PHYSICS (A)

5. A ring having charge +Q and radius R and a long

1. If point A of rod is moving with velocity v0 in right thin rod having charge density + λ are kept as
direction then speed of B is : shown in figure. Electrostatic force applied by ring
on the rod is:

(A) v0tan θ (B) v0cot θ

v0 v0 Qλ
(C) (D) (A) 4 π ε R
cos θ sin θ 0

2. Trajectory of a particle in a projectile motion is Qλ

(B)
x2 2 π ε 0R
given by y = x – , where x and y are in meters.
80 Qλ
The horizontal range is (C)
π ε 0R
(A) 40 m (B) 20 m (D) Zero
(C) 60 m (D) 80 m 6. Two rods each of length 6L carry charge Q are
3. A block slides down an inclined plane of angle ϕ placed as shown in figure. Find magnitude of
with constant velocity v0. If it is then projected up electric field at point P, which is at a distance of 5L
the same inclined plane with an initial speed v0 , from centre of each rod.
the distance in which it will come to rest is:
v20 v20
(A) (B)
g tan ϕ 4 g sin ϕ
v20 v20
(C) (D)
2g 2 g sin ϕ
4. Two blocks A (1kg) and B (3kg) rest over the other
on a smooth horizontal plane (A over B). The
coefficient of static and dynamic friction between
A and B is the same and equal to 0.75. The
maximum horizontal force in newton that can be 1 √ 3Q
applied to A in order that both A and B do not have (A) .
64 π ∈ 0 L2
relative motion is : [g = 9.8 m/s2] √ 5Q
(B)
(A) 19.6 4 π ∈ 0 L2
1 Q
(B) 14.7 (C) 2 π ∈ .
0 L2
(C) 9.8 3Q
(D)
(D) 4.9 5 π ∈ 0 L2

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7. Four charges are placed at the circumference of dial 11. A parachutist falls freely from a stationary
clock as shown in figure. If the clock has only hour helicopter above ground. He covers as much
hand, then the resultant force on a charge q0 placed distance in the last second of his motion (before
at the centre, points in the direction which show the landing on trampoline) as covered in the first three
time as : – seconds. The parachutist has fallen for a time of :
(A) 3 sec (B) 5 sec
(C) 7 sec (D) 9 sec
12. A football is hit by a footballer in X-Y plane with
Y axis along vertical. Two seconds after hit, the
velocity of the footballer makes an angle 45° with
(A) 1:30 (B) 7:30 (C) 4:30 (D) 10:30 X axis.
Four seconds after hit, it moves horizontally.
8. The ratio of flux through surfaces S1 and S2 is:
The velocity just after hit is 20 n m/s. Find n.
√

(A) 5 (B) 3 (C) 4 (D) 2

13. A ping pong ball is thrown by a boy from a point
O with speed 20 m/s as shown. The incline plane is
(A) 1 : 1 (B) – 3 : 1 hit by the ball along the normal to the incline
(C) 3 : 1 (D) – 1 : 3 after two seconds. Find the value of x, is β = π ( β
x
is the angle of incline in degree)
9. The charge per unit length of the four quadrant
of the ring is 2 λ , −2 λ , λ and − λ respectively.
The electric field at the centre is:

(A) 4 (B) 3
(C) 2 (D) 1
−λ ^ λ ^ 14. A Cyclist is moving with uniform velocity on a
(A) 2 π ε R i (B) 2 π ε R j
0 0 straight road on a bridge. Beneath the bridge, there
√ 2λ ^ is a river in which a swimmer is moving at 4 km/hr
(C) i (D) None
4 π ε 0R due east observes that the cyclist is moving due
10. A small iron ball is moving under the influence of North. Another swimmer moving at 1
moving magnet along a straight line such that at km/hr due south claims that the cyclist is moving
time t its displacement from a fixed point O on the towards north-east. What is the speed of the cyclist
line is 3t2 – 2 . The velocity of the ball when t = 2 in ground frame ?
is: (A) 3 km/hr (B) 4 km/hr
(A) 8 m/s (B) 4 m/s (C) 12 m/s (D) 0 (C) 5 km/hr (D) 6 km/hr
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15. Find the tension in the string connecting 5kg and 19. The block shown in the diagram has a mass of 2
1kg. microgram and a charge of 2 × 10 – 9C. If the block
is given an initial velocity of 2m/s in x direction at t
= 0 and an electric field of 2 N/C in x direction is
switched on at that moment, then R will be (g = 10
m/s2).

