements about DNA is not correct? (a) It has a double helix structure. (b) It undergoes replication. (c) The two strands in a DNA molecule are exactly similar. (d) It contains the pentose sugar, 2-deoxyribose. 35. Photoelectric effect is the phenomenon in which (a) photons come out the metal when hit by a beam of electrons (b) photons come out of the nucleus of an atom under the action of an electric field (c) electrons come out of metal with a constant velocity which depends on frequency and intensity of incident light (d) electrons come out of metal with different velocities not greater than a certain value which depends upon frequency of incident light and not on intensity. 36. Consider the following statements : I. Cationic polymerisation occurs in monomers with electron donating substituents. II. Anionic polymerisation occurs in monomers with electron withdrawing substituents. III. Head-to-head chain growth polymerisation occurs in polystyrene. The correct statements are (a) I and II (b) I and III (c) II and III (d) I, II and III 37. The correct IUPAC name of the compound is (a) 3-(1-ethylpropyl)hex-1-ene (b) 4-ethyl-3-propylhex-1-ene (c) 3-ethyl-4-ethenylheptane (d) 3-ethyl-4-propylhex-5-ene. 38. In a face-centred cubic arrangement of A and B atoms in which A atoms are at the corners of the unit cell and B atoms are at the face centres, one of the A atoms is missing from one corner in unit cell. The simplest formula of the compound is (a) A7B3 (b) AB3 (c) A7B24 (d) A8/7B3 39. Borax is used as a buffer since (a) its aqueous solution contains equal amount of weak acid and its salt

(b) it is easily available (c) its aqueous solution contains equal amount of strong acid and its salt (d) none of these. 40. An organic aromatic compound having molecular formula C7H8O does not give characteristic colour with neutral FeCl3 but bubbles of hydrogen gas are formed when it is treated with metallic sodium. The compound is

(a)

(b)

(c)

(d)

41. Which of the following is not an example of green chemistry? (a) Catalytic dehydrogenation of the diethanol amine without using cyanide and formaldehyde. (b) Replacement of CFCs by CO2 as blowing agent in the manufacture of polystyrene foam sheets. (c) Reacting methylamine and phosgene to produce methyl isocyanate. (d) Replacement of organotins by ‘sea-nine’ as anti fouling compound in sea marines. 42. The decreasing order of basic character of K2O, BaO, CaO and MgO is (a) K2O > BaO > CaO > MgO (b) K2O > CaO > BaO > MgO (c) MgO > BaO > CaO > K2O (d) MgO > CaO > BaO > K2O

O 43. CH3 C CH CH2 Identify A and B. A OH

NaCN/HCN 5–10°C

A

NaCN, HCN 80°C

B

B OH

(a) CH3 C CH CH3 CN OH O

CH3 C CH2 CH2 CN OH O

(b) CH3 C CH CH3 CN

CH3 C CH CH3 CN

Test-1

5 OH

(c) CH3 C CH CH2

O CH3 C CH2CH2CN

CN

(d) None of these. 44. A mixture of 1.57 moles of N2, 1.92 moles of H2 and 8.13 moles of NH3 is introduced into a 20 L reaction vessel at 500 K. At this temperature, the equilibrium constant, Kc for the reaction, N2(g) + 3H2(g) 2NH3(g) is 1.7 × 102. Select the correct statement. (a) The reaction is at equilibrium. (b) The reaction goes in the direction of reactants. (c) The reaction goes in the direction of product. (d) None of these. 45. The equivalent conductances of two strong electrolytes at infinite dilution in H2O (where ions move freely through a solution) at 25°C are given below: L°CH COONa = 91.0 S cm2/equiv. 3 L°HCl = 426.2 S cm2/equiv. What additional information/quantity one needs to calculate L° of an aqueous solution of acetic acid? (a) L° of chloroacetic acid (ClCH2COOH) (b) L° of NaCl (c) L° of CH3COOK (d) the limiting equivalent conductance of H+ (l°H+).

46.

47.

48.

49.

NUMERICAL VALUE TYPE Amount of of potassium dichromate in grams required to oxidise 20.0 g of Fe2+ in FeSO4 to Fe3+ if the reaction is carried out in an acidic medium is ____. (Molar masses of K2Cr2O7 and FeSO4 are 294 and 152 respectively.) The vapour density of a metal sulphate is 90 and its oxide contains 60 per cent metal. The atomic weight of metal is ____. The mass of a non-volatile solute (in g) which should be dissolved in 114 g octane to reduce its vapour pressure to 80% is ____. (Given : Molar mass of solute 40 g mol–1) An open vessel contains 200 mg of air at 17°C. The weight percent of air that would be expelled if the vessel is heated to 117°C is ____.

50. The standard heat of formation of CH4(g), CO2(g) and H2O(g) are –76.2, –394.8 and –241.6 kJ mol–1 respectively. The amount of heat evolved (in kJ) by burning 1 m3 of methane measured at NTP is x × 104. The value of x is ____. 51.

52.

53.

54.

MATHEMATICS Let n be a fixed positive integer. Define a relation R in the set Z of integers by aRb if and only if a – b divides n. The relation R is (a) reflexive (b) symmetric (c) transitive (d) an equivalence relation The value of a for which the system of equations a3x + (a + 1)3y + (a + 2)3z = 0, ax + (a + 1)y + (a + 2)z = 0, x + y + z = 0, has a non zero solution is (a) – 1 (b) 0 (c) 1 (d) None of these The function f(x) = 5 + 36x + 3x2 – 2x3 is decreasing in the interval (a) (–2, 3) (b) (2, –3) (c) (–2, –3) (d) (2, 3) The last digit in the expansion of 7300 is (a) 7 (b) 9 (c) 1 (d) 3 1

55.

57.

58.

59.

−1  2x   dx is equal to 2  

1+ x   (a) 0 (b) p (c) p/2 (d) p/4 The value of p for which the function  (4x − 1)3 , x≠0   x2   x f (x ) =  sin log 1 +  p 3    12(log 4)3 , x=0  may be continuous at x = 0, is (a) 1 (b) 2 (c) 3 (d) 4 Points (3, 3), (h, 0), (0, k) are collinear and a/h + b/k = 1/3. Then (a) a = 3, b = 2 (b) a = 3, b = 3 (c) a = 1, b = 1 (d) a = 2, b = 2 If iz3 + z2 – z + i = 0, then |z| is equal to (a) 0 (b) 1 (c) 2 (d) None of these 1 + sin A − cos A = 1 + sin A + cos A A A A A (a) sin (b) cos (c) tan (d) cot 2 2 2 2 0

56.

d 

∫ dx sin 

6

Very-Similar Practice Tests

60. The four arithmetic means between 3 and 23 are (a) 5, 9, 11, 13 (b) 7, 11, 15, 19 (c) 5, 11, 15, 22 (d) 7, 15, 19, 21 61.

lim

(1+ 2 + 3 + ... + n)(13 + 23 + 33 + ... + n3)

= (12 + 22 + 32 + ... + n2 )2 9 7 3 5 (a) (b) (c) (d) 8 8 8 8 If the planes x = cy + bz, y = az + cx, z = bx + ay pass through a line, then a2 + b2 + c2 + 2abc is (a) 0 (b) 1 (c) 2 (d) 3 The solution of the differential equation dy 1 + y 2 is = dx 1 + x 2 (a) y = tan–1x + c (b) x = tan–1y + c (c) tan(xy) = c (d) y – x = c(1 + xy) In a class of 100 students there are 70 boys whose average marks in a subject are 75. If the average marks of the complete class is 72, then what is the average of the girls? (a) 73 (b) 65 (c) 68 (d) 74 The negation of the proposition: “If a quadrilateral is a square, then it is a rhombus” is (a) If a quadrilateral is a square, then it is a rhombus. (b) If a quadrilateral is a square, then it is not a rhombus. (c) A quadrilateral is a square and it is not a rhombus. (d) A quadrilateral is not a square and it is a rhombus. A purse contains 4 copper and 3 silver coins, and a second purse contains 6 copper and 2 silver coins. A coin is taken out from any purse, the probability that it is a copper coin is (a) 3/7 (b) 4/7 (c) 3/4 (d) 37/56 The area bounded by the parabola y = 4x2, x2 y= and the line y = 2 is 9

69. Let a and b be the roots of equation x2 – (a – 2)x – a – 1 = 0, then a2 + b2 assumes the least value if (a) a = 0 (b) a = 1 (c) a = –1 (d) a = 2

10 2 5 2 sq. units sq. units (b) 3 3 15 2 20 2 (c) sq. units (d) sq. units 3 3

75. If

n→ ∞

62.

63.

64.

65.

66.

67.

68. If the circles (x – 1)2 + (y – 3)2 = r2 and x2 + y2 – 8x + 2y + 8 = 0 intersect in two distinct points, then (a) 2 < r < 8 (b) r = 2 (c) r < 2 (d) r > 2

(a)

70. If tan θ =

x sin φ

1 − x cos φ x then = y sin φ (a) sin θ sin φ (c) 1 − cos θ

and tan φ =

y sin θ 1 − y cos θ

,

sin θ sin φ sin θ (d) 1 − cos φ (b)

NUMERICAL VALUE TYPE  1 2 1 71. If the adjoint of a 3 × 3 matrix P is  4 1 1 ,    4 7 3 then the sum of squares of possible values of determinant of P is _____. 72. The number of polynomials of the form x3 + ax2 + bx + c which are divisible by x2 + 1 where a, b, c ∈ {1, 2, 3, ..., 10} is K, then 10K is _____. 73. If the sum to infinity of a decreasing G.P. with the common ratio x is k such that |x| < 1; x ≠  0. The ratio of the fourth term to the second term is 1/16 and the ratio of third term to the square of the second term is 1/9. Find the value of k. 74. The plane 2x – 2y + z = 3 is rotated about the line where it cuts the xy plane by an acute angle a. If the new position of plane contains the point (3, 1, 1), then cosa equal to _____. the

points

with

position

vectors

10i + 3j, 12i − 5j and λi +11j are collinear,

then

3 l is equal to _____. 2

Telegram @unacademyplusdiscounts

Join Us on Telegram for More Such Books https://telegram.me/unacademyplusdiscounts

Join us from the above link or search ''unacademyplusdiscounts'' in Telegram

8

Very-Similar Practice Tests

VERY SIMILAR

PRACTICE TEST 2 Time : 3 hrs.

Max. Marks : 300

PHYSICS 1. Figure shows the distance-time graph of the motion of a car. It follows from the graph that x the car is (a) at rest x = 1.2t2 (b) in uniform motion (c) in non-uniform motion t (d) uniformly accelerated. 2. Half-life of a radioactive substance is 20 minute. The time between 20% and 80% decay will be (a) 20 min (b) 30 min (c) 40 min (d) 25 min 3. A particle is projected at 60° to the horizontal with a kinetic energy K. The kinetic energy at the highest point is K K (a) K (b) zero (c) (d) 4 2 4. Two waves coming from two coherent sources, having different intensities interfere. Their ratio of maximum intensity to the minimum intensity is 25. The intensities of the sources are in the ratio (a) 25 : 1 (b) 25 : 16 (c) 9 : 4 (d) 5 : 1 5. If the energy, E = Gphqcr, where G is the universal gravitational constant, h is the Planck’s constant and c is the speed of light, then the values of p, q and r are, respectively 1 −1 −5 −1 1 5 and (a) , and (b) , 2 2 2 2 2 2 1 −1 −3 −1 1 3 and , and (c) (d) , 2 2 2 2 2 2 6. A body floats in water with one-third of its volume above the surface of water. If it is placed in oil, it floats with half of its volume

above the surface of the oil. The specific gravity of oil is 3 5 4 (b) (c) (d) 1 (a) 2 3 3 7. In the circuit shown, the value of 2.25 A R 1.5 A E

(a) R = 15 W (c) E = 36 V

R

30 

(b) R = 30 W (d) E = 180 V

8. Given below is the circuit diagram of an AM demodulator. For good demodulation of AM signal of carrier frequency u, the value of RC should be

AM signal

C

R Output

(a) RC = 1 (b) RC < 1 υ υ (c) RC ≤ 1 (d) RC >> 1 υ υ 9. The third overtone of an open organ pipe is in resonance with the second overtone of a closed organ pipe. If the length of the open pipe is 8 cm, then the length of the closed pipe is (a) 10 cm (b) 8 cm (c) 12 cm (d) 5 cm 10. The ratio of de Broglie wavelength of a proton and an a particle accelerated through the same potential difference is (a) 3 2 (b) 2 2 (c) 2 3 (d) 2 5 11. Two massless springs of force constants k1 and k2 are joined end to end. The resultant force constant K of the system is

Test-2

k1 + k2 k1k2 k1k2 (c) k1 + k2 (a)

9

(b) k1 + k2 (d)

k1k2 k1 − k2

12. The current gain of a transistor in a common base arrangement is 0.98. Find the change in collector current corresponding to a change of 5.0 mA in emitter current. What would be the change in base current? (a) 4.9 mA, 0.1 mA (b) 4.9 mA, 0.2 mA (c) 5.9 mA , 0.3 mA (d) 5.9 mA, 0.8 mA 13. A particle is executing linear simple harmonic motion. The fraction of the total energy to its 1 potential energy, when its displacement is 2 of its amplitude is 1 1 1 1 (a) (b) (c) (d) 2 8 4 16 14. A convex lens of focal length 20 cm made of glass of refractive index 1.5 is immersed in water having refractive index 1.33. The change in the focal length of lens is (a) 62.2 cm (b) 5.82 cm (c) 58.2 cm (d) 6.22 cm

The amount of heat required in the process in energy units is (a) 5 × 104 Dm (b) (33/4) × 104 Dm 4 (c) (65/4) × 10 Dm (d) (5/4) × 104 Dm 19. The instantaneous magnetic flux f in a circuit is f = 4t2 – 4t + 1 Wb The total resistance of the circuit is 10 W. At 1 t = s, the induced current in the circuit is 2 (a) 0 A (b) 0.6 A (c) 0.4 A (d) 0.2 A 20. The rms value of the electric field of the light coming from the sun is 720 N C–1. The average total energy density of the electromagnetic wave is (a) 3.3 × 10–3 J m–3 (b) 4.58 × 10–6 J m– 3 (c) 6.37 × 10–9 J m–3 (d) 81.35 × 10–12 J m– 3. NUMERICAL VALUE TYPE 21. A geostationary satellite is orbiting the earth at a height of 6R from the surface of the earth, where R is the radius of the earth. The time period of another satellite at a height of 2.5R from the surface of the earth is 2 × n hours. The value of n is _____.

15. A black body has maximum wavelength lm at 2000 K. Its corresponding wavelength at 3000 K will be 3 81 2 λm (a) λm (b) λm (c) 16 λm (d) 2 16 3 81 16. The plates of a parallel plate capacitor are charged up to 100 V. A 2 mm thick plate is inserted between the plates, then to maintain the same potential difference, the distance between the capacitor plates is increased by 1.6 mm. The dielectric constant of the plate is (a) 5 (b) 1.25 (c) 4 (d) 2.5

22. A solid sphere of radius R has a charge Q distributed in its volume with a charge density r = kr a, where k and a are constants and r is the distance from its centre. If the electric field at r = R/2 is 1/8 times that at r = R, the value of a is _____.

17. A body starting from rest moves with constant acceleration. The ratio of distance covered by the body during the 5th second to that covered in 5 seconds is 9 1 3 25 (a) (b) (c) (d) 25 25 25 9 18. The specific heat c of a solid at low temperature shows temperature dependence according to the relation c = DT 3 where D is a constant and T is the temperature in kelvin. A piece of this solid of mass m kg is taken and its temperature is raised from 20 K to 30 K.

24. Three blocks of masses m1, m2 and m3 are connected by massless string as shown in the figure on a frictionless table. They are pulled with a force F = 60 N. If m1 = 10 kg, m2 = 20 kg T and m3 = 30 kg, then the ratio 2 is _____. T1

23. An ideal monoatomic gas is compressed  1  th of its initial volume. adiabatically to   8 If the initial temperature of the gas is Ti (in Kelvin) and the final temperature is aTi , then the value of a will be _____.

