SECTION - I (Single Correct Choice Type)

Tliis Section contains 8 multiple choice questions. Each question has four choices A), B), C) and D) out of which ONLY ONE is correct.

1. The correct structure of e thylene dia mine tetra ace tic acid (EDTA) is

HOOC-CH2    ch2-cooh Vch=cht/" A)    /    \ HOOC-CHi    CH2-COOH

HOOC    COOH N-CHZ'CH-N B)    /    \ HOOC    COOH

---

ANSWER: C

2. The ionization isomer of [Cr(H O) Cl(WOJ]Cl is

_2- 4-    2.

A) [Cr(H_a0)_t(0₂N)]Cl

B)    |Cr(H,0)₄Cl₂|(TO₂)

C)    [Cr(H,0)₄Cl(0N0)]Cl

D)    [Cr(H₃0)₄C1₂(NOJ 1 -HO

ANSWER: B

3. The synthesis of 3-octyne is achieved by adding a bromoalkane into a mixture of sodium amide and an alkyne. The bromoalkane and alkyne respectively are

A) BrCHCfCflCHCf and CH₃CH,C=CH

B)    BrCH₂ CHCH and CHCHCHC = CH

C)    BrCH₂CH₂CH₂CH_nCH₃ and CH₃C = CH

D)    BrCH,,CH_nCHj and CH₃CIt,C = CH

ANSWER: D

A)    Ring (a) is pyranose with a-gjycosidic link

B)    Ring (a} is liiranose with a -gjycosidic link

C)    Ftiiae (b) is liiranose with a -glvcosidic link

D)    Ring (b) is pyranose with [3 -glycosiclic link

ANSWER: A

C) $Br and CHOH

ANSWER: D

6. Plots showing the variation of the rate constant (k) with temperature (T) are given below. The plot that follows Arrhenius equation is

ANSWER: A

7. The species winch by definition lias ZERO standard molar enthalpy of formation at 298 K is

ANSWER: B

8. The bond energy (in kcal mol *) of a C-C single bond is approximately A) 1    B) 10    C) 100    D) 1000

SECTION - IT] (Multiple Correct Choice Type)

9. The reagent(s) used for softening the temporary hardness of water is(are) A) Ca₃(P0₄)₂    B) Ca(OH)₂    C) Na₂C0₃    D) NaOCl

ANSWER: B

ANSWER: A and C

11. In the Newman projection for 2,2-dimethylbutane

X and Y can respectively be A) H and H    B) H and C₂H.

D) CH and CH,

ANSWER: B and D

12. Among the following, the intensive property is (properties are)

A) molar conductivity B) electromotive force

C) resistance    D) heat capacity

ANSWER: A and B

13. Aqueous solutions of HK0₃. KOH* CH,COOH, and CH₃COONa of identical concentrations axe prodded. The pair(s) of solutions which form a buffer upon mixing is (are)

A) HN03 and CH3COOH C) HNO and CH COONa '    3    3

B) KOH and CH3COONa D) CH COOH and CH COONa '    3    3

---

ANSWER: C and D

SECTION - III (Paragraph Type)

Paragraph for Questions 14 to 16

Copper is the most noble of the first row transition, metals and occurs in small deposits in several countries. Ores of copper include chalcanthite (CuS0₄ oHO), atacamite (Cu₂C1(OH)₃), cuprite (Cu_aO), copper glance (Cu₂S) and malachite (CuOHCOJ. However, 80% of the world copper production comes from the ore clialcopyrite (CuFeS₂). The extraction of copper from clialcopyrite involves partial roasting, removal of iron and self-reduction.

14. Partial roasting of chal copy rite produces

A)    Cu₂S and FeO

B)    Cu₂0 and FeO

C)    CuS and Fe₂O_a

D)    CuO and Fe₂0₃

ANSWER: A

15. Iron is removed from clialcopyrite as

A) FeO

D) FeSiO_s

ANSWER: C

Paragraph for Questions 17 to IS

The concentration of potassium ions inside a biological cell is at least twenty times higher tlian the outside. The resulting potential difference across the cell is important in several processes such as transmission of nerve impulses and maintaining the ion balance. A simple model for such a concentration cell involving a metal M is:

M[s)|M⁺(aq; 0.05 molar) || M⁺(aq; 1 molar) |M(s)

For the above electrolytic cell the magnitude of the cell potential |E_ceU| = 70 mV.

