Assam CEE Sample Paper

Sample Paper

Full Test

Q.No. 1 Charge is distributed within a sphere of radius R with a volume charge density ρ(r) = A

r
2 e
−2r/a

where A and a are constants. If Q is the total charge of this charge distribution, the radius R is:

(A) alog ( 1
Q
)
1−
2πaA

(B) alog (1 − 2πaA
Q
)

(C) a

2
log (1 −
Q

2πaA
)

(D) a

2
log |
1
Q
)
1−
2πaA

Q.No. 2 A ratio of the 5th term from the beginning to the 5th term from the end in the binomial expansion of
10

(2
1/3
+
2(3)
1
1/3
) is:

1

(A) 4(36) 3 : 1

1

(B) 1 : 2(6) 3

1

(C) 2(36) 3 : 1

(D) 1 : 4(16)
1
3

Q.No. 3 The maximum area (in sq. units) of a rectangle having its base on the x-axis and its other two vertices
on the parabola, y=12-x² such that the rectangle lies inside the parabola, is:

(A) 36

(B) 18√3

(C) 20√2

(D) 32

Q.No. 4 Correct statements among a tod regarding silicones are : (a) They are polymers with hydrophobic
character. (b) They are biocompatible. (c) In general, they have high thermal stability and low dielectric
strength. (d) Usually, they are resistant to oxidation and used as greases.

(A) (a), (b), (c) and (d)

(B) (a) and (b) only

(C) (a), (b) and (c) only

(D) (a), (b) and (d) only

Q.No. 5 The combustion of benzene (l) gives CO₂(g) and H₂O(l). Given that heat of combustion of benzene at
constant volume is −3263.9 kJ mol⁻¹ at 25⁰ C; heat of combustion (in kJ mol⁻¹) of benzene at constant pressure
will be : (R=8.314 JK⁻¹ mol⁻¹)

(A) 4152.6

(B) -452.46

(C) 3260

(D) -3267.6

Q.No. 6 If the system of linear equations x+ky+3z=0 3x+ky−2z=0 2x+4y−3z=0 has a non-zero
solution (x, y, z), then xz/y² is equal to :
(A) -10

(B) 10

(C) -30

(D) 30

Q.No. 7 Let a,b and c be the 7th, 11th and 13th terms respectively of a non-constant A.P. If these are also the
three consecutive terms of a G.P., then a/c is equal to

(A) 2

(B) ½

(C) 4

(D) 7/13

^ →
→ = 2^i + λ ^j + 3k, → = 3^i + 6^j + (λ − 1)k
Q.No. 8 Let a 1 b = 4^ j + 6k and c
i + (3 − λ )^
2
^
3
^
be three vectors such
that →b = 2a
→ and a
→ is perpendicular to c→. Then a possible value of (λ , λ , λ ) is :
1 2 3

(A) (− 1

2
, 4, 0)

(B) ( 1

2
, 4, −2)

(C) (1,3,1)

(D) (1,5,1)

Q.No. 9 A solution of sodium sulfate contains 92 g of Na⁺ ions per kilogram of water. The molality of Na⁺
ions in that solution in mol kg⁻¹ is:

(A) 8

(B) 4

(C) 12

(D) 16

Q.No. 10 From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and
arranged in a row on a shelf so that the dictionary is always in the middle. The number of such arrangements
is :

(A) at least 1000

(B) less than 500

(C) at least 500 but less than 750

(D) at least 750 but less than 1000

Q.No. 11 A power transmission line feeds input power at 2300 V to a step down transformer with its primary
windings having 4000 turns. The output power is delivered at 230 V by the transformer. If the current in the
primary of the transformer is 5A and its efficiency is 90%, the output current would be:

(A) 25 A

(B) 50 A

(C) 45 A

(D) 35 A

Q.No. 12 The pitch and the number of divisions, on the circular scale, for a given screw gauge are 0.5 mm and
100 respectively. When the screw gauge is fully tightened without any object, the zero of its circular scale lies
3 divisions below the mean line. The readings of the main scale and the circular scale, for a thin sheet, are 5.5
mm and 48 respectively, the thickness of this sheet is :

(A) 5.950 mm

(B) 5.755 mm

(C) 5.725 mm

(D) 5.740 mm

Q.No. 13 'The value of c in the Lagrange's mean value theorem for the function f(x) = x3 + 8x + 11, when x ∈
[0, 1] is :

(A) 4−√ 5

3

(B) 4−√ 7

3

(C) 2/3

(D) √ 7−2

3

Q.No. 14 An emf of 20 V is applied at time t = 0 to a circuit containing in series 10 mH inductor and 5 Ω
resistor. The ratio of the currents at time t = ∞ and at t = 40 s is close to : (Take e2=7.389)

(A) 1.06

(B) 1.15

(C) 1.46

(D) 0.84
2 2 2 2 2 2 2 2 2 2
9(1 +2 +3 ) 12(1 +2 +3 +4 ) 15(1 +2 +…+5 )
Q.No. 15 The sum of the following series 1 + 6 + 7
+
9
+
11
+ ⋯

upto 15 terms is

(A) 7510

(B) 7820

(C) 7830

(D) 7520

Q.No. 16 Which of the following arrangements does not represent the correct order of the property stated
against it ?

