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© Target Publications Pvt. Ltd. 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.

STD. XII Sci.

Printed at: India Printing Works, Mumbai

Follows the revised HSC syllabus prescribed by the Maharashtra State Board of Secondary and Higher Secondary Education, Pune.

A collection of2013

to 2019

Physics Chemistry Mathematics Biology

Board Questions

Includes all board questions from 2013 to 2019 and several other relevant questions from previous years.

TEID: 13797P.O. No. 144757 Balbharati Registration No.: 2018MH0022

Salient Features • Subjects covered: Physics, Chemistry, Mathematics and Biology

• Includes Board question papers of March, July 2019

• Also covers questions from previous curriculum which fall under the current

revised syllabus

• Board questions include: MCQs, Theory questions and Numericals.

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Preface ‘Target’s: Std. XII Sci. Board Questions’ is a compilation of all the questions (MCQs + theory + numericals) that

have been asked in the previous years HSC Maharashtra Board Papers of science stream for Physics, Chemistry,

Mathematics and Biology. The book has been prepared with an aim to help the students get quick access to all the previous years board

questions. The book covers questions from more than 10 years till date. Only those questions from previous years

which fall under the current revised syllabus prescribed by Maharashtra State Board of Secondary and Higher

Secondary Education are included. Furthermore, we have also included Board Question Papers of March, July 2019

examinations. Constructive criticism and feedback for improving the book are always appreciated. Please write to us on :

mail@targetpublications.org

Best of luck to all the aspirants! Yours faithfully,

Publisher Edition: Third

Disclaimer This reference book is transformative work based on textual contents published by Bureau of Textbook. We the publishers are making this reference book which constitutes as fair use of textual contents which are transformed by adding and elaborating, with a view to simplify the same to enable the students to understand, memorize and reproduce the same in examinations. This work is purely inspired upon the course work as prescribed by the Maharashtra State Board of Secondary and Higher Secondary Education, Pune. Every care has been taken in the publication of this reference book by the Authors while creating the contents. The Authors and the Publishers shall not be responsible for any loss or damages caused to any person on account of errors or omissions which might have crept in or disagreement of any third party on the point of view expressed in the reference book. © reserved with the Publisher for all the contents created by our Authors. No copyright is claimed in the textual contents which are presented as part of fair dealing with a view to provide best supplementary study material for the benefit of students.

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Chapter No. Units Page No. Physics - I 1

1 Circular Motion 2 2 Gravitation 6 3 Rotational Motion 10 4 Oscillations 14 5 Elasticity 19 6 Surface Tension 22 7 Wave Motion 25 8 Stationary Waves 30 9 Kinetic Theory of Gases and Radiation 34

Physics – II 39 10 Wave Theory of light 40 11 Interference and Diffraction 43 12 Electrostatics 48 13 Current Electricity 52 14 Magnetic Effect of Electric Current 55 15 Magnetism 58 16 Electromagnetic Induction 60 17 Electrons and Photons 64 18 Atoms, Molecules and Nuclei 67 19 Semiconductors 71 20 Communication Systems 73

Chemistry – I 75 1 Solid State 76 2 Solutions and Colligative Properties 78 3 Chemical Thermodynamics and Energetics 81 4 Electrochemistry 84 5 Chemical Kinetics 87 6 General Principles and Processes of Isolation of Elements 90 7 pBlock Elements 92

Chemistry – II 95 8 d and fBlock Elements 96 9 Coordination Compounds 98 10 Halogen Derivatives of Alkanes and Arenes 100 11 Alcohols, Phenols and Ethers 102 12 Aldehydes, Ketones and Carboxylic Acids 104 13 Compounds Containing Nitrogen 107 14 Biomolecules 109 15 Polymers 111 16 Chemistry in Everyday Life 112 Maths – I 113

1 Mathematical Logic 114 2 Matrices 116 3 Trigonometric Functions 118 4 Pair of Straight Lines 120 5 Vectors 122 6 Three Dimensional Geometry 124 7 Line 125 8 Plane 126 9 Linear Programming 128

CONTENT

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Maths – II 129 1 Continuity 130 2 Differentiation 132 3 Applications of Derivatives 134 4 Integration 136 5 Definite Integral 138 6 Applications of Definite Integral 139 7 Differential Equations 140 8 Probability Distribution 142 9 Binomial Distribution 144 Biology – I 146

