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[SECTION -I](Single Correct Choice Type)This 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 ethylenedialninetetraacetic acid (EDTA) is
HOOC`.."CHZ CH2"COOH\ I
C) /N-CH2-CH2-N\
HOOC""CH2 CH2-COOH
COON
HOOC-CH2\N_CCH~_CH___N/H
D) Ml ` | ` \' ' CH2 CH2 -COOH
HOOC'
ANSWER: C
[CI`(H2O)4C1(NO2)]CIis
C) [CI`O)4C1(ONO)]CI
ANSWER: B
3 . of
B) BrCH~CH2CH3 mld CH3CCII2C -=CH
D ) BrCH2CH2C H2CH3 and CH3C fI2C @ CH
ANSWER: D
4) The correct statement about the following disaccharide is
o H cHzOH O H
/CI|20 OH fB)
ANSWER: A
D) OH and CH3Br
ANSWER: D
6. Plots showing the variation of the rate constant Ck) with temperature CT) areen below. e plot that follows Arrhenius equation is
A)
C)
1
k
1
D)
ANSWER: A7. The species which by definition has ZERO standard mo enpy of formation
at 298 K is
A} Br!2 (gJ B} C(7 (g) C) H2O lg) D) CH4 (gJ
ANSWER: B
8. The bond energy (In kea1 mol-IJ of a C-C slngle bond Is approtelyA) 1 B) 10 C) 100 D) 1000
ANSWER: C
9. The reagent(s) used for softening the tempor hardness of water is(are)A) Ca3(PO4)2 B) Ca(OH)2 C) Na2CO3 D) NaOCI
ANSWER: B
11. In the Newman projection for 2.2-dimethv.Ibutane
X and Y can respectively be
A) H and H B) H and C2H5
C) C2H5 d H D) CH3 mld CH3
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 HNO3 , KOH. C H3 C O O H, and C H3C O ONa of identicalconcentrations are provided. The pair(s) of solutions which form a buffer upon g is(are)
A) HNO3 and CH3COOH B) KOH and CH3COONa
B) HNO3 and CH3COONa D) CHsCOOH and CH3COONa
ANSWER: C and D
14. Partial roasting of chalcopyrite produces
B) CuQ{O and FeO
ANSWER: A
15. Iron is removed from chalcopyrite
A) FeO B) FeS
B) Fe2O3 C) FeSi
O3ANSWER: D
SECTION II- PARAGRAPH TYPE
16. In self-reduction, the reducing species is
A )S B)O 2-
ANSWER: C
Paragraph for guestions 17 to 18The concentration of potassium ions inside a biological cell is at least twenty timeshigher than the outside. The resulting potential difference across the cell is importantin several processes such as transmission of nerve impulses and maintaining the ionbalance. A simple model for such a concentration cell involving a metal M is:M(s) |M+ aq: 0.05 molar) ||M- aq: 1 molar) IM(s)For the above electrolytic cell the magnitude of the cell potential IE ] = 70 mV.
17. FOl` file above cell
A) E < 0: D G > 0 B) E > 0: DG < 0B) E < 0: D Go > 0 D) E > 0: DGo < 0
ANSWER: B
18. If the 0.05 molar solution of M+ is replaced by a 0.0025 molar M+ solution. thenthe tude of the cell potential would be
A) 35 mV B) 70 mV
B) 140 mV D) 700 mV
ANSWER: C
19.
20.
