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

Date: 04/10/2022
Time: 3 hours Max. Marks: 300

PRAVEEN-XIII (22-23) [FL] - MPT-1

Physics
Single Choice Question

Q1 The position vector of a particle changes with time according to the relation
. What is the magnitude of the acceleration at t = 1?
a)    50 b)    100 c)    40 d)    25

Q2 A ball is thrown upward with an initial velocity V 0 from the surface of the earth. The
motion of the ball is affected by a drag force equal to mγv2 (where m is mass of the
ball, v is its instantaneous velocity and γ is a constant). Time taken by the ball to rise
to its zenith is :
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a)    b)    c)    d)   

Q3 A shell is fired from a fixed artillery gun with an initial speed u such that it hits the
target on the ground at a distance R from it. If t1 and t2 are the values of the time
taken by it to hit the target in two possible ways, the product t1t2 is :
a)    b)    c)    d)   

Q4 Two particles are projected from the same point with the same speed u such that they
have the same range R, but different maximum heights, h1 and h2. Which of the
following is correct?
a)    R 2 = 4 h 1 h 2 b)    R 2 = 16 h 1 h 2 c)    R 2 = 2 h 1 h 2 d)    R 2 = h 1 h 2

Q5 Two motor cars are moving along two roads perpendicular to each other towards point
of intersection of the two roads. Their velocities at a particular time are V1,V2
respectively while their distance from the crossing are S1 and S2 respectively. If the
acceleration of the two cars be f1 and f2 respectively, then they shall avoid collision, if
a)    (S 1 f 2 – S 2 f 1 ) 2 ≠ 2(V 2 f 1 – V 1 f 2 ) (V 2 S 1 – V 1 S 2 )
b)    (S 1 V 2 – S 2 V 1 ) 2 ≠ 2(f 1 S 2 – f 2 S 1 ) (V 2 f 1 – V 1 f 2 )
c)    (V 2 f 1 – V 1 f 2 ) 2 ≠ 2(S 1 V 2 – S 2 V 1 ) (f 1 S 2 – f 2 S 1 )
d)    (S 1 V 1 – S 2 V 2 ) (f 1 S 2 – f 1 S 1 ) (V 2 f 1 – V 1 S 2 ) ≠ 0

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Q6 Two identical trains take 3 sec to pass one another when going in the opposite
direction but only 2.5 sec if the speed of one is increased by 50 %. The time one
would take to pass the other when going in the same direction at their original speed
is :
a)    10 sec b)    12 sec c)    15 sec d)    18 sec

Q7 A particle is moving in a straight line whose acceleration versus time graph is given.
Assume that initial velocity is in the direction of acceleration. Then which of the
statement is correct between time t = 0 to t = t0.

a)    Velocity first increases then decreases, displacement always increases

b)    Velocity and displacement both, first increases and then decreases
c)    Displacement increases and velocity decreases
d)    Displacement and velocity both always increases

Q8 A point moves in a straight line with retardation ‘d’ which depends on velocity of
particle ‘v’ as d = , where C is a positive constant. If initial velocity of the particle
is v0 then total distance travelled by the particle before stopping is :
a)    b)    c)    d)   

Q9
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Three elephants A, B and C are moving along a straight line with constant speed in
same direction as shown in figure. Speed of A is 5 m/s and speed of C is 10 m/s.
Initially separation between A & B is ‘d’ and between B & C is also d. When ‘B’
catches ‘C’ separation between A & C becomes 3d. Then the speed of B will be -

a)    7.5 m/s b)    15 m/s c)    20 m/s d)    5 m/s

Q10 Particles A and B are moving with constant velocity in two perpendicular directions as
shown in the diagram at t = 0. Find the velocity of separation at t = 0, t = 1 sec
respectively.

a)    b)    c)    d)    4.8 m/s, 4.8 m/s

5 m/s, m/s 4.8 m/s, m/s 4.8 m/s, m/s

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Q11 In given figure, a smooth square platform ABCD is moving towards right with a
uniform speed m/s. At what angle θ must a particle be projected from B with
speed 20 m/s so that it strikes the point A?