(A) Ni2+ < Co2+ < Fe2+ < Mn2+ : ionic size

(B) Co3+ < Fe3+ < Cr3+ < Sc3+ : stability in aqueous solution

(C) Sc < Ti < Cr < Mn : number of oxidation states

(D) V2+ > Cr2+ > Mn2+ > Fe2+ : paramagnetic behaviour

Q.No. 17 In a hydrogen like atom electron makes transition from an energy level with quantum number n to
another with quantum number (n – 1). If n >> 1, the frequency of radiation emitted is proportional to

(A) 1/n2

(B) 1/n3/2

(C) 1/n3

(D) 1/n

Q.No. 18

(A) 2

(B) 4

(C) -1

(D) -2

Q.No. 19 The above p-v diagram represents the
thermodynamic cycle of an engine, operating with an ideal monoatomic gas. The amount of heat extracted
from the source in a single cycle is

(A) (13/2)p0 v

(B) (11/2)p0 v

(C) 4 p0 v

(D) p0 v

Q.No. 20 The pH of rain water , is approximately :

(A) 7.5

(B) 6.5

(C) 7.0

(D) 5.6

Q.No. 21 A uniform metallic wire has a resistance of 18Ω and is bent into an equilateral triangle. Then, the
resistance between any two vertices of the triangle is :

(A) 2Ω

(B) 8Ω

(C) 4Ω

(D) 12Ω

Q.No. 22 The integral

(A)

(B)

(C)

(D)

Q.No. 23 Three point particles of masses 1kg , 1.5kg and 2.5 kg are placed at three corners of a right angle
triangle of sides 4.0 cm, 3.0 cm and 5.0 cm as shown in the figure. The center of mass of the system is at a

point :

(A) 0.6 cm right and 2.0 cm above 1kg mass

(B) 1.5 cm right and 1.2 cm above 1kg mass

(C) 2.0 cm right and 0.9 cm above 1kg mass

(D) 0.9 cm right and 2.0 cm above 1kg mass
√ −1

Q.No. 24 lim x→1
−
√π− 2 sin

√ 1−x
x

(A) √π

(B) 1

√ 2π

(C) √ π

2

(D) √ 2

π

Q.No. 25

(A) 64kΩ ± 10%

(B) 530kΩ ± 5%

(C) 5.3MΩ ± 5%

(D) 6.4MΩ ± 5%

Q.No. 26 The sum of the co-efficients of all odd degree terms in the expansion of (x+√x³-1)⁵+(x-
√x³-1)⁵ ,(x>1) in:
(A) -1

(B) 0

(C) 1

(D) 2

Q.No. 27 A paramagnetic substance in the form of a cube with sides 1 cm has a magnetic dipole moment of
J/T when a magnetic intensity of 60 × 10 A/m is applied. Its magnetic susceptibility is :
−6 3
20 × 10

(A) 3.3 x 10-2

(B) 4.3 x 10-2

(C) 2.3 x 10-2

(D) 3.3 x 10-4

Q.No. 28 A galvanometer, whose resistance is 50 ohm, has 25 divisions in it. When a current of 4 x A passes

through it, its needle (pointer) deflects by one division.To use this galvanometer as a voltmeter of range 2.5 V,
it should be connected to a resistance of:

(A) 200 ohm

(B) 6250 ohm

(C) 6200 ohm

(D) 250 ohm

Q.No. 29 Let y=y(x) be the solution of the differential sinx dy/dx+y cosx=4x,x∊(0,π). If y(π/2)=0, then y(π/6)
is equal to:

(A) 4/9√3 π²

(B) -8/9√3 π²

(C) -8/9 π²

(D) -4/9 π²

Q.No. 30 The values of K /K for the following reactions at 300 K are, respectively : (At 300 K,
p c

3 −1
RT = 262dm atmmol ) N 2 (g) + O 2 (g) = 2NO(g) N 2 O 4 (g) = 2NO 2 (g) N 2 (g) + 3H 2 (g) = 2NH 3 (g)

3 −1
262dm atmmol
(A) 6 −2
2
606.0dm atm mol

−2 −3 −1
1, 1 × 10 dm atm mol
(B) 6 −2
2
606dm atm mol

3 −1
1, 262dm atm mol ,
(C) 6 2 −2
606.0dm atm mol

3 −1
1, 262dm atmmol .
(D) −3 −6 2
−2
1.65 × 10 dm atm mol

Q.No. 31 A thin lens made of glass (refractive index = 1.5) of focal length f = 16 cm is immersed in a liquid of
refractive index 1.42. If its focal length in liquid is f1, then the ratio f1/ f is closest to the integer :

(A) 1

(B) 9

(C) 5

(D) 17

Q.No. 32 Two coherent sources produce waves of different intensities which interfere. After interference, the
ratio of the maximum intensity to the minimum intensity is 16. The intensity of the waves are in the ratio :

(A) 16:9

(B) 5:3

(C) 25:9

(D) 4:1

Q.No. 33 Consider the statement: ′′
P (n) : n
2
− n + 41 is prime." Then which one of the following is true?

(A) P(5) is false but P(3) is true.

(B) Both P(3) and P(5) are false.