(A) 10 N (B) 25 N (C) 35 N (D) 40 N

16. Calculate the relative acceleration of A w.r.t B if B
is moving with acceleration a0 towards right.

(A) 4m
(B) 1m
a0
(A) (C) 2m
2
a0 (D) 3m
(B)
4
5a0
20. An insulating long light rod of length L pivoted at
(C) its centre O and balanced with a weight W at a
2
5a0 distance x from the left end as shown in figure.
(D)
4 Charges q and 2q are fixed to the ends of the rod.
17. In the figure, on cutting the string OA find the Exactly below each of the charges at a distance h a
tension between m and 3m blocks at that instant. positive charge Q is fixed. Then x is

QLq + ε 20 h2 LW
(A) 0 (B) 4 mg (C) 5 mg (D) 2 mg (A)
h2 W
18. The electric field 0.400 m from a very long uniform QLq + ε 0 h2 LW
line of charge is 840 N/C. How much charge is (B)
ε 0 h2 W
contained in a 2.00 -cm section of the line ? 4QLq + ε 0 h2 LW
(C)
(A) 1.49 nC (B) 2.5 nC 8 π h2 W
QLq + 4 π ε 0 h2 LW
(C) 3.49 nC (D) 4.7 nC (D)
8 π ε 0 h2 W

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 PHYSICS (B)
This section contains 10 questions Candidates have to 3. 2 insects are moving with constant speed on a
attempt any 5 questions out of 10. If more than 5 square frame at t = 0, their positions are shown. If
questions are attempted, then only first 5 attempted magnitude of average acceleration of A, in the time
questions will be evaluated. kv2 √2
The answer to each question is an Integer Value Type A catches B is ( ), what is the value of k?
3ℓ
questions.
For each question, enter the correct integer value (In
case of non-integer value, the answer should be
rounded off to the nearest Integer).
Answer to each question will be evaluated according to
the following marking scheme:
Full Marks : +4 If correct answer is selected.
Zero Marks : 0 If none of the option is selected. 4. Two friends A and B are standing on a river bank L
Negative Marks : –1 If wrong option is selected. distance apart. They decide to meet at point C on
1. the other bank exactly opposite to B. Both of them
Two point charges q1 = 2µC and q2 = 1µC are
start rowing the boats simultaneously which can
placed at distances b = 1 cm and a = 2 cm from the travel with velocity v = 5 km/hr in still water. It
origin of the y and x axes as shown in figure. The was found that both reached C at same time.
electric field vector at point P(a,b) will subtend an Assume path of boats as straight lines ( ℓ = 3 km &
angle θ with the x-axis given by tan θ = K. Find speed of river, u = 3 km/hr). If the time taken by A
4
value of K. & B is 't' (in hours). Find the value of t.
3

5. A block of mass M is pulled along horizontal

frictionless surface by a rope of mass m. If tension
2. Electric field due to a uniformly charged ring of at the middle point of rope & force applied by
radius √ 5 m at a certain point on its axis is 1 V/m string on the block is in ratio 3 : 2 then find the
and electric potential at the same point is 6V. If the value of M/m.
distance of this point from centre of the ring is x (in
m), find the smallest value of x.

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6. Figure shows a massless pan connected to an ideal 9. An aeroplane is accelerating in sky horizontally. A
spring (Figure). On the pan a small mass 'm = 5 kg' box kept on the floor at that instant in front of the
first compartment slides to the end of the same
is kept. The mass is connected to another mass 'M
compartment through the passage and hits the wall
= 2 kg' through a thread passing through the hole in of the compartment after 2 sec. The box comes to
the pan. Initially the system is in equilibrium. Find rest after hitting the wall of the compartment in 0.1
the acceleration of 'm' (in m/s2) just after the string sec. What is the force (N) with which the box hits
is cut. the wall ? (Assuming passage is frictionless)
(Given: mass of the box = 5 kg and length of
compartment= 40 m)
10. A uniform electric field E = 500 N/C passes
through a hemispherical surface of radius R = 2m
as shown is figure. The net electric flux (in SI
units) through the hemispherical surface only is
N π × 102 . Then find the value of N.

7. Block on the smooth sphere is in equilibrium (it

implies that net force is zero). If sphere applies a
force of 30N on the block and weight of the block
is 50 N.Tension T in the string is 5x newton then
the value of x.

