11th Science | JEE Main: Mathematics MCQs Book

16 Pages·2015·0.85 MB·English

Useful for all Agricultural, Medical, Pharma cy and Engineering Entrance Examinations
held across India.

STD XI Sci.
.

Triumph Physics

Based on Maharashtra Board Syllabus

Fourth Edition: October 2014

First Edition: July 2014

Salient Features

• Exhaustive subtopic wise coverage of MCQs

• Important formulae provided in each chapter

• Hints included for relevant questions

• Various competitive exam questions updated till the latest year
  • Includes solved MCQs from JEE (Main), AIPMT, CET 2014
  • Evaluation test provided at the end of each chapter

Solutions/hints to Evaluation Test available in downloadable PDF format at

www. targetpublications.org

Printed at: India Printing Works Mumbai
No part of this book may be reproduced or transmitted in any form or by any means, C.D. ROM/Audio Video Cassettes or electronic, mechanical
including photocopying; recording or by any information storage and retrieval system without permission in writing from the Publisher.

TEID : 770
Preface

“Std. XI: Sci. Triumph Physics” is a complete and thorough guide to prepare students for a competitive
level examination. The book will not only assist students with MCQs of Std. XI but will also help them to prepare for
JEE, AIPMT, CET and various other competitive examinations.
The content of this book is based on the Maharashtra State Board Syllabus. Formulae that form a vital part of
MCQ solving are provided in each chapter. Notes provide important information about the topic. Shortcuts provide
easy and less tedious solving methods. Mindbenders have been introduced to bridge the gap between a text book
topic and the student’s understanding of the same. A quick reference to the notes, shortcuts and mindbenders has been
provided wherever possible.
MCQs in each chapter are divided into three sections:
Classical Thinking: consists of straight forward questions including knowledge based questions.
Critical Thinking: consists of questions that require some understanding of the concept.
Competitive Thinking: consists of questions from various competitive examinations like JEE, AIPMT, CET, CPMT etc.
Hints have been provided to the MCQs which are broken down to the simplest form possible.
An Evaluation Test has been provided at the end of each chapter to assess the level of preparation of the
student on a competitive level.
An additional feature of pictorial representation of a topic is added to give the student a glimpse of various
interesting physics concept.
The journey to create a complete book is strewn with triumphs, failures and near misses. If you think we’ve
nearly missed something or want to applaud us for our triumphs, we’d love to hear from you.
Please write to us on : [email protected]

Best of luck to all the aspirants!

Yours faithfully
Authors

Sr. No. Topic Name Page No.
1 Measurements 1
2 Scalars and Vectors 28
3 Projectile Motion 55
4 Force 91
5 Friction in Solids and Liquids 126
6 Sound Waves 161
7 Thermal Expansion 184
8 Refraction of Light 218
9 Ray Optics 256
10 Electrostatics 284
11 Current Electricity 323
12 Magnetic Effect of Electric Current 356
13 Magnetism 382
14 Electromagnetic Waves 403
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Tar et Publications Pvt. Ltd. Chapter 01: Angle and It’s Measurement

01 
Angle and It’s Measurement

Syllabus

1.1 Directed angles and systems of
Roller coasters, all about the angles!
measurement of angles

1.2 Relation between degree
measure and radian measure

1.3 Length of an arc and area of
sector

Roller coasters are the best example, when we look

at the real life situation for measuring and drawing

the angles. It involves reading the angles of rises and

falls on roller coasters.

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Tar et Publications Pvt. Ltd. Std. XI : Triumph Maths

Formulae Shortcuts

1. Sexagesimal system (Degree measure): 1. The angle between two consecutive digits of a
i. 1 right angle = 90 degree (= 90°) π
clock = 30° = radians.
ii. 1° = 60 minutes (= 60′) 6

iii. 1′ = 60 seconds (= 60′′)
2. Angle moved by hour hand in one hour = 30°.

2. Relation between degree measure and
3. Angle moved by hour hand in one minute
radian measure:
°
⎛ π ⎞c = ⎛1⎞ .
i. 1° = ⎜ ⎟ = 0.01746 radian ⎜⎝2⎟⎠
⎝180⎠

(cid:68) 4. Angle moved by minute hand in one minute
⎛180⎞
ii. lc = = 57° 17′ 48′′(approx)
⎜ ⎟ = 6°.
⎝ π ⎠
⎛ πx ⎞c ⎛180y⎞(cid:68) 5. If the difference between measures of two
iii. x° = ⎜ ⎟ and yc = ⎜ ⎟ directed angles is an integral multiple of 360°,
⎝180⎠ ⎝ π ⎠
then the two directed angles are co−terminal
3. Length of an arc and area of sector: angles.
If in a circle of radius r an arc of length S
subtends an angle of θ radian at the centre, 24-hour clock

then S = r θ and

S arc
i. Angle in radian, θc = =
r radius
1
ii. Area of corresponding sector = r2θ.
2