(D) Both P(3) and P(5) are true.

Q.No. 34 If A =

(A) (

(B) [

(C) (1,

(D) (0,

(A) 3/2

(B) 4/3

(C) 2/3

(D) ⅓
3

2

5

2

(B) tanθ =

(C) tanθ =
, 3]

, 4)

5

2

3

2
]

]

⎢⎥
(C) P(3) is false but P(5) is true.

⎡

⎣
− sin θ

−1
1 sin θ

1

− sin θ
1

1
⎤
sin θ
⎦
; then for all θ ∈ ( 3π

4

Q.No. 35 Energy of an electron is given by E= -2.178 x 10-18J. Wavelength of light required to excite an
electron in an hydrogen atom from level n = 1 to n = 2 will be.

(A) 2.816 × 10-7 m

(B) 6.500 × 10-7 m

(C) 8.500 × 10-7 m

(D) 1.214 × 10-7 m

Q.No. 36 Let x + y

√3

1

2

2√ 3
2

1
k k k
= a , (a, k > 0) and dy

dx
+ (
y

x
)
1
3
= 0
,

then k is

Q.No. 37 An L-shaped object, made of thin rods of uniform mass density, is suspended with a string as shown
in figure. If AB = BC, and the angle made by AB with downward vertical is θ, then:

(A) tanθ =
5π

4
), det (A) det ( A) lies in the interval :

(D) tanθ = 1

3

Q.No. 38 An unbiased coin is tossed 5 times. Suppose that a variable X is assigned the value k when k
consecutive heads are obtained for k =3,4,5 otherwise X takes the value -1. Then the expected value of X is :

(A) 3/16

(B) 1/8

(C) -(3/16)

(D) -(⅛)

Q.No. 39 The locus of the mid-points the perpendiculars drawn from points on the line, x = 2y to the line x =
y is :

(A) 2x - 3y = 0

(B) 5x - 7y = 0

(C) 3x - 5y = 0

(D) 7x - 5y = 0

Q.No. 40 In amplitude modulation, sinusoidal carrier frequency used is denoted by ωc and the signal
frequency is denoted by ωm. The bandwidth (∆ωm) of the signal is such that ∆ωm<<ωc. Which of the
following frequencies is not contained in the modulated wave ?

(A) ωm

(B) ωc

(C) ωm+ωc

(D) ωc−ωm

Q.No. 41 The number of all possible positive integral values of a for which the roots of the quadratic equation,
6x − 11x + α = 0 are rational numbers is :
2

(A) 2

(B) 3

(C) 5

(D) 4

Q.No. 42 Let y = y(x) be the solution curve of the differential equation, (y − x)
2 dy

dx
= 1 . This curve
intersects the x-axis at a point whose abscissa is :

(A) 2 - e

(B) - e

(C) 2

(D) 2 + e

Q.No. 43 Which of the following statements is false ?

(A) Wheatstone bridge is the most sensitive when all the four resistances are of the same order of magnitude.

(B) In a balanced wheatstone bridge if the cell and the galvanometer are exchanged, the null point is
disturbed.

(C) A rheostat can be used as a potential divider.

(D) Kirchhoff’s second law represents energy conservation.

Q.No. 44 An urn contains 5 red and 2 green balls. A ball is drawn at random from the urn. If the drawn ball is
green, then a red ball is added to the urn and if the drawn ball is red, then a green ball is added to the urn; the
original ball is not returned to the urn. Now, a second ball is drawn at random from it. The probability that the
second ball is red, is:

(A) 27/49

(B) 32/49

(C) 21/49

(D) 26/49

Q.No. 45 If the point (2, α, β) lies on the plane which passes through the points (3, 4, 2) and (7,0, 6) and is
perpendicular to the plane 2x - 5y=15, then 2α − 3β is equal to :

(A) 7

(B) 12

(C) 17

(D) 5

Q.No. 46 The amplitude of a damped oscillator decreases to 0.9 times its original magnitude is 5s. In another
10s it will decrease to α times its original magnitude, where α equals.

(A) 0.81

(B) 0.729

(C) 0.6

(D) 0.7

Q.No. 47 A simple pendulum of length 1 m is oscillating with an angular frequency 10 rad/s. The support of
the pendulum starts oscillating up and down with a small angular frequency of 1 rad/s and an amplitude of
m. The relative change in the angular frequency of the pendulum is best given by :
−2
10

(A) 1 rad/s

(B) 10 −5
rad/s

(C) 10 −3
rad/s

(D) 10 −1
rad/s

Q.No. 48 The area of the region A = {(x, y) : 0 ≤ y ≤ x|x| + 1 and −1 ≤ x ≤ 1} in sq. units, is :

(A) 2

(B) 2/3

(C) 1/3

(D) 4/3

Q.No. 49 The coagulating power of electrolytes having ions Na+, Al3+ and Ba2+ for arsenic sulphide sol
increases in the order

(A) Na+ < Ba2+ < Al3+

(B) Ba2+ < Na+ < Al3+

(C) Al3+ < Na+ < Ba2+

(D) Al3+ < Ba2+ < Na+

Q.No. 50 For 1 molal aqueous solution of the following compounds, which one will show the highest freezing
point ?

