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Competishun
52/6, Opposite Metro Mas Hospital, Shipra Path, Mansarovar

Date: 29/10/2022
Time: 3 hours Max. Marks: 180

PRAVEEN-XIII (22-23) [FL] - ACT-1 - PAPER-1

Physics
Multiple Choice Question

Q1 In a situation, a board is moving with a velocity v with respect to earth, while a man A
and man B are running with a velocity 2v with respect to earth and both men are
running from the opposite ends of the board at the same time, as shown. Length of the
board is L. If they meet after time T, then

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a)    value of T is L/4v
b)    value of T is L/2v
c)    Displacement of man B with respect to board in time T is 3L/4
d)    Displacement of man A with respect to board in time T is L/4

Q2 An object is moving in the xy plane with the position vector is given by and
velocity vector is . Consider a point O at origin .Distance of object from
origin in decreasing, if
a)    v x > 0, v y < 0 & x < 0, y > 0 b)    v x < 0, v y > 0 & x > 0, y < 0
c)    xv x + yv y < 0 d)    – xv x + yv y < 0

Q3 Two refracting media are separated by a spherical interface as shown in the figure. P P
′ is the principal axis, μ1 and μ2 are the refractive indices of medium of incidence and
medium of refraction respectively. Then:

a)    if μ2 > μ1, then there cannot be a real image of real object

b)    if μ 2 > μ 1 , then there cannot be a real image of virtual object
c)    if μ 1 > μ 2 , then there cannot be a virtual image of virtual object
d)    if μ 1 > μ 2 , then there cannot be a real image of real object

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Q4 In the figure shown radius of curvature of either surface of equi convex half lens is 40
cm and refractive index 1.5. Its one side is silvered. A plane mirror is also placed. A
small object O is placed such that there is no parallax between final image formed by
lens and mirror. If transverse length of final image formed by lens system is twice that
formed by mirror. Choose the correct options :

a)    a = 2.5 cm
b)    b = 5 cm
c)    Distance of image from object is 15 cm
d)    Image formed by lens system is virtual

Q5 A bead of mass m is kept at a distance a from the axis of rotation of a smooth

massless tube. The tube is rotated on a smooth horizontal surface along a vertical axis
perpendicular to the length L of the tube and passing through one of its end 'O' with
constant angular velocity ω.

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a) The speed of the bead relative to tube when it is at distance r from axis of rotation
   is ω
b) The speed of the bead relative to tube when it is at distance r from axis of rotation
   is ω
c) The work done by the centrifugal force in the frame of the tube when the bead
   reaches at distance r from the axis starting from radius a is mω2(r2 – a2)
d) The work done by the centrifugal force in the frame of the tube when the bead
   reaches at distance r from the axis starting from radius a is mω2 (r2 – a2)

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Q6 A car is accelerating on a horizontal road with acceleration = 20 m/s2. A box that is

placed inside the car, of mass m = 10 kg is put in contact with the vertical wall as
shown. The friction coefficient between the box and the wall is μ = 0.6.

a)    The acceleration (with respect to ground) of the box will be 20 m/sec2

b)    The friction force acting on the box will be 100 N
c)    The contact force between the vertical wall and the box will be 100 N
d) The net contact force between the vertical wall and the box is only of
   electromagnetic in nature.

Numerical

Q7 A car is travelling in steady rain with constant acceleration in a straight line. When it
begins to move the driver sees that the raindrops make an angle of 37° with the
vertical. After 20 s, the driver observes that the raindrops make an angle of 53° with
vertical in same direction. The acceleration of the car is x cm/s2. Find the value of 2x.
Rain is falling at 3 m/s relative to the ground.
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A river is flowing with velocity 5 km/hr relative to the ground as shown in the figure.
A boat starts from A and reaches the other bank by covering shortest possible
distance. Velocity of boat in still water is 3 km/hr. The distance (in m) boat covers is
s. The value of is

Q9 Two inclined planes OA and OB of inclinations to the horizontal α and β, each equal
to 30° are placed as shown in the figure. A particle is projected at an angle of 90° with
plane OA from point A and its strikes the plane OB at point B normally. If the speed
of projection in m/s is x. Fill the value of 8x. (given that OA = OB = 20 cm and g = 10
m/s2)