ANSWER: 2
ANSWER: 5
ANSWER: 122. Amongst the following the total number of compounds soluble in aqueous NaOH is
ANSWER: 4
SECTION- IV(INTEGER TYPE)
23. Amongst the following, the total number of compounds whose aqueous solutlonturns red litmus paper blue is
ANSWER: 3
24) Based on VSEPR theoly. the number of 90 degree F-Br-F anes in BrF5 is
ANSWER: either 0 or 8
25. The value of n in the molecular formula Be 3Si6Ol3 Is
ANSWER: 326. A student performs a titration with different burettes and finds titre values of
25.2 Inf. 25.25 and 25.0 inf. e number of ant figures in the etitre value is
ANSWER: 3
27 . The concentration of R In the reaction R P was measured as a function oftime and the following data is obtained:
ANSWER: o
28. The number of neutrons emitted when 2U undergoes controlled nuclear fission
ANSWER: 4
1 .O O. 7 5 0.40 0.10
t(n.) O . O 0.05 0.12 0.18
| SECTION -I| (Single Correct Choice Type)
29. If the angles A, B and C of a triangle are in an arithmetic progression and if a. band c denote the lengths of the sides opposite to A, B and C 1`espectively, then
a cthe value of the expression a/c sin2C+ c/a sin2A is
1Al
/3B) C)1
ANSWER: D
x y"Z30. Bquation of the plane containing the straight line == and perpendicular to
xVz xyzthe plane containing the straight lines =-=-2 and ==-3 is
A) x + 2y ~- 2z=0 B) 3x+ 2y 2z=o C) x - + z=0 D) 5X+ 2y - 4z=0
ANSWER: C
31. Let wbe a complex cube root of uni~ with w=l. A fan` die is tllrowll three tilnes.If rl , r2 and r3 are the numbers obtained on the die. then the probabih mat
1
Al I
IB)
2C)
ANSWER: C
ID)
A) parallelogram, which Is neither a rhombus nor a rectangleB) squareC) rectangle, but not a squareDJ rhombus, but not a squareANSWER: A
33. The number of 3x3 matrices A entries are either O or 1 and for the
Ix| II|A|y|=|o| has exactlv two distinct solutions, is
Izl IO|A)0 B) 28 ` 1 C) 168 D) 2
ANSWER: A
1B) --
' 12
ANSWER: B
1C)
'24
ID) --
' 64
A)
35. Let p and q be real numbers such that p = 0 p 3 # q and p 3 # - q . If a and b arenonzero complex number sans a + b = - p and a3 + b3 = q , then a quadratic
a equation ha-b and as Its roots is
A) (p3 + q) x 2 - (p 3 + 2q)x + (p3 + q) = 0 B) (p3 + q) x 2 - (p 3 - 2q)x + (p3 + q) = 0
B) (p 3 - q ) x2 - (5p 3 - 2q) x + (p 3 - q) = 0 D) (p 3 - q) x 2 - (5p 3 + 2q) x + (p 3 - q) = 0
ANSWER: B
36. Let f, g and 11 be real-valued functions deflned on the Interval lo, ll by
f (x) = ex2 + e-x2 , g(x) = Xex2 + e-x2 and h(x) = X2ex2 + e-x2 . If a. b and c denote.
respe ely. the absolute um of f, g and h on IO, 11, then
ANSWER: D
| SECTION - II | Multiple Correct Choice Type)
37. let A and B be o distinct points on the parabola y2 - 4x. If the axis of theparabola touches a circle of radl'us r ha AB as its diameter, then the slope ofthe line joining A and B can be
1 1A) - - B) -
1. r
2C)-
r
2DJ -
1
ANSWER: C and D
38. Let ABC be a triangle such that ACE= and let a, b and c denote the lengths of< 6
the sides opposite to A. B and C respe . e s) of x for ch
a = x2 + x + 1. b = X2 - 1 and c = 2x + 1 is (are)
ANSWER: B
39. Let 21 and Z2 be tw"o mstmct complex numbers and let z = (1 - t) 21 + tZ2 for somereal number t th O < t < 1. If Arg(w) denotes the principal argument of anonzero complex number w. then
A) |z ` Ell + |z - 22| = |21 - 22|
C} Z ` 21 Z - z = OZ 2 ` zl 22 ` 21
Bl Arg (z - zl) =Arg (z ~- 22)
D) Arg (z ~- zl) - Arg(22 - Zl)
ANSWER: A and C and D
40. Let f be a real-valued function defined on the interval (0. ) byx
f(x) = In x+ "l t dt , Then which of the renewing statement(s) is (are) true ?