T1 m1

T2 m2

F = 60 N m3

25. A capacitor and a coil in series are connected to a 6 volt AC source. By varying the frequency of the source, maximum current of 600 mA is

10

Very-Similar Practice Tests

observed. If the same coil is now connected to a cell of emf 6 V and internal resistance of 2 W, then the current through it will be _____ A.

29. Which of the following is not the product of dehydration of

?

OH

CHEMISTRY 26. When copper pyrites is roasted in excess of air, a mixture of CuO and FeO is formed. FeO is present as impurities. This can be removed as slag during reduction of CuO. The flux added to form slag is (a) SiO2, which is an acidic flux (b) lime stone, which is a basic flux (c) SiO2, which is a basic flux (d) CaO, which is a basic flux. 27. Which of the following structure is correctly drawn according to fundamental idea of VSEPR theory?

(a)

(b)

(c)

(d)

30. In the hydrolytic equilibrium, A– + H2O HA + OH– –5 Ka = 1.0 × 10 . The degree of hydrolysis of a 0.001 M solution of the salt is (a) 10–2 (b) 10–3 (c) 10–4 (d) 10–5 31. Which of the following is a biodegradable polymer? (a) ( CH2 C CH CH2 ) n

(a)

Cl

CN

(b) ( CH2 CH CH CH2 CH2 CH ) n (c) ( O CH CH2 C O CH CH2 C )n

(b)

O

CH3 –

Cl

H



: Cl Cl

F

F 

(d)

Si

( = 90°)

F F 28. Identify Z in the following reactions : C6H5NH2

NaNO2/HCl 280 K

X

CuBr/HBr

Z

Br

Br

Br (a)

(b)

Br

Br Br

Br (c)

(d)

O

Br

33. The structure given below represents O H S CH3 CH2 C NH CH3 N COOH O H (a) Penicillin-F (b) Penicillin-G (c) Penicillin-K (d) Ampicillin Me

34. H C CO2H Ph

Br

H O

(d) ( N (CH2)6 N C (CH2)4 C ) n 32. Which of the following reactions is not associated with the Solvay process of manufacture of sodium carbonate? H2CO3 (a) CO2 + H2O (b) NH3 + H2CO3 NH4HCO3 (c) NaCl + NH4HCO3 NaHCO3 + NH4Cl (d) 2NaOH + CO2 Na2CO3 + H2O

( = 90°)

I

:

(c)

Cl

CH2 CH3 O

NH3 

A

The end product C is

Br2 + KOH

B

HONO

C

Test-2

11

OH (a)

(b)

OH OH (c)

(d)

35. The ions O2–, F–, Na+, Mg2+ and Al3+ are isoelectronic. Their ionic radii show (a) a decrease from O2– to F– and then increase from Na+ to Al3+ (b) a significant increase from O2– to Al3+ (c) a significant decrease from O2– to Al3+ (d) an increase from O2– to F– and then decrease from Na+ to Al3+. 36. If the freezing point of a 0.01 molal aqueous solution of a cobalt(III) chloride-ammonia complex (which behaves as a strong electrolyte) is –0.0558°C, formula of complex is [Kf of water = 1.86 K kg mol–1] (a) [Co(NH3)5Cl]Cl2 (b) [Co(NH3)4Cl2]Cl (c) [Co(NH3)3Cl3] (d) [Co(NH3)6]Cl3 37. Which of the given values is twice of the equivalent mass of the oxidising agent of the given reaction, 3S + 2H2O SO2 + 2H2S (a) 64 (b) 32 (c) 16 (d) 48 38. The energy absorbed by each molecule (A2) of a substance is 4.4 × 10–19 J and bond energy per molecule is 4.0 × 10–19 J. The kinetic energy of the molecule per atom will be (a) 2.2 × 10–19 J (b) 2.0 × 10–19 J –20 (c) 4.0 × 10 J (d) 2.0 × 10–20 J 39. Which of the following represents physical adsorption? (a) x/m

(b) x/m T

T

(b) Endothermic reaction with negative entropy change and low temperature (c) Exothermic reaction with positive entropy change and high temperature (d) Exothermic reaction with negative entropy change and low temperature 41. Sodium extract of which of the following compounds does not form blood red ppt. with aqueous FeCl3? (a) NH2NH2 (b) NH2 C NH2

O (c) CH3 CH CH2NH2 SH (d) Both (a) and (b) 42. Growth of fish is not as healthy in warm water as in cold water because (a) the amount of D.O. in warm water is higher than in cold water (b) warm water is not liked by fish (c) cold water contains more marine plants (d) the amount of D.O. in warm water is less than in cold water. 43. White phosphorus on reaction with lime water gives calcium salt of an acid (A) along with a gas (X). Which of the following statements is correct? (a) (A) on heating gives (X) and O2. (b) The bond angle in (X) is less than that in case of ammonia. (c) (A) is a dibasic acid. (d) (X) is more basic than ammonia. 44. MnO4– is of intense pink colour, though Mn is in (+7) oxidation state. It is due to (a) oxygen gives colour to it. (b) charge transfer when oxygen gives its electron to Mn making it Mn (+VI) hence, coloured. (c) charge transfer when Mn gives its electron to oxygen. (d) none of the above is correct. 2HCl

(c) x/m

(d) x/m T

T

40. Which of the following reactions is said to be entropy driven? (a) Endothermic reaction with positive entropy change and high temperature

A 45. CH3 C C H (a) CH3 C C H (b) CH3 C C CH3 (c) CH3 CH CH2 (d)

Zn

B ; B is

12

Very-Similar Practice Tests

NUMERICAL VALUE TYPE 46. A metal (atomic mass = 75 g mol–1) crystallizes in cubic lattice and the edge length of unit cell is 5Å. If the density of the metal is 2 g cm–3 then the radius of metal atom (in pm) is _____. 47. Out of N2O, SO2, I3+, I3–, H2O, NO2–, N3–, the number of linear species is _____. 48. The rate constant for the first order decomposition of H2O2 is given by the following equation : 1.0 × 104 log k = 14.2 − K T The multiplication of Ea for this reaction and rate constant k if its half-life period is 200 minutes is _____. 49. The total number of cyclic isomers possible for a hydrocarbon with the molecular formula C4H6 is ____. 50. The number of possible isomers of the complex, Pt(NH3)2(SCN)2 is ____. MATHEMATICS 51. The range of the function π π f (x ) = sin[ x], − ≤ x ≤ where [x] denotes 4 4 the greatest integer is (a) {0} (b) {0, –1} (c) {0, ± sin1} (d) {0, –sin1} 52. The least value of natural number n satisfying C(n, 5) + C(n, 6) > C(n + 1, 5) is (a) 11 (b) 10 (c) 12 (d) 13 53. If tangent to the curve y2 = x3 at its point (m2, m3) is also normal to the curve at (M2, M3), then what is the value of mM ? 2 4 (a) − (b) − (c) − 1 (d) 1 9 9 3 54. If the (r + 1)th term in the expansion of  a + 3 b 

b  3  a

21

has the same power of a

and b, then the value of r is (a) 9 (b) 10 (c) 8

(d) 6

π /2

dx is 1 + cot x 0 (b) p/2 (c) 0

55. The value of ∫ (a) p/4

(d) p

56. If f(x) = a|sinx| + be|x| + c|x|3 and if f(x) is differentiable at x = 0, then (a) b = 0, c = 0, a is any real (b) a = 0, b = 0, c is any real (c) c = 0, a = 0, b is any real (d) a + b = 0 57. The minor axis of the ellipse with foci (± 2, 0) 1 and eccentricity is 3 (a) 4 (b) 3 (c) 8 2 (d) 4 2 58. If x2 – 2x cosq + 1 = 0 then, x2n – 2xn cos nq + 1 is equal to (a) cos 2nq (b) sin 2nq (c) 0 (d) R – {0} 59. In an experiment with 15 observations on x, the following results were available. Sx2 = 2830, Sx = 170 One observation that was 20 was found to be wrong and was replaced by the correct value 30. Then the corrected variance is (a) 78 (b) 188.66 (c) 177.33 (d) 8.33 60. If sinx + sin2x = 1, then the value of cos12x + 3cos10x + 3cos8x + cos6x – 2 is equal to (a) 0 (b) 1 (c) – 1 (d) 2   61. lim  x + x + x − x  = x →∞   (a) ∞ 62. If

(b) 0

(c) 1

(d)

1 1 1 are in A.P., then , , p+q r + p q+r

1 2

(a) p, q, r are in A.P. (b) p2, q2, r2 are in A.P. 1 1 1 (c) , , are in A.P. p q r (d) None of these 1+ i 1− i i 63. 1 − i i 1+ i = i 1+ i 1− i (a) –4 –7i (c) 3 + 7i

(b) 4 + 7i (d) 7 + 4i

64. The locus of the midpoint of the intercept of the line xcosa + ysina = p between the coordinate axes is (a) x–2 + y–2 = 4p–2 (b) x–2 + y–2 = p–2 (c) x2 + y2 = 4p–2 (d) x2 + y2 = p2

Test-2

65. The area of the region bounded by the curves 1 y = x 3 , y = , x = 2 is x 1 + log e 2 (a) 4 – loge2 (b) 4 15 (c) 3 – loge2 (d) − log e 2 4 66. If tanq – cotq = a and sinq + cosq = b, then (b2 – 1)2(a2 + 4) is equal to (a) 2 (b) – 4 (c) 3 (d) 4 67. For the binomial distribution (p + q)n, whose mean is 20 and variance is 16, pair (n, p) is 2  1 (a)  100,  (b)  100,     5 5 1 2 (c)  50,  (d)  50,     5 5 68. If n is a natural number, then (a) 12 + 22 + ..... + n2 < n3/3 (b) 12 + 22 + ..... + n2 = n3/3 (c) 12 + 22 + ..... + n2 > n3 (d) 12 + 22 + ..... + n2 > n3/3

13 (a) y 1 − y 2 + x 1 − x 2 = a (b) x 1 − y 2 + y 1 − x 2 = a (c) x 1 − y 2 − y 1 − x 2 = a 2 2 (d) y 1 − y − x 1 − x = a

NUMERICAL VALUE TYPE 71. If 2 – i is a root of the equation ax2 + 12x + b = 0 (where a and b are real), then the value of ab is _____ . k

2π   2π cos 3 − sin 3  1 0 72. If   =  then the  sin 2π cos 2π  0 1  3 3  least value of k equals (k ≠ 0)

69. If the lines

73. The shortest distance between the z-axis and the line, x + y + 2z – 3 = 0, 2x + 3y + 4z – 4 = 0 is _____ .      74. If (a × b )2 + (a ⋅ b )2 = 144 and | a | = 4, then  | b | is ____.

70. If a is an arbitrary constant, then the solution

75. The sum of the terms of an infinitely decreasing G.P. is equal to the greatest value of the function f (x) = x3 + 3x – 9 on the interval [–4, 3] and the difference between the first and second terms is f ′(0). Then the value of 3 r (where r is common ratio) is _____ .

y −2 1− x z −3 = = and 3 2α 2 x −1 6−z are perpendicular, then = y −1 = 3α 5 the value of a is −10 −10 10 (a) (b) (c) (d) 10 11 7 7 11 1 − y2 dy of the differential equation + =0 dx 1 − x2 is

Telegram @unacademyplusdiscounts

Join Us on Telegram for More Such Books https://telegram.me/unacademyplusdiscounts

Join us from the above link or search ''unacademyplusdiscounts'' in Telegram

Test-3

15

VERY SIMILAR

PRACTICE TEST 3 Time : 3 hrs.

Max. Marks : 300

PHYSICS B 1. A bob of mass M is suspended by a massless string of length L. The horizontal velocity v at position A is just L  sufficient to make it reach the v point B. The angle q at which A the speed of the bob is half of that at A, satisfies π π π (i) (b) (iv) > (ii) > (iii) > (i) (c) (i) > (iii) > (ii) > (iv) (d) (i) > (ii) > (iii) > (iv) 36. If M is an element of actinoids series, the degree of complex formation decreases in the order (a) M 4+ > M3+ > MO22+ > MO2+ (b) MO2+ > MO22+ > M3+ > M 4+ (c) M 4+ > MO22+ > M3+ > MO2+ (d) MO22+ > MO2+ > M 4+ >M3+ 37. For compounds with the same anion, the hydration energies of Na+, K+, Rb+, Cs+ and Li+ follow the order (a) Cs+ > Rb+ > K+ > Na+ > Li+ (b) Li+ > Na+ > K+ > Rb+ > Cs+ (c) K+ > Na+ > Li+ > Cs+ > Rb+ (d) Li+ > K+ > Na+ > Cs+ > Rb+ 38. In which of the following reactions will there be no change in the oxidation number of nitrogen? (a) HNO3 + 2H2SO4 → NO2+ + H3O+ + 2HSO4– (b) 2N2O4 + 2KI → 2KNO3 + 2NO + I2 (c) 2KNH2 + N2O → KN3 + KOH + NH3 (d) 4NO2 + O2 + 2H2O → 4HNO3 39. Which among the following statements are correct with respect to adsorption of gases on a solid? (i) The extent of adsorption is equal to kpn according to Freundlich isotherm. (ii) The extent of adsorption is equal to kp1/n according to Freundlich isotherm. (iii) The extent of adsorption is equal to (1 + bp)/ap according to Langmuir isotherm. (iv) The extent of adsorption is equal to ap/(1 + bp) according to Langmuir isotherm. (a) (i) and (iii) (b) (i) and (iv) (c) (ii) and (iii) (d) (ii) and (iv)

40. For which of the following processes, q = DU (a) O → A (b) O → D (c) O → B (d) O → C 41. When a brown compound of Mn (A) is treated with HCl, it gives a gas (B). The gas (B) taken in excess reacts with NH3 to give an explosive compound (C). The compounds A, B and C are (a) A = MnO2, B = Cl2, C = NCl3 (b) A = MnO, B = Cl2, C = NH3Cl (c) A = Mn3O4, B = Cl2, C = NCl3 (d) A = MnO3, B = Cl2, C = NCl2 42. The empirical formula of an organic compound containing carbon and hydrogen is CH2. The mass of one litre of this organic gas is exactly equal to that of one litre of N2. Therefore, the molecular formula of the organic gas is (a) C2H4 (b) C3H6 (c) C6H12 (d) C4H8 43. H2O2 cannot oxidise (a) Na2SO3 (b) KI (c) PbS (d) O3 44. An electric current is passed through an aqueous solution (buffered at pH = 6.0) of alanine (pI = 6.0) and ariginine (pI = 10.2). The two amino acids can be separated because (a) alanine migrates to anode, and arginine to cathode (b) alanine migrates to cathode and arginine to anode (c) alanine does not migrate while arginine migrates to cathode (d) alanine does not migrate while arginine migrates to anode. 45. Which one of the following is a non-steroidal hormone? (a) Estradiol (b) Prostaglandin (c) Progesterone (d) Estrone NUMERICAL VALUE TYPE 46. In the given reaction, the total number of carboxylic groups in the product is _____.

20

Very-Similar Practice Tests

47. The change in pH if 0.02 mol CH3COONa is added to 1.0 L of 0.01 M HCl is _____. (Ka of CH3COOH = 1.8 × 10–5) 48. A greenish yellow gas reacts with an alkali metal hydroxide to form a halate which can be used in fire works safety matches. The halate molecule formed has x number of oxygen atoms. The value of x is _____.

56. The

solution of differential equation 1 dy y + = under the condition dx x log e x x y = 1 when x = e is 1 (a) 2 y = log e x + log e x 2 (b) y = log e x + log e x (c) ylogex = logex + 1 (d) y = loge x + e

49. A certain metal was irradiated with light of frequency 3.2 × 1016 sec–1. The photoelectrons emitted have twice the kinetic energy as photoelectrons emitted when the same metal is irradiated with a light of frequency 2 × 1016 sec–1. The threshold frequency of the metal is x × 1015 sec–1. The value of x is _____.