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Q10 The backside of a truck is open and a box of 40 kg is placed 5 m away from the rear
end. The coefficient of friction of the box with the surface of the truck is 0.15. The
truck starts from rest with acceleration 2 m s–2. Calculate the distance (in m) covered
by the truck when the box falls off.
Q11 A police car is travelling in a straight line with a constant speed, υ. A truck travelling
in the same direction with constant velocity, passes the police car at, t = 0. The
police car starts accelerating 10 s after passing the truck, at a constant rate of 3 m s–2,
while the truck continues to move at a constant speed. If the police car takes 10 s
further to catch the truck, find the value of υ (m/s)
Q12 If pulley is ideal and string is massless then reading of weighing machine is kg
then calculate x. : (g = 10 m/s2)

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Q13 Consider the arrangement shown in figure. Pulleys and string are ideal. There is no
friction between smaller and bigger block. Both blocks have same mass m. The
minimum coefficient of friction between bigger block and ground for which both
blocks remains in equilibrium is μ, then 70μ is :

Q14 As shown in the figure, water is filled inside a beaker and a point object ‘O’ is
kept at the bottom. Find the distance of the image formed due to reflection from the
mirror. Assume paraxial rays.

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Single Choice Question

Q15 Two concave refracting surfaces each with radius of curvature R = 35 cm and
refractive indices μ1 and μ2 respectively, are placed facing each other in air as shown
in figure. A point object 'O' is placed at a distance R/2 from one of the surface as
shown. Answer the following :

Distance of image after refraction from 1st surface (μ1 = 1.5) is equal to :
a)    45 cm towards left of P 1 b)    45 cm towards right of P 1
c)    30 cm towards left of P 1 d)    30 cm towards right of P 1

Q16 Two concave refracting surfaces each with radius of curvature R = 35 cm and
refractive indices μ1 and μ2 respectively, are placed facing each other in air as shown
in figure. A point object 'O' is placed at a distance R/2 from one of the surface as
shown. Answer the following :

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Separation between the images of 'O' formed by each refracting surfaces is equal to :
(μ2 = 1.5)
a)    8 cm b)    4 cm
c)    2 cm d)    cannot be determined

Q17 Two particles are projected horizontally in opposite direction from a point on a
smooth inclined plane with velocity u1 and u2 as shown in figure. Angle of incline is θ
with horizontal.

Time when their velocities will become perpendicular is -

a)    b)    c)    d)   

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Q18 Two particles are projected horizontally in opposite direction from a point on a
smooth inclined plane with velocity u1 and u2 as shown in figure. Angle of incline is θ
with horizontal.

The separation between the particles when their velocities become perpendicular to
each other is :
a)    b)    c)    d)   

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Chemistry
Multiple Choice Question

Q19 Amongs the species given below which will have same mass?
a)    0⋅1 mol of sulphur dioxide b)    0⋅1 mol of N 2 O
c)    0⋅1 mol of CO 2 d)    Avogadro number of CO molecules

Q20 Which of the following contains same number of sulphur atoms as present in 1 g S ?
a)    1g S 2 b)    1g S 6 c)    1g S 8 d)    1 mol of SO 2

Q21 Which of the following is/are aromatic compounds :

a)    b)    c)    d)   

Q22 Identify correct structure of 4-ethylidene-3,7-dimethyldeca-1,7-diene

a)    b)    c)    d)   

Q23 Select the structure in which incorrect numbering has been done for IUPAC name of
the compound :
a)    b)    c)    d)   

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Q24 A nonpolarmolecule AX 4 have all bond angles equal then which of the following
conclusions are correct?
a)    Molecule may be tetrahedral.
b)    Molecule may be square planar.
c)    Central atom 'A' must have at least six valence electrons.
d)    Central atom 'A' has either zero lone pair or two lone pairs

Numerical

Q25 Calculate molecular diameter for a gas if its molar excluded volume is 3.2 π ml. (in
nenometer). Give the answer by multiplying with 100. (Take NA = 6.0 × 1023)

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Q26 If wave functions, ψ(r, θ, φ) of 2s and 2pz electrons in a hydrogen atom are
given by
ψ(2s) = K1 and

ψ(2pz) = k2 cosθ,
where a0 = 53 pm and let constants k1 = k2 . If the probability of finding the
electron in 2s orbital in a small spherical volume of radius r0 (r0 << a0) around r
= a0 is P1 and of electron in 2pz orbital in same spherical volume around r = a0
at θ = 300 is P2 then Find (P1 – P2) × 15:
Q27 How many products (structural isomers) are formed by monochlorination of
following compound ?

Q28 How many alkene on hydrogenation give 2,3-dimethyl pentane ?