(A) [Co(H₂O)₆]Cl₃

(B) [Co(H₂O)₅Cl]Cl₂. H₂O

(C) [Co(H₂O)₄Cl₂]Cl . 2H₂O

(D) [Co(H₂O)₃Cl₃]. 3H₂O

Q.No. 51 Amongst the following statements , that which was not proposed by Dalton was :

(A) Chemical reactions involve reorganization of atoms. These are neither created nor destroyed in a chemical
reaction.

(B) all the atoms of a given element have identical properties including identical mass. Atoms of different
elements differ in mass.

(C) When gases combine or reproduce in a chemical reaction they do so in a simple ratio by volume provided
all gases are at the same T and P.

(D) matter consists of indivisible atoms.

Q.No. 52

(A) −74.8 kJ mol−1

(B) −144.0 kJ mol−1

(C) 74.8 KJ mol-1

(D) 144.0 KJ mol-1

Q.No. 53

(A) (I) < (III) < (II)

(B) (II) < (III) < (I)

(C) (III) < (II) < (I)

(D) (II) < (I) < (III)

Q.No. 54 The graph between angle of deviation (δ) and angle of incidence (i) for a triangular prism is
represented by:

(A)

(B)

(C)

(D)

Q.No. 55 The following results were obtained during kinetic studies of the reaction 2A+B Products

The time (in minutes) required to consume half of A is:

(A) 5

(B) 1

(C) 10

(D) 100

Q.No. 56 A copper wire is stretched to make it 0.5% longer. The percentage change in its electrical resistance
if its volume remains unchanged is :

(A) 2.0 %

(B) 1.0 %

(C) 0.5 %

(D) 2.5 %

Q.No. 57 The increasing basicity order of the following compounds is :

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

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

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

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

Q.No. 58 At a given instant, say t=0, two radioactives substances A and B have equal activities. The ratio RB

RA

of their activities after time t itself decays with time t as e . If the half-life of A is In2, the half-life of B is:
−3t

(A) ln2/4

(B) In2/2

(C) 4ln2

(D) 2ln2

Q.No. 59 Consider three boxes, each containing 10 balls labelled 1, 2, ...., 10. Suppose one ball is randomly

drawn from each of the boxes. Denote by n the label of the ball drawn from the ith box, (i=1, 2, 3). Then, the
i

number of ways in which the balls can be chosen such that n₁ < n₂ < n₃ is:

(A) 120

(B) 164

(C) 240

(D) 82

Q.No. 60 The recommended concentration of fluoride ion in drinking water is up to 1 ppm as fluoride ion is
required to make teeth enamel harder by converting [3Ca₃(PO₄)₂.Ca(OH)₂] to :

(A) [CaF₂]

(B) [3(CaF₂).Ca(OH)₂]

(C) [3Ca₃(PO₄)₂.CaF₂]

(D) [3{Ca(OH)₂}.CaF₂]

Q.No. 61 If ∫f (x) dx =Ψ(x) , then ∫x5f(x3) dx is equal to

(A) (1/3)x3Ψ(x3) - 3 ∫x3Ψ(x3) dx + C

(B) (1/3)x3Ψ(x3) - ∫x2Ψ(x3) dx + C

(C) (1/3)[x3Ψ(x3) - ∫x3Ψ(x3) dx] + C

(D) (1/3)[x3Ψ(x3) - ∫x2Ψ(x3) dx ]+ C

Q.No. 62 The anodic half-cell of lead-acid battery is recharged using electricity of 0.05 Faraday. The amount
of PbSO₄ electrolyzed in g during the process is : (Molar mass of PbSO₄ =303 g mol⁻¹)

(A) 15.2

(B) 11.4

(C) 7.6

(D) 22.8

Q.No. 63

(A) 1/16

(B) 1/8

(C) 1/4

(D) 1/24

Q.No. 64 Chlorine on reaction with hot and concentrated sodium hydroxide gives :

(A) Cl −
and ClO
−

3

(B) Cl −
and ClO 2
−

(C) G −
and ClO
−

(D) ClO − and ClO
3
−

2

Q.No. 65 At 100°C, copper (Cu) has FCC unit cell structure with cell edge length of x Å . What is the
approximate density of Cu in g (cm ) at this temperature ? [Atomic Mass of Cu=63.55 u)
−3

(A) 205

x
3

(B) 211

x
3

(C) 105

x
3

(D) 422

x
3

Q.No. 66 A vertical closed cylinder is separated into two parts by a frictionless piston of mass m and of
negligible thickness. The piston is free to move along the length of the cylinder. The length of the cylinder
above the piston is , and that below the piston is ,, such that > . Each part of the cylinder contains n moles of
an ideal gas at equal temperature T. If the piston is stationary, its mass, m, will be given by: (R is universal gas
constant and g is the acceleration due to gravity)

(A) RT

ng
[
l 1 −3l 2

l1 l2
]

(B) nRT

g
[
1

l2
+
l1
1
]

(C) RT

g
[
2l 1 +l 2

l1 l2
]

(D) nRT

g
[
l 1 −l 2

l1 l2
]