57. In the expansion of  x −  , the constant  x term is (a) –20 (b) 20 (c) 30 (d) –30

50. Out of the following compounds, the number of compounds that cannot be prepared by Kolbe’s electrolytic method is _____. Ethane, Butane, Methane, Propane, Pentane, Hexane, Ethene, Ethyne

58. A plane which passes through the point x−3 y−6 z −4 is (3, 2, 0) and the line = = 1 5 4 (a) x – y + z = 1 (b) x + y + z = 5 (c) x + 2y – z = 0 (d) 2x – y + z = 5

MATHEMATICS 51. If the function f : [1, ∞) → [1, ∞) is defined by f(x) = 2x(x –1), then f –1(x) is

1 (a)    

x(x −1)

2 1 (b) (1 + 1 + 4 log 2 x ) 2 1 (c) (1 − 1 + 4 log 2 x ) 2 (d) none of these 52. If sinq + cosecq = 2, the value of sin10q + cosec10q is (a) 10 (b) 210 (c) 29 (d) 2 53. The sides of a triangle are x = 2, y + 1 = 0 and x + 2y = 4. Its circumcentre is (a) (4, 0) (b) (2, –1) (c) (0, 4) (d) (2, 3) 54. The number of values of a for the which the function f(x) = (x + 1) |x – a| is differentiable " x ∈ R, is (a) 0 (b) 1 (c) 2 (d) more than 2 55.

If both the roots of the equations ax2 + px + q = 0

and bx2 + lx + m = 0 (a ≠ b) are common, then (a) pm = lq (c) p2l = m2q

(b) pq = lm (d) pm2 = lq2.



59. Suppose f ( x) =

1

6

k

is a probability distribution 2x of a random variable X that can take values 0, 1, 2, 3, 4. Then k is equal to (a) 16/15 (b) 15/16 (c) 31/16 (d) none of these

60. If for the curve y = 1 + bx – x2, the tangent at (1, –2) is parallel to x-axis, then b = (a) 2 (b) –2 (c) 1 (d) –1 61. Given that 0 < x < ∞

∑ (−1)k tan2k x k =0

∞

π π π and and 0 is (b) ap

69. lim

1 2

(b)

(c) m2 – n2 = m2 + n2 (d) m2 − n2 = 4 mn

=

(b) x3 + w (d) x3

(a) x3 + 1 (c) x3 + w2

(a) 1

(c) 2p

68. Let L be the line of intersection of the planes 2x + 3y + z = 1 and x + 3y + 2z = 2. If L makes an angle a with the positive x-axis, then cos a equals

3 −4  A= , then det(A2005) equals to 1 −1 _____.

72. If

73. If logx y, logz x, logy z are in G.P., xyz = 64 and x3, y3, z3 are in A.P., then x + y – z is _____.    74. Let a , b , c be non-zero vectors such that    1    (a × b ) × c = | b || c | a. If q is the angle 3  π sin     4  = _____. between b and c , then sin θ 2

75. The value of

∫ [x 0

places, is _____.

2

] dx, upto two decimal

Telegram @unacademyplusdiscounts

Join Us on Telegram for More Such Books https://telegram.me/unacademyplusdiscounts

Join us from the above link or search ''unacademyplusdiscounts'' in Telegram

23

Test-4

VERY SIMILAR

PRACTICE TEST 4 Time : 3 hrs.

Max. Marks : 300

PHYSICS 1. A part of circuit in a steady state along with the currents flowing in the branches, the values of resistances etc., is shown in the figure. 1A

4V

3Ω

3Ω 5Ω

2A 1Ω

4µ F 3V

1Ω 2Ω

2A

4Ω

3Ω 1A

Calculate the energy stored in the capacitor C(4 mF). (a) 0.73 mJ (b) 0.7 mJ (c) 0.8 mJ (d) 8.0 J 2. When two bar magnets have their like poles tied together, they make 12 oscillations per minute and when their unlike poles are tied together, they make 4 oscillations per minute. Find the ratio of their magnetic moments. 2 3 5 4 (a) (b) (c) (d) 3 2 4 5 3. A ceiling fan rotates about its own axis with some angular velocity. When the fan is switched off, the angular velocity becomes th

1 of the original in time t and n   4 revolution are made in that time. The number of revolutions made by the fan during the time internal between switch off and rest are (Angular retardation is uniform) 4n 8n 16n 32n (a) (b) (c) (d) 15 15 15 15

4. If the radius of the opening of a dropper is r = 5 × 10–4 m, density of liquid r = 103 kg m–3, g = 10 m s–2 and surface tension T = 0.11 N m–1, the radius of the drop when the drop detaches from the dropper is approximately (a) 1.4 × 10–3 m (b) 3.3 × 10–3 m –3 (c) 2.0 × 10 m (d) 4.1 × 10–3 m 5. Two small particles of equal masses start moving in opposite directions from a point A in a horizontal circular orbit. Their tangential velocities are v and 2v respectively, as shown in the figure. Between collisions, the particles move with constant speeds. After making how many elastic collisions, other than that at A, these two particles will again reach the point A? (a) 4 (b) 3 (c) 2 (d) 1 6. The figure shows two identical copper blocks of mass 1.5 kg. When they were not in contact, block L was at temperature 60°C and block R was at temperature 20°C. But, when the blocks are bring in contact, they come to the equilibrium temperature 40°C. What is the net entropy change of the two block system during the irreversible process? (Specific heat of copper = 386 J/kg K) (a) 2.4 J/K (b) 3.6 J/K (c) 4.2 J/K (d) 5.2 J/K 7. There is a stream of neutrons with a kinetic energy of 0.0327 eV. If the half-life of neutrons is 700 s, what fraction of neutrons will decay before they travel a distance of 10 m? (a) 4.6 × 10–5 (b) 3.9 × 10–6 –5 (c) 9.2 × 10 (d) 7.8 × 10–6

24

Very-Similar Practice Tests

8. A modulated signal cm(t) has the form cm(t) = 30 sin 300pt + 10 (cos 200pt– cos 400pt). The carrier frequency uc, the modulating frequency (message frequency) um, and the modulation index m are respectively given by (a) uc = 200 Hz; um = 50 Hz; m = 1/2 (b) uc = 150 Hz; um = 50 Hz; m = 2/3 (c) uc = 150 Hz; um = 30 Hz; m = 1/3 (d) uc = 200 Hz; um = 30 Hz; m = 1/2 9. Three very large plates of same area are kept parallel and close to each other. They are considered as ideal black surfaces and have very high thermal conductivity. The first and third plates are maintained at temperatures 2T and 3T respectively. The temperature of the middle (i.e. second) plate under steady state condition is 1/ 4

1/ 4

 65  (a)   2

 97  (b)   4

T

T

13. The magnetic flux f through a stationary loop of wire having a resistance R varies with time as f = at2 + bt (a and b are positive constants). The average emf and the total charge flowing in the loop in the time interval t = 0 to t = t respectively are aτ2 + bτ aτ2 + bτ (b) aτ + b, R 2R aτ + b aτ2 + bτ (c) , 2 R aτ2 + bτ (d) 2(aτ + b), 2R 14. The expression of the trajectory of a projectile is given as y = px – qx2, where y and x are respectively the vertical and horizontal displacements, and p and q are constants. The time of flight of the projectile is (a) aτ + b,

1/ 4

1/ 4  97  (c)   T (d) (97 ) T 2  10. For the circuit as 1/p H 100 W C shown in figure, if the value of rms Box current is 2.2 A, the power factor Vrms = 220 V, w = 100p s–1 of the box is 3 1 (b) 1 (c) (d) (a) 1 2 2 2 11. In a photoemissive cell, with exciting wavelength l, the fastest electron has speed v. If the exciting wavelength is changed to 3l/4, the speed of the fastest emitted electron will be 1/2

4 (a) less than v   3

15.

16.

1/2

(b) v  4    3

1/2

3 (c) v   4

4 (d) greater than v   3

2 p2 p2 2p (b) (c) (d) p qg 2q 4q qg Two full turns of the circular scale of a screw gauge cover a distance of 1 mm on its main scale. The total number of divisions on the circular scale is 50. Further, it is found that the screw gauge has a zero error of – 0.03 mm. While measuring the diameter of a thin wire, a student notes the main scale reading of 3 mm and the number of circular scale divisions in line with the main scale as 35. The diameter of the wire is (a) 3.32 mm (b) 3.73 mm (c) 3.67 mm (d) 3.38 mm A pipe of length 85 cm is closed from one end. Find the number of possible natural oscillations of air column in the pipe whose frequencies lie below 1250 Hz. The velocity of sound in air is 340 m s–1. (a) 4 (b) 12 (c) 8 (d) 6 A large solid sphere with uniformly distributed positive charge has a smooth narrow tunnel through its centre. A small particle with negative charge, initially at rest far from the sphere, approaches it along the line of the tunnel, reaches its surface with a speed v, and passes through the tunnel. Its speed at the centre of the sphere will be (a) 0 (b) v (c) 2v (d) 1.5v Suppose an electron is attracted towards the origin by a force k/r, where k is a constant (a)

1/2

12. A projectile is fired vertically upward from the surface of earth with a velocity of kve, where ve is the escape velocity and k < 1. Neglecting air resistance, the maximum height to which it will rise, measured from the centre of the earth, is (R = radius of earth) 1 − k2 R k2 R (a) (b) (c) (d) R R k2 1 − k2

17.

18.

25

Test-4

and r is the distance of the electron from the origin. By applying Bohr model to this system, the radius of nth orbit of the electron is found to be rn and the kinetic energy of the electron is found to be Tn. Then which of the following is true? 1 (a) Tn ∝ 2 n (b) Tn is independent of n; rn ∝ n 1 (c) Tn ∝ ; rn ∝ n n 1 2 (d) Tn ∝ and rn ∝ n n 19. Let there be a spherically symmetric charge distribution with charge density varying 5 r  as ρ(r) = ρ0  −  for r ≤ R, and r(r) = 0 4 R for r > R, where r is the distance from the origin. The electric field at a distance r (r < R) from the origin is given by 4πρ0r  5 r  ρ r 5 r   −  (a) 0  −  (b)   3ε0  3 R  3ε0 4 R ρ0r  5 r  4ρ0r  5 r  (d)  −   −  4ε0  3 R  3ε0  4 R  A block of mass m is placed on a surface with x3 y = . If the a vertical cross section given by 6 coefficient of friction is 0.5, the maximum height above the ground at which the block can be placed without slipping is 1 1 2 1 m (b) m (c) m (d) m (a) 2 6 3 3 NUMERICAL VALUE TYPE A proton of mass m = 1.67 × 10–27 kg moves uniformly in a space where there are uniform, mutually perpendicular electric and magnetic fields with Ez = 4.5 × 104 V m–1 and Bx = 40 mT at an angle f = 60° with the x-axis in the xyplane. The pitch of the trajectory after the electric field is switched off is _____ m. A ball falls from height h. After 1 second, another ball falls freely from a point 20 m below the point from where the first ball falls. If both of them reach the ground at the same time, then value of h is _____m. A body undergoes no change in volume. Poisson’s ratio is ______ . (c)

20.

21.

22.

23.

24. In the given circuit, the value of b is 200. When IC = 2.5 mA, then VBC will be ______ V.

+20V 5.0 kW C

120 kW B

E

25. In Young’s double slit experiment, the y-coordinates of central maxima and tenth maxima are 2 cm and 5 cm respectively. When the apparatus is immersed in a liquid of refractive index 1.5, will be ______ cm. CHEMISTRY 26. Which among the following is a tetrabasic acid? (a) Orthophosphorous acid (b) Orthophosphoric acid (c) Hypophosphorous acid (d) Pyrophosphoric acid 27. Match the entries of List I with appropriate entries of List II and select the correct answer using the codes given below the lists. List I List II (Pollutants) (Effects) (P) Oxides of 1. Global warming sulphur (Q) Nitrogen 2. ‘Blue baby’ dioxide syndrome (R) Carbon 3. Respiratory dioxide diseases (S) Nitrates in 4. Red haze in traffic and congested areas drinking water (a) P-3, Q-4, R-2, S-1 (b) P-3, Q-4, R-1, S-2 (c) P-2, Q-1, R-4, S-3 (d) P-3, Q-1, R-2, S-4 28. How does H2O2 differ from O3 in its chemical action? (a) In oxidising PbS to PbSO4 (b) In liberating I2 from KI (c) In decolourising acidified KMnO4 (d) In oxidising K4[Fe(CN)6] to K3[Fe(CN)6] 29. The IUPAC name of the given compound is OH (a) 2,4,4-trimethylhex-5-ene-5-ol (b) 3,3,4,4-tetramethylbut-1-en-2-ol (c) 3,3,5-trimethylhex-1-en-2-ol (d) none of the above. 30. M is the molecular mass of KMnO4. The equivalent mass of KMnO4 when it is converted into K2MnO4 is (a) M (b) M/3 (c) M/5 (d) M/7

26

Very-Similar Practice Tests

31. The heat of formation of CH3OCH3(g) is [Given : B.E.H – H = 103 kcal, B.E.C – H = 87 kcal B.E.C – O = 70 kcal, B.E.O O = 177 kcal; Heat of vaporisation of 1 gram atom of carbon = 125 kcal.] (a) –14.5 kcal (b) – 15.4 kcal (c) + 14.5 kcal (d) + 15.4 kcal 32. Which of the following involves both calcination and carbon reduction processes to obtain metal from its ore? (a) Zinc from zinc carbonate (b) Calcium from calcium carbonate (c) Copper from copper sulphide (d) None of these 33. A solid ‘X’ on heating gives CO2 and a residue. The residue with H2O form ‘Y’. On passing an excess of CO2 through ‘Y’ in H2O, a clear solution of ‘Z’ is obtained. On boiling ‘Z’, ‘X’ is reformed. ‘X’ is (a) Ca(HCO3)2 (b) CaCO3 (c) Na2CO3 (d) K2CO3 34. A solution of a metal ion when treated with KI gives a red precipitate which dissolves in excess of KI to give a colourless solution. Moreover, the solution of metal ion on treatment with a solution of cobalt(II) thiocyanate gives rise to deep blue crystalline precipitate. The metal ion is (a) Pb2+ (b) Hg2+ (c) Cu2+ (d) Co2+ 35. Which of the following is not stabilised by hyperconjugation? +

(a) CH3 CH2 (c)

+

+

CH2

(b) (d)

+

36. An organic compound ‘A’ having molecular formula C2H3N on reduction gave another compound ‘B’. Upon treatment with nitrous acid, ‘B’ gave ethyl alcohol. On warming with chloroform and alcoholic KOH, it formed an offensive smelling compound ‘C’. The compound ‘C’ is (a) CH3CH2NH2 (b) CH3CH2N C (c) CH3C N (d) CH3CH2OH 37. (R) in the given reaction sequence is

+ CH3COCl

anhyd. AlCl3

(R )

(P)

HCN

H2O/dil. acid

(Q )

OH

OH

CH CH3 (a)

HOOC C CH3

(b)

OH

NH2

Cl C CH3 (c)

HOOC C CH3

(d)

38. The correct IUPAC name of the following alkene is

(a) Z-3-methyl-4-propyl-3-octene (b) E-3-methyl-4-propyl-3-octene (c) E-4-butyl-3-methyl-3-heptene (d) E-2-ethyl-3-propyl-2-heptene. 39. Which one of the following statements is not true? (a) For first order reaction, straight line graph of log (a – x) versus t is obtained for which slope = – k/2.303. (b) A plot of log k vs 1/T gives a straight line graph for which slope = – Ea/2.303R. (c) For third order reaction, the product of t1/2 and initial concentration a is constant. (d) Units of k for the first order reaction are independent of concentration units. 40. Which of the following has highest molar conductivity? (a) Diamminedichloroplatinum(II) (b) Tetraamminedichlorocobalt(III) chloride (c) Potassium hexacyanoferrate(II) (d) Pentacarbonyliron(0) 41. Match the species in column I with the shapes in column II and select the correct option. Column I Column II + (A) H3O (i) Linear (B) HC CH (ii) Angular (C) ClO2– (iii) Tetrahedral (D) NH+4 (iv) Pyramidal (a) A-(i), B-(ii), C-(iv), D-(iii) (b) A-(iv), B-(i), C-(ii), D-(iii) (c) A-(i), B-(ii), C-(iii), D-(iv) (d) A-(iv), B-(ii), C-(i), D-(iii)