AJ f _(x) exists for all xe (O . )B) f '(x) exists for an xe (O ) and f' is continuous on (O.). but not
differentiable on (O. )
C) dlere exlsts a > 1 such that /f' (x)I<If(xJ/ for all Xe (a . )
DJ there exists b > o such that If(xJ/+If'(x)/ b for aH x CO )
ANSWER: B and C
C)O
ANSWER: A
Paragraph for Questions 42 to 44
prime ntmlber and Tp be the foHowing set of 2x2 matrices
~ A~ ~ : a,b,c E lo. L 2. ,...p-1}}
p be odd
42. The number of A in Tp such that A is either symmetric or skew-symmetric or
both. and det (A) dl Bible by p isA) (p ~- 1)2 8) 2 (p - 1) C) (p - IJ2 + 1 DJ 2p - 1
ANSWER: D
43. The number of A HI Tp such that the trace of A is not divisible by p but det (A) isdivisible by p is(Note : The trace of a matrix is the sum of its dl Dual entries.)
A) (p - 1) (p2 - p + 1) B) p3 - (p - 1)2 C) (p - 1)2 D) (p - 1) (p2 - 2)
ANSWER: C
44) The number of A in Tp such that det CA) is not divisible by p is
A) 2p2 B) p3 5p C) p3 - 3p D) p3 - p2
ANSWER: D
Paragraph for questions 45 to 46
e
45.
2 2X v
circle X2 + y2 - ax = O and hyperbola -- - = I intersect at the points A and B.w` ^ 9 4 ^
~tion of a coroman ~ ent wl'tll positive slope to the circle as wen as to thehyperbola is
ANSWER: C
46. Equation of the circle with AB as its diameter is
A) x2 + y2 - l2x + 24 = O B) x3 + y2 + l2x + 24 = O
ANSWER: A
ANSWER: 3
ANSWER: 2
X2 y2 1
0. The line 2x + y = 1 is tangent to the herbola - 2 = 1 . If this line passesa o
ANSWER: 2
ANSWER: 6
to X.
ANSWER: 4
53. Let wbe the complex number cos + i sin -2p . Then the number of distinct^ 3 3
z+1 w w2complex numbers z satisg w z + w2 I = D is equal to
w2 1 z + w
ANSWER: 1
ANSWER: 3
55. The number of all possible ues of 0 , where O < 0 < p . for which the system ofequations
+ z) cos 3 o= ) sin 3 02cos30 2sin30
xsin3O=--+--y z
sin 30 = + ) cos 3 0 + y sin 30
is equal to the cube of the abscissa of P, then the value of f(-3) is equal to
ANSWER: 9
| SECTION -I | (Single CoHect Choice e)
57 . Consider a thin square sheet of side L andthickness t. made of a material of resistivity p . ~The resistance between two opposite faces. vshown b the shaded areas in the figure Is
A) directlv ProPortional to L B) directly proportional to tC) indePendent of L DJ independent of t
ANSWER: C
58. A real gas behaves like an ideal gas if itsAJ pressure and temperature are both highBJ pressure and temperature are both lowCJ pressure Is high and temperature is lowDJ pressure is low and temperature is high
ANSWER: D
59. Incandescent bulbs are des~ed by keeping in mind that the resistance of theirfilament increases with the increase in temperature. If at room temperature.100 W. 60 W and 40 W bulbs have filament re sistance s Rloo . R6o and R4OI ,respectively. the relation between these resistances is
1 1 1A) Rl = R + B) Rloo = R4o + R6o
1 1 1C) Bl00 > R6o > D) > >
ANSWER: D
60. To ~ Ohm's law, a student is provided with a test~ resistor RF. a Iligfl resistanceR], a small resistance R2, two identical galvanometers Gl and G2, and a variablevoltage source V. The correct circuit to out the experiment is
A) B)
C) D J
ANSWER: C
An AC voltage source of ~ le frequencomlected in series wl'th a capacl~tance C and an(inductance zero). en w is increasedA) tlle bulb glows B) tlle bulb glows brigflterC) total impedance of tlle circuit is unchangedDJ total impedance of tlle circuit illcreases
ANSWER: B
w andelectric
fixedbulb
amphtude VDof resistance
ls
R61.