1
i.e., Area = × r × s
2

4. The sum of interior angles of a polygon of n

sides = (n − 2) × 180°

= (n − 2) × π

5. Each interior angle of a regular polygon of n

⎛ 2⎞(cid:68) π(n−2)
sides = 180 ⎜1− ⎟ = radian
⎝ n⎠ n

6. In a regular polygon:
i. All the interior angles are equal
ii. All the exterior angles are equal
iii. All the sides are equal

iv. Sum of all the exterior angles is 360°

v. Each exterior angle

360°
=
numberofexteriorangles The angle between two numbers on the clock is
c
⎛π⎞
vi. Each interior angle
⎜ ⎟ .
⎝12⎠
=180°− exterior angle

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Tar et Publications Pvt. Ltd. Chapter 01: Angle and It’s Measurement

10. The minute hand rotates through an angle of
Classical Thinking
_______ in one minute.

(A) 6° (B) 30°
1.1 Directed angles and systems of
(C) 60° (D) 1°
measurement of angles

11. 45° 30′ is equal to
1. A radian is a
(A) terminal angle ⎛46⎞o
(A) 95° (B) ⎜ ⎟
(B) co-terminal angle ⎝ 2 ⎠
(C) quadrantal angle
⎛91⎞o
(D) constant angle (C) (D) 50°
⎜ ⎟
⎝ 2 ⎠
2. In circular system, the unit of measurement of
an angle is a 12. Minute hand of a clock gains _______ on hour
(A) degree (B) radian hand in one minute.
(C) minute (D) second (A) 5°30′ (B) 59°

(C) 5°50′ (D) 360°
3. If the initial ray and directed ray are opposite
rays, then directed angle formed is called as 13. Which of the following pairs of angles are not
(A) zero angle (B) straight angle coterminal?
(C) co-terminal angle (D) standard angle (A) 330°, − 60° (B) 405°, − 675°

(C) 1230°, − 930° (D) 450°, − 630°
4. The measure of quadrantal angles is an

integral multiple of
14. If the measure of an angle is 1105°, then it
(A) 360° (B) 180° will lie in
(C) 90° (D) 60° (A) 1st quadrant (B) 2nd quadrant

(C) 3rd quadrant (D) 4th quadrant
5. _____ part of one degree is called one minute.
⎛1⎞th 15. If the measures of angles of a quadrilateral are
(A) 60th (B)
⎜ ⎟ in the ratio 2 : 3 : 7 : 6, then their measures in
⎝6⎠
degrees will be
⎛ 1 ⎞th ⎛ 1 ⎞th (A) 20°, 40°, 60°, 80°
(C) (D)
⎜ ⎟ ⎜ ⎟
⎝30⎠ ⎝60⎠ (B) 40°, 60°, 80°, 100°

(C) 40°, 60°, 140°, 120°
6. If the terminal arm of a directed standard
(D) 40°, 60°, 160°, 120°
angle lies along any one of the co-ordinate
axes, then it is called 1.2 Relation between degree measure and
(A) co-terminal angle radian measure

(B) quadrantal angle
16. 240º is equal to
(C) zero angle
(D) constant angle (A) ⎛⎜⎜⎜⎝43π⎞⎠⎟⎟⎟c (B) ⎛⎜⎜⎜⎝34π⎞⎠⎟⎟⎟c
7. (74.87)° =
(A) 74°52′52′′ (B) 74°52′12′′ ⎛4π⎞′ ⎛3π⎞′′
(C) 74°12′52′′ (D) 74°0′52′′ (C) ⎜⎜⎜⎝ 3 ⎠⎟⎟⎟ (D) ⎜⎜⎜⎝ 4 ⎠⎟⎟⎟

8. If the angles of a triangle are in the ratio
17. The radian measure of an angle of –260° is
1 : 2 : 3, then the angles in degrees are
(A) 40°, 50°, 90° (B) 30°, 60°, 90° ⎛−13π⎞c ⎛−13π⎞c
(A) (B)
⎜ ⎟ ⎜ ⎟
(C) 35°, 45°, 90° (D) 20°, 70°, 90° ⎝ 12 ⎠ ⎝ 9 ⎠