27

Test-4

42. In which of the following polymers ethylene glycol is one of the monomer units? (a)

(c)

(b) [ CH2 CH ] 2 n

(d)

(c) CH2 CH CH CH2 CH CH2 n

(d)

O CH CH2 C O CH CH2 C O CH2CH3 O CH3 n

43. At temperature of 298 K the emf of the following electrochemical cell Ag(s)|Ag+(0.1 M)||Zn2+(0.1 M)|Zn(s) will be (given E°cell = –1.562 V) (a) –1.532 V (b) –1.503 V (c) 1.532 V (d) –3.06 V 44. The pKa of acetylsalicylic acid (aspirin) is 3.5. The pH of gastric juice in human stomach is about 2-3 and the pH in the small intestine is about 8. Aspirin will be (a) unionised in the small intestine and in the stomach (b) completely ionised in the small intestine and in the stomach (c) ionised in the stomach and almost unionised in the small intestine (d) ionised in the small intestine and almost unionised in the stomach. 45. p-Cresol reacts with chloroform in alkaline medium to give a compound ‘A’ which adds hydrogen cyanide to form the compound ‘B’. Compound ‘B’ on acidic hydrolysis gives chiral carboxylic acid. The structure of the carboxylic acid is

NUMERICAL VALUE TYPE 46. The unit cells present in a cube-shaped ideal crystal of NaCl of mass 1 g are x × 1021. The value of x is ____. 47. 0.008 g of starch is required to prevent coagulation of 10 mL of gold sol when 1 mL of 10% NaCl solution is present. The gold number of starch sol is ____. 48. A hydrocarbon (X) having molecular weight 70 gives a single monochloride but three dichlorides on chlorination in the presence of ultraviolet light. The number of C-atoms in hydrocarbon (X) is ____. 49. In the disproportionation reaction, 3HClO3 → HClO4 + Cl2 + 2O2 + H2O the equivalent mass of the oxidising agent is ____. (Molar mass of HClO3 = 84.45) 50. A diatomic molecule has a dipole moment of 1.2 D. If the bond distance is 1.0 Å, 1/x of an electronic charge exists on each atom. The value of x is ____. MATHEMATICS 51. Domain of the function f(x) = sin–1(2x2 + 3x + 1) is : (a) (–1, 1) (b) (–∞, ∞) (c)

(a)

 3   − 2 , 0



1 2

(d)  −∞, −  ∪ (2, ∞)  

cos θ − sin θ −1  , A is given by  sin θ cos θ 

52. If A =  (a) –A π

(b)

53.

∫e

sin2 x

(b) AT

(c) –AT

(d) A

(c) 1

(d) p

cos3 xdx

0

(a) 0

(b) –1

28

Very-Similar Practice Tests

 x2 −1  54. If lim  − ax − b  = 2, then a − b = x → ∞ x +1 (a) 1 (b) 2 (c) 3 (d) 4 55. The line passing through the points (5, 1, a) and (3, b, 1) crosses the yz-plane at the point  17 −13  . Then   0, , 2 2  (a) a = 8, b = 2 (b) a = 2, b = 8 (c) a = 4, b = 6 (d) a = 6, b = 4 56. The first 3 terms in the expansion of (1 + ax)n, (n ≠ 0) are 1, 6x and 16x2. Then the value of a and n are respectively (a) 2 and 9 (b) 3 and 2 (c) 2/3 and 9 (d) 3/2 and 6 57. sin36°sin72°sin108°sin144° = (a) 1/4 (b) 1/16 (c) 3/4 (d) 5/16 x decreases in the 58. The function f (x) = 1 + x2 interval (a) (– ∞, – 1] ∪ [1, ∞) (b) (– 1, 1) (c) (– ∞, ∞) (d) none of these 59. A pair of fair dice is thrown independently three times. The probability of getting a score of exactly 9 twice is (a) 8/729 (b) 8/243 (c) 1/729 (d) 8/9 60. If the product of the roots of the equation x 2 − 2 2 kx + 2 e 2 log k − 1 = 0 is 31, then the roots of the equation are real for k = (a) – 4 (b) 1 (c) 4 (d) 0 61. The length of the latus rectum of the hyperbola 16x2 – 25y2 + 400 = 0 is (a)

32 5

62. Let I =

(b)

16 5

(c)

25 4

(d)

25 2

2

∫ (x − [x])dx ,

−2

where [x] represents

the greatest integer in x not greater than x. Then the value of I is (a) 4 (b) 3 (c) 2 (d) 1 63. The number of ways in which four letters of the word ‘MATHEMATICS’ can be arranged is given by (a) 136 (b) 192 (c) 1680 (d) 2454 64. The foot of the perpendicular from the point (2, 4) upon x + y = 4 is (a) (1, 3) (b) (3, –1) (c) (2, 2) (d) (4, 0) 65. The value of tan20° + 2tan50° – tan70° is equal to

(a) 1 (c) tan50°

(b) 0 (d) None of these

66. If a, b, c are in A.P., then

(a − c)2

= (b2 − ac) (a) 1 (b) 2 (c) 3 (d) 4 67. If p : The earth is round, q : 3 + 4 = 7, then (~p) ∨ (~q) is (a) It is not that the earth is round or 3 + 4 = 7 (b) The earth is round and 3 + 4 = 7 (c) It is not that the earth is round or it is not that 3 + 4 = 7 (d) The earth is round or 3 + 4 = 7 68. The mean deviation from the mean of the data 3, 10, 10, 4, 7, 10, 5 is (a) 2 (b) 2.57 (c) 3 (d) 3.75 69. The solution of the differential equation dy

e dx = x +1, when y(0) = 3, is (a) y = xlogx – x + 2 (b) y = (x + 1)log|x + 1| – x + 3 (c) y = (x + 1)log|x + 1| + x + 3 (d) y = xlogx + x + 3 70. The function f : R – {0} → R,

1 2 − can be made continuous 2 x x e −1 at x = 0 by defining f(0) as (a) 2 (b) –1 (c) 0 (d) 1 f (x ) =

NUMERICAL VALUE TYPE 71. If ( 5 + 3 i)33 = 249 z, then modulus of the complex number z is equal to ______.

1 72. The value of 1 1

a b c

bc 1 ca − 1 ab 1

a

a2

b

b2

c

c2

is ______. ^

^

^

73. The distance of the point i + 2 j + 3 k from

 ^ ^ ^

the plane r ⋅ ( i + j + k ) = 5 measured parallel ^

^

^

to the vector 2 i + 3 j − 6 k is _____ .       74. a ·[( b + c ) × ( a + b + c )] equals ______. 75. The smallest natural number m > 90 for which n = 111  ......  1 is not a prime number  is ______. m times

Telegram @unacademyplusdiscounts

Join Us on Telegram for More Such Books https://telegram.me/unacademyplusdiscounts

Join us from the above link or search ''unacademyplusdiscounts'' in Telegram

30

Very-Similar Practice Tests

VERY SIMILAR

PRACTICE TEST 5 Time : 3 hrs.

Max. Marks : 300

PHYSICS 1. In a particular system, the unit of length, mass and time are chosen to be 10 cm, 10 g and 0.1 s respectively. The unit of force in this system will be equivalent to (a) 0.1 N (b) 1 N (c) 10 N (d) 100 N 2. A cyclotron is operated at an oscillator frequency of 24 MHz and has a dee radius R = 60 cm. What is magnitude of the magnetic field B (in tesla) to accelerate deuterons (mass = 3.34 × 10–27 kg)? (a) 9.5 (b) 7.2 (c) 5.0 (d) 3.2 3. The speed of a projectile at its maximum 3 times its initial speed. If the height is 2 range of the projectile is P times the maximum height attained by it, then P equals 4 3 (a) (b) 2 3 (c) 4 3 (d) 3 4 4. The total intensity of the earth’s magnetic field at equator is 5 units. What is its value at the poles? (a) 5 (b) 4 (c) 3 (d) 2 5. A uniform solid cylinder has a radius R and length L. If the moment of inertia of this cylinder about an axis passing through its centre and normal to its circular face is equal to the moment of inertia of the same cylinder about an axis passing through its centre and perpendicular to its length, then (a) L = R (b) L = 3R (c) L =

R 3

(d) L =

3 R 2

6. A coil of inductance 300 mH and resistance 2 W is connected to a source of voltage 2 V. The current reaches half of its steady state value in time t is (a) 0.05 s (b) 0.1 s (c) 0.15 s (d) 0.3 s 7. A body is projected up with a velocity equal to 3  4 

th

of the escape velocity from the surface

of the earth. The height it reaches is (Radius of the earth = R) (a) 10 R (b) 9 R (c) 9 R (d) 10 R 9 7 8 3 8. Radius of a circular ring is changing with time and the ring is placed in a uniform magnetic field perpendicular to its plane. The variation of r with time t as shown in the figure. The magnitude of induced emf (e) is best represented by

(a)

(b)

(c)

(d)

9. A gaseous mixture consists of 16 g of helium and 16 g of oxygen. The ratio CP /CV of the mixture is (a) 1.4 (b) 1.54 (c) 1.59 (d) 1.62

Test-5

31

10. A ray incident at a point at an angle of incidence of 60° enters a glass sphere of refractive index µ = 3 and is reflected and refracted at the further surface of the sphere. The angle between the reflected and refracted rays at this surface is (a) 50° (b) 60° (c) 90° (d) 40° 11. An air column in a pipe which is closed at one end, will be in resonance with the vibrating body of frequency 166 Hz, if the length of the air column is (a) 0.5 m (b) 1.0 m (c) 1.5 m (d) 2.0 m 12. Two coherent monochromatic light beams of intensities I and 4I are superimposed. The maximum and minimum possible intensities in the resulting beam are (a) 5I and I (b) 5I and 3I (c) 9I and I (d) 9I and 3I 13. If the work done in stretching a wire by 1 mm is 2 J, the work necessary for stretching another wire of same material but with double radius of cross-section and half the length by 1 mm is (a) 16 J

(b) 8 J

(c) 4 J

(d)

1 J 4

14. The incident intensity on a horizontal surface at sea level from sun is about 1 kW m–2. Assuming that 50 percent of this intensity is reflected and 50 percent is absorbed, the radiation pressure on this horizontal surface is (a) 5 × 10–11 Pa (b) 5 × 10–6 Pa (c) 1 × 10–6 Pa (d) 1 × 10–11 Pa 15. A parallel plate capacitor of capacity 100 mF is charged by a battery of 50 volts. The battery remains connected and if the plates of the capacitor are separated so that the distance between them becomes double the original distance, the additional energy given to the battery by the capacitor in joules is 125 × 10−3 (a) (b) 12.5 × 10–3 2 (c) 1.25 × 10 –3 (d) 0.125 × 103 16. Given that a photon of light of wavelength 10,000 Å has an energy equal to 1.23 eV. When light of wavelength 5000 Å and intensity I0 falls on a photoelectric cell, the surface current is 0.40 × 10–6 A and the stopping potential is 1.36 V, then the work function is (a) 0.43 eV (b) 0.55 eV (c) 1.10 eV (d) 1.53 eV

17. A glass capillary tube of inner diameter 0.28 mm is lowered vertically into water in a vessel. The pressure to be applied on the water in the capillary tube so that water level in the tube is same as that in the vessel in N m–2 is (Surface tension of water = 0.07 N m–1 and atmospheric pressure = 105 N m–2) (a) 103 (b) 99 × 103 3 (c) 100 × 10 (d) 101 × 103 18. The largest wavelength in the ultraviolet region of the hydrogen spectrum is 122 nm. The smallest wavelength in the infrared region of the hydrogen spectrum (to the nearest integer) is (a) 802 nm (b) 823 nm (c) 1882 nm (d) 1648 nm 19. Mean free path of a gas molecule is (a) inversely proportional to number of molecules per unit volume (b) inversely proportional to diameter of the molecule (c) directly proportional to the square root of the absolute temperature (d) directly proportional to the molecular mass 20. A disc passes through a pin at the rim and is capable of oscillating freely. The period of oscillation of the disc is (a) T = 2 π

2R 3g

(c) T = 2 π 3 R 2g

(b) T = 2 π

A O

4R 3g

(d) none of these

NUMERICAL VALUE TYPE 21. There are two radioactive substances A and B. Decay constant of B is two times that of A. Initially, both have equal number of nuclei. After n half lives of A, rate of disintegration of both are equal. The value of n is _____. 22. Two masses of 10 kg and 20 kg respectively are connected by a massless spring. A force of 200 N is applied on the 20 kg mass as shown in the figure. At the instant shown, the 10 kg mass has acceleration 12 m s–2. For 20 kg mass the acceleration is _____ m s–2. 10 kg

20 kg

200 N

32

Very-Similar Practice Tests

23. One end of a spring of natural length l0 = 0.1 m and spring constant k = 80 N m–1 is fixed to the ground and the other end is fitted with a smooth ring of mass m = 2 g, which is allowed to slide on a horizontal rod fixed at a height h = 0.1 m. Initially the spring makes an angle of 37° with the vertical when the system is released from rest. 0.1 m

{

37°

When the spring becomes vertical, if the speed of ring is v, then the value of v is _____m s–1. 4 (Given cos 37° = ) 5 24. In the network shown in the figure, the value of current through 4 V battery is _____ A. 3 4V

1

2V

1

25. In brass, the velocity of longitudinal wave is 100 times the velocity of the transverse wave. If Y = 1 × 1011 N m–2, then stress in the wire is x × 107 N m–2. The value of x _____. CHEMISTRY 1 2B, rate of A 2 disappearance of A is related to rate of appearance of B by the expression −d [ A] 1 d [B] −d [ A] d [ B] (b) (a) = =4 dt dt dt 4 dt −d [ A] 1 d [ B] −d [ A] d [ B] (c) (d) = = dt 2 dt dt dt

26. For a reaction

27. For the reduction of NO3– ion in an aqueous solution, E° is +0.96 V. Values of E° for some metal ions are given below : V2+(aq) + 2e– → V; E° = –1.19 V Fe3+(aq) + 3e– → Fe; E° = – 0.04 V Au3+(aq) + 3e– → Au; E° = +1.40 V Hg2+(aq) + 2e– → Hg; E° = +0.86 V The pair of metals that is not oxidised by NO–3 in aqueous solution is (a) V and Hg (b) Hg and Fe (c) Fe and Au (d) Fe and V

28. For an octahedral complex, which of the following d-electron configurations will give maximum CFSE? (a) d 6 (High spin) (b) d 5 (Low spin) (c) d 4 (Low spin) (d) d 7 (High spin) 29. Which one of the following compounds has the trigonal bipyramidal geometry with three equatorial positions occupied by lone pairs of electrons? (a) AlCl3 (b) XeF2 (c) Pt(NH3)2Cl2 (d) CH3MgBr

30.

