Vmc Booster Test With Solns
April 18, 2017 | Author: amogh kumar | Category: N/A
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7/7/2015
Question Revision
Question 1. A given function g(x) is defined as [A]
. The value of g(2) equals :
1
[B] [C] [D]
22010 2
Your Answer:
Correct Answer: D Explanation:
Question 2. If sec A tan B + sec B tan A = 91, then the value of (sec A sec B + tan A tan B) 2 is equal to : [A] [B] [C] [D]
8282 4141 8280 4041
Your Answer:
Correct Answer: A Explanation:
Question 3. If C1, C2, C3...... is sequence of circles such that Cn + 1 is the director circle of Cn. If the radius of C1 is a units, then the area bounded by the circle Cn and Cn + 1 is : http://www.vidyamandir.com/questionRevision.do?actionName=displayQuestionList&testIds=8ac8f545499972ab01499a0c257f3d5e&tName=JEE%202016%2…
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[A] [B] [C] [D]
None of these
Your Answer:
Correct Answer: C Explanation:
Question 4. If
are the roots of the equation
, then equation whose roots are
,
,
is : [A] [B] [C] [D] Your Answer:
Correct Answer: B Explanation:
Question 5. The maximum value of [A] [B] [C]
,
is :
1 + sin 1 cos 1 1 + cos 1
[D] Your Answer:
Correct Answer: A Explanation:
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Question 6. Consider the equation
where
. It is given that x 1, x 2 and x 1 x 2 are the real roots of the
equation. If b + c = 2(a + 1), then x 1x 2 is equal to : [A] [B] [C]
1 2
[D] Your Answer:
Correct Answer: B Explanation:
Question 7. If
are three values lying in
for which
, then
is equal to : [A] [B] [C] [D]
1 2 3 4
Your Answer:
Correct Answer: C Explanation:
Question 8. An even polynomial function f (x) satisfies a relation and
, then the value of
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is : [A] [B] [C] [D]
3 15 7 1
Your Answer:
Correct Answer: C Explanation:
Question 9. Let
be an even function for all
, then the sum of all
possible values of a is : (where [.] and {.} denote greatest integer function and fractional part functions, respectively) [A] [B] [C] [D]
17/6 53/6 31/3 35/3
Your Answer:
Correct Answer: D http://www.vidyamandir.com/questionRevision.do?actionName=displayQuestionList&testIds=8ac8f545499972ab01499a0c257f3d5e&tName=JEE%202016%2…
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Explanation:
Question 10. Let
. If x 1, x 2, x 3 are three distinct real numbers such that f (x 1) = f (x 2) = f (x 3) = 0, then
If
then g(x) is identically equal to : [A]
x
[B] [C] [D] Your Answer:
Correct Answer: B Explanation:
Question 11. Let
. If x 1, x 2, x 3 are three distinct real numbers such that f (x 1) = f (x 2) = f (x 3) = 0, then
If [A] [B]
then g (x) is identically equal to:
1 x
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[C]
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x2
[D] Your Answer:
Correct Answer: C Explanation:
Question 12. If line L intersects the sides BC, CA and AB of a triangle ABC at P, Q, R respectively, then
is equal to :
[A] [B] [C] [D]
1/2 1
Your Answer:
Correct Answer: A Explanation:
Question 13.