9. An hour hand rotates through _______ in one ⎛−12π⎞c ⎛−26π⎞c
minute. (C) ⎜ ⎟ (D) ⎜ ⎟
⎝ 9 ⎠ ⎝ 9 ⎠
(cid:68) (cid:68)
⎛1⎞ ⎛1⎞
(A) (B) 18. Taking πc = 3.14159, 1c =
⎜ ⎟ ⎜ ⎟
⎝3⎠ ⎝2⎠ (A) 60° (B) 180°
(C) 30° (D) 6° (C) 57.3° (D) 0°

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2πc 26. If the radian measures of two angles of a
19. If xc = 340° and y° = − , then x and y is
3π 4π
5 triangle are , , then the radian measure
equal to 5 5
7πc of third angle is
(A) x = , y = 72° πc 2πc
9 (A) (B)
17πc 15 15
(B) x = , y = −72° πc 4πc
9 (C) (D)
9πc 5 15
(C) x = , y = −72°
7 27. The sum of two angles is 5πc and their
17πc difference is 60°. The angles in degrees are
(D) x = , y = −27°
(A) 400°, 480° (B) 340°, 420°
9
(C) 480°, 420° (D) 440°, 460°

20. – 37° 30′ =
1.3 Length of an arc and area of sector
5πc ⎛5π⎞c
(A) (B) –
⎜ ⎟ 28. The length of the arc subtended by an angle
24 ⎝24⎠
7π
7πc ⎛7π⎞c of radians on a circle of radius 20 cm is
(C) (D) –⎜ ⎟ 4
24 ⎝24⎠
80π

(A) cm (B) 35π cm
21. The radian measure of an angle of 75° is 7
5πc πc (C) 20π cm (D) 7π cm
(A) (B)
12 12 29. If two circular arcs of the same length subtend
4πc 7πc angles of 60° and 80° at their respective
(C) (D)
3 12 centres, then the ratio of their radii is

3 4
−19πc (A) (B)
22. is equal to 4 3
9
3 9
(A) −360° (B) −380° (C) (D)
2 16
(C) −340° (D) −300°

30. If the arcs of the same length of two circles
23. The exterior angle of a regular pentagon in
subtend 75° and 140° at the centre, then the
radian measure is
ratio of the radii of the circles is
πc 2πc
(A) (B) (A) 28:15 (B) 11:13
5 5
(C) 22:15 (D) 21:13

3πc 4πc
(C) (D) 31. An arc of a circle of radius 77 cm subtends an
5 5
angle of 10° at the centre. The length of the arc is
24. If the difference between two acute angles of a 121
(A) cm (B) 88 cm
2πc 9
right angled triangle is , then the angles in
5 (C) 111 cm (D) 77 cm

degrees are 32. The perimeter of a sector of a circle, of area
(A) 81°, 9° (B) 35°, 55° 36π sq.cm., is 28 cm. The area of sector is
(C) 20°, 40° (D) 50°, 30° equal to

(A) 12 sq.cm (B) 16 sq.cm
25. The measures of angles of a triangle are in the
(C) 48 sq.cm (D) 96 sq.cm
ratio 2 : 3 : 5. Their measures in radians are
πc 3πc πc πc 3πc πc 33. A pendulum 14 cm long oscillates through an
(A) , , (B) , ,
angle of 18°. The length of path described by
5 10 2 5 10 3
its extremity is
πc 5πc 3πc πc 3πc πc
(C) , , (D) , , (A) 4.6 cm (B) 4.4 mm
6 12 4 4 10 2
(C) 4.8 cm (D) 4.4 cm

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Tar et Publications Pvt. Ltd. Chapter 01: Angle and It’s Measurement

10. The radian measure of the interior angle of a
Critical Thinking
regular dodecagon is

5πc 3πc πc 4πc
1.1 Directed angles and systems of (A) (B) (C) (D)
measurement of angles 6 2 4 3

11. The radian measure of the interior angle of a
1. π radians = ______ right angles
regular heptagon is
1
(A) 0 (B) 1 (C) (D) 2 πc 3πc 5πc 7πc
2 (A) (B) (C) (D)

7 7 7 5
2. Angles with measure 45° and −315° are
(A) zero angles. (B) straight angles. 12. If the measures of angles of a quadrilateral are
(C) co-terminal angles. (D) standard angles. in the ratio 2 : 5 : 8 : 9, then their measures in

radians, will be
3. ____ is the largest unit in Sexagesimal system.
πc 5πc 3πc 3πc πc 5πc 2πc 2πc
(A) Degree (B) Radian (A) , , , (B) , , ,
(C) Minute (D) Second 6 12 2 4 3 12 3 5

