JEE Questions for Maths Miscellaneous Quiz 12

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127
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247
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186
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313

If the velocity of a particle moving in a straight line is given by v² = se^s, then its acceleration is

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2)
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0%

The position at any time t, of a particle moving along x-axis is given by the relation s = t³ – 9t² + 24t + 6, where s denotes the distance in metre from the origin. The velocity v of the particle at the instant when the acceleration becomes zero, is given by

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v = 3
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v = –3
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v =
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v = –6

If the law of motion of a particle moving in a straight line is given by ks = log(1/v) then its acceleration a is given by

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2)
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None of these

The law of motion of a particle moving in a straight line is given by s = 1/2 vt, where v is the velocity at time t and s is the distance covered. Then acceleration is

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A function of
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A function of s
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A function of v
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Constant

If the displacement of a particle varies with time as √x = t + 7, then
(a) The velocity of the particle is inversely proportional to t
(b) The velocity of the particle is proportional to t
(c) The velocity of the particle is proportional to
(d) The particle moves with a constant acceleration

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b and d
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a only
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d only
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a only

The x and y displacement of a particle in the xy-plane at any instant are given by x = at² and y = 2at, where a is a constant. The velocity of the particle at any instant is given by

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2)
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A particle moves in a straight line with a velocity given by dx/dt = x + 1. The time taken by the particle to traverse a distance of 99 metres is

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2)
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A particle is moving in a straight line with uniform acceleration covers d₁ and d₂ in t₁ and t₂ sec. Then the acceleration is

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2)
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0%

If a particle has two velocities each equal to u in magnitude and their resultant is also of magnitude u, then the angle between the two velocities is

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60o
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300o
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900o
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1200o

If two velocities u and v are inclined at such an angle that the resultant of 2u and v inclined at the same angle is at right angle to v, then the resultant of u and V is of magnitude

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2u
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v
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2v
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u

If a particle having simultaneous velocities 3 m/sec, 5 m/sec. and 7 m/sec. at rest, then the angle between the first two velocities is

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120o
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150o
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60o
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90o

The greatest and least magnitudes of the resultants of two velocities of constant magnitudes are ii and v respectively. If a particle has these velocities inclined at an angle 2a, then the resultant velocity is of magnitude

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2)
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None of these

If the distance S covered by a particle in time t is proportional to the cube root of its velocity, then the acceleration is

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A constant
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2)
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The average speed of a bicycle over a journey of 20 km; if it travels the first 10 km at 15 km/hr and the second 10 km at 10 km/hr, is

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12 km/hr
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10 km/hr
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15 km/hr
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None of these

If OP makes 4 revolutions in one second, the angular velocity in radians per second is

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2)
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0%

A velocity 1/4 m/s is resolved into two components along OA and OB making angles 30^o and 45° respectively with the given velocity, then the components along OB is

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2)
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0%

Two straight railways converge to a level crossing at an angle x and two trains are moving towards the crossing with velocities u and v. If a and b are the initial distances of the trains from the crossing, the least distance between them will be after time t given by

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2)
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None of these

The velocity v of a particle is at any time related to the distance travelled by the particle by the relation v = as + b, where a > 0 and b ≤ a/2. Which of the following statements will be true for this motion (Given s = 0 when t = 0)?

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The particle will experience a retardation if b > 0
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The particle will be at rest at t = 0
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The motion of the particle is under constant acceleration

A particle moving in a straight line is subject to a resistance which produces a retardation kv³, where v is the velocity and k is a constant. lits is the initial velocity of the particle, then

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2)
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0%

A particle moves towards east from a point A to a point B at the rate of 4 km/h and then towards north from B to C at the rate of 5 km/h. If AR = 12 km and BD 5 km, then its average speed for its journey from A to C and resultant average velocity direct from A to C are respectively

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2)
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0%

A particle of mass m is projected from a fixed point 0 into the air with velocity u in a direction making an angle x with the horizontal. Then the motion of the particle describes a parabola with the latus rectum is

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2)
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0%

Given that the force acting on a material point is inversely proportional to the velocity of the moving point. Then the K.E. of the point is a function of time

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Exponential
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Linear
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Second degree
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Non-linear

A man crosses a 320 m wide river perpendicular to the current in 4 minutes. If in still water he can swim with a speed 5/3 times that of the current then the speed of the current in m/mm is

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30
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40
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50
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60

A train of length 200 rn travelling at 30 rn/sec overtakes another of length 300 m travelling at 20 rn/sec. The time taken by the first tram to pass the second is

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30 sec
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50 sec
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10 sec
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40 sec

A train A is moving towards east with a velocity of 30 km/h and another train B is moving on parallel lines towards west with a speed of 40 km/h. The velocity of train A relative to train B is

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10 km/h
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70 km/h towards eas
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70 km/h towards west
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None of these