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The range of
where [.] denotes the greatest
integer function and n is a natural number is : [A]
[B]
[C]
[D]
Your Answer:
Correct Answer: D Explanation:
Question 14. A ray of light travels along the line
and strikes a plane mirror lying along the line
. The equation of the straight
line containing the reflected ray is : [A] [B] [C] [D] Your Answer:
Correct Answer: B Explanation:
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Question 15. Two points P and Q are taken on the line joining the points A(0, 0) and B(3a, 0) such that AP = PQ = QB. Circles are drawn on AP, PQ and QB as diameters. The locus of the point S, the sum of the squares of the lengths of the tangents from which to the three circles is equal to b2, is : [A] [B] [C] [D] Your Answer:
Correct Answer: B Explanation:
Question 16. If
and
, then :
[A] [B] [C] [D] Your Answer:
Correct Answer: B Explanation:
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Question 17. If
, then
[Hint: You may use
[A] [B] [C]
(where
, is equal to :
]
1 x0
[D] Your Answer:
Correct Answer: C Explanation:
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Question 18. Two circles are such that one is inscribed in and the other is circumscribed about a square A1A2A3A4. If the length of each side of the square is a units and P, Q are two points respectively on these circles, then
equals :
[A]
[B] [C] [D]
a2 2a2
Your Answer:
Correct Answer: C Explanation:
Question 19. If [x] and {x} represent integral and fractional part of x, then the function defined by [A] [B] [C] [D]
is :
2[ x ] + {x} 4 x x 4[x] + 1000 {x}
Your Answer:
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Correct Answer: C Explanation:
Question 20. If ax = bc, by = ca, c z = ab, then the value of [A] [B] [C] [D]
is :
2 10 1 3
Your Answer:
Correct Answer: A Explanation:
Question 21. For each natural number k, let Ck denote the circle with radius k cm and centre at the origin, on the circle Ck a particle moves k cm in the anticlockwise direction. After completing its motion on Ck , the particle movies to Ck +1 in the radial direction. The motion of the particle continues in this manner. The particle starts at (1, 0). If the particle cross the positive direction of Xaxis for the first time on the circle Cn, then n is greater than : [A] [B] [C] [D]
4 5 6 7
Your Answer:
Correct Answer: A , B , C Explanation:
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Question 22. are the roots of equation ax 2 + 2hx + b = 0. While b1 = 0. If C and D divides AB in the ratio of [A] [B] [C]
2 0
[D]
Independent of a, b, h, a1, b1,h1
Your Answer:
respectively and also ab1, hh1, a1b are in A.P., then
are those of a1x 2 + 2h1x + is equal to :
Correct Answer: B , C , D Explanation:
Question 23. In a right angled triangle, the length of the sides are a and b (where 0 bp bp In general, as the number of lone pair of electrons on central atom increases, value of bond angle from normal bond angle also increases The number of lone pair on O in H2O is 2 while on N in NH3 is 1.
[D]
In cumulated diene,
Your Answer:
; there are 2 sp2, 1 sp and 1 sp3 hybrid carbon atoms
Correct Answer: A , C , D Explanation: NA
Question 51. An elastic ball strikes a moving elevator with a velocity v. if the elevator has a speed v, the maximum height attained by the ball after the collision measured from the point of collision is:
[A]
[B]
[C]
[D]
Your Answer:
Correct Answer: D Explanation: Vsep = eVapp V1 v = 2v V1 = 3v Hence height w.r.t point of collision
Question 52. The acceleration of a particle varies with time as
speed of the particle at t = 4sec, if the particle was moving along + ve xaxis
with a speed of 4 m/s at t = 0 sec [A] [B] [C] [D]
28 26 30 24
Your Answer:
Correct Answer: D Explanation:
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Question 53. Block A of mass m and block B of mass M are connected by a massless spring over a pulley on a rough plane with coefficient of friction as force F is applied on block A to the left. Find the minimum value of M to move the block A towards right:
. A
[A]
[B]
[C]
[D] Your Answer:
Correct Answer: A Explanation:
Question 54. In the figure shown two blocks of equal mass m = 10 kg attached to the two ends of a light spring of spring constant K = 100 N/m. Both the blocks are placed over a rough horizontal fixed surface.