1 Genetic Basis of Inheritance 147 2 Gene: It’s Nature, Expression and Regulation 149 3 Biotechnology: Process and Application 150 4 Enhancement in Food Production 152 5 Microbes in Human Welfare 153 6 Photosynthesis 155 7 Respiration 156 8 Reproduction in Plants 157 9 Organisms and Environment - I 159 Biology – II 161

10 Origin and Evolution of Life 162 11 Chromosomal Basis of Inheritance 164 12 Genetic Engineering and Genomics 165 13 Human Health and Diseases 167 14 Animal Husbandry 168 15 Circulation 169 16 Excretion and Osmoregulation 170 17 Control and Co-ordination 171 18 Human Reproduction 173 19 Organisms and Environment – II 175 Board Question Paper

March 2019

Physics 177 Chemistry 180 Maths 183 Biology 187

July 2019

Physics 190 Chemistry 193 Maths 196 Biology 199

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14

14

Std. XII Sci.: Board Questions (Physics)

p 1. The displacement of a particle performing

linear harmonic motion in one time period is [Mar 11]

(A) A (B) 2A (C) zero (D) 4A 2. The total work done by a restoring force in

simple harmonic motion of amplitude A and angular speed , in one oscillation is _______.

[Mar 08]

(A) 12

mA22 (B) zero

(C) mA22 (D) 12

mA 3. Two springs of force constants K1 and K2 (K1

> K2) are stretched by same force. If W1 and W2 be the work done stretching the springs then _______. [Mar 16]

(A) W1 = W2 (B) W1 < W2 (C) W1 > W2 (D) W1 = W2 = 0 4. An amplitude of a simple pendulum of a

period T and length L in increased by 5%. The new period of that pendulum will be _______.

[Mar 09]

(A) T8

(B) T4

(C) T2

(D) T 5. In simple harmonic motion, acceleration of the

particle is zero, when its _______. [Oct 08, July 18]

(A) velocity is zero (B) displacement is zero (C) both velocity and displacement are zero (D) both velocity and displacement are

maximum 6. For the particle perfoming linear S.H.M. from

general position, the state of the particle giving its position and direction of motion of a time to zero (t = 0) is called [Oct 11]

(A) phase of S.H.M. (B) final phase of S.H.M. (C) angular speed of S.H.M. (D) epoch of S.H.M. 7. The maximum velocity of a particle

performing linear S.H.M. is 0.32 m/s and its maximum acceleration is 2.56 m/s2, the amplitude of S.H.M. is _______. [Mar 10]

(A) 0.02 m (B) 0.03 m (C) 0.04 m (D) 0.05 m 8. The average displacement over a period of

S.H.M. is _______. [Oct 14] (A = amplitude of S.H.M.) (A) 0 (B) A (C) 2A (D) 4A 9. A particle executing linear S.H.M. has

velocities v1 and v2 at distances x1 and x2 respectively from the mean position. The angular velocity of the particle is [Oct 13]

(A) 2 21 22 22 1

x xv v

(B) 2 22 12 21 2

v vx x

(C) 2 21 22 22 1

x xv v

(D) 2 22 12 22 1

v vx x

10. The phase difference between displacement

and acceleration of a particle performing S.H.M. is _______. [Mar 14]

(A) rad2 (B) rad

(C) 2 rad (D) 3 rad2

11. If the particle starts its motion from mean

position, the phase difference between displacement and acceleration is _______.

[Mar 18]

(A) 2 rad (B) π2

rad

(C) rad (D) π4

rad 12. Two particles perform linear simple harmonic

motion along the same path of length 2A and period T as shown in the graph below. The phase difference between them is _______.

[Mar 13]

(A) zero rad (B)

4 rad

(C) 2 rad (D) 3

4 rad

04 Oscillations

Multiple Choice Questions

T4

Disp

lace

men

t

O

A

A

X

T2

3T4

T

A2

Time

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15

Chapter 04: Oscillations

13. The motion of a simple pendulum is _______. [Oct 09]

(A) oscillatory but not periodic (B) periodic but not oscillatory (C) neither periodic nor oscillatory (D) periodic as well as oscillatory 14. A particle of mass 0.1 kg executes S.H.M.

under a restoring force F = 10x newton. Speed of particle at mean position is 6 m/s. The amplitude of oscillations is

[Feb 13 old course] (A) 0.6 m (B) 0.4 m (C) 0.2 m (D) 0.1 m 15. The tension in the string of a simple pendulum

is maximum, when the bob of the simple pendulum is _______. [Oct 11]

