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TEST - 1 TARGET : JEE (IITs) 2014 Date : 14-02-2013

COURSE CODE : CLINIC CLASSES VIKAAS(JA) & VIPUL(JB) Duration : 1 Hour

Max. Marks : 80

Please read the instructions carefully. You are allotted 5 minutes specifically for this purpose.

Physics - Rectilinear Motion, Projectile motion INSTRUCTIONS 2.

No additional sheets will be provided for rough work.

3.

Blank paper, clipboard, log tables, slide rules, calculators, cellular phones, pagers and electronic gadgets in any form are not allowed.

4.

The answer sheet, a machine-gradable Objective Response Sheet (ORS), is provided separately.

5.

Do not Tamper / mutilate the ORS or this booklet.

6.

Do not break the seals of the question-paper booklet before instructed to do so by the invigilators.

7.

Write your Name, Roll No. and Sign in the space provide on the back page of this booklet.

B. Filling the bottom-half of the ORS : Use only Black ball point pen only for filling the ORS. Do not use Gel / Ink / Felt pen as it might smudge the ORS. 8.

Write your Roll no. in the boxes given at the top left corner of your ORS with black ball point pen. Also, darken the corresponding bubbles with Black ball point pen only. Also fill your roll no on the back side of your ORS in the space provided (if the ORS is both side printed).

9.

Fill your Paper Code as mentioned on the Test Paper and darken the corresponding bubble with Black ball point pen.

10. If student does not fill his/her roll no. and paper code correctly and properly, then his/her marks will not be displayed and 5 marks will be deducted (paper wise) from the total. 11. Since it is not possible to erase and correct pen filled bubble, you are advised to be extremely careful while darken the bubble corresponding to your answer. 12. Neither try to erase / rub / scratch the option nor make the Cross (X) mark on the option once filled. Do not scribble, smudge, cut, tear, or wrinkle the ORS. Do not put any stray marks or whitener anywhere on the ORS. 13. If there is any discrepancy between the written data and the bubbled data in your ORS, the bubbled data will be taken as final. C. Question paper format and Marking scheme : 14. The question paper consists of 1 parts. The part consists of Two Sections. 15. For each question in Section–I, you will be awarded 3 marks if you darken the bubble(s) corresponding to the correct choice for the answer and zero mark if no bubbled is darkened. In case of bubbling of incorrect answer, minus one (–1) mark will be awarded. 16. For each question in Section–II, you will be awarded 5 marks if you darken the bubble corresponding to the correct answer and zero marks if no bubble is darkened. In case of bubbling of incorrect answer, minus one (–1) mark will be awarded.

DO NOT BREAK THE SEALS WITHOUT BEING INSTRUCTED TO DO SO BY THE INVIGILATOR

A. General : 1. This Question Paper contains 22 questions.

PHYSICS

PART I : PHYSICS SECTION - I Straight Objective Type This section contains 15 multiple choice questions. Each question has choices (A), (B), (C), and (D) out of which ONLY ONE is correct. 1.

A particle moves along a path ABCD as shown in the figure. Then the magnitude of net displacement of the particle from position A to D is : (A) 10 m (B) 5 2 m (C) 9 m (D) 7 2 m

2.

A particle starts from rest with uniform acceleration a. Its velocity after ‘n’ second is ‘v’. The displacement of the body in the last two second is (A)

2v (n 1) n

(B)

v (n 1) n

(C)

v (n 1) n

(D)

2v (2n 1) n

3.

The displacement of a particle moving in a straight line is given by x = 16t – 2t2 (where, x is in metres and t is in second). Find the distance travelled by the particle in 8 seconds [starting from t = 0] is : (A) 24 m (B) 40 m (C) 64 m (D) 80 m

4.

Two objects moving along the same straight line are leaving point A with an acceleration a, 2 a & velocity 2 u, u respectively at time t = 0. The distance moved by the object with respect to point A when one object overtakes the other is : (A)

6u2 a

(B)

2u 2 a

(C)

4u2 a

(D) none of these

Space for Rough Work

RESONANCE

JA&JBTEST140213C0-2

PHYSICS

5.

A truck travelling due north at 50 km/hr turns west and travels at the same speed. What is the change in magnitude of velocity. (A) 50 2

6.