8. The two blocks, m = 20 kg and M = 80kg, shown in

figure are free to move, the coefficient of static
friction between the blocks is μ s = 0.5, but the
surface beneath M is frictionless. What is the
minimum horizontal force F(N) required to hold m
against M?

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 CHEMISTRY (A)
This section contains 20 questions. Each question has 6. 896 mL of a mixture of CO and CO2 weigh 1.28g
4 options for correct answer. Multiple-Choice at 1 atm and 273 K. Calculate the volume of CO2 in
Questions (MCQs) Only one option is correct. For the mixture.
each question, marks will be awarded as follows: (A) 448 ml (B) 672 ml
Full Marks : +4 If correct answer is selected. (C) 224 ml (D) 500 ml
Zero Marks : 0 If none of the option is selected.
Negative Marks : –1 If wrong option is selected. 7. If a piece of iron gains 10% of its weight due to
partial rusting into Fe2O3 the percentage of total
1. What approximate volume of 0.40 M Ba(OH)2 iron that has rusted is [Fe = 56]
must be added to 50.0 mL of 0.30 M NaOH to get
a solution in which the molarity of the OH – ions is (A) 33.33 (B) 13
0.50 M? (C) 23.3 (D) 25.67
(A) 33 mL (B) 66 mL 8. Calculate the mass of anhydrous HCl in 10 mL of
(C) 133 mL (D) 100 mL concentrated HCl (density = 1.2 g/ mL) solution
having 37% HCl by weight,
2. The difference between the wave number of 1st line
of Balmer series and last line of paschen series for (A) 4.44 g (B) 4.44 mg
Li2+ ion is : (C) 4.44 × 10 – 3 mg (D) 0.444 μ g
(A) RH (B) 5RH 9. 1st excitation energy for the hypothetical H-like
36 36 sample is 24 eV, then which one is incorrect-
(C) 4RH (D) RH
4 (A) Ionisation energy of sample is 36 eV.
3. The third ionization enthalpy is minimum for : (B) Ionisation energy of sample is 32 eV.
(A) Fe (B) Ni (C) Binding energy of 3rd excited step is 2 eV.
(C) Co (D) Mn (D) Second excitation energy of the sample is
4. A certain substance 'A' tetramerises in water to the 28.44 eV.
extent of 80%. A solution of 2.5 g of A in 100 g of 10. An electron, initially at rest, is accelerated through
water lowers the freezing point by 0.3ºC. The a potential difference of 100 volt. It has debroglie
molar mass of A is :- wavelength λ 1 Aº. It then get retarded through 19
(A) 122 (B) 31 volt and then has a wave length λ 2Aº. A
(C) 244 (D) 62 further retardation throught 32 volt change the
5. In a reaction carried out at 400 K, 0.0001% of the wavelength to λ 3Aº., then calculate λ 3 − λ 2 .
λ1
total number of molecules are in activated state. 7
The energy of activation of reaction is - (A)
90
(A) 110.5 Kcal/mol (B) 27
90
(B) 7.37 Kcal/mol 20
(C)
(C) 9.21 Kcal/mol 63
2
(D) 11.05 Kcal/mol (D)
10
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11. Which of the following is wrong :- 15. Two components A and B form an ideal solution.
(A) NH3 < PH3 < AsH3 ⇒ Acidic character The mole fractions of A and B in ideal solution are
XA and XB while that in vapour phase, these
(B) Li < Be < B < C ⇒ IE1 components have their mole fractions as YA and
(C) Al2O3 < MgO < Na2O < K2O ⇒ Basic 1
YB. Then, the slope and intercept of plot of vs.
YA
character 1
will be :-
(D) Li+ < Na+ < K+ < Cs+ ⇒ Ionic radius XA
PBo PBo − PAo
12. Which of the following has been arranged in order (A) ,
PAo PBo
of decreasing freezing point :- (Assume α = 1)
PBo PAo − PBo
(A) 0.05 M KNO3 > 0.04 M BaCl2 > 0.140 M (B) ,
PAo PAo
sucrose > 0.075 M CuSO4 PBo PBo
(C) ,
(B) 0.04 M BaCl2 > 0.140 M sucrose > 0.075 M PAo PBo − PAo
CuSO4 > 0.05 M KNO3 PAo
(D) PAo − PBo ,
(C) 0.075 M CuSO4 > 0.140 M sucrose > 0.04 M PBo
BaCl2 > 0.05 M KNO3 16. The polarimeter readings in a experiment to
(D) 0.075 M CuSO4 > 0.05 M KNO3 > 0.140 M measure the rate of inversion of cane sugar (Ist
sucrose > 0.04 M BaCl2 order reaction) were as follows -
13. At a given temperature, total vapour pressure in Time (min) 0 30 ∞
Torr of a mixture of volatile components A and B Rotation due to –
is given by 30º 20º
solution 15º
PTotal = 120 – 75 XB Identify the true statements :
hence, vapour pressure of pure A and B [Given : log 2 = 0.3, log3 = 0.48, log 7 = 0.84,
respectively (in Torr) are : (loge 10) = 2.3]
(A) 120, 75 (A) The half life of the reaction is 75 min
(B) 120, 195 (B) The solution is optically inactive at 15 min
(C) 120, 45 (C) The half life of the reaction is 60 min
(D) 75, 45 (D) The solution is optically active throughout the
14. 12.2 gm benzoic acid (M = 122) in 100 g H2O has course of reaction.
elevation of boiling point of 0.27°C, Kb = 0.54 K 17. Reaction A + B —→ C + D follow's following
1 1
kg/mole. If there is 100% association, the no. of rate law : rate = k [A]+ 2 [B]+ 2 Starting with initial
molecules of benzoic acid in associated state is : conc. of one mole of A and B each, what is the time
(A) 1 taken for amount of A of become 0.25 mole. Given
k = 2.31 × 10 – 3 sec – 1.
(B) 2
(A) 300 sec. (B) 600 sec.
(C) 3
(C) 900 sec. (D) none of these
(D) 4
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18. A reactant (A) forms two products : 20. For a reaction 2A + B → Product, rate law is
k1 −d[A]
A −→ B, Activation Energy Ea1 = K[A]. Concentration of reactant A at
k1 dt
A −→ C , Activation Energy Ea2 1
time t = , where C0 is initial concentration of A
If Ea2 = 2Ea1 , then k1 and k2 are related as K
(If arrhenious constant is same for both reactions) -
(A) C0
(A) k1 = 2k2 eEa2 /RT
e
(B) k1 = k2 eEa1 /RT (B) C0e
(C) k2 = k1 eEa2 /RT (C) C0
10
(D) k1 = Ak2 eEa1 /RT
(D) 10C0
19. For reaction 2A →B + 3C; if
d[A] d[B] d[C]
− = k1 [A]2 ; = k2 [A]2 ; = k3 [A]2
dt dt dt
the correct reaction between k1, k2 and k3 is:
(A) k1 = k2 = k3
(B) 2k1 = k2 = 3k2
(C) 4k1 = k2 = 3k2
k1 k
(D) = k2 = 3
2 3