17. For the above cell

ANSWER: B

18. If the 0.05 molar solution of M⁺ is replaced by a 0.0025 molar M⁺ solution, then the magnitude of the cell potential would be

ANSWER: 2

20. The total number of cyclic isomers possible for a hydrocarbon with the mole culm'

formula CH is

4 b

ANSWER: 5

ANSWER: 1

22. Amongst the following, the total number of compounds soluble in aqueous NaOH is

23. Amongst the following, the total number of compounds whose aqueous solution turns red litmus paper blue Is

ANSWER: 3

24.    Based on VSEPR theory. the number of 90 degree F-Br-F angles in BrF is

ANSWER: either 0 or 8

25.    The value of n in the molecular formula Be_nAl₂Si₆O_ia is

ANSWER: 3

26.    A student performs a titration with different burettes and finds titre values of 25.2 niL, 25.25 mL, and 25.0 mL. The number of significant figures in tlie average titre value is

ANSWER: 3

27.    The concentration of R in the reaction R > P was measured as a function of time and the following data is obtained:

SECTION - 11 (Single Correct Choice Type)

29. If the angles A, B and C of a triangle are in an arithmetic progression and if a. b and c denote the lengths of the sides opposite to A, B and C respectively, then

the value of the expression sin2C+siii2A is

ANSWER: D

30. Equation of the plane containing the straight line -j and perpendicular to

ANSWER: C

31. Let cobe a complex cube root of unity with col. A fail' die is thrown three times. If r , r₂ and r are the numbers obtained on the die, then the probability that

of¹ +0)¹² +of³ =0 is

ANSWER: C

A)    parallelogram, which is neither a rhombus nor a rectangle

B)    square

C)    rectangle, but not a square

D)    rhombus, but not a square

ANSWER: A

A) 0 B) 2s - 1    C) 168 D) 2

ANSWER: A

ANSWER: B

C) (_p³-_q)x²-Op³-2q)x + (p³-q) = 0 D) (p³-q)x²

ANSWER: B

36. Let f, g and h be real-valued functions defined on the interval [O', 1] by

2    1    T    1    2    2

f (x) = e^K + e^_x" . g(x) = xe^x" + e^_x~ and h(x) = x²e^s + e^K . If a, b and c denote, respectively, the absolute maxiinum of f, g and h oil [0, 1], then

(Multiple Correct Choice Type)

37. Let A and B be two distinct points on the parabola v² = 4x. If the axis of the parabola touches a circle of radius r having AB as its diameter, then the slope of the line joining A and B can be

ANSWER: C and D

TT

38. Let ABC be a triangle such that ZACB= and let a, b and c denote the lengths of

6

the sides opposite to A, B and C respectively. The value(s) of x for which

a = + x + 1, b = x- - 1 and c = 2x + 1 is (are)

A) -{l + S )    B) \+S    C) 2+S

ANSWER: B

39. Let Zj and z₂ be two distinct complex numbers and let z = (1 - t) z_l + tz₂ for some real number t with 0 < t < 1. If Arg(w) denotes the principal argument of a nonzero complex number w, then

40. Let f be a real-valued function defined on the interval (0 * DO ) by x _

f(x) = *n x+ j + smt dt. Tlien which of the following stateinent(s) is (are) true ?

0

ANSWER: B and C

ANSWER: A

(Paragraph Type)

42. The number of A in T such that A is either svmmetric or skew-symmetric or

P    ^L'    

both, and det (A) divisible by p is

A) (p - l)²    B) 2 (p - 1)    C) (p - l)² + 1    D) 2p - 1

ANSWER: D

43. The number of A in T such tliat the trace of A is not divisible by p but det (A) is divisible by p is

[Note : The trace of a matrix is the sum of its diagonal entries.]