a)    60º b)    c)    30º d)   
cos–1 sin–1

Q12 A particle is projected from point A. A fly is standing at a tower at point B as shown
in figure. When particle passes from B, fly starts flying in horizontal direction with
constant speed of 2 m/sec. Both will meet at the same horizontal level at point C.
Then : (g = 10 m/sec2)

a)    –1 b)    angle of projection is tan–1 (2)

angle of projection is tan
c)    angle of projection is 45º d)    None of these

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Q13 A river is flowing with a speed of 1km/hr. A swimmer wants to go to point C starting
from A. He swims with a speed of 5 km/hr at an angle θ w.r.t. river. If AB = BC = 400
m, then the value of θ is :

a)    37º b)    30º c)    53º d)    45º

Q14 A man is moving with 10 m/s towards west on a horizontal ground. He observed that
the rainfall is falling vertically down wards. Now he increases his speed to 15 m/s and
find that now the rainfall is falling at an angle of 45° towards him. The speed of the
rain with respect to ground is :
a)    b)    10 m/s c)    d)    None of these

Q15 A particle is moving in a circle of radius r with speed v as shown in the figure. The
magnitude of change in velocity in moving from P to Q is :

a)    2 v cos 40º b)    2 v sin 20º c)    2 v cos 20º d)    none of these

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Q16 A body falls from a height, h = 200 m. The ratio of the distance travelled in every 2 s,
during £ = 0 to t = 6s of the journey is
 
a)    1 : 4 : 9 b)    1 : 2 : 4 c)    1 : 3 : 5 d)    1 : 2 : 3

Q17 A body is at rest at, x = 0. At, t = 0, it starts moving in the positive indirection with a
constant acceleration. At the same instant another body passes through, x = 0 moving
in the positive x-direction with a constant speed. The position of the first body is
given by x1 (t) after time, t and that of the second body by, x2 (t) after the same time
interval. Which of the following graphs correctly describes (x1 – x2) as a function of
time t?
a)    b)   

c)    d)   

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Q18 Given below are the equations of motion of four particles A, B, C and D
xA = 6t – 3; xB = 4t2 – 2t + 3;
xC = 3t3 – 2t2 + t – 7;
xD = 7 cos 60° – 3 sin 30°
The particle moving with constant non–zero acceleration is
a)    A b)    B c)    C d)    D

Q19 Which of the following statement is incorrect :

a)    velocity is the rate of change of position with time
b)    relative velocity is the rate of change of relative position with time
c)    velocity of separation is rate of change of distance between two points with time
d) for collision of two particles A and B moving with constant velocity, the velocity
   of B relative to A should be from particle A to particle B

Q20 A man wearing a hat of extended length 12 cm is running in rain falling vertically
downwards with speed 10 m/s. The maximum speed with which man can run, so that
rain drops do not fall on his face (the length of his face below the extended part of the
hat is 16 cm) will be :
a)    7.5 m/s b)    13.33 m/s c)    10 m/s d)    zero

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Numerical

Q21 A particle is projected up with 15 m/s perpendicular to the incline. (see fig.). If the
particle hits the incline at a distance R (in meter) from the point of projection then
find the value of  R5
? (g = 10 m/s2)

Q22 Consider a car moving on a straight road as shown in figure. At some time t = t 0 when
car is 48 m from pole A. Speed and acceleleration of car are 10 m/sec and 4 m/sec2
respectively. If car takes equal time in reaching to A from this position and B from A
than find out the distance between pole A and B. (Assume acceleration of car is
constant)

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Q23 A particle moves along X axis. At t = 0 it was at x = – 1. It’s velocity varies with time
as shown in the figure. Find the number of times the particle passes through the
origin.