πc 5πc 2πc 4πc πc 5πc 2πc 3πc
4. The measure of co-terminal angles always (C) , , , (D) , , ,
differ by an integral multiple of 6 12 3 3 6 12 3 4
(A) 90° (B) 180° 13. The difference between two acute angles of a
5 . T(Ch)e an2g7l0e° b etween minu(tDe )h an3d6 a0n°d hour hand right angled triangle is ⎛⎜⎜⎜⎝9π⎞⎠⎟⎟⎟c. The angles in
of a clock at 8:30 is
degrees are
(A) 80° (B) 75° (C) 60° (D) 105° (A) 50º, 30º (B) 25º, 45º

(C) 20º, 40º (D) 55º, 35º
6. The angle of measure −1560° lies in
(A) 1st quadrant (B) 2nd quadrant 14. If the sum of two angles is 1 radian and the
(C) 3rd quadrant (D) 4th quadrant difference between them is 1°, then the

smaller angle is
7. The angle between two hands of a clock at
quarter past one is ⎛90 1⎞ο ⎛90 1⎞ο
(A) − (B) +
⎜ ⎟ ⎜ ⎟
⎛ 1⎞ο ⎝ π 2⎠ ⎝ π 2⎠
(A) 60° (B) ⎜52 ⎟
⎝ 2⎠ ⎛180 ⎞ο ⎛180 ⎞ο
(C) −1 (D) +1
⎜ ⎟ ⎜ ⎟
⎛π⎞c ⎛ 1⎞ο ⎝ π ⎠ ⎝ π ⎠
(C) (D) 7
⎜ ⎟ ⎜ ⎟
⎝3⎠ ⎝ 2⎠ 15. 5°37′30″ =

⎛π⎞c ⎛π⎞c
1.2 Relation between degree measure and (A) (B)
⎜ ⎟ ⎜ ⎟
radian measure ⎝4⎠ ⎝8⎠

8. The radian measure of an angle of 19° 30′ is ⎛ π ⎞c ⎛ π ⎞c
(C) (D)
⎜ ⎟ ⎜ ⎟
equal to ⎝16⎠ ⎝32⎠

⎛12π⎞c ⎛13π⎞c
(A) ⎜⎜⎜⎝130⎠⎟⎟⎟ (B) ⎜⎜⎜⎝120⎠⎟⎟⎟ 1.3 Length of an arc and area of sector
16. The length of an arc of a circle of radius 5 cm
(C) ⎜⎜⎜⎝⎛43π⎠⎞⎟⎟⎟c (D) ⎛⎜⎜⎜⎝1132π⎞⎠⎟⎟⎟c subten3dπing a central angle mea7suπring 15º is
(A) cm (B) cm
12 12
9. At 3:40, the hour hand and minute hands of a
clock are inclined at 5π π
(C) cm (D) cm
(A) ⎛⎜⎜⎜⎝1138π⎞⎠⎟⎟⎟c (B) ⎛⎜⎜⎜⎝9π⎞⎠⎟⎟⎟c 17. The ar1e2a of a sector, whose ar4c length is 25π
(C) ⎛⎜⎜⎜⎝38π⎞⎠⎟⎟⎟⎟c (D) ⎛⎜⎜⎜⎝56π⎞⎠⎟⎟⎟c (cAm) and1 9t2h5e .a5nπg sleq .ocfm t he s(eBc)t or 1is8 6705°π, swqi.lcl mbe
(C) 937.5π sq.cm (D) 75π sq.cm

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18. In a circle of diameter 66 cm, the length of a
Competitive Thinking
chord is 33 cm. The length of minor arc of the

chord is
1.1 Directed angles and systems of
(A) 33π cm (B) 11π cm
measurement of angles
(C) 22π cm (D) 5.5π cm

1. At 2.15 O’clock, the hour and the minute
19. A railway engine is travelling along a circular
hands of a clock form an angle of
railway track of radius 1500 meters with a
[AMU 1992]
speed of 66 km/ hour. The angle turned by the
engine in 10 seconds is 1ο
(A) 5° (B) 22
15c 7c 2
(A) (B)
7 15 (C) 28° (D) 30°