A) (p - 1) (p² - p + 1)    B) p³ - (p - l)²    C) (p - l)² D) (p - 1) [p² - 2)

44. The number of A in T_p such tliat det (A) is not divisible by p is

A) 2p²    B) p³ - 5p    C) p³ - 3p    D) p³ - p²

ANSWER: D

45. Equation of a common tangent with positive slope to the circle as well as to the hyperbola is

ANSWER: B

48. The maximum value of the expression -~ is

siii 0 + 3 siii 0 cos0 + 5cos 0

ANSWER: 2

. j. . , p . . _t i - 2j . r 2i + j+ 3k _tl

49. If a and b are vectors m space given by a = f= and b =-f=-, then the

Vl4

ANSWER: 5

2 2 x y

50. Tlie line 2x4 v= 1 is tangent to the hyperbola r--- 1. If this line passes

   "    a b

through the point of intersection of the nearest directrix and the x-axis, then the

eccentricity of the hyperbola is

ANSWER: 2

ANSWER: 6

52. For any real number x, let [x] denote the largest integer less tlian or equal to x. Let f be a real valued function defined on the interval [-10, 10] bv

10 Then the value of I f(x) cos nx dx is 10 '-io

[ x - [x] if [x] is odd, f(x) 11 + [x] - x if [x] is even

---

ANSWER: 4

complex numbers z satisfying

2k 2jt cos + 1 Sill 3 3 z +1 0) to2 0) Z + <02 1 9 0) 1 z + to

= 0 is equal to

ANSWER: 1

k 1    1    100²    I o    \

term is- and the coimnon ratio is . Then die value of -+ Y k - 3k + 1 Si.

k! k 100!

k=i

is

ANSWER: 3

55. The number of all possible values of 0 , where 0 < 9 < Tl, for wliich the system of equations

(y + z) cos 3 0= (xyz| sin 3 0

2 cos 36 2 sin30 x sm 30 =-+-

y z

(xyz) sin 3 0 = (y + 2z) cos 3 0 + y sin 3 0 have a solution (x y₀, with y₀ z₀ 0, is

ANSWER: 3

56. Let f be a real-valued differentiable iimction on R (the set of all real numbers) such diat f(l) = 1. If the y-intercept of the tangent at any point P(x, y) on tlie curiae y = f(x)

is equal to the cube of the abscissa of P, then the value of f(-3) is equal to

ANSWER: 9

57. Consider a thin square sheet of side L and thickness t made of a material of resistivity p . The resistance between two opposite faces, shown by the sliaded areas in the figure is

A) directly proportional to L C) independent of L

B) directly proportional to t D) independent of t

---

ANSWER: C

58. A real gas behaves like an ideal gas if its

A)    pressure and temperature are both high

B)    pressure and temperature are both low

C)    pressure is high and temperature is low

D)    pressure is low and temperature is high

ANSWER: D

59. Incandescent bulbs are designed by keeping in mind that the resistance of their filament increases with the increase in temperature. If at room temperature, 100 W, 60 W and 40 W bulbs have filament resistances R_10D, R_eo and R₄₀,

respectively, the relation between these resistances is

1

60. To verify Ohm's law, a student is provided with a test resistor R,., a high resistance R₂, a small resistance R, two identical galvanometers G_L and G₂, and a variable voltage source V. The correct circuit to cany out the experiment is

ANSWER: C

61. An AC voltage source of variable angular frequency to and fixed amplitude V_Q is connected in series with a capacitance C and an electric bulb of resistance R (inductance zero). When to is increased

A)    the bulb glows dimmer

B)    the bulb glows brighter

C)    total impedance of the circuit is unchanged

D)    total impedance of the circuit increases

ANSWER: B

62. A thin flexible wire of length L is connected to two adjacent fixed points and carries a current I in the clockwise direction, as shown in tlie figiu'e. When the system is put in a uniform magnetic field of strength B going into the plane of the paper, the wire takes the sliape of a circle. The tension in the wire is