Q24 A ship is moving in a sea with a constant velocity of 50 m/sec and a helicopter is
flying horizontally with a constant velocity of 150 m/sec in the same direction at 2 km
height. Motion of the helicopter and the ship are in same vertical plane. When the
helicopter is x km behind the ship horizontally, a packet is dropped from the
helicopter so that it can reach the ship. Find the value of 10 x. (Neglect air resistance,
take g = 10 m/sec2)
Q25 A bird is at a point P (4m, –1m, 5m) and sees two points P1 (–1m, – 1m, 0m) and P2
(3m, – 1m, – 3m). At time t = 0, it starts flying in a plane of the three positions, with a
constant speed of 1 m/s in a direction perpendicular to the straight line P1 P2 till it
sees P1 and P2 collinear at time t. Find the time t. ( in s)

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Q26 A particle in projected from point A horizontally with speed 5 m/s from height 20 m.
At the same time another particle from B at a height 30 m is projected such that two
meet on the ground at exactly midpoint between the two bases. There find the velocity
of the particle at B (in m/s) in nearest integer. (Take g = 10 m/s2)

 
Q27 A swimmer wants to reach point B on the opposite bank of a river flowing at a speed
m/s as shown in figure. What minimum speed (in m/s) relative to water should the
swimmer have from point A so that he can reach the point B ?

Q28 A particle moving along a straight line with a constant acceleration of – 4 m/s2 passes
through a point A on the line with a velocity of + 8 m/s at some moment. Find the

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Q29
distance travelled by the particle in 5 seconds after that moment.
A particle is projected from ground with an initial velocity 20 m/sec making an angle
60° with horizontal. If R1 and R2 are radius of curvatures of the particle at point of
projection and highest point respectively, then find the value of .

Q30 The velocity of a particle is given by in m/s for time interval t = 0 to t =

10 sec. Find the distance travelled by the particle in given time interval.

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Chemistry
Single Choice Question

Q31 X and Y are two elements which form X 2 Y 3 and X3Y4. If 0.20 mol of X2Y3 weighs
32.0 g and 0.4 mol of X3Y4 weighs 92.8 g, the atomic weights of X and Y are
respectively
a)    16.0 and 56.0 b)    8.0 and 28.0 c)    56.0 and 16.0 d)    28.0 and 8.0

Q32 2KΙ + Ι2 + 22 HNO3 ⎯→ 2HΙO3 + 2KΙO3 + 22NO2 + 10H2O

If 3 mole of KΙ & 2 moles Ι2 are reacted with excess of HNO3. Volume of NO2
gas evolved at NTP is
a)    739.2 Lt b)    1075.2 Lt c)    44.8 Lt d)    67.2 Lt

Q33 Minimum amount of Ag 2CO3 (s) required to produce sufficient oxygen for the
complete combustion of C2H2 which produces 11.2 ltr of CO2 at S.T.P after
combustion is: [Ag = 108]
Ag2CO3 (s) ⎯→ 2Ag (s) + CO2 (g) + 1/2 O2 (g)
C2H2 + 5/2 O2 ⎯→ 2CO2 + H2O
a)    276 g b)    345 g c)    690 g d)    1380 g

Q34 Which of the following equations is a balanced one :

a)    5BiO 3 – + 22H + + Mn 2+ ⎯→ 5Bi 3+ + 7H 2 O + MnO 4 –
b)    5BiO 3 – + 14H + + 2Mn 2+ ⎯→ 5Bi 3+ + 7H 2 O + 2MnO 4 –

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c)    2BiO 3 – + 4H + + Mn 2+ ⎯→ 2Bi 3+ + 2H 2 O + MnO 4 –
d)    6BiO 3 – + 12H + + 3Mn 2+ ⎯→ 6Bi 3+ + 6H 2 O + 3MnO 4 –

Q35 The strength of 10– 2 M Na2CO3 solution in terms of molality will be (density of
solution = 1.10 g mL–1). (Molecular weight of Na2CO3 = 106 g mol–1)
a)    9.00 × 10 – 3 b)    1.5 × 10 –2 c)    5.1 × 10 –3 d)    11.2 × 10 – 3