(B) 50

(C) 0

(D) None of these

A football is rolling down a hill of unknown shape. The speed of the football at different times is noted as given below (Football always remains in contact with hill) : Time 0 sec 1 sec 2 sec 3 sec 4 sec

Instantaneous speed 0 4m/s 8 m/s 16 m/s 24 m/s

The correct shape of the hill is depicted in :

(A)

7.

(B)

(C)

(D)

A frictionless wire is fixed between A and B inside a sphere of radius R. A bead slips along the wire. The time taken by the ball to slip from A to B will be (A) 2 R / g

(C)

2 gR g cos

(B) gR / g cos (D)

2 gR cos g

Space for Rough Work

RESONANCE

JA&JBTEST140213C0-3

PHYSICS

8.

A particle is thrown upwards from ground. It experiences a constant air resistance force which can produce a retardation of 2 m/s2 . The ratio of time of ascent to the time of descent is : [ g = 10 m/s2 ] (A) 1 : 1

9.

2 3

(C)

2 3

(D)

3 2

Initially car A is 10.5 m ahead of car B. Both start moving at time t = 0 in the same direction along a straight line. The velocity time graph of two cars is shown in figure. The time when the car B will catch the car A, will be

(A) t = 21 sec 10.

(B)

(B) t = 2 5 sec

(C) 20 sec.

(D) None of these

Position (Km) - Time (min.) graph is shown for two cars ‘A’ and ‘B’. Both collide at time t = 150 minute. Then the distance of position ‘R’ of accident from the starting point ‘Q’ of car A will be. (Initial distance between the two cars is 500 km) (Position in the graph shows the distance of the two cars from the point ‘Q’) -

(A) 200 km

(B) 300 km

(C) 250 km

(D) 400 km

Space for Rough Work

RESONANCE

JA&JBTEST140213C0-4

PHYSICS

11.

Three particles are projected from a tower on inclined plane with same speed u as shown in figure. Mark the correct option : (A) A will collide the inclined plane with more speed than B and C (B) A will collide the inclined plane with more speed than A and C (C) C will collide the inclined plane with more sped than A and B (D) All will collide the inclined plane with same speed

12.

CE and DF are two walls of equal height (20 meter) from which two particles A and B of same mass are projected as shown in the figure. A is projected horizontally towards left while B is projected at an angle 370 (with horizontal towards left) with velocity 15 m/sec. If A always sees B to be moving perpendicular to EF, then the range of A on ground is :

(A) 24 m

13.

(C) 26 m

(D) 28 m

A particle travels according to the equation x = at3, y = bt3. The equation of the trajectory is (A) y

14.

(B) 30 m

ax 2 b

(B) y

bx 2 a

(C) y

bx a

(D) y

bx 3 a

The maximum height attained by a projectile thrown over a horizontal ground is increased by 5%, keeping the angle of projection constant. What is the percentage increase in the horizontal range? (A) 20% (B) 15% (C) 10% (D) 5%

Space for Rough Work

RESONANCE

JA&JBTEST140213C0-5

PHYSICS

15.

A particle is projected from surface of the inclined plane with speed u and at an angle with the horizontal. After some time the particle collides elastically with the smooth fixed inclined plane for the first time and subsequently moves in vertical direction. Starting from projection, find the time taken by the particle to reach maximum height. (Neglect time of collision). (A)

2u cos g

(B)

2u sin g

(C)

u (sin cos ) g

2u (D) g

SECTION - II Multiple Correct Answers Type This section contains 7 multiple correct answer(s) type questions. Each question has 4 choices (A), (B), (C) and (D), out of which ONE OR MORE is/are correct. 16.

A particle moves with constant speed v along a regular hexagon ABCDEF in the same order. Then the magnitude of the average velocity for its motion from A to : (A) F is

17.

v 5

(B) D is

v 3

(C) C is

v 3 2

(D) B is v.

A particle moves along a straight line and its velocity depends on time 't' as v = 4t – t2. Here v is in m/sec. and t is in second. Then for the first 5 seconds : (A) Magnitude of average velocity is

(C) Average speed is

11 m/s 5

5 m/s 3

(B) Average speed is

13 m/s 5

(D) Average acceleration is – 1m/s2|

Space for Rough Work

RESONANCE

JA&JBTEST140213C0-6

PHYSICS

18.