Q.No. 67 The galvanometer deflection, when key K₁, is closed but K₂, is open, equals θ₀ (see figure). On
closing K₂, also and adjusting R₂ to 5Ω, the deflection in galvanometer becomes . The resistance of the
θ0

5

galvanometer is, then, given by [Neglect the internal resistance of battery]:

(A) 25Ω

(B) 22Ω

(C) 5Ω

(D) 12Ω

Q.No. 68 For the following reactions

(A) μB > μA and ke(A) > ke(B)

(B) μA > μB and ke(B) > ke(A)

(C) μB > μA and ke(B) > ke(A)

(D) μA > μB and ke(A) > ke(B)

Q.No. 69 The highest value of the calculated spin-only magnetic moment (in BM) among all the transition
metal complexes is :

(A) 5.92

(B) 6.93

(C) 4.90

(D) 3.87

Q.No. 70 A mass of 10 kg is suspended by a rope of length 4 m. from the ceiling. A force F is applied
horizontally at the midpoint of the rope such that the top half of the rope makes an angle of 45° with the
vertical. Then F equals : (Take g = 10 ms-2 and the rope to be massless)

(A) 100 N

(B) 90 N

(C) 70 N

(D) 75 N

Q.No. 71 Let S be the set of all real values of such that a plane passing through the points

(−λ , 1, 1), (1, −λ , 1) and (1, 1, −λ ) also passes through the point (-1,-1,1). Then S is equal to :
2 2 2

(A) {1, -1}

(B) {3, -3}

(C) {√3}
√ √

(D) {√3, -√3}

Q.No. 72 A plano convex lens of refractive index μ and focal length f is kept in contact with another plano
1 1

concave lens of refractive index μ and focal length f2. If the radius of curvature of their spherical faces is R
2

each and f = 2f , then μ and μ are related as :
1 2 1 2

(A) 2μ − μ 2 1
= 1

(B) 3μ − 2μ 2 1 = 1

(C) μ + μ 1 2
= 3

(D) 2μ − μ 1 2 = 1

Q.No. 73 A block of mass m, lying on a smooth horizontal surface, is attached to a spring (of negligible mass)
of spring constant k. The other end of the spring is fixed, as shown in the figure. The block is initially at rest in
its equilibrium position. If now the block is pulled with a constant force F, the maximum speed of the block is

:

(A) √ mk
F

(B) F

π√ mk

(C) πF

√ mk

(D) √ mk
2f

Q.No. 74 If the third term in the binomial expansion of (1+xlog2x)5 equals 2560, then a possible value of x is :

(A) 3
2
√ 21

(B) 2

3
√ 21

(C) 1/4

(D) 2√21

Q.No. 75 The equation of the circle passing through the foci of the ellipse x2/16 + y2/9 = 1 , and having centre
at (0, 3) is

(A) x2 + y2 -6y +7 = 0

(B) x2 + y2 -6y -5 = 0

(C) x2 + y2 -6y +5 = 0

(D) x2 + y2 -6y -7 = 0

Q.No. 76 The top of a water tank is open to air and its water level is maintained. It is giving out 0.74 m water
per minute through a circular opening of 2 cm radius in its wall. The depth of the centre of the opening from
the level of water in the tank is close to :

(A) 9.6 m

(B) 6.0 m

(C) 2.9 m

(D) 4.8 m

Q.No. 77 A circular loop of radius 0.3 cm lies parallel to a much bigger circular loop of radius 20 cm. The
centre of the small loop is on the axis of the bigger loop. The distance between their centres is 15 cm. If a
current of 2.0 A flows through the smaller loop, then the flux linked with bigger loop is

(A) 6 × 10-11 weber

(B) 3.3 × 10-11 weber

(C) 6 × 10-9 weber

(D) 9.1 × 10-11 weber

Q.No. 78 A water sample has ppm level concentration of the following metals : Fe=0.2; Mn=5.0; Cu=3.0;
Zn=5.0. The metal that makes the water sample unsuitable for drinking is :

(A) Mn

(B) Zn

(C) Cu

(D) Fe

Q.No. 79 In the circuit shown, find C if the effective capacitance of the whole circuit is to be 0.5 uF. All

values in the circuit are in uF.

(A) 6

5
μF

(B) 4 μF

(C) 7

11
μF

(D) 7
10
μF

Q.No. 80 A rod, of length L at room temperature and uniform area of cross section A, is made of a metal
having coefficient of linear expansion ∝/°C. It is observed that an external compressive force F, is applied on
each of its ends, prevents any change in the length of the rod, when its temperature rises by ΔTK. Young's
modulus, Y, for this metal is :

(A) AαΔT
2F

(B) AαΔT
F

(C) 2AαΔT
F

(D) F

Aα(ΔT−273)

Q.No. 81 Experimentally it was found that a metal oxide has formula M0.98O. Metal M, is present as M2+ and
M3+ in its oxide. Fraction of the metal which exists as M3+ would be:

(A) 4.08%

(B) 6.05%

(C) 5.08%

(D) 7.01%

Q.No. 82 The magnetic field associated with a light wave is given, at the origin, by B=Bₒ [sin(3.14x 10⁷)ct +
sin(6.28 x 10⁷)ct]. If this light falls on a silver plate having a work function of 4.7 eV, what will be the
maximum kinetic energy of the photo electrons ? (c = 3 × 10 ms , h = 6.6 × 10 J )
8 −1 −34
−S