Q36 What is the molarity of H2SO4 solution that has a density 1.84 g/cc at 35ºC and
contains 98% by weight-
a)    4.18 M b)    8.14 M c)    18.4 M d)    18 M

Q37 Li metal is one of the few substances that reacts directly with molecular
nitrogen. The balanced equation for reaction is :
6Li(s) + N2(g) ⎯→ 2Li3N(s)
How many grams of the product, lithium nitride, can be prepared from 3.5g of
lithium metal and 8.4 g of molecular nitrogen ?
a)    21.00 g of Li 3 N. b)    21.00 g of Li 3 N. c)    5.83 g of Li 3 N. d)    10.50 g of Li 3 N.

Q38 Equal weights of mercury and Ι2 are allowed to react completely to form a mixture of
mercurous and mercuric iodide leaving none of the reactants. Calculate the ratio of the
weights of Hg2Ι2 and HgΙ2 formed.
a)    1 : 0.653 b)    0.732 : 1 c)    1 : 0.523 d)    1 : 0.523

Q39 100 ml of 0.15 M solution of Al 2(SO4)3 , the density of the solution is 1.5 g/ml.
Report the no. of Al3+ ions in this weight.
a)    1.8 × 10 25 ions b)    6 × 10 22 ions c)    1.8 × 10 23 ions d)    1.8 × 10 22 ions

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Q40 When 25 g of Na2SO4 is dissolved in 103 Kg of solution, its concentration will b

a)    2.5 ppm b)    25 ppm c)    250 ppm d)    100 ppm

Q41
The name of is :

a)    Isohexane b)    2,2,4-Trimethylpentane
c)    Neoocatne d)    Isoheptane

Q42

What is incorrect about the given structure?

a)    It has six D.U. b)    It has six D.U.
2 2
c)    It has ten sp –sp C–C σ bond d)    All are incorrect.

Q43 Which of the following alkane has longest Carbon chain :

a)    b)   

c)    d)   

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Q44 Which of the following groups is attached to the cyclohexane ring in the following
compound.

a)    Methyl b)    n-Propyl c)    Iso-propyl d)    Neo-pentyl

Q45 Which of the following alkyl group are possible from Iso-butane ?
a)    Iso-Butyl & n-butyl b)    Sec. butyl & Ter. butyl
c)    n-butyl & Ter. butyl d)    Iso-butyl & Ter. butyl

Q46 Which of the following has longest chain of carbon :

a)    b)   

c)    d)   

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Q47 How many isopropyl groups are present in the parent chain?

a)    3 b)    5 c)    4 d)    2

Q48 When Dinitrogen pentaoxide (N2O5, a white solid) is heated, it decomposes into
nitrogen dioxide and oxygen. If a sample of N2O5 produces 1.6g O2, then how many
grams of NO2 are formed?
(not balanced)
a)    9.2g b)    4.6g c)    2.3g d)    18.4g

Q49 1 mole of an organic compound containing C, H and O on complete combustion

produces 134.4 L of CO2 gas at STP and 108 g H2O. Then, the molecular formula of
organic compound could be:
a)    C 6 H 6 O 6 b)    C 6 H 12 O 6 c)    C 6 H 6 O d)    C 8 H 12 O 2

Q50 The hydrated salt Na2CO3.xH2O undergoes 63% loss in mass on heating and becomes
anhydrous.Calculate the value of x.
a)    10 b)    12 c)    11 d)    16

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Numerical

Q51 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 ?
Q52 A drop (0.05 mL) of 12 M HCl is spread over a thin sheet of aluminium foild
(thickness 1 mm and density of Al = 2.7 g/mL). Assuming whole of the HCl is used to
dissolve. At what will be the maximum area of hole produced in foild (in cm2).
[Report your answer after multiplying by 10].
Q53