(A) at the extreme position (B) midway between mean and extreme

position

(C) at rd1

3

of amplitude from the mean

position (D) at the mean position 16. If the metal bob of a simple pendulum is

replaced by a wooden bob of the same size, then its time period will ______. [Mar 15]

(A) increase (B) remain same (C) decrease (D) first increase and then decrease 17. A seconds pendulum is suspended in an

elevator moving with constant speed in downward direction. The periodic time (T) of that pendulum is _______. [Oct 15]

(A) less than two seconds (B) equal to two seconds (C) greater than two seconds (D) very much greater than two seconds 18. The acceleration of a particle in S.H.M. is

_______. [Mar 12] (A) maximum = a2, when it passes through

mean position (B) maximum = a2, when it attains the

extreme position (C) minimum = a, when it passes through

its mean position (D) minimum = a, when it attains the

extreme position 19. In a damped harmonic oscillator, periodic

oscillations have _______ amplitude. [Mar 17] (A) gradually increasing (B) suddenly increasing (C) suddenly decreasing (D) gradually decreasing

1. Define: i. Phase of S.H.M. ii. Angular S.H.M. [Mar 97, 04] 2. Define amplitude and phase of S.H.M.

[Oct 2000] 3. Obtain the differential equation of linear

S.H.M. [Mar 96, 03; Oct 02; Mar 17] 4. Using differential equation of linear S.H.M,

derive an expression for velocity of a particle performing linear S.H.M. Discuss the condition for maximum and minimum velocity. [Oct 98]

5. Derive an expression for velocity of a particle

performing linear S.H.M using differential equation. Hence find the expression for maximum velocity. [Oct 96, 02]

6. State the differential equation of linear S.H.M.

Hence obtain an expression for velocity and displacement of a particle performing linear S.H.M. [Mar 98]

7. State the differential equation of linear simple

harmonic motion. Hence obtain the expression for acceleration, velocity and displacement of a particle performing linear S. H. M. [Mar 18]

8. Show that linear S.H.M is the projection of

U.C.M on any diameter. [Mar 97, 11] 9. Define linear S.H.M. Show that S.H.M. is a

projection of U.C.M. on any diameter. [Mar 16]

10. Define phase of S.H.M. Show variation of

displacement, velocity and acceleration with phase for a particle performing linear S.H.M. graphically, when it starts from extreme position. [Oct 14]

11. State the expressions for displacement,

velocity and acceleration of a particle performing linear S.H.M and starting from extreme positive position. Hence draw their graphs w.r.t. time. [Oct 97]

12. Represent graphically the displacement,

velocity and acceleration against time for a particle performing linear S.H.M when it starts from the extreme position. [Mar 2000]

13. A particle performing S.H.M. starts from

extreme position. Plot the graph of velocity and displacement against time. [Mar 12]

Theory Questions

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16

16

Std. XII Sci.: Board Questions (Physics)

14. Show graphically the variation of velocity and acceleration in S.H.M. with phase, if motion starts from extreme position. [Oct 11]

15. Define linear simple harmonic motion. Assuming the expression for displacement of a particle starting from extreme position, explain graphically the variation of velocity and acceleration w.r.t. time. [July 17]

16. Explain graphical representation of displacement, velocity and acceleration when particle starts its S.H.M from mean position.

[Mar 08; Oct 10] 17. Give graphical representation of S.H.M when

particle starts from the positive extreme position. [Oct 09]

18. When particle oscillates with S.H.M. along a linear path, the magnitudes of its acceleration are “” and “” at shorter displacement “x1” and at longer displacement “x2” respectively. If the velocities at these displacements are v1 and v2 respectively and both points are on the same side from the mean position, show that

the distance between two position is 2 21 2v v

[Oct 06] 19. Discuss analytically the composition of two

S.H.M’s of the same period and parallel to each other. Hence obtain the expression for resultant amplitude when the phase difference is

i. 0 ii. 180 [Oct 96]

20. Discuss analytically the composition of two S.H.M’s of equal periods and parallel to each other. Find the resultant amplitude when the phase difference is

i. Zero ii. 90. [Mar 05]

21. Define angular S.H.M. State its differential equation. [Mar 10]

22. Discuss the composition of two S.H.M’s along the same path having same period. Find the resultant amplitude and intial phase. [Oct 15]

23. Two S.H.M’s are represented by x1 = A1 sin (t + 1) and x2 = A2 sin(t + 2). Obtain the expressions for the displacement, amplitude and initial phase of the resultant motion. [Mar 08]

24. Assuming the general expression for the displacement in S.H.M, obtain an expression for the velocity and the acceleration of a particle performing S.H.M. [Oct 99]

25. Show that average velocity of a particle performing S.H.M. in one oscillation is 2

(maximum velocity). [Oct 02] 26. Represent graphically the variation of K.E.,

P.E. and T.E. of a particle performing linear S.H.M. with respect to displacement.