The correct order towards electrophilic substitution reaction is (a) (iv) > (iii) > (ii) > (i) (b) (i) > (ii) > (iii) > (iv) (c) (iii) > (ii) > (i) > (iv) (d) (iii) > (iv) > (i) > (ii) 31. We have three aqueous solutions of NaCl labelled as ‘A’, ‘B’ and ‘C’ with concentrations 0.1 M, 0.01 M and 0.001 M, respectively. The value of van’t Hoff factor for these solutions will be in the order (a) iA < iB < iC (b) iA > iB > iC (c) iA = iB = iC (d) iA < iB > iC 32. A solution of sulphur dioxide in water reacts with H2S precipitating sulphur. Here sulphur dioxide acts as (a) an oxidising agent (b) a reducing agent (c) an acid (d) a catalyst. 33. CH3(CH2)4CH3

A C

What is D ? (a)

(b)

(c)

(d)

B D

Test-5

34. Among the following molecules : (i) XeO3 (ii) XeOF4 (iii) XeF6 those having same number of lone pairs on Xe are (a) (i) and (ii) only (b) (i) and (iii) only (c) (ii) and (iii) only (d) all of these. 35. A white solid (X) on heating evolves CO2 and gives a white residue (Y) which is soluble in water. (Y) also gives CO2 when treated with dilute acid. (X) and (Y) are respectively (a) Na2CO3 and NaHCO3 (b) NaHCO3 and Na2CO3 (c) CaCO3 and CaHCO3 (d) CaHCO3 and CaCO3 36. For the process,  H2O(l) (1 bar, 373 K) ↽ ⇀  H2O(g) (1 bar, 373 K), the correct set of thermodynamic

33 (b) On hydrolysis (+)-lactose gives equal amount of D(+)-glucose and D(+)galactose. (c) (+)-Lactose is a b-glycoside formed by the union of a molecule of D(+)-glucose and a molecule of D(+)-galactose. (d) (+)-Lactose is a reducing sugar and does not exhibit mutarotation. 41. Which of the following is used is Clark’s method for the removal of temporary hardness? (a) Na2CO3 (b) Ca(OH)2 (c) Na2Al2Si2O8 ⋅ xH2O (d) Na2[Na4(PO3)6] 42. Final product of the given reaction sequence is

parameters is (a) DG = 0, DS = +ve (b) DG = 0, DS = –ve (c) DG = +ve, DS = 0 (d) DG = –ve, DS = +ve. 37. Following are the properties related to adsorption : I. Reversible II. Results into unimolecular layer III. Low heat of adsorption IV. Occurs at low temperature and decreases with increasing temperature. Which of the above properties are for physical adsorption? (a) I, II, III only (b) I, III, IV only (c) II, III, IV only (d) I, III only 38. Which of the following chemicals are used to manufacture methyl isocyanate that caused “Bhopal Gas Tragedy”? (i) Methylamine (ii) Phosgene (iii) Phosphine (iv) Dimethylamine (a) (i) and (ii) (b) (iii) and (iv) (c) (i) and (iii) (d) (ii) and (iv) 39. A solution of (+)-2-chloro-2-phenylethane in toluene racemises slowly in the presence of a small amount of SbCl5, due to the formation of (a) carbanion (b) carbene (c) free radical (d) carbocation. 40. Which one of the following statements is not true regarding (+) lactose? (a) (+)-Lactose, C12H22O11 contains 8 –OH groups.

(a)

(b)

(c)

(d)

43. Which of the following statements is correct for the periodic classification of elements? (a) Atomic size gradually increases from left to right in a period of representative elements. (b) Across a transition series, atomic size gradually but somewhat irregularly decreases and then increases at the end of the series. (c) Electron gain enthalpies of third period elements, sulphur and chlorine are less negative than those of oxygen and fluorine of second period in respective groups. (d) Ionisation potential gradually but irregularly decreases across a period in representative elements. 44. Which of the following reactions does not give N-ethyl cyclopentyl amine as a major product? (a)

34

Very-Similar Practice Tests

(b)

52. The value of sum

13

∑ (in + in+1) ,

where

n=1

i = −1 equals (b) i – 1 (c) –i (d) 0 ax –ax 53. The function f (x) = e + e , a > 0 is monotonically increasing for (a) – 1 < x < 1 (b) x < – 1 (c) x > – 1 (d) x > 0 (a) i

(c) (d) 45. Which of the following crystals has unit cell such that a ≠ b ≠ c and a ≠ b ≠ g ≠ 90°? (a) K2Cr2O7 (b) NaNO3 (c) KNO3 (d) K2SO4

54.

NUMERICAL VALUE TYPE 46. The number of ethers in the given list which cannot be prepared by Williamson’s synthesis is_____. CH3OCH2CH3, C6H5OCH3, C6H5OCH2CH3, (C6H5)2O,(CH3)3COCH3, (CH3)3COCH2CH3, (CH3)3COC(CH3)3, (C2H5)2O,C6H5CH2OC6H5 47. At 400 K, the root mean square speed of a gas X (molecular weight = 40) is equal to the most probable speed of gas Y at 60 K. The molecular weight of Y is______. 48. At a certain temperature and total pressure of 105 Pa, iodine vapour contains 40% by 2I(g). The Kp for volume of I atoms, I2(g) 4 the equilibrium is x × 10 . The value of x is _______. 49. The molarity of a sulphuric acid solution in which the mole fraction of water is 0.86, is______. 50. To stop the flow of photoelectrons produced by electromagnetic radiation incident on a certain metal, a negative potential of 300 V is required. If the photoelectric threshold of metal is 1500 Å, the frequency of the incident radiation is x × 1016 Hz. the value of x is_______. .MATHEMATICS 51. Let U be a universal set and A ∪ B ∪ C = U. Then ((A – B) ∪ (B – C) ∪ (C – A))′ = (b) A ∩ B ∩ C (a) A ∪ B ∪ C (c) A ∪ ( B ∩ C )

(d) A ∩ ( B ∪ C )

55.

56.

57.

a +1 a + 2 a + p If a + 2 a + 3 a + q = 0, then p, q, r are a+3 a+4 a+r in : (a) AP (b) GP (c) HP (d) none of these If a and b are solutions of sin2x + a(sinx) + b = 0 as well as that of cos2x + c(cosx) + d = 0, then sin(a + b) is equal to 2 2 2bd (b) a + c (a) 2ac b2 + d2 2 2 2ac (c) b + d (d) 2 a + c2 2bd 2 sin(π cos x) = lim x →0 x2 (a) –p (b) p (c) π (d) 1 2 If x1 and x2 are means of two distribution such that x1 < x2 and x is the mean of the joint distribution then x +x (b) x > x2 (a) x = 1 2 2 (c) x < x1 (d) x1 < x < x2 x

58. If

∫ 0

(a)

1

f (t )dt = x + ∫ tf (t )dt , then f ( x) = x

1 1 1 1 (b) (c) (d) x − 1 1+ x x 1− x

 α  |tan x| −1 ; b. α β γ 3

75. The value of x in the given equation x

4 −3

x−

1 2

=3

x+

1 2

− 22 x −1 is

Telegram @unacademyplusdiscounts

Join Us on Telegram for More Such Books https://telegram.me/unacademyplusdiscounts

Join us from the above link or search ''unacademyplusdiscounts'' in Telegram

Test-6

37

VERY SIMILAR

PRACTICE TEST 6 Time : 3 hrs.

Max. Marks : 300

PHYSICS 1. The number of significant figures in the numbers 4.8000 × 104 and 48000.50 are respectively (a) 5 and 6 (b) 5 and 7 (c) 2 and 7 (d) 2 and 6 2. The length of a potentiometer wire is l. A cell of emf e is balanced at a length l/5 from the positive end of the wire. If length of the wire is increased by l/2. At what distance will the same cell give a balance point? 2 3 3 4 (a) l (b) l (c) l (d) l 15 15 10 10 3. A body A starts from rest with an acceleration a1. After 2 seconds, another body B starts from rest with an acceleration a2. If they travel equal distances in the 5th second, after the start of A, then the ratio a1 : a2 is equal to (a) 5 : 9 (b) 5 : 7 (c) 9 : 5 (d) 9 : 7 4. A particle of charge q and mass m moves in a circular orbit of radius r with angular speed w. The ratio of the magnitude of its magnetic moment to that of its angular momentum depends on (a) w and q (b) wq and m (c) q and m (d) w and m 5. A machine gun is mounted on a 2000 kg car on a horizontal frictionless surface. At some instant, the gun fires 10 bullets/second and each of mass 10 g with a velocity of 500 m s–1. The acceleration of the car is (a) 0.025 m s–2 (b) 0.25 m s–2 –2 (c) 0.50 m s (d) 500 m s–2 6. What will happen to the inductance L of a solenoid when the number of turns and the

length are doubled keeping the area of crosssection same? (b) L (c) 2L (d) 4L (a) L 2 7. A bomb moving with velocity ^

^

^

(40 i + 50 j − 25 k ) m s −1 explode into two pieces of mass ratio 1 : 4. After explosion

the smaller piece moves away with velocity ^

^

^

(200 i + 70 j + 15 k ) m s–1. The velocity of

larger piece after explosion is (a) 45 ^j − 35 k^

(b) 45^i − 35 ^j

(c) 45 k^ − 35 ^j

(d) −35^i + 45 k^

8. A ray of light is incident normally on one of the faces of a prism of apex angle 30° and refractive index 2. The angle of deviation of the ray is (a) 0° (b) 12.5° (c) 15° (d) 22.5° 9. Particles of masses m, 2m, 3m … nm grams are placed on the same line at distance l, 2l, 3l … nl cm from a fixed point. The distance of centre of mass of the particles from the fixed point in centimetre is (b) l (a) (2n + 1)l n +1 3 2 2l 1 n ( n + ) l (c) (d) 2 n(n2 + 1) 10. When one of the slits of Young’s experiment is covered with a transparent sheet of thickness 4.8 mm, the central fringe shifts to a position originally occupied by the 30th bright fringe. What should be the thickness of the sheet if the central fringe has to shift to the position occupied by 20th bright fringe? (a) 3.8 mm (b) 1.6 mm (c) 7.6 mm (d) 3.2 mm

38

Very-Similar Practice Tests

11. A gas expands with temperature according to the relation V = KT2/3. Calculate work done when the temperature changes by 60 K? (a) 10R (b) 30R (c) 40R (d) 20R 12. The electric field (in N C–1) in an electromagnetic wave is given by x  E = 50sin ω  t −  .  c

The energy stored in a cylinder of crosssection 10 cm2 and length 100 cm along the x-axis will be (a) 5.5 × 60–12 J (b) 1.1 × 10–11 J –11 (c) 2.2 × 10 J (d) 1.65 × 10–11 J 13. A liquid X of density 3.36 g cm–3 is poured in a U-tube, which contains Hg. Another liquid Y is Y X poured in left arm 8 cm with height 8 cm, upper levels of X and Y are same. What is the density of Y? (a) 0.8 g cm–3 (b) 1.2 g cm–3 –3 (c) 1.4 g cm (d) 1.6 g cm–3

10 cm

14. A common emitter amplifier has a voltage gain of 50, an input impedance of 100 W and an output impedance of 200 W. The power gain of the amplifier is (a) 500 (b) 1000 (c) 1250 (d) 100 15. The Poisson’s ratio of a material is 0.4. If a force is applied to a wire of this material, there is a decrease of cross-sectional area by 2%. The percentage increase in its length is (a) 3% (b) 2.5% (c) 1% (d) 0.5% 16. A signal wave of frequency 12 kHz is modulated with a carrier wave of frequency 2.51 MHz. The upper and lower side band frequencies are respectively (a) 2512 kHz and 2508 kHz (b) 2522 kHz and 2488 kHz (c) 2502 kHz and 2498 kHz (d) 2522 kHz and 2498 kHz 17. Three rods of same dimensions have thermal conductivities 3K, 2K and K respectively. They are arranged as shown below 50°C 3K T 2K 100°C K 0°C

What will be the temperature T of the junction? 100 200 °C (a) (b) °C 3 3 50 (c) 75°C (d) °C 3 18. The mass of deuteron (1H2) nucleus is 2.014102 u. If the masses of proton and neutron are 1.007825 u and 1.008665 u respectively, nucleus the binding energy per nucleon of 1H2 nucleus is (a) 2.2 MeV (b) 1.1 MeV (c) 0.5 MeV (d) 0.25 MeV 19. An electric dipole of length 1 cm is placed with the axis making an angle of 30° with an electric field of strength 104 N C – 1. If it experiences a torque of 10 2 N m, the potential energy of the dipole is (a) 0.245 J (b) 2.45 J (c) 0.0245 J (d) 24.5 J 20. A rod is oscillating from a support, freely. The period is (a) T = 2π l

g

(b) T = 2 π 2l g (c) T = 2 π

l 3g

(d) T = 2 π

2l 3g

NUMERICAL VALUE TYPE 21. A parallel plate capacitor is maintained at a certain potential difference. When a 3 mm thick slab is introduced between the plates, in order to maintain the same potential difference, the distance between the plates is increased by 2.4 mm. The dielectric constant of the slab is ____. 22. A silver sphere of radius 1 cm and work function 4.7 eV is suspended from an insulating thread in free-space. It is under continuous illumination of light of wavelength 200 nm. As photoelectrons are emitted, the sphere gets charged and acquires a potential. The maximum number of photoelectrons emitted from the sphere is A × 10Z (where 1 < A < 10). The value of Z is ______.

Test-6

39

23. The activity of a freshly prepared radioactive sample is 1010 disintegrations per second, whose mean life is 109 s. The mass of an atom of this radioisotope is 10–25 kg. The mass of the radioactive sample is ______ mg. 24. The period of revolution of planet A around the sun is 8 times that of B. The distance of A from the sun is ______ times that of B from the sun. 25. In a car race sound signals emitted by the two cars are detected by the detector on the straight track at the end point of the race. Frequency observed are 330 Hz and 360 Hz and the original frequency is 300 Hz of both cars. Race ends with the separation of 100 m between the cars. Assume both cars move with constant velocity and velocity of sound is 330 m s–1. The time taken by winning car is ______ s. CHEMISTRY 26. Aniline is treated with bromine water to give an organic compound ‘X’ which when treated with NaNO2 and HCl at 0°C gives a water soluble compound ‘Y’. Compound ‘Y’ on treatment with Cu2Cl2 and HCl gives compound ‘Z’. Compound ‘Z’ is (a) o-bromochlorobenzene (b) p-bromochlorobenzene (c) 2, 4, 6-tribromophenol (d) 2, 4, 6-tribromochlorobenzene. 27. Temporary hardness and permanent hardness in water can be removed respectively by addition of (a) CaO, CaCO3 (b) CaO, Na2CO3 (c) Na2CO3, CaO (d) NaHCO3, CaCl2 28. According to adsorption theory of catalysis, the speed of the reaction increases because (a) concentration of the reactant molecules at active centres of the catalyst becomes high due to adsorption (b) in the process of adsorption, the activation energy of molecules becomes large (c) adsorption produces heat which increases the speed of the reaction (d) adsorption lowers the activation energy of the reaction. 29. Formation of a solution from two components can be considered as

(i) Pure solvent → separated solvent molecules, DH1 (ii) Pure solute → separated solute molecules, DH2 (iii) Separated solvent and solute molecules → solution, DH3 Solution so formed will be ideal if (a) DHsolution = DH1 + DH2 – DH3 (b) DHsolution = DH1 – DH2 – DH3 (c) DHsolution = DH3 – DH1 – DH2 (d) DHsolution = DH1 + DH2 + DH3 30. During the extraction of Cu in the blast furnace at the roasting step, (a) Cu2S gets converted to Cu2O if temperature is below 800°C (b) Cu2S gets converted to Cu2O if temperature is above 800°C (c) FeS remains unaffected and gets converted to FeO only at temperature above 1000°C (d) FeSiO3 is formed and removed. 31. If we consider that 1/6, in place of 1/12, mass of carbon atom is taken to be the relative atomic mass unit, the mass of one mole of a substance will (a) decrease to half (b) increase two fold (c) remain unchanged (d) be a function of the molecular mass of the substance. 32. Match the polymers given in column I with their chemical names given in column II.