Phenylthiohydration(PTH)
Is a derivative of amino acid how many number of sp2 hybridised carbon atoms in
given structure.
Q54 Give the value of degree of unsaturation for given compound :
C12H17ClF2N2O4
Q55 The number of substituent present on main chain of given compound :

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Q56 Howmany of the following compounds have different number of carbons in parent
carbon chain
(1) n-propyl alcohol & isopropyl alcohol
(2) n-butyl alcohol & isobutyl alcohol
(3) n-butyl alcohol &  ter.butyl alcohol

Q57 Number of carbons in parent carbon chain of following compound :

Q58 The number of substituents are present on parent chain of given compound

Q59 How many compounds are hydrocarbon in the following?

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Q60 How many of following IUPAC names of given strutures are correct.

(1) 3,4-Diethyl-2,5-dimethyloctane

(2) 5-Ethyl-1-methyl-2-propylcyclohexane

(3) 1,2,4-Tribromo-3,5,6-trichlorocyclohexane

(4) 4-Bromo-2-chloro-4-methyl-2-nitrohexane

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Mathematics
Single Choice Question

Q61 Let A and B be two sets, then (A ∪ B)′ ∪ (A′ ∩ B) is equal to

a)    A′ b)    A c)    B′ d)    None of these

Q62 Two finite sets have m and n elements. The total number of subsets of the first set is
56 more than the total number of subsets of the second set. The values of m and n are
a)    7, 6 b)    6, 3 c)    5, 1 d)    8, 7

Q63 The value of cot 70° + 4 cos 70° is

a)    1 b)    √ –
3 c)    2√ –
3 d)    1

√3 2√ 3

Q64 If θ < x < π and cos x + sin x =

1
, then tan x is
2

a)    (4–√ 7)

b)    (4+√ 7)
– 3

c)    (1+√ 7)

d)    (1–√ 7)

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Q65
4

If x lies in second quadrant, then (

√ 1+sin x + √ 1–sin x

√ 1+sin x – √ 1–sin x
)  is equal to
a)    sin x
b)    tan  x
c)    sec  x
d)    cosec  x

2 2 2 2

Q66 The maximum value of cos (cos (cos (sin x))) for all x ∈ R is
a)    1 b)    cos 1 c)    cos (cos 1) d)    cos (cos (cos 1))

Q67 If sin (x) + sin2 (x) = 1 and λ = cos2 (x) + cos4 (x). Then 
λ+3
is equal to :
2–λ

a)    3 b)    4 c)    5 d)    2

Q68 If A + B + C = π and ∑cos A cosec B cosec C = k, then k is equal to

a)    √ –
2 b)    3 c)    2 d)    √ –
3

Q69 If a cos θ – b sin θ = c, then (a sin θ + b cos θ) equals to (given a2 + b2 > c2)
a)    a 2 + b 2 + c 2 b)    a 2 – 6 2 – c 2 c)    √−−
2
−−−−−
2
a + b + c
−− −
2 d) ± √− −
2
−−−−
2
a + b –c
−−−
2

  

Q70 The number of all possible triplets (a1, a2, a3) such that a1 + a2 cos 2x + a3 sin2 x = 0
holds for all x is –
a)    0 b)    1 c)    2 d)    Infinite

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Q71
n+1

Given, cos 2mθ cos 2m+1θ ..... cos 2nθ =  sin 2

n–m+1
θ
m
where 2mθ ≠ kπ, n, m ∈ I,
2 sin 2 θ

then  is equal to
 
a)    1
b)    1
c)    1
 sin  10
π
d)    √ 5–1
128 256 512
512
 sin  3π
10

Q72 If A > 0, B > 0 and A + B = π

6
, then the minimum positive value of (tan A + tan B), is
:
–
a)    √ –
3  –  √ 2

b)    4 – 2 √ –3

c)    2

√3

–
d)    2 – √ 3

Q73 Solution of inequatity log x

(x2 – 10x + 22) > 0 is -
log ( )
2
2

– –
a)    (– ∞ , 3) b)    (5 –√ 3, 3) ∪ (5 + √3 , 7)
–
c)    (0, 5– √3 ) ∪ (3, 4) d)    (7, ∞ )