[Oct 08; Mar 09] 27. Obtain an expression for potential energy of a

particle performing S.H.M. What is the value of potential energy at

a. mean position? b. extreme position? Draw the graph showing the variation of

potential energy with displacement. [Oct 2000; Mar 01; Feb 13 old course]

28. Obtain an expression for potential energy of a particle performing simple harmonic motion. Hence evaluate the potential energy

a. at mean position and b. at extreme position. [Mar 15] 29. Assuming the expression for potential energy

and kinetic energy for a particle performing simple harmonic motion, obtain the expression for its total energy. State any one conclusion from this expression. [Oct 99]

30. Represent graphically the variations of K.E, P.E. and T.E. of a particle performing linear S.H.M. with respect to displacement.

[Oct 08; Mar 09] 31. Prove the law of conservation of energy for a

particle performing simple harmonic motion. Hence graphically show the variation of kinetic energy and potential energy w. r. t. instantaneous displacement. [Mar 17]

32. State an expression for K. E. (kinetic energy) and P. E. (potential energy) at displacement ‘x’ for a particle performing linear S.H. M. Represent them graphically. Find the displacement at which K.E. is equal to P. E.

[Mar 14] 33. Obtain the expression for the total energy of the

particle performing linear S.H.M. at a distance x, from the mean position. Hence show that the total energy is inversely proportional to the square of its period. [Oct 03]

34. Define ideal simple pendulum. Show that the period of a simple pendulum does not depend upon its mass. [Mar 99]

35. Derive an expression for the period of a simple pendulum. What is second’s pendulum?

[Mar 06]

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17

Chapter 04: Oscillations

36. State laws of simple pendulum. [Oct 97] 37. Draw a neat labelled diagram of a simple

pendulum at displaced position. [Feb 13 old course]

38. Define an ideal simple pendulum. Show that, under certain conditions, simple pendulum performs linear simple harmonic motion.

[Mar 13] 39. Derive an expression for the period of motion

of a simple pendulum. On which factors does it depend? [Oct 13]

40. Define practical simple pendulum. Show that motion of bob of pendulum with

small amplitude is linear S.H.M. Hence obtain an expression for its period. What are the factors on which its period depends? [July 16]

41. Show that for a small amplitude, the motion of a simple pendulum is linear S.H.M. Hence find its period. [Mar 11]

42. Define an ideal simple pendulum. Show that the motion of a simple pendulum under certain conditions is simple harmonic. Obtain an expression for its period. [Mar 10, July 18]

1. When the length of a simple pendulum is

increased by 22 cm, the period changes by 20 %. Find the original length of simple pendulum. [g = 9.8 m/s2] [Mar 99]

2. Determine the length of a second’s pendulum at a place, where the acceleration due to gravity is 9.77 m/s2. [Mar 2000]

3. A clock regulated by seconds pendulum, keeps correct time. During summer, length of pendulum increases to 1.005 m. How much will the clock gain or loose in one day?

[g = 9.8 m/s2 and = 3.142] [July 17] 4. When the length of a simple pendulum is

decreased by 20 cm, the period changes by 10%. Find the original length of the pendulum.

[Mar 14] 5. The period of a simple pendulum increases by

10% when its length is increased by 21 cm. Find the original length and period of the pendulum. [g = 9.8 m/s2] [Oct 09]

6. A simple pendulum of length 1 m has a mass of 10 g and oscillates freely with amplitude 2 cm. Find its potential energy at extreme position. [g = 9.8 m/s2]

[July 18, Similar in Mar 97]

7. A particle of mass 0.2 kg performs S.H.M of amplitude 0.1 m and period 3.14 second. Find its kinetic energy and potential energy when it is at a distance of 0.03 m from mean position.