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 CHEMISTRY (B)
This section contains 10 questions Candidates have to 6. Consider the following first order decomposition
attempt any 5 questions out of 10. If more than 5 reaction :
questions are attempted, then only first 5 attempted A4(g) → 4A(g)
questions will be evaluated.
The answer to each question is an Integer Value Type
questions.
For each question, enter the correct integer value (In
case of non-integer value, the answer should be
rounded off to the nearest Integer). The half-life of the reaction (in minutes) is :
Answer to each question will be evaluated according to [Given : log 2 = 0.3, log 5 = 0.7]
the following marking scheme: 7. A compound H2X with molar weight of 80 g is
Full Marks : +4 If correct answer is selected.
dissolved in a solvent having density of 0.4 g mL – 1,
Zero Marks : 0 If none of the option is selected.
Negative Marks : –1 If wrong option is selected. Assuming no change in volume upon dissolution, the
1. How many of the following can react with bases : molality of a 3.2 molar solution is
Mn2O7, ZnO, Al2O3, BeO, Na2O, Cl2O7, PbO2, 8. The Henry's law constant for the solubility of
As2O3
nitrogen gas in water at 298 K is 2 × 105 atm. The
2. In the saturated aqueous solution of PbCl2 the mole fraction of nitrogen in air is 0.4. If the number
D
freezing point decreases by ( )°C then ‘D’ is
of moles of nitrogen from air dissolved in 20 moles
100
(Given Ksp of PbCl2 = 4 × 10 – 6, Kf, water = 2K- of water at 298 K and 10 atm pressure of air is x ×
kg/mole. 10 – 4 then calculate value of x.
3. 75 g ethylene glycol is dissolved in 500 gram 9. A solution is prepared by dissolving 0.6 g of urea
water. The solution is placed in a refrigerator
(molar mass = 60g mol-1) and 1.8g of glucose
maintained at a temperature of 263 K. What
amount of ice will separate out at this temperature? (molar mass = 180 g mol-1) in 100 ml of water at
(Kf water = 1.86 K molality – 1 , Freezing point of 27°C. The osmotic pressure of the solution is (R =
water = 273 K) 0.082) L atm K-1 mol-1)
4. An ideal solution is made by mixing 3 moles of 10. For a first order reaction A → B + C all the
liquid A (P°A = 100 torr) and 5 moles of liquid B reactant and product molecules are in gaseous state.
(P°B = 200 torr), at what pressure in torr 6 moles of If the initial pressure of the reactant molecule is
liquid mixture will be vaporised?
100mm and after 30 minutes the total pressure of
5. A reaction is of first order. After 100 minutes 75g the mixture containing molecules of all three A, B
of the reactant A are decomposed when 100 g are & C is 140 mm then find the time interval at which
taken initially, calculate the time required (in
the initial pressure of A will be reduced to 50 mm.
minutes) when 150 g of the reactant A are
(log10 3 = 0.5, log10 2 = 0.3)
decomposed, the initial weight taken is 200 g.