Q29 In given pairs no. of pairs in which Ι compound is more stable than ΙΙ.
(i)                                       (ii) >

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(iii)                    (iv) >

(v) >                                  (vi) >

Q30 For one mole of a van der Waals gas when b = 0 and T = 300 K, the PV vs.1/V
plot is shown below. The value of the vanderWaals constant a (atm.liter2 mol–
2 ), If your answer is x then what will be the value of 10x.

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Q31 CN– ion is oxidised by a powerful oxidising agent to NO3– and CO2 or CO32–
depending on the acidity of the reaction mixture.
CN– ⎯→ CO2 + NO3– + H+ + ne–
What is the number (n) of electrons per mole of CN– involved in the process ?
Q32 1 g of dry green algae absrobs 4.7 × 10–3 mole of CO2 per hour by photosynthesis. If
the fixed carbon atoms were all stored after photosynthesis as starch (C6H10O5)n.
Aproximately how long (in hour) would it take for the algae to double their own
weight assuming phtosynthesis takes place at a constant rate?

Single Choice Question

Q33 (Q) gives positive iodoform test and also give red precipitate with fehling
solution. Hydrogenation of (P) results benzenoid compound (S). Compound
(S) gives three monochloro products (only structural) on monochlorination.

The structure of the aromatic compound P is :

a)    b)    c)    d)   

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Q34 (Q) gives positive iodoform test and also give red precipitate with fehling
solution. Hydrogenation of (P) results benzenoid compound (S). Compound
(S) gives three monochloro products (only structural) on monochlorination.

The structure of the product Q is :

a)    b)    c)    d)   

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Q35 One of the important approach to the study of real gases involves the analysis of a
parameter Z called the compressibility factor Z = where P is pressure, V m is
molar volume, T is absolute temperature and R is the universal gas constant. Such a
relation can also be expressed as Z = (where V m ideal and V m real are the molar
volume for ideal and real gas respectively). Gas corresponding Z > 1 have repulsive
tendencies among constituent particles due to their size factor, whereas those
corresponding to Z < 1 have attractive forces among constituent particles. As the
pressure is lowered or temperature is increased the value of Z approaches 1. (reaching
the ideal behaviour)

a)    Allconclusions are true b)    Conclusions I, II & IV are true

c)    Conclusions I, II & IV are true d)    Conclusions III & IV are true

Q36 One of the important approach to the study of real gases involves the analysis of a
parameter Z called the compressibility factor Z = where P is pressure, V m is
molar volume, T is absolute temperature and R is the universal gas constant. Such a
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relation can also be expressed as Z = (where V m
volume for ideal and real gas respectively). Gas corresponding Z > 1 have repulsive
ideal and V m real are the molar

tendencies among constituent particles due to their size factor, whereas those
corresponding to Z < 1 have attractive forces among constituent particles. As the
pressure is lowered or temperature is increased the value of Z approaches 1. (reaching
the ideal behaviour)
For a real gas ‘G’ Z > 1 at STP Then for ‘G’ :
Which of the following is true :
a)    1 mole of the gas occupies 22.4 L at NTP
b) 1 mole of the gas occupies 22.4 L at pressure higher than that at STP (keeping
   temperature constant)
c) 1 mole of the gas occupies 22.4 L at pressure lower than that at STP (keeping
   temperature constant)
d)    None of the above

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Mathematics
Multiple Choice Question

Q37 Which of the following function are defined for all x

a)    sin[x] + cos [x] ([x] denotes greatest integer ≤ x)
b)    sec –1 (1 + sin 2 x)
c)    tan (log x)
−−−−−−−−−−−−−−
d)   
 √ 98 + cosx + cos2x

Q38 If f(x) = (h1(x) –h1(–x)) (h2(x) – h2(–x))…… (h2n+1(x) – h2n + 1(–x))

where h1(x), h2(x), ……. hn(x) are defined everywhere & f(200) = 0, then f(x) is
a)    one-one b)    many one c)    odd d)    even

Q39 If f(x) = sin{[x + 5] + {x – {x –{x}}} for x ∈ (0, π ) is invertible, where {.} and [.]
4

represent fractional part and greatest integer functions respectively, then f–1(x) is-
a)    sin –1 x b)    π – cos –1 x c)    sin –1 {x} d)    cos –1 {x}
2