A ball is projected horizontally from top of a 80 m deep well with velocity 10 m/s. Then particle will fall on the bottom at a distance of (all the collisions with the wall are elastic) : 10m/s

80m

A

B 7m

(A) 5 m from A

(B) 5 m from B

(C) 2 m from A

(D) 2 m from B

19.

A particle is projected on a smooth fixed incline plane. Initial velocity of particle is along inclined and at an angle 53º with horizontal line AB. Then: [g = 10 m/s2] (A) minimum speed of particle during it's motion on inclined is 15 m/s (B) maximum height of particle from ground is 30 m (C) particle returns back to line AB after 5 sec. (D) Range of particle along line AB is 120 m

20.

Two particles are projected under gravity with speed 4m/s and 3m/s simultaneously from same point and at angles 53º and 37º with the horizontal surface respectively as shown in figure. Then :

(A) Their relative velocity is along vertical direction. (B) Their relative acceleration is non-zero and it is along vertical direction. (C) They will hit the surface simultaneously (D) Their relative velocity is constant and has magnitude 1.4 m/s. Space for Rough Work

RESONANCE

JA&JBTEST140213C0-7

PHYSICS

21.

A particle projected from O and moving freely under gravity strikes the horizontal plane passing through O at a distance R from starting point O as shown in the figure. Then: (A) there will be two angles of projection if Rg < u2 (B) the two possible angles of projection are complementary (C) the product of the possible times of flight from O to A is 2R/g (D) there will be more than two angles of projection if Rg = u2

22.

Two balls are thrown from an inclined plane at angle of projection with the plane one up the incline plane and other down the incline as shown in the figure. If R1 & R2 be their respective ranges, then:

(A) h1=h2

(B) R2 R1 = T 12

(C) R2 R1 = g sin T 22 (D) R2 R1 = g sin T 12 [ here T 1 & T 2 are times of flight in the two cases respectively ]

Space for Rough Work

RESONANCE

JA&JBTEST140213C0-8

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TEST - 1 TARGET : JEE (IITs) 2014 Date : 14-02-2013

COURSE CODE : CLINIC CLASSES VIKAAS(JA) & VIPUL(JB) Duration : 1 Hour

Max. Marks : 80

Please read the instructions carefully. You are allotted 5 minutes specifically for this purpose.

Physics - Rectilinear Motion, Projectile motion INSTRUCTIONS 2.

No additional sheets will be provided for rough work.

3.

Blank paper, clipboard, log tables, slide rules, calculators, cellular phones, pagers and electronic gadgets in any form are not allowed.

4.

The answer sheet, a machine-gradable Objective Response Sheet (ORS), is provided separately.

5.

Do not Tamper / mutilate the ORS or this booklet.

6.

Do not break the seals of the question-paper booklet before instructed to do so by the invigilators.

7.

Write your Name, Roll No. and Sign in the space provide on the back page of this booklet.

B. Filling the bottom-half of the ORS : Use only Black ball point pen only for filling the ORS. Do not use Gel / Ink / Felt pen as it might smudge the ORS. 8.

Write your Roll no. in the boxes given at the top left corner of your ORS with black ball point pen. Also, darken the corresponding bubbles with Black ball point pen only. Also fill your roll no on the back side of your ORS in the space provided (if the ORS is both side printed).

9.

Fill your Paper Code as mentioned on the Test Paper and darken the corresponding bubble with Black ball point pen.

10. If student does not fill his/her roll no. and paper code correctly and properly, then his/her marks will not be displayed and 5 marks will be deducted (paper wise) from the total. 11. Since it is not possible to erase and correct pen filled bubble, you are advised to be extremely careful while darken the bubble corresponding to your answer. 12. Neither try to erase / rub / scratch the option nor make the Cross (X) mark on the option once filled. Do not scribble, smudge, cut, tear, or wrinkle the ORS. Do not put any stray marks or whitener anywhere on the ORS. 13. If there is any discrepancy between the written data and the bubbled data in your ORS, the bubbled data will be taken as final. C. Question paper format and Marking scheme : 14. The question paper consists of 1 parts. The part consists of Two Sections. 15. For each question in Section–I, you will be awarded 3 marks if you darken the bubble(s) corresponding to the correct choice for the answer and zero mark if no bubbled is darkened. In case of bubbling of incorrect answer, minus one (–1) mark will be awarded. 16. For each question in Section–II, you will be awarded 5 marks if you darken the bubble corresponding to the correct answer and zero marks if no bubble is darkened. In case of bubbling of incorrect answer, minus one (–1) mark will be awarded.