XXX	X X	X X	X
X X J<		X X	X
XXX	X X	x\<	X
x jk x	X X	X k	X
XXX	X X	X *	X
X XX	X X	X jfe	X
X x\	X X	/x	X
XXX		X X	X

ANSWER: C

ANSWER: A

(Multiple Correct Choice Type)

ANSWER: A and D

66. A student uses a simple pendulum of exactly 1m length to determine g, the acceleration due to gravity. He uses a stop watch with, the least count of 1 sec for this and records 40 seconds for 20 oscillations. For tliis observation, which of the following statement(s) is (are) true ?

A)    Error AT in measuring T, the time period, is 0.05 seconds

B)    Error AT in measuring T, the time period, is 1 second

C)    Percentage error in the determination of g is 5%

D)    Percentage error in the determination of g is 2.5%

67. A point mass of 1 kg collides elastically with a stationary point mass of 5 kg. After their collision, the 1 kg mass reverses its direction and moves with a speed of 2 ms^-1. Which of the following statement(s) is [are) correct for the system of these two masses ?

A)    Total momentum of the system is 3 kg ms-¹

B)    Momentum of 5 kg mass after collision is 4 kg ms^-1

C)    Kinetic energy of the centre of mass is 0.75 J

D)    Total kinetic energy of the system is 4 J

ANSWER: A and C

68. A ray OP of monochromatic light is incident on the face AB of prism ABCD near vertex B at an incident angle of 60 (see figure). If the refractive index of the material of the prism is . which of the following is (are) correct ?

A)    The ray gets totally internally reflected at face CD

B)    The ray comes out tluough face AD

C)    The angle between the incident ray and the emergent ray is 90

D)    The angle between the incident ray and the emergent ray is 120

ANSWER: A and B and C

69. One mole of an ideal gas in initial state A undergoes a cyclic process ABCA. as shown in the figure. Its pressure at A is P_Q. Choose the correct option(s) from the following

A)    Internal energies at A and B are the same

B)    Work done by the gas in process AB is P_QV n 4

P₀

C)    Pressure at C is

4:

T₀

D)    Temperature at C is

SECTION - III (Paragraph Type)

Paragraph for Questions 70 to 72

When a particle of mass m moves on the x-axis in a potential of the form V(x) = kx², it performs simple harmonic motion. The corresponding time period is

proportional to , as can be seen easily using

dimensional analysis. However, the motion of a particle can be periodic even when its potential energy increases

on both sides of x = 0 in a way different from kx- and its total energy is such that the particle does not escape to infinity. Consider a particle of mass m moving on the x-axis. Its potential energy is V(x) = ax⁴ (a>0) for |x| near the origin and becomes a constant equal to V for |x| > Xj. (see figure).

70. If the total energy of the particle is E, it will perform periodic motion only if

ANSWER: B or C or (B and C) Option C implies option B.

71. For periodic motion of small amplitude A, the time period T of this particle is proportional to

ANSWER: B

72. The acceleration of this particle for |x|> is

A) proportional to V_D

D) zero

Paragraph for Questions 73 to 74

Electrical resistance of certain materials, known as superconductors, clianges abruptly from a nonzero value to zero as their temperature is lowered below a critical temperature T_c(0). An interesting property of superconductors is that their critical temperature becomes smaller than T_c (0) if they are placed in a magnetic field, i.e., the critical temperature T_c (B) is a function of die magnetic field strength B. The dependence of T_c (B) on B is shown in the figure.

73. In the graphs below, the resistance R of a superconductor is shown as a function of its temperature T for two different magnetic fields B (solid line) and B,, (dashed line). If B₂ is larger than Bj, which of the following graphs shows the correct variation of R with T in these fields ?