Column I Column II Nylon 6 1. Polyvinyl chloride PVC 2. Polyacrylonitrile Acrilan 3. Polycaprolactum Natural rubber 4. cis-Polyisoprene P–1, Q–2, R–3, S–4 P–4, Q–3, R–1, S–2 P–3, Q–1, R–4, S–2 P–3, Q–1, R–2, S–4 33. Consider the following equilibrium in a 2NO2(g). closed container, N2O4(g) At a fixed temperature, the volume of the reaction mixture is halved. For this change, which of the following statements holds true regarding the equilibrium constant (Kp) and degree of dissociation (a)? (a) Neither Kp nor a changes. (b) Both Kp and a change. (c) Kp changes but a does not. (d) Kp does not change but a changes P. Q. R. S. (a) (b) (c) (d)

40

Very-Similar Practice Tests

34. The detergent which is used as a germicide is (a) sodium lauryl sulphate (b) cetyltrimethylammonium chloride (c) lauryl alcohol ethoxylate (d) sodium-2-dodecylbenzenesulphonate.

:

35. Which of the following is an anti-aromatic compound? CH3 (b) (a) N H

40. In kinetic study of a chemical reaction, slopes are drawn at different times in the plot of concentration of reactants versus time. The magnitude of slopes with increase of time (a) remains unchanged (b) increases (c) decreases (d) increases and decreases periodically

(c)

(d)

36. A 1.0 M solution with respect to each of metal halides AX3, BX2, CX3 and DX2 is electrolysed using platinum electrodes. If E ° 3 + = 1.50 V, E ° 2 + = 0.34 V, A

/A

B

/B

E ° 3 + = −0.74 V, E ° 2 + = −2.37 V, C /C D /D the correct sequence in which the various metals are deposited at the cathode, is (a) A, B, C, D (b) D, C, B, A (c) A, B, C (d) C, B, A 37. Schottky defect occurs mainly in electrovalent compounds where (a) positive ions and negative ions are of different size (b) positive ions and negative ions are of same size (c) positive ions are small and negative ions are big (d) positive ions are big and negative ions are small. 38. The correct IUPAC name of the compound [Cr(NH3)5(NCS)] [ZnCl4], is (a) pentaammineisothiocyanatochromium (III) tetrachloridozincate(II) (b) pentaammineisothiocyanatozinc chloridochromate(III) (c) pentaammineisothiocyanatochromate(II) (d) isothiocyanatopentaamminechromium (II) zincchlorido(IV). 39. Consider the given curve, the correct y relationship among N T1 and T2 is N (a) T1 > T2 (b) T2 > T1 (c) T1 = T2 (d) can’t be predicted.

T2 T1 z Speed

41. Phenol is converted into bakelite by heating it with formaldehyde in the presence of an alkali or an acid. Which statement is true regarding this reaction? (a) The electrophile in both cases is CH2 O. (b) The electrophile in both cases is +

CH2 OH. (c) The electrophile is CH2 O in the + presence of an alkali and CH2 OH in the presence of an acid. (d) It is a nucleophilic substitution reaction. 42. The correct order of bond order values among the following species is (i) NO– (ii) NO+ (iii) NO (iv) NO2+ (v) NO2– (a) (i) < (iv) < (iii) < (ii) < (v) (b) (iv) = (ii) < (i) < (v) < (iii) (c) (v) < (i) < (iv) = (iii) < (ii) (d) (ii) < (iii) < (iv) < (i) < (v) 43. An organic compound ‘X’ on treatment with pyridiniumchlorochromate in dichloromethane gives compound ‘Y’. Compound ‘Y’ reacts with I2 and alkali to form triiodomethane. The compound ‘X’ is (a) C2H5OH (b) CH3CHO (c) CH3COCH3 (d) CH3COOH 44. An element X belongs to fourth period and fifteenth group of the periodic table. Which of the following statements is true? (a) It has a completely filled s-orbital and a partially filled d-orbital. (b) It has completely filled s-and p-orbitals and a partially filled d-orbital. (c) It has completely filled s-and p-orbitals and a half-filled d-orbital. (d) It has a half-filled p-orbital and completely filled s-and d-orbitals.

Test-6

41

45. The standard reduction potential values of three metallic cations, X, Y and Z are 0.52, – 3.03 and –1.18 V respectively. The order of reducing power of the corresponding metals is (a) Y > Z > X (b) X > Y > Z (c) Z > Y > X (d) Z > X > Y NUMERICAL VALUE TYPE 46. Among the following, the total number of alkyl halides that would react by SN1 mechanism is ______ . CH3Br, CH3CH2Br, CH3CH2CH2I, (CH3)3CBr, BrCH2CH CH2, C6H5CH2Br, (CH3)3CCH2Br, C6H5 CHBr CH3, CH3CH CHCH2Cl 47. 2 moles of a perfect gas at 27°C is compressed reversibly and isothermally from a pressure of 1.01 × 105 Nm–2 to 5.05 × 106 Nm–2. The free energy change is x × 104 joule. The value of x is ______ . 48. Titanium shows magnetic moment of 1.73 B.M. in its compound. The oxidation number of Ti in the compound is ______ . 49. In the compound beryl, number of oxygen atoms shared by one silicate tetrahedron is ______ . 50. In a compound C, H and N are present in 9 : 1 : 3.5 by weight. If molecular weight of the compound is 108, the number of N atoms present in the molecular formula will be ______ . .MATHEMATICS 51. Let g(x) = 1 + x – [x], [x] is the greatest integer not greater than x. −1, x < 0  If f (x) =  0, x = 0 , then for all x, f(g(x))  1, x > 0  equals (a) x (b) 1 (c) f(x) (d) g(x) 52.

∫

2x 1− 4

x

53. Let f (x) = lim

1 + x 2n

n→∞

, then

(a) f(x) is continuous at x = 1 (b)

lim f ( x ) = log e 3

x →1+

(c) (d)

lim f ( x ) = − sin1

x →1+

lim f ( x ) does not exist

x →1−

π 3π 5π 7π is equal to 54. cos cos cos cos 8 8 8 8 (a) (c)

1 2

(b)

1 8

(d)

1− 2 2 2 1+ 2 2 2

55. If S.D. of a variate x is s then the S.D. of ax + b (∀ a, b, p ∈ R) is p (a)

a a σ (b) σ (c) p x p x

p p σ x (d) σ x a a

56. In how many ways n books can be arranged in a row so that two specified books are not together? (a) n! – (n – 2)! (b) (n – 1)! (n – 2) (c) n! – 2(n – 1) (d) (n – 2)n! 57. If a, b, c are respectively the pth, qth, rth terms a p 1 of an A.P., then b q 1 = c r 1 (a) 1

(b) –1

(c) 0

(d) pqr

58. The angle between the lines 3x = 6y = 2z and 3x + 2y + z – 5 = 0 = x + y – 2z – 3 is π π π π (a) (b) (c) (d) 4 6 2 3

dx =

1 (a) (log2)sin–1 2x + C (b) sin −1 2 x + C 2 1 (c) sin −1 2 x + C (d) 2log2 sin–12x + C log 2

log e (2 + x ) − x 2n sin x

1/3

59. lim

(cos x )

x →0

(a)

1 3

1/2

− (cos x )

sin2 x (b)

1 6

(c)

= 1 2

(d)

1 12

42

Very-Similar Practice Tests

60. Let y = 4x 2 and (a) a < (c) a > −

x2 a

2

−

1

y2 = 1 intersect iff 16

(b) a < −

2 1

1 2

(d) none of these

2

61. If 1, log 9(31− x + 2), log 3(4.3x − 1) are in A.P. then x equals (a) log34 (b) 1 – log34 (c) 1 – log43 n

62. If P(n) : “49 + 16 + k is divisible by 64 for all n ∈ N” is true, then the least negative integral value of k is (a) – 1 (b) – 2 (c) – 3 (d) – 4 dy 63. If sin x + y cos x = x sin x, then (y – 1) dx

(b) c + x cos x (d) c + x sin x

64. The image of the line 2x – y = 1 in the line x + y = 0 is 1 (a) x + 2 y = − (b) x – 2y = 1 3 2 1 (c) x + 3 y = − (d) 2x + y = 3 3 x

65. The determinant

(a) (b)

C1

x

y z

68. In the expansion of (1 + x + x3 + x4)10, the coefficient of x4 is (a) 40C4 (b) 10C4 (c) 210 (d) 310 69. The

(d) log43 n

sin x = (a) c – x sin x (c) c – x cos x

67. A is one of 6 horses entered for a race, and is to be ridden by one of two jockeys B and C. It is 2 to 1 that B rides A, in which case all the horses are equally likely to win. If C rides A, his chances of winning is tripled. What are the odds against winning of A? (a) 5 : 13 (b) 5 : 18 (c) 13 : 5 (d) none of these

C2

x

C3

C1

y

C2

y

C3 =

C1

z

C2

z

C3

1 xyz(x + y)( y + z)(z + x) 3 1 xyz(x + y − z)( y + z − x) 4

1 xyz(x − y)( y − z)(z − x) 12 (d) none of these (c)

66. If y = a ln x + bx2 + x has its extreme values at x = –1, 2 then a + b = 3 (a) 2 (b) (c) 1 (d) 1 2 2

x

∫

solution dt

=

2

2 t t −1

(a)

3 2

for

x

of

the

equation

π is 2

(b) 2 2

(c) − 2 (d) p

70. If z1, z2 and z3 are complex numbers such that 1 1 1 |z1| = |z2| = |z3| = + + = 1 , then z1 z2 z3 |z1 + z2 + z3| is (a) equal to 1 (b) less than 1 (c) greater than 3 (d) equal to 3 NUMERICAL VALUE TYPE 71. If 3x 2 − 7x − 30 + 2x 2 − 7x − 5 = x + 5 , then x is equal to ______.  72. The projection of a = 3ɵi − ɵj + 5kɵ on  b = 2ɵi + 3ɵj + kɵ is ______. 73. The value of ______.

56 ∞ 2k   is tan −1  π ∑  2 + k 2 + k 4  k =1

74. If the foot of perpendicular from the point (1, –5, –10) to the plane x – y + z = 5 is the point (a, b, c), then | a + b + c | is ______. tan x tan y tan z and x + y + z = p, = = 2 3 5 38 tan2x + tan2y + tan2z = , then K = ______. K

75. If

Telegram @unacademyplusdiscounts

Join Us on Telegram for More Such Books https://telegram.me/unacademyplusdiscounts

Join us from the above link or search ''unacademyplusdiscounts'' in Telegram

44

Very-Similar Practice Tests

VERY SIMILAR

PRACTICE TEST 7 Time : 3 hrs.

Max. Marks : 300

PHYSICS 1. An electron of mass m and charge e initially at rest gets accelerated by a constant electric field E. The rate of change of de-Broglie wavelength of this electron at time t (Ignoring relativistic effects) is −h −mh −h −eEt (a) (b) (c) (d) 2 2 eEt h eEt eEt 2. A liquid is kept in a cylindrical vessel which is rotated along its axis. The liquid rises at the sides (as shown in figure). If the radius of the vessel is 0.05 m and the speed of rotation is 2 rad s–1, find the difference in the height of the liquid at the centre of the vessel and its sides. (a) 20 cm (b) 4 cm (c) 2 cm (d) 0.2 cm 3. A 10 watt source of sound of frequency 1  kHz sends out waves in air. The displacement amplitude at a distance of 10 m from the source is (Given speed of sound in air is 340 m s–1 and density of air is 1.29 kg m–3) (a) 0.62 mm (b) 1.6 mm (c) 0.96 mm (d) 4.2 mm 4. A telephone cable at a place has four long straight horizontal wires carrying a current of 4.0 A in the same direction east to west. The earth’s magnetic field at the place is 0.39 G, and the angle of dip is 35°. The magnetic declination is nearly zero. What is the resultant magnetic field at points 4.0 cm below the cable? (a) 0.25 G (b) 2.32 G (c) 1.93 G (d) 3.11 G 5. The change in the gravitational potential energy when a body of mass m is raised to

a height nR above the surface of the earth is (here R is the radius of the earth)  n   n  mgR mgR (b)  (a)    n − 1   n + 1 (c) nmgR

(d)

mgR n

6. 3 moles of a monatomic gas (g = 5/3) is mixed with 1 mole of a diatomic gas (g = 7/5). The value of g for the mixture will be (a) 9/11 (b) 11/7 (c) 12/7 (d) 15/7 7. Three identical spherical shells, each of mass m and radius r are placed as shown in figure. Consider an axis XX′ which is touching to two shells and passing through diameter of third shell. Moment of inertia of the system consisting of these three spherical shells about XX′ axis is 16 2 (b) 4mr2 (a) mr 5 11 2 (c) (d) 3mr2 mr 5 8. A particle moves in x-y plane. The position vector of particle at any time t is  r = {(2t )ɵi + (2t 2 )ɵj} m. The rate of change of q at time t = 2 s (where q is the angle which its velocity vector makes with positive x-axis) is 2 (a) (b) 1 rad s −1 rad s −1 17 14 6 4 rad s −1 (c) (d) rad s −1 5 7

Test-7

9. A magnetic flux through a stationary loop with a resistance R varies during the time interval t as f = at (t – t). Determine the amount of heat generated in the loop during that time. The inductance of the loop is to be neglected. 3 2 3 3 3 aτ (a) aτ (b) a τ (c) a τ (d) 3 R 3R 3R 3R 10. A force F acting on a body depends on its displacement S as F ∝ S–1/3. The power delivered by F will depend on displacement as (a) S2/3 (b) S1/2 (c) S0 (d) S–5/3 11. The figure shows the cross-section of a long conducting cylinder of inner radius a and outer radius b. The cylinder carries a current whose current density J  =  Cr2 where C is a constant. What is the magnitude of the magnetic field B at a point r, where a < r < b? µ0 πC 2 2 (r − a ) (a) B = 4r 2 µ0C 4 4 (b) B = 2 (r − a ) 4r µ0 πC 2 2 (r − a ) (c) B = 4r µC (d) B = 0 (r 4 − a 4 ) 4r 12. The system of three blocks as shown in figure is pushed by a force F. All surfaces are smooth except between B and C. Coefficient of friction between B and C is m. Minimum value of F to prevent block B from slipping is

 3   5  (a)  2µ  mg (b)  2µ  mg 3 5 (c) µmg (d) µmg 2 2 13. A student measures the distance traversed in free fall of a body, initially at rest, in a given time. He uses this data to estimate g, the acceleration due to gravity. If the maximum percentage errors in measurement of the distance and the time are e1 and e2 respectively, the percentage error in the estimation of g is (a) e2 – e1 (b) e1 + 2e2 (c) e1 + e2 (d) e1 – 2e2

45 14. Suppose C be the capacitance of a capacitor discharging through a resistor R. Suppose t1 is the time taken for the energy stored in the capacitor to reduce to half its initial value and t2 is taken for the charge to reduce to onet fourth its initial value. Then the ratio 1 will be t2 1 (a) 2 (b) 1 (c) (d) 1 2 4 15. Charges +q and –q are placed at points A and B respectively which are a distance 2L apart, C is the midpoint between A and B. The work done in moving a charge +Q along the semicircle CRD is

qQ 2 πε0 L qQ (c) − 6 πε0 L (a)

qQ 6 πε0 L qQ (d) 4 πε0 L (b)

16. A nucleus with mass number 220 initially at rest emits an a particle. If the Q value of the reaction is 5.5 MeV, the kinetic energy of the a particle is (a) 4.4 MeV (b) 5.4 MeV (c) 5.6 MeV (d) 6.5 MeV 17. A galvanometer has 30 divisions and a sensitivity 16 mA/div. It can be converted into a voltmeter to read 3 V by connecting resistance nearly (a) 6 kW in series (b) 6 kW in parallel (c) 500 W in series (d) 500 W in parallel 18. The following figure shows a logic gate circuit with two inputs A and B and the output Y. The voltage waveforms of A, B and Y are as given. Logic gate circuit

46

Very-Similar Practice Tests

The logic gate is (a) NOR gate (c) AND gate

(b) OR gate (d) NAND gate

19. The focal length of a plano convex lens is f and its refractive index is 1.5. It is kept over a plane glass plate with its curved surface touching the glass plate. The gap between the lens and the glass plate is filled with a liquid. As a result, the effective focal length of the combination becomes 2f. Then the refractive index of the liquid is (a) 1.5 (b) 2 (c) 1.25 (d) 1.33 20. If the modulation index of an AM wave is changed from 0 to 1, the transmitted power is (a) unchanged (b) doubled (c) increased by 50% (d) zero NUMERICAL VALUE TYPE 21. A cylindrical tube of radius r and length l, fitted with a cork is shown in figure. The coefficient of friction between the cork and the tube is m. The tube contains an ideal gas at temperature T, and atmospheric pressure P0. The tube is slowly heated, the cork pipe out when temperature is doubled. Assume uniform temperature throughout gas at any instant. If the is normal force per unit length exerted by PA the cork on the periphery of tube is 0 then nµr the value of n is ________. 22. The amplitude of a damped oscillator becomes half in one minute. The amplitude after 3 minute will be 1/x times the original, where x is ________. 23. If two coherent sources are placed at a distance 3 l from each other, symmetric to the centre of the circle of radius R as shown in the figure (R >> l), then number of bright fringes shown on the screen placed along the circumference is________. 24. A string is stretched between fixed points separated by 75 cm. It is observed to have resonant frequencies of 420 Hz and 315 Hz.