62. A thin flexible wire of lengtfl L is connected to two adjacent fixed points andcarries a current I in the cl e direction, as sho in the figtlre. en thestem is put in a uniform magnetic field of strength B going into the plane of the
paper the e kes the shape of a ch`cle. The tension m the e I`s
IBLB)
IBLC)
ANSWER: C
IBLDJ
A) IBL
63. A block of mass m is on an inclined plane of ar!gle 0 . The coefficientof friction between the block and the plane is and tanq >m . Theblock is held statio by app a force P parallel to the plane.The direction of force pointing up the plane is taken to be positive.As P is varied from P I= l1lg(sin O - m cos 0 ) to P2= mg(sinO + m cosq ),the frictional force f versus P graph look like
f I JB)
DJ
ANSWER: A
64. A thin uniform annular disc (seefigure) of mass M has outerradius 4R and inner radius SR.The work required to take a unitmass from point P on its axis to'lllfini 'IS
ANSWER: A
| SECTION - II|(Multiple Correct Choice Type)
65. A few electric field lines for a stem of two charges91 and 92 fixed at two different points on the x-axisare shown in the . These lines suggest that
Al |91| > |92|Bl | 91 | < |92 |CI at a finite distance to the left~ of 91 the electric field~ is zeroD) at a ~finite distance to the ~t of g the electn'c field is zero
ANSWER: A and D
A student uses a simple pendulum of exactly Iln length to deterlnine g. theacceleration due to gravity. He uses a stop watch with the least count of 1 secfor this and records 40 seconds for 20 oscillations. For this observation, which of
66.
A) En`o1` DT in meas T, the time perl`od is 0.05 seconds
BI En`or DT In meas T, the tlme period is 1 second
DJ Percentage elTor in the detel`lnination of g is 2.5%
ANSWER: A and C
67 . A point mass of 1 kg collides elastically with a stationary point mass of 5 kg. Aftertheir co~ the 1 kg mass leverses its direction and moves with a speed of 2 ms-I.Wln'ch of the following statement(s) is (are) correct for the system of these twomasses ?
A) Total momentum of the system is 3 kg ms-lB)Momentum of 5 kg mass after collision is 4 kg ms-1C) etic energy of the centre of mass is O75 JD)Total kinetic energy of the system Is 4 J
ANSWER: A and C
68. A ray OP of monochromatic light is lucident on theface AB of prism ABCD near vertex B at an incident
angle of Goo (see figure). If the refractive it1dex of thematerial of the prism is which of the following is
(are) correct ?
A) The ray gets totally intel'nafly reflected at face CD
B) The ray comes out through face AD
o
C) The angle between the incident ray and the emergent ray is goo
ANSWER: A and B and C
One mole of an ideal gas in initial state A undergoesa cyclic process ABCA, as shown in the figure. Itspressure at A is Po. Choose the correct op6on(s) from
the following
A) Internal enel'gles at A and B are the sameB) Work done by the gas in process AB is PoVo en 4
PoCJ Pressnre at C is
ToD) Temperature at C ~Is
69.
ANSWER: A and B and C and D
aph for Questions 70 to 72
When a particle of mass m moves on the x-axis in apotential of the form V(xJ = kX2 , it performs simpleharmonic motion~ e corresponding time period is
Julproportional to \i -k . as can be seen easily using
dimensional analysis. However. the motion of a particlecan be periodic even when its potential energy increaseson both sides of x = 0 in a way different from and itstotal energy is such that the particle does not escape toinfinity. Consider a particle of mass m moving on thex-axis. Its potential energy is V(xJ - a Ca >OJ for [x[near the origin and becomes a constant equal to Vo for[x[ (see figurel.
70. If the total enc of the parUcle is E it `vifl perform periodic motion olllv ifAl E < 0 B) E > 0 C) Vo > E > 0 D) E > Va
ANSWER: B or C or (B and C)Option C implies option B.