(A) 5 eV

(B) 8.52 eV

(C) 6.82 eV

(D) 7.72 eV
2
Q.No. 83 All x satisfying the inequality (cot −1
x) − 7 (cot
−1
x) + 10 > 0 , lie in the interval :

(A) (−∞, cot 5) ∪ (cot 4, cot 2)

(B) (cot 2, ∞)

(C) (−∞, cot 5) ∪ (cot 2, ∞)

(D) (cot 5, cot 4)

Q.No. 84 The major product of following reaction is :

(A) RCOOH

(B) RCHO

(C) RCONH₂

(D) RCH₂NH₂

Q.No. 85 Two lines x−3

1
=
y+1

3
=
z−6

−1
and x+5

7
=
y−2

−6
=
z−3

4
intersect at the point R. The reflection of R
in the xy-plane has coordinates :

(A) (2, -4,7)

(B) (-2,4,7)

(C) (2,4,7)

(D) (2, -4, -7)

Q.No. 86 The reaction, MgO(s) +C(s) >Mg(s) +CO(g), for which Δ H = +491.1 kJ mol and
r
∘ −1

Δ S
r
∘
= 198.0JK
−1
mol , is not feasible at 298 K. Temperature above which reaction will be feasible is :
−1

(A) 2380.5 K

(B) 2480.3 K

(C) 2040.5 K

(D) 1890.0 K

Q.No. 87 A 100 V carrier wave is made to vary between 160 V and 40 V by a modulating signal. What is the
modulation index?

(A) 0.4

(B) 0.5

(C) 0.6

(D) 0.3

Q.No. 88 The equation of the plane containing the straight line and perpendicular to the plane
x y z
= =
2 3 4

containing the straight lines = = and = = is :
x y z x y z

3 4 2 4 2 3

(A) x+2y – 2z=0

(B) x-2y+z=0

(C) 3x +2y-3z=0

(D) 5x +2y - 4z=0

Q.No. 89 For reaction 2H2(g) + 2NO(g) → N2(g) + 2H2O(g) the Observed rate expression is, rate =
kf[NO]2[H2]. The rate expression for the reverse reaction is :

(A) Kb[N2][H2O]2

(B) Kb[N2][H2O]2/[NO]

(C) Kb[N2][H2O]

(D) Kb[N2][H2O]2/[H2]

Q.No. 90 Homoleptic octahedral complexes of a metal ion M ′
with three monodentate ligands L , L and
3+1
1 2

L absorb wavelengths in the region of green, blue and red respectively. The increasing order of the ligand
3

strength is :

(A) L 3
< L1 < L2

(B) L 1
< L2 < L3

(C) L 2
< L1 < L3

(D) L 3
< L2 < L1

Q.No. 91 The output of the given logic circuit is :
–
AB (A)
–
AB (B)
–
AB + AB (C)
–
–
AB + AB (D)

Q.No. 92 A telephonic communication service is working at carrier frequency of 10 GHz. Only 10% of it is
utilized for transmission. How many telephonic channels can be transmitted simultaneously if each channel
requires a bandwidth of 5 kHz ?

(A) 2×103

(B) 2×104

(C) 2×105

(D) 2×106

Q.No. 93 Ge and Si diodes start conducting at 0.3 V and 0.7 V respectively. In the following figure if Ge
diode connection are reversed, the value of V₀. changes by : (assume that the Ge diode has large breakdown

voltage)

(A) 0.4 V

(B) 0.2 V

(C) 0.6 V

(D) 0.8 V

Q.No. 94

(A) 66

(B) 68

(C) 34

(D) 33

Q.No. 95 An unbiased coin is tossed. If the outcome is a head then a pair of unbiased dice is rolled and the
sum of the numbers obtained on them is noted. If the toss of the coin results in tail then a card from a well-
shuffled pack of nine cards numbered 1, 2, 3, ..., 9 is randomly picked and the number on the card is noted.
The probability that the noted number is either 7 or 8 is :

(A) 19/72

(B) 19/36

(C) 15/72

(D) 13/36

Q.No. 96 A metal ball of mass 0.1 kg is heated upto 500°C and dropped into a vessel of heat capacity
800JK and containing 0.5 kg water. The initial temperature of water and vessel is 30°C. What is the
−1

approximate percentage increment in the temperature of the water ? [ Specific Heat Capacities of water and
metal are, respectively, 4200Jkg K and 400Jkg K J Jkg-IK-1]
−1 −1 −1 −1

(A) 30%

(B) 20 %

(C) 25 %

(D) 15%

Q.No. 97 If Re ( z−1

2z+i
) = 1 where z = x+iy, then the point (x,y) lies on a:

(A) circle whose centre is (-½, -3/2)

(B) straight line whose slope is -(⅔)

(C) straight line whose slope is is 3/2

(D) circle whose diameter is √5/ 2

Q.No. 98 Arrange the following amines in the decreasing order of basicity :

(A) 1 > III > II

(B) III > II > I

(C) III > I > II

(D) I > II > III

Q.No. 99 The equation of the line passing through (-4, 3, 1), parallel to the plane x+2y-z-5=0 and intersecting
the line is
x+1 y−3 z−2
= =
−3 2 −1