There are no other resonant frequencies between these two. Then, the lowest resonant frequency for this string is________ Hz. 25. An ideal choke draws a current of 8 A when connected to an AC supply of 100 V, 50 Hz. A pure resistor draws a current of 10 A when connected to the same source. The ideal choke and the resistor are connected in series and then connected to the AC source of 150 V, 40 Hz. The current in the circuit _______ A. CHEMISTRY 26. An oxide AxOy has molecular weight 288 u. Atomic weights of A and O respectively are 12 and 16. The formula of the compound, if A is 50% by weight is (a) A3O5 (b) A5O3 (c) A12O9 (d) A9O12 27. 3-Octyne is synthesized by adding a bromoalkane in a mixture of sodium amide and an alkyne. The bromoalkane and alkyne are respectively (a) BrCH2CH2CH2CH2CH3 and CH3CH2C CH (b) BrCH2CH2CH3 and CH3CH2CH2C CH (c) BrCH2CH2CH2CH2CH3 and CH3C CH (d) BrCH2CH2CH2CH3 and CH3CH2C CH 28. Molar conductivity of 0.025 mol L–1 methanoic acid is 46.1 S cm2 mol–1. The degree of dissociation and dissociation constant will be (Given : l°H+ = 349.6 S cm2 mol–1 and l°HCOO– = 54.6 S cm2 mol–1) (a) 11.4%, 3.67 × 10–4 (b) 22.8%, 1.83 × 10–4 (c) 52.2%, 4.25 × 10–4 (d) 1.14%, 3.67 × 10–6 29. Mg

Z

Air Heat H2O

X+Y Solution

H2O

Z

Colourless gas CuSO4

(A)

Blue coloured solution

Substances X, Y, Z and A are respectively (a) Mg3N2, MgO, NH3, CuSO4·5H2O (b) Mg(NO3)2, MgO, H2, CuSO4·5H2O (c) MgO, Mg3N2, NH3, [Cu(NH3)4]SO4 (d) Mg(NO3)2, MgO2, H2O2, CuSO4·5H2O

Test-7

30. The statements that are true of silicates among the following are 1. Each silicon atom has four Si — O bonds arranged tetrahedrally. 2. Because of the availability of d-orbitals in Si, water molecules can coordinate with Si and bring about hydrolysis readily. 3. Si — O bonds are strong; hence silica is inert having high melting point. 4. Each oxygen atom in SiO2 is shared by 4 silicon atoms in the tetrahedra. (a) 1, 2, 4 (b) 1, 3, 4 (c) 1, 3 (d) 1, 2, 3, 4 31. The CMC of a given soap in water is 10–3 mol litre–1. A 10–4 mol litre–1 solution of this soap in water is a (a) lyophilic sol (b) lyophobic sol (c) true solution (d) none of these. 32. Which of the following statements is false? (a) The lower the concentration of D.O., the more polluted is the water sample. (b) The tolerable limit of lead in drinking water is 50 ppb. (c) Water is considered pure if it has BOD less than 5 ppm. (d) In COD determination, the pollutants resistant to microbial oxidation are not oxidised by oxidising agents like K2Cr2O7. 33. Which of the following statements is not true? (a) In vulcanisation the rubber becomes harder and stronger. (b) Natural rubber has ‘trans’ configuration at every double bond. (c) Buna-S is a copolymer of 1,3-butadiene and styrene. (d) Natural rubber is 1,4-polymer of isoprene. 34. Match the lists I and II and pick the correct matching from the codes given below. List I List II (A) [Ag(CN)2]– 1. Square planar and 1.73 B.M. (B) [Cu(CN)4]3– 2. Linear and zero (C) [Cu(CN)6]4– 3. Octahedral and zero (D) [Cu(NH3)4]2+ 4. Tetrahedral and zero (E) [Fe(CN)6]4– 5. Octahedral and 1.73 B.M.

47 (a) (b) (c) (d)

A - 2, B - 4, C - 5, D - 1, E - 3 A - 5, B - 4, C - 1, D - 3, E - 2 A - 1, B - 3, C - 4, D - 2, E - 5 A - 4, B - 5, C - 2, D - 1, E - 3

35. Which of the following structures is enantiomeric with the molecule (I) given below : H CH3 C H5C2 Br (I)

H C (a) H3C

(b) Br

C2H5

C2H5 Br

Br

H

C

C (c) H3C

H

C Br

H

CH3

C2H5

(d) H5C2

CH3

36. In which of the following, the order is not in accordance with the property mentioned? (a) Li < Na < K < Rb – Atomic radius (b) F > N > O > C – Ionisation enthalpy (c) Si < P < S < Cl – Electronegativity (d) F < Cl < Br < I – Electronegativity 37. An alkene gives two moles of HCHO, one mole of CO2 and one mole of CH3COCHO on ozonolysis. What is its structure? (a) CH2 C CH CH2 CH3 CH3 (b) CH2 CH CH CH CH2 (c) CH2 C C CH3 CH3 CH3

(d) CH2 C C CH CH2 38. At 1400 K, Kc = 2.5 × 10–3 for the reaction : CH4(g) + 2H2S(g) CS2(g) + 4H2(g) A 10 L reaction vessel at 1400 K contains 2.0 mol of CH4, 3.0 mol of CS2, 3.0 mol of H2 and 4.0 mol of H2S. In which direction does the reaction proceed to reach equilibrium? (a) Forward (b) Backward (c) May be forward or backward (d) Reaction is in equilibrium

48

Very-Similar Practice Tests

39. Consider the given A B diagram for 1 mole of 10 L a gas: The process A → B V 2L C represents 100 K 150 K (a) isobaric change T (b) isothermal change (c) adiabatic change (d) isochoric change. 40. The decreasing order of boiling points of the following hydrides is (a) H2O > SbH3 > AsH3 > PH3 > NH3 (b) H2O > NH3 > SbH3 > AsH3 > PH3 (c) H2O > SbH3 > NH3 > AsH3 > PH3 (d) H2O > PH3 > AsH3 > SbH3 > NH3 41. Pick out the wrong statement(s). (i) Vapour pressure of a liquid is the measure of the strength of intermolecular attractive forces. (ii) Surface tension of a liquid acts perpendicular to the surface of the liquid. (iii) Vapour pressure of all liquids is same at their freezing points. (iv) Liquids with stronger intermolecular attractive forces are more viscous than those with weaker intermolecular force. (a) (ii), (iii) and (iv) (b) (ii) and (iii) (c) (i), (ii) and (iii) (d) (iii) only 42. Five-membered ring structures of fructose are given below. Mark the incorrect statement.

P. Q. R. S. (a) (b) (c) (d)

List I List II P.E. of electron in 1. –54.4 eV atom–1 ground state K.E. of electron in 2. +13.6 eV atom–1 ground state Total energy of in 3. –108.8 eV atom–1 ground state Ionization energy 4. +54.4 eV atom–1 of He+ in lowest excited state P - 1, Q - 2, R - 3, S - 4 P - 4, Q - 1, R - 2, S - 3 P - 4, Q - 2, R - 1, S - 3 P - 3, Q - 4, R - 1, S - 2

44. In acidic medium, KMnO4 oxidises FeSO4 solution. Which of the following statements is correct? (a) 10 mL of 1 N KMnO4 solution oxidises 10 mL of 5 N FeSO4 solution. (b) 10 mL of 1 M KMnO4 solution oxidises 10 mL of 5 M FeSO4 solution. (c) 10 mL of 1 M KMnO4 solution oxidises 10 mL of 1 M FeSO4 solution. (d) 10 mL of 1 N KMnO4 solution oxidises 10 mL of 0.1 M FeSO4 solution. 45. If an impurity in a metal has a greater affinity for oxygen and is more easily oxidised than the metal, then the purification of metal may be carried out by (a) poling (b) zone refining (c) electrolytic refining (d) cupellation NUMERICAL VALUE TYPE 46. Out of the following, the total number of antihistamine drugs is_____. Dimetapp, Phenelzine, Alitame, Equanil, Novestrol, Morphine, Seldane, Bithionol.

(a) The five-membered ring structures are named as furanose structures. (b) The cyclic structures represent two anomers of fructose. (c) Five-membered ring structures are named as pyranose structures. (d) These are also called Haworth structures.

47. The total number of molecules that do not follow octet rule among the following is_____. CO, PCl5, PCl3, AlCl3, SF6, BF3, NH3

43. Match the List I with List II for singly ionized helium atom if total energy of electron in first orbit in H-atom is –13.6 eV atom–1 and select the correct answer using the code given below the lists.

49. Liebermann’s nitroso reaction is given by x° amines only. The value of x is_____.

48. Among the following, the number of underlined elements having +6 oxidation state is_____. PO43–, H2S2O8, H2SO5, OF2, Cr2O72–, CrO5

50. The composition of a sample of wustite is Fe0.93O1.00. The percentage of the ion present in the form of Fe (III) is_____.

Test-7

49 MATHEMATICS

51. The domain of the function f (x ) = is (a) (–∞, 0) (c) (–∞, ∞)

1 | x | −x

(b) (–∞,∞) – {0} (d) (0, ∞)

52. If A and B are square matrices of the same order such that (A + B)(A – B) = A2 – B2, then (ABA–1)2 = (a) A2B2 (b) A2 (c) B2 (d) I 1

3

53. If k ∫ x. f (3x)dx = ∫ t ⋅ f (t )dt , then the value of 0

k is (a) 9

n(n + 1) n(n + 1) (d) 4 2 2cosβ − 1 60. If cosα = ,(0 < α < π, 0 < β < π), 2 − cosβ α β then tan cot is equal to 2 2 (a) 1 (b) 2 (c) 3 (d) none of these (c)

 ln(1 + x )1+ x 1  61. lim  − = x →0  x x2 (a) 0

0

(b) 3

(c)

1 9

(d)

1 3

x 54. The function f (x ) = is differentiable 1 + x in (a) R (b) R – {0} (c) [0, ∞) (d) (0, ∞) 55. The ratio between the sum of n terms of two A.P.’s is 3n + 8 : 7n + 15. Then the ratio between their 12th terms respectively is (a) 5 : 7 (b) 7 : 16 (c) 12 : 11 (d) none of these 56. The distance of the point (4, 2, 5) from the x −1 y + 2 z +1 line is = = 6 3 2 (a) 3 (b) 4 (c) 5 (d) 2 57. The coefficient of 1/x in the expansion of n

 1 (1 + x )n  1 +  is  x (2n)! n! (b) (n − 1)!(n + 1)! (n − 1)!(n + 1)! 2n! (c) (d) none of these (2n − 1)!(2n + 1)!

(a)

58. The number of real values of k, such that the lines x – 2y + 3 = 0, kx + 3y + 1 = 0 and 4x – ky + 2 = 0 are concurrent, is (a) 0 (b) 1 (c) 2 (d) infinite 59. If a variate assumes the values 0, 1, 2, ...., n with frequencies nC0 , nC1 , nC2 ,..., nCn then mean square deviation about the value x = 0 is 2 n(n −1) (a) (b) n (n − 1) 2 4

(b) 1

(c) 2 100

62. Given z = (1 + i 3 ) equals (a) 2100 (b) 250 63.

∫e

x

(d) 1/2 2 Re(z )

, then

3 Im(z )

(c) 2/3

(d) 3/2

−1   cosec −1 x + dx is equal to    x x2 − 1 

(a) ex cosec–1x + C (c) ex sec–1x + C

(b) ex sin–1x + C (d) ex cos–1x + C

64. If a, b, c are positive integers, then the determinant a2 + x ab ac ab

∆=

ac 3

b2 + x bc

(a) x (c) (a2 + b2 + c2)

bc

is divisible by

2

c +x (b) x2 (d) None of these

65. “If Ram secures 100 marks in math then he will get a mobile”. The converse is (a) If Ram get a mobile then he will not secures 100 marks. (b) If Ram not get a mobile then he will secures 100 marks. (c) If Ram will get a mobile then he secures 100 marks in Math. (d) None of these 66. The solution of the differential equation ydx + (x + x2y)dy = 0 is 1 (a) + log | y | = c xy 1 (b) − + log | y | = c xy 1 (c) + 2 log | y | = c (d) log|y| = cx xy

50

Very-Similar Practice Tests

67. If the tangent drawn at a point (t2, 2t) on the parabola y2 = 4x is same as normal drawn at x2 y2 ( 5 cos α, 2 sin α) on the ellipse + = 1, 5 4 then which of the following is not true ? 1 −1 (a) t = ± (b) α = − tan 2 5 −1 (c) α = tan 2

(d) none of these

68. The least value of the function f (x) = ax + b/x, a > 0, b > 0, x > 0 is a (a) ab (b) 2 b (c) 2

b a

(d) 2 ab

69. The probability that sin–1(sinx) + cos–1(cosy) is an integer x, y ∈ {1, 2, 3, 4}, is 3 (b) (a) 1 16 16 15 (c) (d) none of these. 16

70. The number of numbers that can be formed with the help of the digits 1, 2, 3, 4, 3, 2, 1 so that odd digits always occupy odd places, is (a) 24 (b) 18 (c) 12 (d) 30 NUMERICAL VALUE TYPE 71. If the lengths of the sides of a right angled triangle ABC right angled at C are in A.P., find 5(sinA + sinB). 72. Let a, b, c be the three roots of the equation x3 + x2 – 333x – 1002 = 0. If P = a3 + b3 + c3, then the value of P = 2006     2 2 73. If | a × b | = 5 and | a ⋅ b | = 3, then | a | | b | is equal to x −1 y +1 z −1 = = 74. If the lines and 2 3 4 x −3 y −k z = = intersect, then the value of 1 2 1 k is 75. If sinq + sin2q + sin3q = 1, then the value of cos6q – 4cos4q + 8cos2q must be

Telegram @unacademyplusdiscounts

Join Us on Telegram for More Such Books https://telegram.me/unacademyplusdiscounts

Join us from the above link or search ''unacademyplusdiscounts'' in Telegram

52

Very-Similar Practice Tests

VERY SIMILAR

PRACTICE TEST 8 Time : 3 hrs.