Q74 The value of 'a' for which the equation ℓn (a ℓnx) = ℓnx has solution is-
a)    1 b)    1 c)    e d)    None of these

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Q75 If x =
e

2
logk b =  13  logbc =
2
e

4
logcd, then logkd is -
a)    6x 3 b)    2x 3 c)    12x 3 d)    None

Q76 If 2 sec 2α = tan β + cot β, then one of the values of (α + β) {where, (α + β) is not
odd multiple of π2 is
a)    π
b)    π
c)    π d)    3π

4 2
4

Q77 The general solution of the equation 2cos 2x + 1 = 3 ⋅ 2–sin x

2

a)    x =  nπ , n  ∈  I b)    x = (2n + 1) π , n  ∈  I
2 4

c)    x = (2n + 1) π3 , n ∈  I d)    None of these

–
Q78 If 1 + sin θ + sin2 θ + sin3 θ + .... ∞ =4+ 2√ 3 , 0 < θ < π, then
a)    θ  =  π b)    θ  =  π c)    θ  =  π  or  π d)    θ  =  π  or  2π
3 6 3 6 3 3

Q79 The general solution of the equation is (∀ n ∈ I)

a)    b)   

c)    d)   

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–
Q80 If cot x + cosec x = , then the value of which lies in [0, 2π) is
π
√3 (x– )
6

a)    π
b)    π
c)    π
d)    π

3 4 2 6

Numerical

Q81 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
Q82 A class has 175 students. The following data shows the number of students
opting for one or more subjects. Mathematics 100; Physics 70; Chemistry 40;
Mathematics and Physics 30; Mathematics and Chemistry 28; Physics and
Chemistry 23; Mathematics, Physics and Chemistry 18. How many students
have offered Mathematics alone?
Q83 In a class of 55 students, the number of students studying different subjects are 23 in
Mathematics, 24 in Physics, 19 in Chemistry, 12 in Mathematics and Physics, 9 in
Mathematics and Chemistry, 7 in Physics and Chemistry and 4 in all the three
subjects. The number of students who have taken exactly one subject is
Q84 (a, b) & (c, d) are solutions of simultaneous equation 5(logyx +logxy) = 26, xy = 64,
then a + b + c + d is equal to –
Q85 If 2 sin2 x – 3 sin x + 1 < 0, then number of solution(s) of the equation cos2 x – 3 cos
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Q86
x + 2 = 0 is/are
The number of real roots of equation (2 sec θ –1) (4 sec θ – 1) = 0 in [0, 2π] is/are
equal to
Q87 If cos 3x + cos 2x = sin
3x
+ sin
x
, 0, ≤ x ≤ 2π then the number of values of x
2 2

is/are
Q88 If sin x + cos4 y + 2 = 4 sin x cos y and 0 ≤ x, y ≤
π

2
, then value of (sin x + cos y) is
equal to
Q89
In any Δ ABC, always greater than

Q90 If A + B + C = π , then cos2 A + cos 2 B + cos2 C + 2 cos A cos B cos C is equal to

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

Ans. A C B B A C D B B C

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

Ans. A A C C B C B B D A

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

Ans. 6 84 4 20 7 7 3 26 8 30

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

Ans. C A B B A C C D D B

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

Ans. B D D C D C A A B A

Que. 51 52 53 54 55 56 57 58 59 60

Ans. 10 2 8 4 12 2 6 3 8 3

Que. 61 62 63 64 65 66 67 68 69 70

Ans. A B B B B C B C D D

Que. 71 72 73 74 75 76 77 78 79 80

Rankers Academy JEE

Ans.

Que.
B

81
B

82
D

83
C

84
D

85
A

86
A

87
D

88
A

89
D

90

Ans. 16 60 22 68 0 0 5 2 9 1

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