(A) x+4

−1
=
y−3

1
=
z−1

1

(B) x+4

3
=
y−3

−1
=
z−1

1

(C) x−4

3
=
y−3

−1
=
z−1

1

(D) x+4

1
=
y−3

1
=
z−1

3

Q.No. 100 The following observations were taken for determining surface tension T of water by capillary
method : diameter of capillary, D=1.25×10−2 m rise of water, h=1.45×10−2m. Using g=9.80 m/s2 and the
simplified relation T = rhg/2 *103 N/m, the possible error in surface tension is closest to :

(A) 0.15%

(B) 1.5%

(C) 2.4%

(D) 10%
2

Q.No. 101 The dimension of B

2μ 0
, where B is magnetic field and μ0 is the magnetic permeability of vacuum,
is

(A) MLT-2

(B) MLT2T-1

(C) ML2T-2

(D) ML-1T-2

Q.No. 102 An electron, a proton and an alpha particle having the same kinetic energy are moving in circular
orbits of radii re, rp, rα respectively in a uniform magnetic field B. The relation between re, rp, rα is :

(A) re > rp = rα

(B) re < rp = rα

(C) re < rp < rα

(D) re < rα < rp

Q.No. 103 The correct match between Item I and Item II is :

(A) (A) → (P); (B) → (R); (C) → (D); (D) → (Q)

(B) (A) → (R); (B) → (P); (C) → (Q); (D) → (S)

(C) (A) → (P); (B) → (R); (C) → (Q); (D) → (S)

(D) (A) → (R); (B) → (P); (C) → (S); (D) → (Q)

Q.No. 104 The distance of the point (1, 3, −7) from the plane passing through the point (1, −1, −1),
having normal perpendicular to both the lines (x-1)/1= (y+2)/-2= (x-4)/3 and (x-2)/2= (y+1)/-1=
(z+7)/-1, is:
(A) 10/√83

(B) 5/√83

(C) 10/√74

(D) 20/√74

Q.No. 105 In a collinear collision, a particle with an initial speed vo strikes a stationary particle of the same
mass. If the final total kinetic energy is 50% greater than the original kinetic energy, the magnitude of the
relative velocity between the two particles, after collision, is :

(A) v o/4

(B) √ 2vo

(C) vo /2

(D) vo/√ 2

Q.No. 106 A man grows into a giant such that his linear dimensions increase by a factor of 9. Assuming that

his density remains same, the stress in the leg will change by a factor of:

(A) 9

(B) 1/9

(C) 81

(D) 1/81

Q.No. 107 The magnetic field in a travelling electromagnetic wave has a peak value of 20 nT. The peak value
of electric field strength is :

(A) 6 V/m

(B) 9 V/m

(C) 12 V/m

(D) 3 V/m

Q.No. 108 The moment of inertia of a uniform cylinder of length l and radius R about its perpendicular
bisector is I. What is the ratio l/R such that the moment of inertia is minimum?

(A)

(B) √3/2

(C) 1

(D) 3/ √2

Q.No. 109 The compound that does not produce nitrogen gas by the thermal decomposition is :

(A) Ba(N₃)₂

(B) (NH₄)₂Cr₂O₇

(C) NH₄NO₂

(D) (NH₄)₂SO₄

Q.No. 110 8 g of NaOH is dissolved in 18 g of H₂O. Mole fraction of NaOH in solution and molality (in mol
kg⁻¹) of the solution respectively are :

(A) 0.167, 22.20

(B) 0.167, 11.11

(C) 0.2, 22.20

(D) 0.2, 11.11

Q.No. 111 Both lithium and magnesium display several similar properties due to the diagonal relationship;
however, the one which is incorrect, is :

(A) both form nitrides

(B) nitrates of both Li and Mg yield NO2 and O2 on heating

(C) both form basic carbonates

(D) both form soluble bicarbonates

Q.No. 112 If

(A) - (a+b+c)

(B) abc

(C) 2(a+b+c)

(D) -2(a+b+c)

∣a − b − c

2b

2c
2a

b − c − a

2c
2a

2b

c − a − b
=

Q.No. 113 The major product 'X' formed in the following reaction is :

(A)

(B)

(C)

(D)
2
= (a + b + c)(x + a + b + c) , x ≠ 0 and

a + b + c ≠ 0, then x is equal to :
:

Q.No. 114 The least count of the main scale of a screw gauge is 1 mm. The minimum number of divisions on
its circular scale required to measure 5μm diameter of a wire is :

(A) 50

(B) 100

(C) 200

(D) 500

Q.No. 115

(A)

(B)

(C)

(D)

Q.No. 116 In a hydrogen like atom, when an electron jumps from the M - shell to the L - shell, the wavelength
of emitted radiation is λ. If an electron jumps from N-shell to the L-shell, the wavelength of emitted radiation
will be:

