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Rao Intelligence Search Exam 2017 / Sample Paper / Std. XII

PhysicsSingle Correct Questions +4 | ‑1

1. In the following assembly of resistors and emf sources, find I.

(A) (B) (C) (D)

2. In the following figure, infinite number of cells are connected in parallel. Find equivalence of thefollowing network between A and B.

(A) (B)

(C) (D)

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3. In the following figure, internal resistance of ammeter is and voltmeter is ideal. The readingof voltmeter is 6 V. R =

(A) (B) (C) (D)

4. Between two plates of a parallel plate capacitor, the space is filled with a dielectric medium ofvarying dielectric constant, where ko and are positive constants and x isdistance from one of the plates which is taken as reference. Area of each plate is A and distance ofseperation between the plates of the capacitor is d.

(A) (B)

(C) (D)

5. In the following circuit shown, find the value of Rx so that for very small variations of Rx currentthrough Rx remains constant.

(A) (B) R (C) (D)

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6. Two identical square loops are almost in contact but electrically isolated. Initially the loops are intwo perpendicular planes and both are free to rotate about the common axis XY passing throughcentres of loops as shown in the figure. Side PS of the loop is above the plane of the paper and QRis behind the plane of the paper. The two loops are excited with currents I1 and I2. Direction ofcurrents are shown in the figure.

Just after the loops excited, from top view

(A) Both the loops rotate in clockwise direction about XY axis.

(B) ABCD rotates in clockwise direction but PQRS rotates in anticlockwisedirection.

(C) ABCD rotates in anticlockwise direction but PQRS rotates in clockwisedirection.

(D) Both the loops rotate in anticlockwise direction about XY axis.

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7.In figure shown, the switch is thrown to position 1 at t = 0. At the switch is thrown toposition 2. Find the charge of the capacitor at the instant when energy stored in capacitor is equalto energy stored in inductor.

(A) (B) (C) (D)

8. Quality factor of the following RLC series circuit at resonance is unity. RMS voltage of the sourceis V. Average power dissipated across the resistor at half of resonance frequently is equal to

(A) (B) (C) (D)

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9. Three infinite conducting plates A, B and C are alligned as shown in the figure. Space between theplates are filled with dielectric media as shown in the figure. Dielectric constant of the mediumbetween A and B is K and dielectric constant of the medium between B and C is 2K. Distance ofseparation between the plates is shown in figure. When the switch S is open, charges given to A, Band C are 2Q, Q and ‑Q respectively. Find the charge on inner surface of C after the switch S isclosed.

(A) (B) (C) (D)

10. In the circuit shown, two inducutors of inductances L1 and L2 are in series.

The turnings of the two coils are in same direction. Mutual inductance between the coils is M. Findthe magnetic energy stored in two inductors together when the current is equals to half of thecurrent at steady state.

(A) (B)

(C) (D)

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11. In the following circuit at certain frequency XL = XC. Current through inductor lags the voltage of

the source by 600. Current through capacitors leads the voltage of the source by 600. RMS voltageof the source in the circuit is V. Resistance of each resistor is R.

RMS value of the current through the source is

(A) (B) (C) (D)

12. Time constant of the following RL circuit is

(A) (B) (C) (D)

13. Following figure represents a modified Youngʹs Double slit experiment apparatus. Below theline xy, right side of the slits, refractive index of the medium is . O is a point on the screenequidistant from S1 and S2. Bright fringe is formed at O if

(A) (B)

(C) (D)

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14. A parallel beam of light is incident on a biconvex lens of focal length parallel to principal axis.A plane mirror is placed right side of the lens as shown in figure. The mirror makes an angle with principal axis.