ANSWER: A

74. A superconductor has T_c (0) = 100 K. When a magnetic field of 7.5 Tesla is applied its T_c decreases to 75 K. For this material one can definitely say that when

A) B = 5 Tesla, T_c (B) = 80 K    B) B = 5 Tesla, 75 K < T_c (B) < 100 K

C) B = 10 Tesla, 75 K < T_c (B) < 100 K D) B = 10 Tesla, T_c (B) = 70 K

SECTION-IV (Integer Type)

75. Tlie focal length of a thin biconvex lens is 20cm. When mi object is moved from a distance of 25cm in front of it to 50cm, the magnification of its image changes

from iii to iii . Tlie ratio

-5    sa    m,

50

ANSWER: 6

76. Ail a-particle and a proton are accelerated from rest by a potential difference of 100V. After this, their de Broglie wavelengths are and X respectively. The

p

ratio t, to the nearest integer, is

ANSWER: 3

77. When two identical batteries of internal resistance IQ each are connected in series across a resistor R. tlie rate of heat produced in R is J_L. When the same batteries are connected in parallel across R tlie rate is J₂. If = 2.25 J₃ then the value of R in Q is

ANSWER: 4

78. Two spherical bodies A (radius 6 cm) and B (radius 18 cm) are at temperatures and T,, respectively. Tlie maximum intensity in the emission spectrum of A is at 500 mil and in that of B is at 1500 mil. Considering them to be black bodies, what will be the ratio of the rate of total energy radiated by A to tliat of B ?

ANSWER: 9

SO. A 0.1 kg mass is suspended from a wire of negligible mass. The length of die wire is lm and its cross-sectional area is 4.9xl0~⁷m-. If the mass is pulled a little in the vertically downward direction and released, it performs simple harmonic motion of angular frequency 140 rad s^-1. If the Young s modulus of tlie material of the wire is nx 1 O'³ Nnr², the value of n is

ANSWER: 4

SI. A biliary star consists of two stars A (mass 2.2MJ and B (mass 11M_Q), where M_n is the mass of the sun. They are separated by distance d and are rotating about their centre of mass, which is stationary. The ratio of the total angular momentum of the binary star to the angular momentum of star B about the centre of mass is

ANSWER: 6

[q

82. Gravitational acceleration on the surface of a planet is _g , where g is the

gravitational acceleration on the surface of the earth. The average mass density of

2 ' die planet is times that of the earth If the escape speed on die surface of die earth

is taken to 1>e 11 kmsr¹, the escape speed on the surface of the planet in kms^-1 will be

ANSWER: 3

S3. A piece of ice (heat capacity = 2100 J kg¹ ,::C^_1 and latent heat = 3.36 x 10⁵ J kgr¹) of mass m grams is at -5C at atmospheric pressure. It is given 420 J of heat so that the ice starts melting. Finally when the ice-water mixture is in equilibrium, it is found that 1 gm of ice has melted. Assuming there is no other heat exchange in the process, the value of m is

ANSWER: 8

S4. A stationary source is emitting sound at a fixed frequency f₀, which is reflected by two cars approaching the source. The difference between the frequencies of sound reflected from the cars is 1.2% of f_c. What is the difference in the speeds of the cars (in km per hour) to the nearest integer ? The cars are moving at constant speeds much smaller tlian the speed of sound which is 330 ms¹.

ANSWER: 7

1. The complex showing a spin-only magnetic moment of 2.82 B.M. is

ANSWER: B

ANSWER: D

were separately subjected to nitration using HNOg/HgSC mixture. The major product formed in each case respectively, is

_vuo

ANSWER: C

5. The packing efficiency of the two-dimensional square unit cell shown below is

A) 39.27%    B) 68.02%    C) 74.05% )) 78.54%

ANSWER: D

the diatomic molecule B₂ is

A)    1 and diamagnetic C) 1 and paramagnetic

B)    0 and diamagnetic D) 0 and paramagnetic

ANSWER: A

SECTION - II )(Integer Type)