71. For periodic motion of small amplitude A, the time pteriod T of this particle ispropol'tional to
ANSWER: B
72. The acceleration of this particle for |x| > is
bJ proportional to
/ VaC) proportional to --InXa
Al proportional to Va
DJ zero
ANSWER: D
Pph for Questions 73 to 74
Electrical resistance of certain materials, known assuperconductors. s abruptly from a nonzero value tozero as their temperature is lowered below a criticaltemperature Tc(0). An interestin g property of superconductorsIs that their critical temperature becomes smafler than Tc (OJif they are placed in a magnetic field , i. e . , the criticaltemperature Tc (B) is a of the ~ 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 functionof its temperature T for two different magnetic flelds Bl (sohd line) and 82 (dashedlineJ. If 82 is larger than Bl, which of the following graphs shows the correct
variation of R with T in these fields ?
ANSWER: A
74. A superconductor has Tc (O) = 100 K Wllen a maglleUc field of 7.5 Tesla is apphed.its Tc decreases to 75 K For this material one can defmitely say that whenA) B = 5 Tesla. Tc (B) = 80 K B) B = 5 Tesla, 75 K < Tc (B) < 100 K
~C) B = 10 Tesla. 75 K < ~ (B) < 100 K DJ B = 10 Tesla, Tr (B) = 70 K
ANSWER: B
75. The focal lengtfl of a thin biconvex lens is 2Ocm. When an object is moved from a
distance of 25cm in~ front of it to 5Ocm. the cation of its image changes
from n-125 to mso" The ratio ~ is
ANSWER: 6
76. An a ~particle and a proton are accelerated from rest by a potential diff~ erence ofIOOV. After this, their de Broglie wavelengths are laand IprespecUvely. The
I "p .
ratlo . to the nearest Integer, Is
ANSWER: 3
77 . \\Ilen two 'Identical battenes of internal resistance 1 each are connected In sen'es
across a resisWr R. the rate of heat produced in R is Jl. When the same batteries are
comlected in parallel across R the rate is J2. If Jl = 2.25 J2 then the value of R in W Is
ANSWER: 4
78. Two spherical bodl~es A (radius 6 cm) and B (radius 18 cm) are at temperatures ~
and T2, respectively. The maximum intensi in the emission spectrum of A is at
500 nm and in that of B is at 1500 mu. Considering them to be black bodies, what
will be the ratio of the rate of total~ enc radiated by A to that of B ?
ANSWER: 9
When two progressive waves yl - 4 sin(2x - 6t) and y2 = 3 sill(2x-6t - -2)psuperimposed, the amplitude of the resultant wave is
ANSWER: 5
80. A 0.1 kg mass I_s suspended from a of negligftlle mass. The lengtfl of the w1re
is Im and It,s cross-sectional~ area is 4.9xlO-7m2. If the mass is pulled a little in
the vertl~cally downward direction and released. it performs simple Ilarmonl_c
of the wire is nxlO9 Nm-2, the value of n is
ANSWER: 4
A bHlaly star consists of two stars A (mass 2.2Ms) and B (mass IlMs), where Ms is
the ma~ss of the sun. They are separated by dl_stance d and are rotating about
their centre of mass. which is statio . e ratio of the total angular momentum
of the b_~ star to the anglllar momentum of star B about the centre of mass is
8 1 .
ANSWER: 6
82. Gravitational acceleration on the surface of a planet is \/g , where g is the11 .-.
gravitational acceleration on the surface of the earth. e average mass densi of2
the planet is -3 times that of the eal If the escape speed on the surface of the earth
ANSWER: 3
83. A piece of ice (heat capaci~ = 2100 J kgl oC-I and latent heat = 3.36 x 105 J kgll of
mass m grams is at C at atmospheric pressure. It is given 420 J of heat so that
the ice starts melting. when tlle l~ce-water mixfure is in equilibrl_um, it is
found that 1 gm of ice has melted. Assuming there is no other heat exchange mthe process. the value of m is
ANSWER: 8
A statio source is emittlllg sound at a flXed frequency fa, which is reflected
by two cars approaching the source. The difference between the frequencies of
sound reflected from the cars is 1.2% of ~. 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 than the speed of sound which is 330 ms-.1
ANSWER: 7