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 MATHEMATICS (A)
This section contains 20 questions. Each question has 5. If a + b + c > 9c and equation ax2 + 2bx – 5c =0
4 options for correct answer. Multiple-Choice 4
has non – real complex roots, then
Questions (MCQs) Only one option is correct. For
each question, marks will be awarded as follows: (A) a > 0, c > 0
Full Marks : +4 If correct answer is selected. (B) a > 0, c < 0
Zero Marks : 0 If none of the option is selected. (C) a < 0, c < 0
Negative Marks : –1 If wrong option is selected.
(D) a < 0, c > 0
1. If ƒ(x) = √ x − 4 + √6 − x , then maximum value of
ƒ(x) is -
6. If α and β are the roots of the equation x2 + 10x –
α 12 + β 12 − 7 ( α 10 + β 10 )
(A) 3 7 = 0 then the value of
2 ( α 11 + β 11 )
(B) √ 2 is :
(C) √ 6 (A) 5
(D) 2 (B) – 5
2. π π (C) 10
In [ − , ] the equation logsin θ cos 2 θ = 2 has
2 2
(D) – 10
(A) No solution
7. Let f(x) = ax2 + bx + c, where a, b, c ∈ R and a ≠
(B) One solution
0, is such that 2a + b + c = 0, then the quadratic
(C) 2 solutions equation f(x) = 0 has :
(D) None of these (A) non-real roots
3. Suppose that, log10(x – 2) + log10y = 0 and (B) 0 and 2 as real roots
√ x + y − 2 = x + y. Then the value of (x + y),
√ √
(C) two equal roots
is
(D) two distinct real roots
(A) 2
8. The range of 'a' for which the roots of the equation
(B) 2 √2
(a2 – a + 1)x2 + 2(a + 1)x + (a2 + a – 2) = 0 are of
(C) 2 + 2 √2 opposite sign is -
(D) 4 + 2 √2 1
(A) a ∈ ( −2,
2
)

4. If x, y, z are non-zero real numbers then the

minimum value of expression (B) a ∈ ( – 1,2)
( x8 + 4x4 + 1) (y 4 + 3y 2 + 1) (z 2 + 2z + 2)
( ) (C) a ∈ R
x4 y 2
equals - (D) a ∈ ( – 2,1)
(A) 12 (B) 24
(C) 30 (D) 48

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9. If p is the smallest value of x satisfying the 15. The number of real solutions of the equation tan(ex)
equation 2x + 15
=8 then the value of 4p is equal = ex + e – x, x > 0, is
2x
to (A) 0
(A) 9 (B) 16 (B) 1
(C) 25 (D) 1 (C) 2
10. If (D) none of these
1 1 1 1
+ + ........... = logm nx
16.
logn m log n m
√
1/4 log 3 n m
√
1/9 1
log10 n m 100
Let ex = y + √ 1 + y2 then y =
√

then x is equal to (ex + e−x )