ANSWER: 6

8. Total number of geometrical isomers for the complex [RhCl(CO)(PPh.3)(NH₃)] is

ANSWER: 3

9. Among the following, the number of elements showing only one non-zero oxidation

ANSWER: 2

10. Silver (atomic weight = 108 g mol^-1) lias a density of 10.5 g cm^-3. The number of silver atoms on a surface of area 10^-12 m² can be expressed in scientific notation as v x lO*. The value of x is

11. One mole of an ideal gas is taken from a to b along two paths denoted by the solid and the dashed lines as shown in the graph below. If the work done along the solid line path is w_s and that along the dotted line path is w_d, then the integer closest to the ratio w_c]/w₅ is

SECTION - ml (Paragraph Type)

V_J

Paragraph for Questions 12 to 14.

Two aliphatic aldehydes P and Q react in the presence of aqueous K₂C0₃ to give compound R, which upon treatment with HCN provides compound S. On acidification and heating* S gives tlie product shown below :

h₃c OH

V*0

ANSWER: A

Paragraph for Questions 15 to 17.

Tlie hydrogen-like species Li²⁺ is in a spherically symmetric state S_x with, one radial node. Upon absorbing light the ion undergoes transition to a state S₉. Tlie state S₂ lias one radial node and its energy is equal to tlie ground state energy of the hydrogen atom.

ANSWER: B

ANSWER: C

17. Tlie orbital angular momentum quantum number of the state S₉ is

SECTION - IV (Matrix Type)

19. All the compounds listed in Column I react with water. Match the result of the respective reactions with the appropriate options listed in Column II.

Column I    Column II

A)    (CH₃)₃SiCL    p) Hydrogen halide formation

B)    XeF₄    q) Redox reaction

C)    Cl₂    r) Reacts with glass

D)    VC1₅    s) Polymerization

t) O, formation

ANSWER: D

ANSWER: B

ANSWER: A

24. Two adjacent sides of a parallelogram ABCD are given by

AB = 2i + lOj + 1 lk and AD = - i + 2j + 2k

The side AD is rotated by an acute angle a in the plane of the parallelogram so that AD becomes AD⁷. If AD' makes a light angle with the side AB, then the cosine of the angle a is given by

ANSWER: B

⁴ <¹

25. A signal which can be green or red with, probability and respectively, is received

by station A and then transmitted to station B, The probability of each station

   3    

receiving tlie signal correctly is . If the signal received at station B is gi'een,

then tlie probability that tlie original signal was green is

26. Two parallel chords of a circle of radius 2 are at a distance *j3 +1 apart. If the chords

K    2 K

subtend at the center, angles of and , where k > 0. then the value of [k] is

k k

[Note : [k] denotes the largest integer less tlian or equal to k]

ANSWER: 3

27.    Consider a triangle ABC and let a, b and c denote the lengths of the sides opposite to vertices A. B and C respectively. Suppose a = 6, b = 10 and the area of the triangle is 15>/3 . If ZACB is obtuse and if r denotes the radius of the incircle of the triangle, then i² is equal to

ANSWER: 3

28.    Let f be a function defined on R (the set of all real numbers) such that ftx}=2010(x-2009)i(x-2010)²(x-2011)P (x-2012)⁴, for allx _E R.

If g is a function defined on R with values in the interval (0, _M) such that

f(x) = ?n (g (x)), for all x e R, then the number of points in R at which g has a local maximum is

ANSWER: 1

29.    Let a-p a₂, a₃, ... , a_n be real numbers satisfying

a_: = 15, 27 - 2a₂ > 0 and a_k = 2a_k_₁ - a_k_₂ for k = 3. 4, .... 11.

A =	2k -1 2k 2Vk ~ 0 21i-1 Vk " 2/k 1 -2k and B = l-2k 0 24k -2Vk 2k -1 -Vk -2Vk 0

If det (adj A) + det(adj B) =10⁶. then [k] is equal to

[Note : adj M denotes the adjoint of a square matrix M and [k] denotes the largest integer less tlian or equal to k].

ANSWER: 4 SECTION - III] (Paragraph Type)

Paragraph for questions 31 to 33.