90c 11c
(C) (D)
11 90 1.3 Length of an arc and area of sector

20. If a pendulum 18 cm long oscillates through 2. The angle subtended at the centre of a circle of
an angle of 32°, then length of the path radius 3 metre by an arc of length 1 metre is
described by its extremity is equal to
5π 16π [MNR 1973]
(A) cm (B) cm
16 5 (A) 20°
8π 6π (B) 60°
(C) cm (D) cm
45 5 1
(C) radian
3
21. If Kalyan is 48 km from Mumbai and the earth
being regarded as a sphere of radius 6400 km, (D) 3 radians

then the nearest second an angle subtended at
the centre of the earth by the arc joining them 3. A circular wire of radius 7 cm is cut and bend
is (Take π = 22/7) again into an arc of a circle of radius 12 cm.
(A) 22°64′ (B) 24°65′ The angle subtended by the arc at the centre is
(C) 23′62′′ (D) 25′46′′
[Kerala (Engg.) 2002]
22. The perimeter of a certain sector of a circle is (A) 50° (B) 210°
equal to half that of the circle of which it is a
(C) 100° (D) 60°
sector. Then the circular measure of sector is
(A) (π + 2) radians (B) (π − 2) radians 4. The radius of the circle whose arc of length 15
(C) (π + 1) radians (D) (π − 1) radians cm makes an angle of 3/4 radian at the centre

23. A wire 96 cm long is bent, so as to lie along is
the arc of a circle of 180 cm radius. The angle [Karnataka CET 2002]
subtended at the centre of the arc in degree is
(A) 10 cm (B) 20 cm
(A) 30° (B) 29° 30′
1 1
(C) 28° 30′ (D) 30° 30′ (C) 11 cm (D) 22 cm

4 2
24. The perimeter of a sector of a circle of area
64 π sq. cm is 56 cm, then area of sector is 5. The distance between 6.00 A. M. and
(A) 140 sq.cm (B) 150 sq.cm 3.15 P. M. by the tip of the 12 cm long hour
(C) 160 sq.cm (D) 170 sq.cm hand in a clock is [SCRA 1999]

25. The length of an arc of a circle of radius 5 cm 35
(A) π cm
subtending an angle of measure 45° is 2
π 5π (B) 18 π cm
(A) cm (B) cm
4 4 37
(C) π cm
π 4π
2
(C) cm (D) cm
5 5 (D) 19 π cm

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Tar et Publications Pvt. Ltd. Chapter 01: Angle and It’s Measurement

Answer Key

Classical Thinking

1. (D) 2. (B) 3. (B) 4. (C) 5. (D) 6. (B) 7. (B) 8. (B) 9. (B) 10. (A)
11. (C) 12. (A) 13. (A) 14. (A) 15. (C) 16. (A) 17. (B) 18. (C) 19. (B) 20. (B)
21. (A) 22. (B) 23. (B) 24. (A) 25. (A) 26. (B) 27. (C) 28. (B) 29. (B) 30. (A)
31. (A) 32. (C) 33. (D)

Critical Thinking

1. (D) 2. (C) 3. (A) 4. (D) 5. (B) 6. (C) 7. (B) 8. (B) 9. (A) 10. (A)
11. (C) 12. (D) 13. (D) 14. (A) 15. (D) 16. (C) 17. (C) 18. (B) 19. (D) 20. (B)
21. (D) 22. (B) 23. (D) 24. (C) 25. (B)

Competitive Thinking

1. (B) 2. (C) 3. (B) 4. (B) 5. (C)

Hints

Classical Thinking 12. In one minute, minute hand covers 6°

(cid:68)
7. 74.87° = 74° + (0.87)° ⎛1⎞
∴ Hour hand covers
⎜ ⎟
= 74° + (0.87 × 60)′ ⎝2⎠
(cid:68)
= 74° + 52.2′ ⎛1⎞
∴ Minute hand gains = 6° −
⎜ ⎟
= 74° + 52′ + (0.2 × 60)′′ ⎝2⎠
= 74°52′12′′ (cid:68)
⎛1⎞
= 5° +
⎜ ⎟
8. Let the angles be x, 2x and 3x. ⎝2⎠
Then, x + 2x + 3x = 180° = 5°30′

….[∵ sum of the angles of a triangle = 180°] 13. Here, 405° − (− 675°) = 1080° = 3(360°),
1230° − (− 930°) = 2160° = 6(360°)
∴ 6x = 180°
and 450° − (− 630°) = 1080° = 3(360°)
∴ x = 30°, 2x = 60° and 3x = 90°
are a multiple of 360°.
10. In 1 minute, minute hand covers 360°
∴ these angles are co-terminal
360°
Now, 330° − (− 60°) = 390°
i.e., in 60 mins, minute hand covers = 6°
60
Which is not a multiple of 360°.

∴ these pair of angles are not co-terminal.
⎛1⎞o
11. 30′ =
⎜ ⎟
⎝2⎠ 14. 1105° = 3 × 360° + 25°
(cid:68) (cid:68) ∵ 0° < 25° < 90°
⎛1⎞ ⎛91⎞
∴ 45°30′ = 45° + =
⎜ ⎟ ⎜ ⎟
⎝2⎠ ⎝ 2 ⎠ ∴ it lies in 1st quadrant

7