(A)
(A) 110 (B) 50 2
(e − e−x )
x
(C) 40 (D) 55 (B)
2
11.
If f (x) =
3x−3
for all x ∈ Q, then the value of (C) ex + e – x
1−x x
3 +3
f(
1
) + f (
2
) + f (
3
) +. . . +f (
108
)
(D) ex – e – x
109 109 109 109
is 17. Let ƒ : ( – 1,1) → be such that ƒ(cos4 θ ) =
2 π π π
(A) 54 (B) 55 for θ ∈ (0, ) ∪ ( , ). Then the
2 − sec2 θ 4 4 2
1
(C) 108 (D) 2 value(s) of ƒ( ) is (are) -
3
12. Let n(A) = 3, n(B) = 3 (where n(S) denotes number 3 3
(A) 1−√ (B) 1+√
of elements in set S), then number of subsets of (A 2 2
× B) having odd number of elements, is : 2 2
(C) 1−√ (D) 1+√
3 3
(A) 64 (B) 128
18. If the domain of the function
(C) 256 (D) 512 1
f (x) = is all Real
13. Let P(x) = kx3
+ 2k2 x2 k3.
+ The sum of all real √ ℓ n{x2 + 2ax + 9 − 3a}
number then the number of integral values of a-
numbers k for which (x – 2) is a factor of P(x), is
(A) 4 (B) 6 (C) 8 (D) 12
(A) 4 (B) 8
19. Solve for x: |x2 – 4x + 3| = |x2 – 5x + 4|
(C) – 4 (D) – 8
7
14. Let P(x) = x6 + ax5 + bx4 + cx3 + dx2 + ex + f be a (A) {1, 5} (B) {
2
, 1}

polynomial such that 3

P(1) = 1; P(2) = 2; P(3) = 3; P(4) = 4; P(5) = 5 and (C) {
2
, 1} (D) {3, 5}
P(6) = 6, then find the value of P(7). 20. The polynomials P(x) = kx3 + 3x2 – 3 and Q(x) =
(A) 700 2x3 – 5x + k, when divided by (x – 4) leave the
(B) 727 same remainder. Then the value of k is
(C) 650 (A) 2 (B) 1
(D) 725 (C) 0 (D) – 1
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 MATHEMATICS (B)
This section contains 10 questions Candidates have to 8. If ƒ(sinx) = sin3x, then ƒ(cos30°) is equal to
attempt any 5 questions out of 10. If more than 5 9. The number of integral value of b satisfying the
questions are attempted, then only first 5 attempted equation a – ab + 5b + 2 = 0, a ∈ I is
questions will be evaluated.
10. If α & β are roots of the equation x2 + x – 3 = 0,
The answer to each question is an Integer Value Type
then value of α 3 – 4 β 2 + 24 is
questions.
For each question, enter the correct integer value (In
case of non-integer value, the answer should be
rounded off to the nearest Integer).
Answer to each question will be evaluated according to
the following marking scheme:
Full Marks : +4 If correct answer is selected.
Zero Marks : 0 If none of the option is selected.
Negative Marks : –1 If wrong option is selected.
1. Let ℓ = (log34 + log29)2 – (log34 – log29)2,
log65 5
m = 0.8(1 + 9log3 8 ) and n is the value of x
x x
satisfy the equation 2(log23) = 3(log32) the
nℓ
determine
m
2. Number of solutions of x ∈ [0, π ] satisfying the
equation
 3
⎛ ⎞
 log √ 3(
√ 3) log 3 3 √
⎜ ⎟
( log √ 3 tan x) ⎜⎷ + ⎟ = −1
⎜
log √ 3 log 3 tan x
⎟

⎝
√ 3 √
⎠

is are
3. (a − 2b)3 + (2b − c)3 + (c − a)3
Value of is :-
(a − 2b)(2b − c)(c − a)
4. The total number of solutions of the equation [x]2 =
x + 2{x}, (where [.], {.} denotes greatest integer
function and fractional part function respectively)
5. If f(x) = 2x – 1, then the number of solutions of the
equation |f(x)| = |f(|x| – 1)| is
6. The number of solution(s) of the 10|x| |x2 – 3|x| + 2|
= 1 is
7. If the range of function f(x) = sgn(x2 – 3x – 10) is
{ – 1} then the maximum number of integers in the
domain of f(x) is/are

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