DO NOT BREAK THE SEALS WITHOUT BEING INSTRUCTED TO DO SO BY THE INVIGILATOR

A. General : 1. This Question Paper contains 22 questions.

PHYSICS

PART I : PHYSICS SECTION - I Straight Objective Type This section contains 15 multiple choice questions. Each question has choices (A), (B), (C), and (D) out of which ONLY ONE is correct. 1.

A particle moves along a path ABCD as shown in the figure. Then the magnitude of net displacement of the particle from position A to D is : (A) 10 m (B) 5 2 m (C) 9 m (D) 7 2 m

2.

A particle starts from rest with uniform acceleration a. Its velocity after ‘n’ second is ‘v’. The displacement of the body in the last two second is (A)

2v (n 1) n

(B)

v (n 1) n

(C)

v (n 1) n

(D)

2v (2n 1) n

3.

The displacement of a particle moving in a straight line is given by x = 16t – 2t2 (where, x is in metres and t is in second). Find the distance travelled by the particle in 8 seconds [starting from t = 0] is : (A) 24 m (B) 40 m (C) 64 m (D) 80 m

4.

Two objects moving along the same straight line are leaving point A with an acceleration a, 2 a & velocity 2 u, u respectively at time t = 0. The distance moved by the object with respect to point A when one object overtakes the other is : (A)

6u2 a

(B)

2u 2 a

(C)

4u2 a

(D) none of these

Space for Rough Work

RESONANCE

JA&JBTEST140213C0-2

PHYSICS

5.

A truck travelling due north at 50 km/hr turns west and travels at the same speed. What is the change in magnitude of velocity. (A) 50 2

6.

(B) 50

(C) 0

(D) None of these

A football is rolling down a hill of unknown shape. The speed of the football at different times is noted as given below (Football always remains in contact with hill) : Time 0 sec 1 sec 2 sec 3 sec 4 sec

Instantaneous speed 0 4m/s 8 m/s 16 m/s 24 m/s

The correct shape of the hill is depicted in :

(A)

7.

(B)

(C)

(D)

A frictionless wire is fixed between A and B inside a sphere of radius R. A bead slips along the wire. The time taken by the ball to slip from A to B will be (A) 2 R / g

(C)

2 gR g cos

(B) gR / g cos (D)

2 gR cos g

Space for Rough Work

RESONANCE

JA&JBTEST140213C0-3

PHYSICS

8.

A particle is thrown upwards from ground. It experiences a constant air resistance force which can produce a retardation of 2 m/s2 . The ratio of time of ascent to the time of descent is : [ g = 10 m/s2 ] (A) 1 : 1

9.

2 3

(C)

2 3

(D)

3 2

Initially car A is 10.5 m ahead of car B. Both start moving at time t = 0 in the same direction along a straight line. The velocity time graph of two cars is shown in figure. The time when the car B will catch the car A, will be

(A) t = 21 sec 10.

(B)

(B) t = 2 5 sec

(C) 20 sec.

(D) None of these

Position (Km) - Time (min.) graph is shown for two cars ‘A’ and ‘B’. Both collide at time t = 150 minute. Then the distance of position ‘R’ of accident from the starting point ‘Q’ of car A will be. (Initial distance between the two cars is 500 km) (Position in the graph shows the distance of the two cars from the point ‘Q’) -

(A) 200 km

(B) 300 km

(C) 250 km

(D) 400 km

Space for Rough Work

RESONANCE

JA&JBTEST140213C0-4

PHYSICS

11.

Three particles are projected from a tower on inclined plane with same speed u as shown in figure. Mark the correct option : (A) A will collide the inclined plane with more speed than B and C (B) A will collide the inclined plane with more speed than A and C (C) C will collide the inclined plane with more sped than A and B (D) All will collide the inclined plane with same speed

12.

