Indian Institute of Technology New Delhi - (IIT) 2010 Iit -jee 2009 - Question Paper
IIT-1 2010
IIT-2 2010
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 |
H
D)
H
HOOCCH? CH2-COOH
pi N-CHj-CHa-N
/ \
HOOCCH2 CH2-COOH
COOH HOOC CH, CH2
\ I /
,NCHCHN
I \
CH2 CH2COOH
HOOC
ANSWER: C
2. The ionization isomer of [Cr(H O) Cl(WOJ]Cl is
_2- 4- 2.
A) [Cr(Ha0)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) BrCH2CH2CH2CHnCH3 and CH3C = CH
D) BrCH,,CHnCHj 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
OCH3 HBr > |
5. In the reaction
a
OCH3 and Hn
A) Hr
the products are B) C-Br and CHaBr
C) $Br and CHOH
D) 4 Von and CH3Br
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
B) Cl, (g)
A) Br (g)
C) HO (g)
D) CH. (g)
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,
C) C,H. and H
2 3
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 (CuaO), 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 Fe2Oa
D) CuO and Fe203
ANSWER: A
15. Iron is removed from clialcopyrite as
A) FeO
B) FeS
D) FeSiOs
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 |EceU| = 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
A) 35 mV C) 140 mV
B) 70 mV
D) 700 mV
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
KCK
FeClr
K2so<
LCOr
(NHj2c2o4
NH,NO
KaCl Zn(NO. LiCN
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 BenAl2Si6Oia 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:
The order of the reaction is
ANSWER: 0
o o it
28. The number of neutrons emitted when 92 U undergoes controlled nuclear fission
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
32. Let P, Q, R and S be the
points o respectively. The
2i j, 4i. 3i +3j and -3i+2j
the plane with position vectors quadrilateral PQRS must be a
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
A) (p3 +q)x2 -(p3 + 2q)x + (pJ +q) = 0 B) (p3 +q) x2 |
(p3-2q)x + (p3+q) = 0 (5p3 +2q) x + (p3 q) = 0
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) = eK + e_x" . g(x) = xex" + e_x~ and h(x) = x2es + eK . 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
SECTION - II
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
D) W3
ANSWER: B
39. Let Zj and z2 be two distinct complex numbers and let z = (1 - t) zl + tz2 for some real number t with 0 < t < 1. If Arg(w) denotes the principal argument of a nonzero complex number w, then
ANSWER: A and C and D
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)
SECTION - III
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 Tp 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
ANSWER: A
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 |
|
= 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 R10D, Reo and R40,
respectively, the relation between these resistances is
1 1
+ -
A)
R-
R-ia 60
100
B) R1D0 = R + 0
1
C) R
D)
R.
Rta R.
100
40
1CD > RSD > R4C
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 GL 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 VQ 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
c?
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 |
IBL
IBL
2n
IBL
4ir
A) IBL
B)
C)
D1
ANSWER: C
ANSWER: A
(Multiple Correct Choice Type)
SECTION - II
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
B |
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 PQ. Choose the correct option(s) from the following
V |
A) Internal energies at A and B are the same
B) Work done by the gas in process AB is PQV 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
V(X)A | |
A' |
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
A) E <0
B) E >0
D) E> V0
C) v;>e>o
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 VD
B) proportional to |
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 Tc(0). An interesting property of superconductors is that their critical temperature becomes smaller than Tc (0) if they are placed in a magnetic field, i.e., the critical temperature Tc (B) is a function of die magnetic field strength B. The dependence of Tc (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 Tc (0) = 100 K. When a magnetic field of 7.5 Tesla is applied its Tc decreases to 75 K. For this material one can definitely say that when
A) B = 5 Tesla, Tc (B) = 80 K B) B = 5 Tesla, 75 K < Tc (B) < 100 K
C) B = 10 Tesla, 75 K < Tc (B) < 100 K D) B = 10 Tesla, Tc (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
IS
-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 JL. 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 11MQ), where Mn 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 fc. 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
2-
2-
B) [NiCl4]2
C) Nl(PPh3)4
A) Ni(CO)4
D) [Ni(CN)4p
ANSWER: B
ANSWER: D
were separately subjected to nitration using HNOg/HgSC mixture. The major product formed in each case respectively, is |
A) HO |
O II f .c_ |
w'V
NO?
COOH
cx
B) MO'
NOi
.COOM
XJ
0
OCHi
iTY
a
C) HO
NOn | |
1ICT v | |
NO, |
COOH
h3 ii r\ i
/Y
Jl,C
D)
NOi
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 ws and that along the dotted line path is wd, then the integer closest to the ratio wc]/w5 is
ANSWER: 2
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
ANSWER: B
ANSWER: A |
Paragraph for Questions 15 to 17.
Tlie hydrogen-like species Li2+ is in a spherically symmetric state Sx 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
A) 0
C)
D) 3
B) 1
ANSWER: B
SECTION - IV (Matrix Type)
r and s t
p and q r
A
B
C
D
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:
A
B
C
D
p and s
p and q and r and t p and q P
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
8
9
A)
B)
C)
D)
9
W5
9
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
3
A) 5
20
23
C)
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]
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
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
29. Let a-p a2, a3, ... , an be real numbers satisfying
a: = 15, 27 - 2a2 > 0 and ak = 2ak_1 - ak_2 for k = 3. 4, .... 11.
If
is equal to
= 90. then the value of
A = |
|
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 =
ANSWER: C
33. Tlie function f'txj is
A) increasing in
t, I raid decreasing in
K'1)
(-H
(
(--i)
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.
11 S\
(T'
8 7 25 5
B)
C)
D)
35. The orthocenter of the triangle PAB is S { 7 25 x
A) 5,
7
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
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
is contained in or equal to
B) The set of points z satisfying |z + 4| + | z 41 = 101 is contained in or equal to
r) the set of points z satisfying | Im z | < 1
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
ANSWER:
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
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
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
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
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
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 aTt, die value of a is
2Mfi |
2m F 1 | | |
iVWWV |
-II- | |
vww |
..... 1 1 | |
2MD |
2|-fF |
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]
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 ?
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
2nr2T
R
2 kR2T
A) 2kiT
C)
D]
B) ZtlRT
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
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.
ANSWER: D
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
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. is dose to
A) 2.4><10-10m B) 1.9x10-10m C) 1.3x10-iam D) 4.4>f10-11m
ANSWER: A
B
C
D
p and r q and s and t p and r and t q and s
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 VT (indicated in circuits) are related as shown in column I. Match the two
Column II
Column I
A) I O.Vj is proportional to I
1 < v > i < |
B: q and r and s and t C: pand q
Attachment: |
Earning: Approval pending. |