[Oct 97; Mar 06]

8. When the displacement in S.H.M is rd1

3of the

amplitude, what fraction of total energy is kinetic energy and what fraction is potential energy? [Mar 2000]

9. A paticle of mass 10 gm executes linear

S.H.M. of amplitude 5 cm with a period of 2 second. Find its potential energy, kinetic

energy th1

6

second after it has passed

through the mean position. [Oct 11] 10. The total energy of a particle of mass 200 g

performing S.H.M is 10–3 joule. Find the maximum velocity and the period if amplitude is 4 cm. [Mar 02]

11. A particle executes linear S.H.M. of period

4 second and amplitude 4 cm. Find the time taken by it to describe a distance of 1 cm from positive extreme position. [Mar 98]

12. A particle executes S.H.M. with a period of

10 seconds. Find the time in which its potential energy will be half of its total energy.

[July 16] 13. The maximum velocity of a particle

performing S.H.M.is 6.28 cm/s. If the length of its path is 8 cm, calculate its period. [Oct 98]

14. For a particle performing linear S.H.M show that

its average speed over one oscillation is a2

,

where ‘a’ is amplitude of S.H.M. [Mar 03] 15. The differential equation for linear S.H.M is

given by 2

2

d xdt

= –4x. If the amplitude is 0.5 m

and initial phase is 6 radian, obtain the

displacement equation of S.H.M and find the velocity at x = 0.3 m for the particle in S.H.M. [Mar 04]

16. The equation of a particle performing S.H.M.

is given by x = 8 sin 5 t3

cm. Determine

the displacement and phase angle of the particle at t = 2 s. [Mar 07]

Numericals

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18

18

Std. XII Sci.: Board Questions (Physics)

17. The displacement of a particle performingS.H.M. is given by

x = 5sin t 12sin t2

cm. Determine

the amplitude, period and initial phase of themotion. [Oct 08]

18. S.H.M. is given by the equationx = 8 sin (4t) + 6 cos (4t) cm.Find its (a) amplitude (b) initial phase (c)period (d) frequency. [Oct 10]

19. The equation of linear S.H.M is

x = 10 sin 4 t6

cm. Write down the

values of amplitude, period and phaseconstant. Also find phase angle 1/24 secondafter the start. [Oct 2000]

20. A load of 100 g increases the length of a lightspring by 10 cm. Find the period of its linearS.H.M (in the vertical direction) if it isallowed to oscillate freely. What will beperiod if the load is increased to 400 g?

[Oct 05]

21. A particle performs S.H.M of amplitude 10 cm, its maximum velocity duringoscillations is 100 cm/s. What is its displacement, when the velocity is 60 cm/s2?

[Mar 01]

22. The period of simple pendulum is found to increase by 50% when the length of thependulum is increased by 0.6 m. Calculate the initial length and initial period of oscillation ata place where g = 9.8 m/s2. [Mar 12]

23. A body of mass 1 kg is made to oscillate on aspring of force constant 16 N/m. Calculate:a. Angular frequency,b. Frequency of vibration [Oct 13]

24. The periodic time of a linear harmonicoscillator is 2 second, with maximumdisplacement of 1 cm. If the particle startsfrom extreme position, find the displacement

of the particle after3 seconds. [Oct 15]

25. A particle in S.H.M. has a period of 2 secondsand amplitude of 10 cm. Calculate theacceleration when it is at 4 cm from itspositive extreme position. [Mar 15]

26. A particle performing linear S.H.M. hasmaximum velocity of 25 cm/s and maximumacceleration of 100 cm/s2. Find the amplitudeand period of oscillation. ( = 3.142)

[Mar 18]

27. The maximum velocity of a particleperforming linear S.H.M. is 016 m/s. If itsmaximum acceleration is 0.64 m/s2, calculateits period. [Oct 14]

28. A particle performs S.H.M of period 12 second and amplitude 8 cm. If initially theparticle is at positive extremity, how much time will it take to cover a distance of 6 cmfrom the extreme position? [Mar 04]

29. A particle performing linear S.H.M. has aperiod of 6.28 seconds and a pathlength of 20 cm. What is the velocity when its displacement is 6 cm from mean position?

[Mar 16]

30. A particle executing S.H.M. has velocities v1and v2 when at distances x1 and x2 respectivelyfrom the mean position. Show that its period is

T = 22 21 22 22 1

x xv v

[Oct 04]

31. A mass M attached to a spring oscillates with a period of 2 second. If the mass is increasedby 2 kg, the period increases by 1 second. Findthe initial mass, assuming that Hooke’s law is obeyed. [Mar 13]

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