Consider the polynomial

f(x)=l+ 2x + 3x² + 4X³.

Let s be the sum of all distinct real roots of f(x) and let t =

33. Tlie function f'txj is

A) increasing in

t, I raid decreasing in

B)    decreasing in t, | and increasing in

C)    increasing in (t, t)

D)    decreasing in (t, t)

ANSWER: B

Paragraph for Questions 34 to 36.

2 2 X V

Tangents are drawn from the point P(3. 4) to the ellipse +-=1

9 4

touching the ellipse at points A and B.

ANSWER: D

36. The equation of the locus of the point whose distances from the point P and the line AB are equal, is

A)    9x² + v²- 6xy - 54x - 62y +241 =0

B)    x² + 9y² + 6xy - 54x + 62y - 241 = 0

C)    9x² + Qy² - 6xy - 54x - 62y - 241 = 0

D)    x² + y² - 2xy + 27x + 31y - 120 = 0

ANSWER: A

SECTION - iv] (Matrix Type)

37. Match the statements in Column-I witii those in Column-II.

[Note: Here z takes values in the complex plane and Im z and Re z denote, respectively, the imaginary part and the real part of z.]

Column I A) The set of points z satisfying

Column II 4 p) an ellipse with eccentricity o

---

|z-i| z|| =|z + i|z |

q) the set of points z satisfying Im z = 0

B) The set of points z satisfying |z + 4| + | z 41 = 10¹ is contained in or equal to

C) If |w| =2, then the set of points    s) the set of points z satisfying |Re z| < 2

1

z-w- is contained in or equal to w    ¹

D) If |w| = 1, then the set of points    t) the set of points z satisfying |z|<3

z = w+ is contained in or equal to w

A:    q and r

B:    p

C:    p and s and t D:    q and r and s and t

A:    t

B:    p and r

C:    either q or (q and s)

D:    r

39.    A Vernier calipers lias 1 mm marks on tlie main scale. It lias 20 equal divisions on the Vernier scale which match with 16 main scale divisions. For this Vernier calipers, the least count is

A) 0.02 mm    B) 0.05 mill    C) 0.1 nun    D) 0.2 mm

ANSWER: D

40.    A hollow pipe of length 0.8 m is closed at one end. At its open end a 0.5 m long uniform string is vibrating in its second harmonic and it resonates with the fundamental frequency of the pipe. If the tension in the wire is 50 N and tlie speed of sound is 320 ms^-1, the mass of tlie string is

A) 5 grams    B) 10 grains    C) 20 grams    D) 40 grams

ANSWER: B

41. A biconvex lens of focal length 15 cm is in front of a plane mirror. Tlie distance between the lens and tlie mirror is 10 cm. A small object is kept at a distance of 30 cm from the lens. Tlie final image is

A)    virtual and at a distance of 16 cm from the mirror

B)    real and at a distance of 16 cm from the mirror

C)    virtual and at a distance of 20 cm from the mirror

D)    real and at a distance of 20 cm from the mirror

ANSWER: B

42. A block of mass 2 kg is free to move along the x-axis. It is at rest and from r = 0 onwards it is subjected to a time-dependent force F(t) in the x direction. The force Fft) varies with t as shown in the figure. The kinetic energy of the block after 4.5 seconds is

F/tJ *

A) 4.50 J    E) 7.50 J    C) 5.06 J    D) 14.06 J

ANSWER: C

43. A tiny spherical oil drop carrying a net charge q is balanced in still air with a

SIjt 5

vertical uniform electric field of strength xlO Vm . When the field is

7

switched off, the drop is observed to fall with terminal velocity 2 x 10^-3 m s^_1.