Q40
Let then :
a)    Maximum value of f(θ ) ∀θ ∈ R is  1

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b)    Maximum

c)    f(0) =  18
value of f(θ ) ∀θ ∈ R is  18
4

d)    Number of principle solutions of f(θ) = 0 is 8

Q41 If the roots of 10x3 – cx2 – 54x – 27 = 0 are in harmonic progression, then
a)    c = 9 b)    one integral root
c)    two positive roots d)    two negative roots

Q42 Let f(x) = ||x2 – 4x + 3| – 2| which of the following is / are correct

a)    f(x) = m has exactly two real solution of different sign  ∀  m > 2
b)    f(x) = m has exactly two real solution  ∀  m  ∈  (2, ∞)  ∪  {0} 
c)    f(x) = m has no solution  ∀  m < 0
d)    f(x) = m has four distinct real solution  ∀  m  ∈  (0, 1)

Numerical

Q43 If both the given equations 2x2 + (λ – 1)x + 8 = 0 and x2 – 8x + λ + 4 = 0 have real
roots, then find the greatest value of λ such that λ3 0 .
 
Q44 The absolute value of maximum possible integral value of a for which the equation x2
+ ax – 4 = 0 has its smaller root in the interval (–1, 2) is

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Q45 If sum of all solutions of the equation (xlog 3 )2  – (3log 10 10

x
) – 2 = 0 is a log
b
c
where a,
b, c ∈N & a, b are prime numbers then a2 × b equals
Q46 In a class of 30 pupils 12 take geography, 16 take physics and 18 take history. If all
the 30 students take at least one subject and no one takes all three, then the number of
pupils taking 2 subjects is
Q47
5 5 5 5 5 5 5 5 5 5
4 +4 +4 +4 6 +6 +6 +6 +6 +6
Let N =  5 5 5
 .  5 5
then the value of log2 N =
3 +3 +3 2 +2

Q48 Let a is real number then minimum number of real roots of equation (x2 + ax + 1) (3x2
+ ax – 3) = 0 can be ⎯⎯
Q49 The maximum value of 12 sin θ – 9 sin2 θ is -

Q50 If the equation |2x3 – 15x2 + 36x – 30| = λ, λ ∈  R has 4 solution, for λ ∈  (α, β ), then
the value of  (α + β ) is

Single Choice Question

Q51 Let f be a function from the set of positive integers to the set of real numbers {f : N →
R} such that
(i) f(1) = 1
(ii) f(1) + 2f(2) + 3f(3) …..+ nf (n) = n(n + 1) f(n) then
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Function f(x) forms-
a)    A.P. b)    G.P. c)    H.P. d)    None of these

Q52 Let f be a function from the set of positive integers to the set of real numbers {f : N →
R} such that
(i) f(1) = 1
(ii) f(1) + 2f(2) + 3f(3) …..+ nf (n) = n(n + 1) f(n) then
Function f(x) is-
a)    2x + 1 b)    x 2 c)    1 d)    None of these
2x+1

Q53 Let graph of y = x2 + 6x + k (k ∈ R) cuts x-axis at two real and distinct points x1 and
x2, while graph of quadratic expression y = ax2 + bx + c (a,b,c ∈ R) neither touches
nor cuts the x-axis, then answer the following questions :
If x1 > 0 and a – 2b + 4c > 0, then product a.k is
a)    positive b)    zero c)    negative d)    can't say

Q54 Let graph of y = x2 + 6x + k (k ∈ R) cuts x-axis at two real and distinct points x1 and
x2, while graph of quadratic expression y = ax2 + bx + c (a,b,c ∈ R) neither touches
nor cuts the x-axis, then answer the following questions :
Set of all possible values of k is
a)    (– ∞, 9] b)    (0, 9) c)    (– ∞, 9) d)    [0, 9)

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Answer Key
Que. 1 2 3 4 5 6 7 8 9 10

Ans. A, C, D A, B, C A, C C, D A, C A, B, C, 14 10 16 20
D

Que. 11 12 13 14 15 16 17 18 19 20

Ans. 15 05 15 40 B B B A B, C A, B, C

Que. 21 22 23 24 25 26 27 28 29 30

Ans. A, D B, C A, C, D A, B, D 20 15 13 05 04 15

Que. 31 32 33 34 35 36 37 38 39 40

Ans. 10 08 C D D B A, B, D B, C A, B, C B, C, D

Que. 41 42 43 44 45 46 47 48 49 50

Ans. A, B, D A, B, C, 12 02 12 16 12 2 4 5
D

Que. 51 52 53 54

Ans. C D C C

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