A car is travelling at a velocity of 10 km/h on a straight road. The driver of the car throws a parcel with a velocity of 10√2 km/hr when the car is passing by a man standing on the side of the road. lithe parcel is to reach the man, the direction of throw makes the following angle with the direction of the car

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2)
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0%

A ship is moving with velocity 12 km/hr in east direction and another ship is moving with velocity 16 km/hr in north direction. The relative velocity of second ship with respect to first ship will b

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20 km/hr
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22 km/hr
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18 km/h
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20√2 km/h

A man is walking towards north with speed 4.5 km/hr. Another man is running towards west with speed 6 km/h. The magnitude and direction of the relative velocity of the second with respect to first is

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0%
2)
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7.5 km/hr south-west
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None of these

Two cars A and B are moving uniformly on two straight roads at right angles to one another at 40 and 20 km/hr respectively. A passes the intersection of the road when B has still to move 50 km to reach it. The shortest distance between the two cars and the time when they are closest arc

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20√2 km, 30 minutes
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20 km, 10 minutes
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20 km, 20 minutes
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None of these

A person travelling towards eastwards at the rate of 4 km/hr finds that the wind seems to blow directly from the north. On doubling his speed it appears to come from north-east. ‘[he velocity and direction of the wind are

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0%
2)
0%
0%
None of these

If a moving particle has two equal velocities inclined at an angle 2α such that their resultant velocity is twice as great as when they are inclined at an angle 2β, then

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2)
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0%

The speed of a boat in a river is u m/sec and that of the current is v m/sec. The boat traverse a distance of d metres down the stream and then comes back to its original position. The average speed of the boat for to and from journey is

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2)
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0%

A 30 m wide canal is flowing at the rate of 20 m/min. A man can swim at the rate of 25 m/min. in still water. The time taken by him to cross the canal perpendicular to the flow is

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1.0 min
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1.5 min
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2.0 min
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2.5 min

If a particle moves in a straight line with uniform acceleration, the distance traversed by it in consecutive seconds are in

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A.P.
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G.P.
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H.P.
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None of these

If a point moves with constant acceleration from A to B in the straight line AB has velocities ii and v at A and B respectively, then the velocity at C, the mid-point of AB is

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2)
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None of these

A particle is moving in a straight line with initial velocity u and uniform acceleration f. If the sum of the distances travelled in tth and (t + 1)th seconds is 100 cm, then its velocity after t seconds, in cm/sec. is

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20
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30
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50
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80

A point moves from rest with constant acceleration. If it covered part of its total distance in its last second of 25 motion, then upto what time is travelled

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5 sec
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2)
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(a) and (b) both are true
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A body starts from rest and moves in a straight line with uniform acceleration F, the distances covered by it in second, fourth and eighth seconds are

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In arithmetic progression
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In geometrical progression
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In the ratio 1 : 3 : 7
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In the ratio 3 :7 : 15

A bullet of mass 0.05 kg travelling at 120 metres/sec penetrates deeply into a fixed target and is brought to rest in 0.01 sec. The distance through which it penetrates the target

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3cm
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6cm
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30 cm
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60 cm

A person travelling on a straight line moves with uniform velocity v₁ for some time and with uniform velocity v₂ for the next equal time. The average velocity p is given by

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2)
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0%

A particle starts with a velocity of 200 cm/sec and moves in a straight line with a retardation of 10 cm/sec². Then the time it takes to describe 1500 cm is

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10 sec, 30 sec
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5 see, 15 sec
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10 sec
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30 sec

A bullet moving at 100 m/sec is fired into a wood-block in which it penetrates 50 cm. If the same bullet moving with the same velocity were fired into a similar piece of wood but only 12.5 cm thick, then the velocity with which it emerges is

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0%
2)
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None of these

Two points A and B move from rest along a straight line with constant acceleration f and f\' respectively. If A takes m sec more than B and describes n unit more than B in acquiring the same speed, then

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2)
0%
0%

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(0, 2)
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(4.8, 0)
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(0, 3)
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None of these

A lizard, at an initial distance of 21 cm behind an insect, moves from rest with an acceleration of 2 cm/s² and pursues the insect which is crawling uniformly along a straight line at a speed of 20 cm/s. Then the lizard will catch the insect afte

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21 sec
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24 sec
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20 sec
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1 sec

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2)
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0%

If a particle is thrown vertically upwards with a velocity of u cm/sec under gravity, then the time for the particle to come to earth again is

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2)
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None of these

If a particle is projected vertically upwards and is at a height t₁ after seconds and again after t₂ seconds, then h

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2)
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0%

A house has multi-storeys. The lowest storey is 20 ft high. A stone which is dropped from the top of the house passes the lowest storey in sec. The height of the house is

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100 ft
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110 ft
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110.25 ft
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None of these

JEE Questions for Maths Miscellaneous Quiz 12 - MCQExams.com

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Practice Maths Quiz Questions and Answers

JEE Questions for Maths Miscellaneous Quiz 12 - MCQExams.com

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Practice Maths Quiz Questions and Answers

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