Given g = 9,8 in s~², viscosity of the air = 1.8 x 10 ⁵ Ws nr² and the density of oil = 900 kg m^-3, tlie magnitude of q is

A) 1.6x 10¹⁹C    B) 3,2 x 10^-19 C C) 4.8 x lO"¹⁹ C D) 8.0 x 10^-19 C

ANSWER: D

ANSWER: A

1

45. A diatomic ideal gas is compressed adiabatically to of its initial volume. In the Initial temperature of the gas is T. (in Kelvin) and the final temperature is aT_t, die value of a is

ANSWER: 4

46. At tune t = 0, a batteiy of 10 V is connected across points A and B in the given circuit. If the capacitors have no charge initially, at wliat time (in seconds) does the voltage across them become 4 V ?

[Take : f.n 5 = 1.6. t.n 3 = 1.1]

ANSWER: 2

47. Image of an object approaching a convex mirror of radius of curvature 20 m along

25 , 50

its optical axis is observed to move from m to m in 30 seconds. What is

3

the speed of the object in km per hour ?

48. A large glass slab (|ll = 5/3) of thickness 8 cm is placed over a point source of light on a plane surface. It is seen tliat light emerges out of the top surface of the slab from a circular area of radius R cm. Wliat is the value of R ?

ANSWER: 6

ANSWER: 8

SECTION - III (Paragraph Type)

Paragraph for questions 50 to 52.

When liquid medicine of density p is to be put in the eye, it is done with the help of a dropper. As the bulb on the top of the dropper is pressed, a drop forms at the opening of the dropper. We wish to estimate the size of the drop. We first assume that the drop formed at the opening is spherical because that requires a minimum increase in its surface energy. To determine die size, we calculate die net vertical force due to the surface tension T when the radius of the drop is R. When this force becomes smaller than the weight of the drop, the drop gets detached from the dropper.

50. If the radius of the opening of the dropper is r, the vertical force due to the surface tension on the drop of radius R (assuming r R) is

51.    If r = 5x 10 111 p = 10^|3 kgm^-3, g = 10' ms\T=0.1 lNm\ the radius of the drop when it detaches from the dropper is approximately

A) 1.4xl0³m    B) 3.3x 10 ^_3 m C) 2.0xlG~³m D) 4.1xl0~³m

ANSWER: A

52.    After the drop detaches, its surface energy is

A) 1.4xlCT⁶J    B) 2.7x10^_6J C) 5.4x10    D) 8.1xlO^_QJ

ANSWER: B

Paragraph for Questions 53 to 55.

The key feature of Bolir's theory of spectrum of hydrogen atom is the quantization of

angular momentum when ail election is revolving around a proton. We will extend

tills to a general rotational motion to find quantized rotational energy of a diatomic

molecule assuming it to be rigid. The rule to be applied is Bohr's quantization condition.

54. It is found that the excitation frequency from ground to the first excited state of

4 u

rotation for the CO molecule is close to xlO Hz. Then the moment of inertia of

K

CO molecule about its center of mass is close to [Take h = 2 jrxlO^-34 J s)

A) 2.76x 1CT⁴⁶ kg m²    B) 1.87x 10⁶ kg in²

C) 4.67x lO^-47 kg m²    D) 1.17xl0⁷kg in²

ANSWER: B

55. In a CO molecule, the distance between C (mass = 12 a.m.u.) and O (mass =16 a.m.u.),

5 -27

where 1 a.m.u.    i^s dose to

A) 2.4><10-¹⁰m    B) 1.9_x10-¹⁰m C) 1.3_x10-^iam D) 4.4>_f10-¹¹m

ANSWER: C

57. You are given many resistances, capacitors and inductors. These are connected to variable DC voltage source (the first two circuits) or an AC voltage source of 50 Hz frequenc

(the next three circuits) in different ways as shown in Column II. When a current

(steady state for DC or mis for AC) flows through the circuit, the corresponding voltage I

and V_T (indicated in circuits) are related as shown in column I. Match the two

Column II

A) I O.Vj is proportional to I

C) Vi =o,v₂ =v

ANSWER: A: r and s and t

B: q and r and s and t C: pand q

D: q and r and s and t

Attachment: indian-institute-of-technology-new-delhi----iit--2010--2550-1.pdf indian-institute-of-technology-new-delhi----iit--2010--2550-2.pdf

Earning:   Approval pending.