Max. Marks : 300

PHYSICS 1. Monochromatic light is incident on a glass prism of angle A. If the refractive index of the material of the prism is m, a ray, incident at an angle q, on the face AB would get transmitted through the face AC of the prism provided  −1  −1  1    (a) θ > cos µ sin  A + sin      µ       −1  −1  1    (b) θ < cos µ sin  A + sin      µ        1   (c) θ > sin µ sin  A − sin −1      µ      −1 

  1   (d) θ < sin µ sin  A − sin −1      µ      −1 

2. The kinetic energy of a particle executing SHM will be equal to (1/8)th of its potential energy when its displacement from the mean position is (where A is the amplitude) (a) A 2

× × × 4. A particle with charge Q, moving with a momentum p, × × × B enters a uniform magnetic p × × × field normally. The magnetic × × × Q field has magnitude B and is d confined to a region of width d, p where d < . The particle is deflected by an BQ angle q in crossing the field. Then

(a) sinθ =

BQd p

(b) sinθ =

p BQd

(c) sinθ =

Bp Qd

(d) sinθ =

pd BQ

5. One end of a uniform rod of length l and mass m is hinged at A. It is released from rest from horizontal position AB as shown in figure. The force exerted by the rod on the hinge when it becomes vertical is

(b) A/2

2 2 2 (d) A A 3 3 3. The current density varies with radial distance r as J = ar2, (where a is a constant) in a cylindrical wire of radius R. The current passing through the wire between radial distance R/3 and R/2 is, (c)

(a) (c)

65 πa R 4 2592 65 πa2 R3 2938

25 πa R 4 (b)

72 2

(d)

81 πa R 4 144

3 mg (b) 3mg (c) 5mg (d) 5 mg 2 2 6. A chain of mass M and length l is suspended vertically with its lower end touching a weighing scale. The chain is released and falls freely onto the scale. Neglecting the size of the individual links, what is the reading of the scale when a length x of the chain has fallen? (a)

Test-8

53

Mgx l 3Mgx (c) l (a)

2Mgx l 4Mgx (d) l (b)

7. A charge is distributed with a linear density l over the length L along radius vector drawn from the point where a point charge q is located. The distance between q and the nearest point on linear charge is R. The electrical force experienced by the linear charge due to q is (a) (c)

qλL 4 πε0 R2 qλL 4 πε0 RL

qλL (b) 4 πε0 R(R + L) (d)

qλL 4 πε0 L2

8. Find the pressure at which temperature attains its maximum value if the relation between pressure and volume for an ideal gas is P = P0 + (1 – a )V2 . 2P0 P 4 P0 (b) 0 (c) P0 (d) 3 3 3 9. If Ka-radiation of Mo (Z = 42) has a wavelength 0.71 Å, the wavelength of the corresponding radiation of Cu(Z = 29) is equal to (a) 1.52 Å (b) 0.71 Å (c) 0.36 Å (d) 2.5 Å 10. The magnetic field of a beam emerging from a filter facing a floodlight is given by B = 12 × 10–8 sin(1.20 × 107 z – 3.60 × 1015 t)T. What is the average intensity of the beam? (a) 1.25 W m–2 (b) 1.72 W m–2 –2 (c) 0.2 W m (d) 0.25 W m–2 11. The escape velocity of a planet is ve. A particle starts from rest at a large distance from the planet, reaches the planet only under gravitational attraction, and passes through a smooth tunnel through its centre. Its speed at the surface of the planet will be (a) ve (b) 2ve

(a) 0.75 cm (c) 7.5 cm

(b) 0.75 m (d) 7.5 m

13. In Young’s double slit experiment, one of the slits is wider than the other, so that the amplitude of the light from one slit is double that from the other slit. If Im be the maximum intensity, the resultant intensity when they interfere at phase difference f is given by I  I  φ φ (a) m 1 + 2 cos2  (b) m 1 + 4 cos2  3  2 5  2 Im  I  φ φ 1 + 8 cos2  (d) m  8 + cos2  9  2 9  2 14. A rectangular loop has a sliding connector PQ of length l and resistance R W and it is moving with a speed v as shown. The set-up is placed in a uniform magnetic field going into the plane of the paper. The three currents I1, I2 and I are (c)

(a)

(c) 1.5 ve

(d)

1.5ve 12. A spherical soap bubble of radius 1 cm is formed inside another bubble of radius 3 cm. The radius of a single soap bubble which maintains the same pressure difference as inside the smaller and outside the larger soap bubble is

Blv Blv ,I= 6R 3R Blv 2 Blv (b) I1 = − I 2 = ,I= R R Blv 2 Blv (c) I1 = I 2 = ,I= 3R 3R Blv (d) I1 = I 2 = I = R 15. A rectangular block of mass m and area of cross-section A floats in a liquid of density r. If it is given a small vertical displacement from equilibrium it undergoes oscillation with a time period T. Then 1 (a) T ∝ (b) T ∝ ρ m 1 1 (c) T ∝ (d) T ∝ ρ A 16. A solid sphere of radius R is charged uniformly. At what distance from its surface is the electrostatic potential half of the potential at the centre? R R (a) R (b) (c) (d) 2R 2 3 (a) I1 = I 2 =

54

Very-Similar Practice Tests

17. A series LR circuit is connected to a voltage source with V(t) = V0 sinwt. After very large L  time, current I(t) behaves as  t 0 >>   R (a)

(b)

(c)

(d) 18. A block of ice at temperature –20°C is slowly heated and converted to steam at 100°C. Which of the following diagram is most appropriate? (a)

(b)

(c)

(d)

19. A modulated signal Cm(t) has the form Cm(t) = 25 sin 300pt + 15 (cos 200pt – cos 400pt). The carrier frequency fc and the modulating

frequency (message frequency) respectively given by (a) fc = 200 Hz; fw = 50 Hz (b) fc = 150 Hz; fw = 50 Hz (c) fc = 150 Hz; fw = 30 Hz (d) fc = 200 Hz; fw = 30 Hz

fw

are

20. Which of the following statements is/are correct? (a) Average speed of a particle in a given time period is never less than the magnitude of average velocity. (b) It is possible to have situations in which   dv d |v | ≠ 0, but = 0. dt dt (c) If the average velocity of a particle is zero in a time interval, then it is possible that the instantaneous velocity is never zero in that interval. (d) All of these. NUMERICAL VALUE TYPE 21. A uniformly tapering conical wire is made from a material of Young’s modulus Y and has a normal, unextended length L. The radii, at the upper and lower ends of this conical wire, have values R and 3R, respectively. The upper end of the wire is fixed to a rigid support and a mass M is suspended from its lower end. The equilibrium extended length, of this wire 1 Mg   is L  1 + . The value of x is ______.  x πYR2  22. A moving coil galvanometer has 150 equal divisions. Its current sensitivity is 10 divisions m A–1 and voltage sensitivity is 2 divisions mV–1. In order that each division reads 1 V, the resistance needed to be connected in series with the coil will be _______ W. 23. A motor cycle starts from rest and accelerates along a straight path at 2 m s–2. At the starting point of the motor cycle there is a stationary electric siren (in m). When the driver hears the frequency of the siren at 94% of its value, the motor cycle was at rest then distance travelled by the motor cycle is _______ m. (Speed of sound = 330 m s–1). 24. A pure germanium semiconductor is doped with donor atoms of density 8 × 10x cm–3 in order to obtain an n-type semiconductor

Test-8

55

whose conductivity is 5 mho cm–1. The value of x is ______. (The mobility of electrons in n-type germanium is 3900 cm2 V–1 s–1 and density of holes is negligible.) 25. Two identical cylindrical vessels with their bases at the same level, each contains a liquid of density 1.3 × 103 kg/m3. The area of each base is 4.0 cm2, but in one vessel, the liquid height is 0.854 m and in the other it is 1.560 m. The work done by the gravitational force in equalizing the levels when the two vessels are connected is ________ J. CHEMISTRY 26. Which of the following arrangements is correct in respect of solubility in water? (a) CaSO4 > BaSO4 > BeSO4 > MgSO4 > SrSO4 (b) BeSO4 > MgSO4 > CaSO4 > SrSO4 > BaSO4 (c) BaSO4 > SrSO4 > CaSO4 > MgSO4 > BeSO4 (d) BeSO4 > CaSO4 > MgSO4 > SrSO4 > BaSO4 27. Under what conditions gases generally deviate from ideal behaviour? (a) At high temperature and low pressure (b) At low temperature and high pressure (c) At high temperature and high pressure (d) At low temperature and low pressure 28. Which silicates is formed from SiO44– tetrahedral units by sharing three oxygen atoms? (a) Sheet silicates (b) Pyrosilicates (c) Linear chain silicates (d) Three dimensional silicates 29. In the reaction, BrO–3(aq) + 5Br–(aq) + 6H+(aq) → 3Br2(aq) + 3H2O(l) the expression of rate of appearance of bromine [Br2] to rate of disappearance of bromide ion [Br–]is − d [Br2 ] 3 d [Br ] (a) =− dt 5 dt − d [Br2 ] 5 d [Br ] (b) =− dt 3 dt

(c) (d)

d [Br2 ] dt d [Br2 ]

=

− 5 d [Br ] 3 dt − 3 d [Br ]

= dt 5 dt 30. In the reaction : S + 3/2 O2 → SO3 + 2x kcal and SO2 + 1/2 O2 → SO3 + y kcal, heat of formation of SO2 is (a) (x + y) (b) (x – y) (c) (2x + y) (d) (2x – y) 31. A student made the following observations in the laboratory : (i) Clean copper metal did not react with 1 molar Pb(NO3)2 solution. (ii) Clean lead metal dissolved in a 1 molar AgNO3 solution and crystals of Ag metal appeared. (iii) Clean silver metal did not react with 1 molar Cu(NO3)2 solution. The order of decreasing reducing character of the three metals is (a) Cu, Pb, Ag (b) Cu, Ag, Pb (c) Pb, Cu, Ag (d) Pb, Ag, Cu 32. The oxidation number of S in the compound KAl(SO4)2⋅12H2O is (a) + 4 (b) + 2 (c) + 6 (d) + 2.5 33. For an ideal solution with p°A > p°B, which of the following is true? (a) (xA)liquid = (xA)vapour (b) (xA)liquid > (xA)vapour (c) (xA)liquid < (xA)vapour (d) (xA)liquid and (xA)vapour do not bear any relationship with each other. 34. Match the list I with list II and select the correct answer using the code given below the lists. List I List II P. Phthalein test 1. Aldehydic group Q. Schiff ’s reagent 2. Amino group test R. Nitrous acid test 3. Alcoholic group S. Xanthate test 4. Phenolic group (a) P - 1, Q - 2, R - 3, S - 4 (b) P - 4, Q - 3, R - 2, S - 1 (c) P - 1, Q - 3, R - 2, S - 4 (d) P - 4, Q - 1, R - 2, S - 3

56

Very-Similar Practice Tests

35. Among the following, the least stable resonance structure is + O (a) +

–

–

(b) + –

(c)

N

+

O – N O –

+

O

+

N O –

(d)

O

+

+

–

O

N

O – 36. In the complexes [Fe(H2O)6]3+, [Fe(CN)6]3–, [Fe(C2O4)3]3– and [FeCl6]3–, more stability is shown by (a) [Fe(H2O)6]3+ (b) [Fe(CN)6]3– 3– (c) [Fe(C2O4)3] (d) [FeCl6]3– 37. X in the above reaction is (a) (b) (c) (d) 38. The atomic weights of two elements A and B are 40 and 80 respectively. If x g of A contains y atoms, how many atoms are present in 2x g of B? y y (a) (b) (c) y (d) 2y 2 4 39. The correct order of basicities of the following compounds is

CH3CH2NH2 (II)

O CH3 C NH2 (IV)

(a) II > I > III > IV (c) III > I > II > IV

(b) I > III > II > IV (d) I > II > III > IV

40. A dihaloalkane ‘X’ having formula C3H6Cl2, on hydrolysis gives a compound, that can reduce Tollens’ reagent. The compound ‘X’ is (a) 1, 2-dichloropropane (b) 1, 1-dichloropropane (c) 1, 3-dichloropropane (d) 2, 2-dichloropropane. 41. Match the list I with list II and select the correct answer using the code given below the lists. List I List II P. sp2 1. ICl4– Q. dsp2 2. Fe(CO)5 3 R. sp d 3. SnCl2 S. sp3d2 4. [Ni(CN)4]2– (a) P - 1, Q - 2, R - 3, S - 4 (b) P - 3, Q - 2, R - 1, S - 4 (c) P - 3, Q - 4, R - 2, S - 1 (d) P - 4, Q - 3, R - 1, S - 2 42. At constant temperature, the equilibrium constant (Kp) for the decomposition reaction, N2O4 2NO2 is expressed by Kp = 4x2P/(1 – x2), where P = pressure and x = extent of decomposition. Which of the following statements is true? (a) Kp increases with increase in P. (b) Kp increases with increase in x. (c) Kp increases with decrease in x. (d) Kp remains constant with change in P and x. 43. In a mixture of PbS, ZnS and FeS, each component is separated from other by using the reagents in the following sequence in froth floatation process (a) potassium ethyl xanthate, KCN (b) potassium ethyl xanthate, KCN, NaOH, CuSO4, acid (c) KCN, CuSO4, acid (d) none of the above. 44. On passing I ampere of current for time t sec through 1 litre of 2 M CuSO4 solution (atomic weight of Cu = 63.5), the amount m of Cu (in g) deposited on cathode will be It (a) m = (63.5 × 96500) It (b) m = (31.25 × 96500)

Test-8

57

(c) m =

I × 96500 (31.25 × t )

31.75 × I × t 96500 45. Amongst the acids, (i) CH CCOOH (ii) CH2 CHCOOH and (iii) CH3CH2COOH, the acid strength follows the sequence (a) (i) < (ii) > (iii) (b) (i) > (ii) > (iii) (c) (i) = (ii) = (iii) (d) (i) = (ii) > (iii) (d) m =

NUMERICAL VALUE TYPE 46. AB crystallises in a rock salt structure with A : B = 1 : 1. The shortest distance between A and B is Y1/3 nm. The formula mass of AB is 6.023 Y a.m.u. where Y is an arbitrary constant. The density (in kg m–3) is ____ . 47. Molarity of commercial 11.2 volume H2O2 solution is ____ . 48. van’t Hoff factor of an electrolyte X3Y2 assuming that it ionizes 25% in the solution is ____ . 49. In 1 L saturated solution of AgCl [Ksp(AgCl) = 1.6 × 10–10], 0.1 mol of CuCl [Ksp(CuCl) = 1.0 × 10–6] is added. The resultant concentration of Ag+ in the solution is 1.6 × 10–x. The value of x is ____ . 50. P4O10 has short and long P—O bonds. The number of short P—O bonds in this compound is ____ . MATHEMATICS 51. Let R = {(3, 3), (6, 6), (9, 9), (12, 12), (6, 12), (3, 9), (3, 12), (3, 6)} be a relation on the set A = {3, 6, 9, 12}. The relation is (a) reflexive and transitive only (b) reflexive only (c) an equivalence relation (d) reflexive and symmetric only 52. Let a1, a2, a3, ... be in A.P. and ap, aq, ar be in G.P. Then aq : ap is equal to q− p r−p (b) (a) r −q q− p r −q (c) (d) 1 q− p

4 53. For the function f (x ) = x 3 − 8 x 2 + 16 x + 5, 3 x = 2 is a point of (a) local maxima (b) local minima (c) point of inflection (d) none of these 54. If (tanx – tany)2, (tany – tanz)2 and (tanz – tanx)2 are in A.P, then (tanx – tany), (tany – tanz) and (tanz – tanx) are in (a) A.P. (b) G.P. (c) H.P. (d) none of these 55. The area bounded by the lines x = 1 and x y + = 4 is y x (a) 4 3

(b) 2 3 1/ x

(c) 8 3

(d) 4

(c) e5

(d) e

2

 1 + 5x 2  56. lim   = x → 0  1 + 3x 2  (a) e2 (b) e3

iθ 57. If −1 + −3 = re , then q is equal to 2π p 2p π (a) (b) − (c) (d) − 3 3 3 3 58. If x is a positive integer, then

x! (x + 1)! (x + 2)! ∆ = (x + 1)! (x + 2)! (x + 3)! is equal to (x + 2)! (x + 3)! (x + 4)! (b) 2(x!)(x + 1)!(x + 2)! (d) None of these

(a) 2(x!)(x + 1)! (c) 2(x!)(x + 3)! 59. If

sin x + sin 2 x + sin 3x sin 2 x sin 3x f (x ) = 3 + 4 sin x 3 4 sin x , 1+ sin x sin x 1 π/2

then the value of ∫ f (x ) dx is 0

(a) 3

(b) 2/3

(c) 1/3

(d) 0

 sin[ x]  α+ , x>0 x  60. f (x ) =  2 , x=0  sin x − x  β + 6   , x