CE and DF are two walls of equal height (20 meter) from which two particles A and B of same mass are projected as shown in the figure. A is projected horizontally towards left while B is projected at an angle 370 (with horizontal towards left) with velocity 15 m/sec. If A always sees B to be moving perpendicular to EF, then the range of A on ground is :

(A) 24 m

13.

(C) 26 m

(D) 28 m

A particle travels according to the equation x = at3, y = bt3. The equation of the trajectory is (A) y

14.

(B) 30 m

ax 2 b

(B) y

bx 2 a

(C) y

bx a

(D) y

bx 3 a

The maximum height attained by a projectile thrown over a horizontal ground is increased by 5%, keeping the angle of projection constant. What is the percentage increase in the horizontal range? (A) 20% (B) 15% (C) 10% (D) 5%

Space for Rough Work

RESONANCE

JA&JBTEST140213C0-5

PHYSICS

15.

A particle is projected from surface of the inclined plane with speed u and at an angle with the horizontal. After some time the particle collides elastically with the smooth fixed inclined plane for the first time and subsequently moves in vertical direction. Starting from projection, find the time taken by the particle to reach maximum height. (Neglect time of collision). (A)

2u cos g

(B)

2u sin g

(C)

u (sin cos ) g

2u (D) g

SECTION - II Multiple Correct Answers Type This section contains 7 multiple correct answer(s) type questions. Each question has 4 choices (A), (B), (C) and (D), out of which ONE OR MORE is/are correct. 16.

A particle moves with constant speed v along a regular hexagon ABCDEF in the same order. Then the magnitude of the average velocity for its motion from A to : (A) F is

17.

v 5

(B) D is

v 3

(C) C is

v 3 2

(D) B is v.

A particle moves along a straight line and its velocity depends on time 't' as v = 4t – t2. Here v is in m/sec. and t is in second. Then for the first 5 seconds : (A) Magnitude of average velocity is

(C) Average speed is

11 m/s 5

5 m/s 3

(B) Average speed is

13 m/s 5

(D) Average acceleration is – 1m/s2|

Space for Rough Work

RESONANCE

JA&JBTEST140213C0-6

PHYSICS

18.

A ball is projected horizontally from top of a 80 m deep well with velocity 10 m/s. Then particle will fall on the bottom at a distance of (all the collisions with the wall are elastic) : 10m/s

80m

A

B 7m

(A) 5 m from A

(B) 5 m from B

(C) 2 m from A

(D) 2 m from B

19.

A particle is projected on a smooth fixed incline plane. Initial velocity of particle is along inclined and at an angle 53º with horizontal line AB. Then: [g = 10 m/s2] (A) minimum speed of particle during it's motion on inclined is 15 m/s (B) maximum height of particle from ground is 30 m (C) particle returns back to line AB after 5 sec. (D) Range of particle along line AB is 120 m

20.

Two particles are projected under gravity with speed 4m/s and 3m/s simultaneously from same point and at angles 53º and 37º with the horizontal surface respectively as shown in figure. Then :

(A) Their relative velocity is along vertical direction. (B) Their relative acceleration is non-zero and it is along vertical direction. (C) They will hit the surface simultaneously (D) Their relative velocity is constant and has magnitude 1.4 m/s. Space for Rough Work

RESONANCE

JA&JBTEST140213C0-7

PHYSICS

21.

A particle projected from O and moving freely under gravity strikes the horizontal plane passing through O at a distance R from starting point O as shown in the figure. Then: (A) there will be two angles of projection if Rg < u2 (B) the two possible angles of projection are complementary (C) the product of the possible times of flight from O to A is 2R/g (D) there will be more than two angles of projection if Rg = u2

22.

Two balls are thrown from an inclined plane at angle of projection with the plane one up the incline plane and other down the incline as shown in the figure. If R1 & R2 be their respective ranges, then:

(A) h1=h2

(B) R2 R1 = T 12

(C) R2 R1 = g sin T 22 (D) R2 R1 = g sin T 12 [ here T 1 & T 2 are times of flight in the two cases respectively ]

Space for Rough Work

RESONANCE

JA&JBTEST140213C0-8

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