At certain instant of time A and B have velocities V1 = 10 m/s towards left and V2 = 20 m/s towards right respectively as shown. If the coefficient of friction between A and ground is instant is:
between 'B' and ground is
then the acceleration of center of mass of the system at that
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[A] [B] [C] [D]
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2 m/s 2 towards left
2 m/s 2 towards left 2 m/s 2 towards left 1 m/s 2 towards right
Your Answer:
Correct Answer: B Explanation: Net force = acm = 1m/s 2
Question 55. A small block enters the top A of the circular path with a horizontal velocity
and gathers speed as it moves down the path. Here g is
the acceleration due to gravity and r is the radius of circular segment. The block leaves the surface at point C. Neglect friction and treat the block as a particle. The angle in the figure is :
[A] [B] [C] [D]
cos 1 (4/9) cos 1 (3/4) cos 1 (1/2) cos 1 (5/6)
Your Answer:
Correct Answer: D Explanation:
Question 56. A particle is moving in a circular path of constant radius r such that its centripetal acceleration is varying with time t, and is proportional to rt2. The power delivered to the particle by the force acting on it will be proportional to : [A] [B] [C] [D]
rt2 rt r 2t r/t
Your Answer:
Correct Answer: C Explanation:
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Question 57. From the uniform circular disc of radius 4 R, three small disc of radius R are cut off. The position vector centre of mass of the new structure will be: (Centre of lower circular cavity lies on xaxis and centre of upper and lower circular cavities lies on yaxis. The centre of each cavity is at distance 3R from centre of disc of radius 4R)
[A] [B] [C] [D] Your Answer:
Correct Answer: C Explanation:
Question 58. A uniform chain of mass m and length l hangs from a hook. Determine the amount of work required to raise the middle link to the hook. [A]
[B]
[C]
[D] Your Answer:
Correct Answer: B Explanation:
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Work done
Question 59. Block A and B each of mass 1 kg are moving with 4 m/sec and 2m/sec respectively as shown. The coefficient of friction for all surface is 0.10. Find the distance by which centre of mass will travel before coming to rest (in m) :
[A] [B] [C] [D]
1 2 4 3
Your Answer:
Correct Answer: D Explanation: acm till 2nd sec = 0 Hence distance After 2nd sec to 4th sec distance by A = 2m Hence COM = 1m Hence = 3m
Question 60. Sphere A is thrown up with velocity 20 m/sec from the ground. Sphere B of same mass in just dropped from a height of 80 m simultaneously at time t = 0 so that both collide in air and suck together. Find the time (in second) after which combined mass will fall to the ground (Calculated from t = 0) (g = 10 m/s 2).
[A] [B] [C] [D]
1 4 6 2
Your Answer:
Correct Answer: B Explanation: NA
Question 61. In the figure shown, a small ring of mass m and a small object of the same mass m are tied to the ends of a light inextensible string of length L = 4m. The ring can slide along a fixed horizontal smooth rod. The string is initially vertical and the object is at its lowest position. Now a horizontal velocity
is given to the object parallel to the rod. Find the maximum height (In metre) attained by the object from initial position :
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[A] [B] [C] [D]
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1m 2m 7m 4m
Your Answer:
Correct Answer: A Explanation:
As
Hence 1m
Question 62. A block A having a mass MA = 5 kg is released from rest at the position P shown and slides freely down the smooth fixed inclined ramp. When it reaches the bottom of the ramp it slides horizontally onto the surface of a cart of mass mc = 5 kg for which the coefficient of friction between the cart and the box is be the initial height of A, determine the position 'x' of the box on the card after it comes to rest relative to cart. (The cart moves on smooth horizontal surface) write x in cm. (Take g = 10 m/s 2)
[A] [B] [C] [D]
x = 150 cm x = 250 cm x = 100 cm x = 300 cm
Your Answer:
Correct Answer: C Explanation:
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The speed of an train increase at a constant rate from zero to v and then remains constant for an interval and finally decreases to zero at a constant rate The total distance travelled by the train is l. The time taken to complete the journey is t. Then : [A]
[B]
[C]
t is minimum when
[D]
t is minimum when
Your Answer:
Correct Answer: B Explanation:
Question 64. A particle is projected at an angle move with speed
with speed
m/s, from the point A, as shown in the figure. At the same time the wedge is made to
m/s towards right as shown in the figure.