(A) 16

25
λ

(B) 25

16
λ

(C) 20

27
λ

(D) 27

20
λ

Q.No. 117 A train moves towards a stationary observer with speed 34 m/s. The train sounds a whistle and its
frequency registered by the observer isf . If the speed of the train is reduced to 17 m/s, the frequency
1

registered is \f . If speed of sound is 340 m/s, then the ratio f / f is :
2 1 2

(A) 20/19

(B) 18/17

(C) 19/18

(D) 21/20

Q.No. 118 A satellite of mass M is in a circular orbit of radius R about the centre of the earth. A meteorite of
the same mass, falling towards the earth, collides with the satellite completely inelastically. The speeds of the
satellite and the meteorite are the same, just before the collision. The subsequent motion of the combined body
will be:

(A) in an elliptical orbit

(B) in the same circular orbit of radius R

(C) in a circular orbit of a different radius

(D) such that it escapes to infinity
1
C (graphite) + O 2 (g) → CO 2 (g) : C (graphite) + O 2 (g) → CO 2 (g) :
Q.No. 119 Given: (i) ∘ −1
(ii) ∘
2

−1
(iii)
ΔrH = xk]mol ΔrH = yk]mol
1
CO(g) + O 2 (g) → CO 2 (g)

∘
2

−1
Based on the above thermochemical equations, find out which one of the
ΔrH = zk]mol

following algebraic relationships is correct?

(A) z = x + y

(B) x = y - z

(C) r = y + z

(D) y = 2z - x

Q.No. 120 If a variable line, 3x+4y-λ=0 is such that the two circles x² + y² - 2x - 2y + 1=0 and x² + y² – 18x –

2y + 78 = 0 are on its opposite sides, then the set of all values of λ is the interval :

(A) (23, 31)

(B) (2,17)

(C) [13, 23]

(D) [12, 21]

Answer Sheet
Q.No Answer
Q.No. 1 (D)
Q.No. 2 (A)
Q.No. 3 (D)
Q.No. 4 (D)
Q.No. 5 (D)
Q.No. 6 (B)
Q.No. 7 (C)
Q.No. 8 (A)
Q.No. 9 (B)
Q.No. 10 (A)
Q.No. 11 (C)
Q.No. 12 (C)
Q.No. 13 (B)
Q.No. 14 (B)
Q.No. 15 (B)
Q.No. 16 (B)
Q.No. 17 (C)
Q.No. 18 (A)
Q.No. 19 (B)
Q.No. 20 (D)
Q.No. 21 (C)
Q.No. 22 (B)
Q.No. 23 (D)
Q.No. 24 (D)
Q.No. 25 (B)
Q.No. 26 (D)
Q.No. 27 (D)
Q.No. 28 (A)
Q.No. 29 (C)
Q.No. 30 (D)

Q.No. 31 (B)
Q.No. 32 (C)
Q.No. 33 (D)
Q.No. 34 (A)

Q.No. 35 (D)
Q.No. 36 (C)
Q.No. 37 (D)
Q.No. 38 (B)
Q.No. 39 (B)
Q.No. 40 (A)
Q.No. 41 (B)
Q.No. 42 (B)
Q.No. 43 (B)
Q.No. 44 (B)
Q.No. 45 (A)
Q.No. 46 (B)
Q.No. 47 (C)
Q.No. 48 (A)
Q.No. 49 (A)
Q.No. 50 (D)
Q.No. 51 (C)
Q.No. 52 (A)
Q.No. 53 (D)
Q.No. 54 (B)
Q.No. 55 (A)
Q.No. 56 (B)
Q.No. 57 (A)
Q.No. 58 (A)
Q.No. 59 (A)
Q.No. 60 (C)
Q.No. 61 (B)
Q.No. 62 (C)
Q.No. 63 (A)
Q.No. 64 (A)
Q.No. 65 (D)
Q.No. 66 (D)
Q.No. 67 (B)
Q.No. 68 (B)
Q.No. 69 (A)

Q.No. 70 (B)
Q.No. 71 (D)
Q.No. 72 (D)
Q.No. 73 (A)

Q.No. 74 (C)
Q.No. 75 (D)
Q.No. 76 (D)
Q.No. 77 (D)
Q.No. 78 (A)
Q.No. 79 (C)
Q.No. 80 (B)
Q.No. 81 (D)
Q.No. 82 (D)
Q.No. 83 (B)
Q.No. 84 (B)
Q.No. 85 (D)
Q.No. 86 (B)
Q.No. 87 (C)
Q.No. 88 (B)
Q.No. 89 (D)
Q.No. 90 (A)
Q.No. 91 (B)
Q.No. 92 (C)
Q.No. 93 (A)
Q.No. 94 (C)
Q.No. 95 (B)
Q.No. 96 (B)
Q.No. 97 (D)
Q.No. 98 (C)
Q.No. 99 (B)
Q.No. 100 (B)
Q.No. 101 (D)
Q.No. 102 (B)
Q.No. 103 (B)
Q.No. 104 (A)
Q.No. 105 (B)
Q.No. 106 (A)
Q.No. 107 (A)
Q.No. 108 (A)

Q.No. 109 (D)
Q.No. 110 (B)
Q.No. 111 (C)
Q.No. 112 (D)

Q.No. 113 (C)
Q.No. 114 (C)
Q.No. 115 (D)
Q.No. 116 (C)
Q.No. 117 (C)
Q.No. 118 (A)
Q.No. 119 (C)
Q.No. 120 (D)