The mirror cuts the principal axis at point ʹOʹ midway between the pole and focus of the convexlens. Choose ʹOʹ as origin, x‑axis is horizontal and towards right. y‑axis is vertically upwards.After reflection from the mirror, the position of image is at

(A) (B) (C) (D)None of these

15. A particle of charge q and mass m is projected with certain high velocity in a uniform magneticfield and in the direction perpendicular to the direction of magnetic field. Assume the particle isspherical in shape and of radius ʹrʹ. The particle experience resistive force and it is given by Stokeʹslaw. The time taken by the particle to complete two cycles is

(A) equals to (B) less than (C) greater than (D) equals to

16. A very large solenoid of turn density n is excited with constant current i. An imaginary coaxialcylinder of length ʹlʹ and radius ʹrʹ is constructed at the centre of the solenoid. The dimensions ofthe imaginary coaxial cylinder are very smaller than linear dimensions of the solenoid. Themagnetic energy stored in the imaginary cylinder is

(A) (B) (C) (D)

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17. A ray of light is incident normally on the face of a prism of refracting angle The refractiveindex of the material of the prism is Angle of deviation of ray of light is

(A) (B) (C) (D)

18. In the figure shown, all resistors are identical Resistance of each resistor is All reistors arearranged along the sides of a prism. At node A, is divided and the currents through AP, AQ andAR are respectively. Identify the correct relations among the following.

(A) (B) (C) (D)

19. Assume that the deBroglie wave associated with an electron can form a standing wave betweenthe atoms arranged in a one dimensional array with nodes at each of the atomic sites. The distancebetween atoms of the array is d. It is found that one such standing wave is formed if d is 2Ao. Asimilar standing wave is again formed if d is increased to 2.5 Ao but not for any intermediatevalue of d. The least value of d for which the standing wave of the type described above can formis

(A) (B) (C) (D)

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20. Which of the following is the appropriate graph of saturation photocurrent V/s intensity ofincident radiation on the emi�er plate of a photocell ?

(A) (B)

(C) (D)

21. Which of the following is incorrect ?

(A)Intensity of X‑rays produced is proportional to number of electrons strikingthe target per unit area per second.

(B) Penetrating power of X‑rays dependent on applied potential difference acrossthe filament and target of X‑ray tube.

(C) Wavelength of a characteristic X‑ray is independent of applied potentialdifference across the X‑ray tube.

(D) Most of the energy of the electron incident on the target is converted to X‑raysand the least part of the energy is converted to heat.

22. A count rate meter is used to measure the activity of a given sample. At one incident the metershows 5400 counts per minute. Five minutes later it shows 2700 counts per minute. The decayconstant is

(A) (B) (C) (D)

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23. A radionuclide X is produced at constant rate and decay constant of X is . At time t=0, numberof nucleus of X is zero.Which of the following is true ?

(A) Number of nucleus produced first increases, reach to maximum and thendecreases.

(B) Maximum number of nuclei produced is equal to

(C) Overall rate of production of X varies exponentially

(D) Half life of radioactive specimen X produced is dependent of rate ofproduction

24. There is a stream of neutrons with a kinetic energy of 0.3350 eV and the half life of neutrons be 693seconds. What fraction of neutrons will remain before they travel a distance of 20m? Mass ofneutron is kg.

(A) (B) (C) (D)

25. 1 Kg of deuterium undergoes complete fusion reaction given by Masses ofdeuterium, helium and neutron are 2.015 amu, 3.017 amu and 1.009 amu respectively. Find theamount of energy released.

(A) (B) (C) (D)

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26. The frequency responses of two RLC series circuit I and II are shown in the following figure. RMSVoltage of the source remains same in both the circuits. R1,L1, and C1, are Resistance, Inductanceand Capacitance of Circuit I . Where as R2, L2 and C2 are Resistance, Inductance and Capacitanceof Circuit II. Which of the following is true ?

(A) (B)

(C) (D)

27. An Infinite number of straight conductors are alligned parallel to z‑axis. Conductor cut x‑axis atx=r, x=2r, x=3r, x=4r, ......... The currents through conductors at x=r, x=3r, x=5r, ............. are in thedirection of positive Z‑ axis. The currents through conductors at x=2r, x = 4r, x=6r, ......... are in thedirection of negative Z‑ axis. The magnitude of current thorugh each conductor is I. The magneticfield at O is

(A) (B) (C) (D)

28. Bandwidth of a RLC series tuning circuit is independent of

(A) Resistance (B) Inductance (C) Capacitance (D) net reactance

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29. In a region of uniform electric and magnetic fields, A positive charged particle ofcharge ʹqʹ and massʹmʹ is released from origin. Find speed of the particle when the particle is at

(A) (B) (C) (D)

30. In the figure shown, light enters into a region at x = O in the direction of positive x‑axis. Refractive

index of the space is given by , where and are positive constants and speedof light in free space is C.