Then the time after which particle will strike will wedge is :
[A]
2 s
[B] [C] [D]
None of these
Your Answer:
Correct Answer: A Explanation:
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Question 65. A sphere of radius R is an contact with a wedge. The point of contact is velocity of
from the ground as shown in the figure. Wedge is moving with
towards left then the velocity of the sphere at this instant will be :
[A] [B] [C] [D] Your Answer:
Correct Answer: B Explanation:
Question 66. Two beads A and B move along a semicircular wire frame as shown in figure. The beads are connected by an inelastic string which always remains tight. At an instant the speed of A is u, and where O is the centre of the semicircular arc. The speed of bead B at that instant is :
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[A] [B] [C]
[D]
Your Answer:
Correct Answer: A Explanation:
Question 67. A smooth chain AB of mass m rests against a surface in the form of a quarter of circle of radius R. If it is released from rest, the velocity of the chain after it comes over the horizontal part of the surface is :
[A] [B] [C] [D] Your Answer:
Correct Answer: C Explanation:
Question 68. A block of mass m is connected to a spring of force constant k. Initially the block is at rest and the spring has natural length. A constant force F is applied horizontally towards right. The maximum speed of the block will be (there is no friction between block and the surface) http://www.vidyamandir.com/questionRevision.do?actionName=displayQuestionList&testIds=8ac8f545499972ab01499a0c257f3d5e&tName=JEE%202016%…
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[A]
[B]
[C]
[D] Your Answer:
Correct Answer: B Explanation:
Question 69. n elastic balls are placed at rest on a smooth horizontal plane which is circular at the ends with radius r as shown in the figure. The masses of the respectively. What is the minimum velocity which should be imparted to the first ball of mass m such that nth
balls are m, ball completes the vertical circle :
[A]
[B]
[C]
[D]
Your Answer:
Correct Answer: A Explanation: Velocity of nth ball =
(To just complete the circle)
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A chain of length l and mass m lies in a pile on the floor. If its end A is raised vertically at a constant speed v 0, the magnitude of the force P applied to end A terms of the length y of chain which is off the floor at any given instant.
[A]
[B]
[C] [D]
None of these
Your Answer:
Correct Answer: A Explanation: Force applied
Question 71. When a chain is lowered onto the ground such that it will be heaped: [A] [B] [C] [D]
The fallen part does not experience reaction force due to the falling part The falling part does not experience reaction force due to the fallen part The fallen part experiences reaction force due to the falling part The reaction force offered by ground must be lesser than the weight of the chain
Your Answer:
Correct Answer: B , C Explanation: NA
Question 72. A block of mass m is pulled by an external agent by an inextensible string with velocity v and acceleration a at point P as shown in the figure then at this instant :
[A]
Kinetic energy of the block is
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[B] [C] [D]
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Power delivered by the external agent is Total power delivered by the string is zero Work done by the string on the block is nonzero
Your Answer:
Correct Answer: A , B , C , D Explanation: Velocity of block will be = V/5 and acceleration of block will be = a/5
Question 73. A bob of a simple pendulum of mass m rests on the inclined plane of a wedge. If the wedge moves with a velocity v and acceleration a, disregarding friction at each surface:
[A]
Tension in the string is
[B]
Acceleration of the bob is
[C]
Tension in the string is greater than
[D]
Normal reaction on the wedge due to the bob is
Your Answer:
Correct Answer: C , D Explanation:
Question 74. A horizontal force F pushes a wedge of mass M on a smooth horizontal surface. A block of mass m is stationary relative to the wedge, then:
[A]
Friction force is equal to mg between M and m
[B]
Minimum coefficient of friction between M and m is
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[C]
Minimum force required to prevent relative sliding between M and m is
[D]
The reaction between M and m is
Your Answer:
Correct Answer: A , B , C Explanation:
Acceleration of both the blocks should be same for no slipping. Reaction between M & m vector sum of f and N
Question 75. Choose the correct statement(s) of the following: [A] [B] [C] [D]
Force acting on a particle for equal time intervals can produce the same change in momentum but different change in kinetic energy Force acting on a particle for equal displacement can produce the same change in kinetic energy but different change in momentum Force acting on a particle for equal time intervals can produce different change in momentum but the same change in kinetic energy Force acting on a particle for equal displacement can produce different change in kinetic energy but the same change in momentum
Your Answer:
Correct Answer: A , B Explanation: NA
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