At what value of x, speed of light

(A) (B) (C) (D)

Chemistry

31. When hydrazoic acid react with Nitrous acid to give

(A) (B) (C) (D)

32. In a solid AB having NaCl structure, A atoms occupy the corners of the cubic unit cell. If all theface centered atoms along one of the axis are removed, then the resultant stoichiometry of thesolid is

(A) AB2 (B) A2B (C) A4B3 (D) A3B4

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33. shows reducing property in __________ medium.

(A) Acidic (B) Alkaline (C) Weak Alkaline (D) Aqueous

34. Seseque oxide in given species is/are

(A) (B) (C) (D)

35. 1g charcoal is placed in 100 ml of 0.5 m CH3COOH to form an adsorbed monolayer of acetic acidmolecule and thereby the molarity of CH3COOH reduces to 0.49. Calculate the surface area ofcharcoal adsorbed by each molecule of CH3COOH.

surface area of charcoal = 3.01 X 102 m2/g

(A) (B) (C) (D)

36. Which gas is adsorbed strongly by charcoal

(A) CO (B) N2 (C) H2 (D)NH3

37. Solution of on mixing with gives

(A) (B) (C) (D)No reaction

38. The coagulating power of electrolytes having ions Na+, Al+3 and Ba2+ for arsenic sulphide sol increases in the order.

(A) Na+


40. Given below are the half cell reaction

The for will be

(A) ‑ 2.69 V the reaction will not occur. (B) ‑2.69 V the reaction will occur

(C) ‑0.33 V the reaction will not occur (D) ‑0.33 V the reaction will occur

41. In the following equillibrium in a closed container the vapourpressure of is 24mm at 250C if pressure of is increased to 48 mm at 250C. Calculate Increase in

pressure of at new equilibrium at 250C

(A) (B) (C) (D)

42. Find the possible pairs of stereoisomers for the compound C2HClBrF?

(A) 1 (B) 2 (C) 3 (D) 4

43. The degree of dissociation is 0.4 at 400k and 1 atm for the gaseous reaction. . Assuming ideal behaviour of all the gases. Calculate the density of equilibrium mixture at 400kand 1 atmosphere. (A) (B)(C) (D)

44. Among the following Oxo acids, the correct decreasing order of acid strength is

(A) HOCl > HClO2 > HClO3 > HClO4 (B) HClO4 > HOCl > HClO2 > HClO3

(C) HClO4 > HClO3 > HClO2 > HOCl (D) HClO2 > HClO4 > HClO3 > HOCl

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45. Which Statement is not true ?

(A) pH of 1 x 10‑8 M HCl is 8 (B)96500 coloumb deposit 1 g equivalentof Cu

(C) Conjugate base of is (D) for all aqueous solution.

46. Find the total number of isomers (including stereoisomers) which can be obtained onmonochlorination of 2 ‑ methyl butane?

(A) 4 (B) 6 (C) 8 (D) 10

47. CsCl crystalises in body centered cubic la�ice if a is the edge length, then which of the followingexpression is correct.

(A) (B) (C) (D)

48.Give the major product for the following reaction :

(A) (B)

(C) (D)

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49. Predict the final product for the transformation :

(A) (B)

(C) (D)

50. Out of the given four structures of organic compounds :

Which two structures are optically inactive?

(A) (i) and (ii) (B) (ii) and (iii) (C) (i) and (iii) (D) (iii) and (iv)

51. For the following three reaction 1,2 and 3 equilibirum constants are given

Which of the following relations is Correct.

(A) (B) (C) (D)

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52. Calculate the concentration of cation vacancies if NaCl is doped with 10‑3 mole % SrCl2

(A) 6.02 X 1018 (B) 5.88 X 1023 (C) 2.65 X 1017 (D) 9.33 X 1027

53. Species which shows paramagnetic behavior is/are

(A) (B) (C) (D) All of these

54. Find the oxidation number of Central atom in X and Y for the given reaction.

(A) (B) (C) (D)

55. on hydrolysis gives

(A) (B) (C) (D) All of these

56. The sides of safety matches contain

(A) Red phosphorous and sand (B)

(C) (D)

57. The oxo‑acid which shows cis‑trans isomerism.

(A) Hyponitrous acid (B) Hypo phosphorous acid

(C) Nitroxylic acid (D) Hypo‑chlorous acid

58. The solubility product of SrF2 in water is 8 x 10‑10.Calculate its solubility in 0.1M NaF aqueoussolution.(A) (B)(C) (D)

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59. Find the basic reagents required for the transformation :

(A) (B)(C) (D)

60. In a galvanic cell, the salt bridge

(A) does not participate chemically in thecell reaction (B)stops the diffusion of ions from oneelectrode to another

(C) is necessary for the occurance of thecell reaction (D)ensures mixing of the two electrolyticsolution

Math

61.If and then the value of is equal to

(A) a (B) b (C) a ‑ b (D) a + b

62.The coefficient of term independent of in the expansion of is

(A) (B) (C) (D)

63.If then is

(A) (B)

(C) (D) None of these

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64. The value of parameter so that the line is normal to may lie in theinterval.

(A) (B) (1, 3) (C) (‑3, 3) (D)None of these

65. then maximum value of xy is

(A) (B) (C) (D)

66. is on such that The area of triangle formed by

and is

(A) 25 (B) (C) (D)Data notsufficient

67. If then what is the probability than X will have 3 at itʹs unit place.

(A) (B) (C) (D)

68.

If

(A) (B) (C) (D)

69. The number of 5 digit numbers of the form in which is

(A) 320 (B) 340 (C) 360 (D) 380

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70. The number of ways in which a commi�ee of 5 can be chosen from 10 candidates so as to excludethe youngest, if it includes the oldest, is

(A) 196 (B) 126 (C) 70 (D) 120

71.The function is monotonically increasing, if

(A) (B) (C) (D)

72. terms is equal to(A) (B)(C) (D)

73.If be the n nth roots of unity, then the value of is

(A) (B) (C) (D)

74.If occurs in the expansion of then

(A) is a multiple of 2 (B) is a multiple of 3

(C) (D) is a multiple of 4

75. equals to

(A) (B) (C) (D)None of these

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76.

, then the value of k is

(A) ‑1006 (B) (C) 1006 (D) 1007

77. The position of a point in time t is given by Itʹs acceleration at time tis

(A) b ‑ c (B) b + c (C) 2 (b ‑ c ) (D)

78.From a city population, the probability of selecting (i) a male or a smoker is . (ii) a male smoker

is and (iii) a male, if a smoker is already selected is . Then probability of selecting a smoker, if amale is first selected, is

(A) (B) (C) (D)

79.A curve passing through the point satisfies then which of thefollowing does not hold good?

(A) f(x) is differentiable at x = 0. (B) f (x) is symmetric w.r.t. origin

(C) f(x) is increasing for x 0. (D) f (x) has two inflexion points.

80.

If then is

(A) (B) (C) 0 (D)Not defined

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81. The point in the interval , where has maximum slope is

(A) (B) (C) (D)

82. If a denotes number of permutations of (x + 2 ) distinct things taken all at a time, b denotes thenumber of permutation of x distinct things taken 11 at a time, and c denotes the number ofpermutation of x ‑ 11 distinct things taken all at a time such that a = 182 bc, then x is

(A) 15 (B) 12 (C) 10 (D) 18

83.

The value of the integral is ([.] : G. I. F. , | . | = modulus)

(A) 0 (B) ‑10 (C) 10 (D)N.O.T.

84.

If then is

(A) = 2 (B) > 2 (C)

RAO IIT ACADEMY Rao Intelligence Search Exam 2017 / Sample Paper / Std. XII

86.The probability that a teacher will give an unannounced test during any class meeting is If astudent is absent twice, the probability that student will miss the paper at least once, is

(A) (B) (C) (D)

87.If such that , then equation

has at least one root lying between

(A) 0, 1 (B) 1, 2 (C) 1, 3 (D) ‑3, 0

88. Sum of coefficients in the expansion of (x‑2y+3z)n is 128, then greatest coefficient in the expansionof (1+x)n is

(A) 35 (B) 20 (C) 10 (D)N.O.T.

89.

The value of the intergral is

(A) 0 (B)

(C) (D)N.O.T.

90.if and then is equal to

(A) (B) (C) (D)

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