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S.B.P. D.A.V. Centenary Public School, Fatehabad. Website: www.davfatehabad.in E. Mail: sbpdavftb@yahoo.co.in, Ph. 01667-222664

Holidays’ Assignments for Summer Vacations (2019-20) for Class XI (Nonmedical)

General Instructions:

1. Get up early in the morning and go out for a walk daily. Play some outdoor game to remain fit.

2. Learn all the prayers and mantras given in student diary.

3. Raise a small kitchen garden by planting seeds.

4. The summer break for Nursery to XII will be from May 24, 2019 to July 1, 2019 (Both days inclusive). School

will reopen on July 2, 2019.

5. Revise the syllabus of all subjects done before summer vacations for Unit Tests to be arranged after

summer break.

6. Submit home work to your teachers on July 2, 2019.

7. Register & Participate in 1st

stage of 5th

Online International Humanity Olympiad by accessing through

our web portal – www.humanityolympiad.org or Android App - Awake Humanity (play store). Every

individual passing the exam (i.e. scoring minimum 40%) will get an e-certificate through e-mail

immediately on their emails. School code is : FATE001

English 1.Revise syllabus for UT.

Hornbill :L 1to 4 Poems:1&2 Snapshots:-L 1&2

Grammar :-Tenses &Modals| Writing Section :-Notice ,Letter Writing ,Advertisement Writing

2.Write 50 difficult or new words from the text you have read.

3(A)Make a beautiful Collage for classified advertisements on the following topics-

(Roll no- 1to20)

a. Accommodation Wanted

b. Bride Groom Wanted

c. Obituary

d. In Memoriam

e. Change of Name

f. Found- a wallet

g. Tour &Travel

(B)Make a beautiful collage with given notices(Roll no-21 to 40…..)

a. Seminar on Career Options after 10th

b. Sudden holidays for a week

c. Donation for flood victims

d. Selections for schools under 19 football team

e. Change in school timing

f. Audition for the selection of play artist for a drama

g. Inviting entries for the school magazine.

4.Complete worksheets from BRAVIA in a good handwriting( use pencil) a. Worksheet 1 to 6 (Reading comprehension)

b. Worksheet 25,26 (Advertisement )

c. Worksheet 51-55 (Article writing) ,Worksheet 21,22 (Notice Writing)

d. Worksheet 41, 42 ,43 ,44(Letter writing)

5.Exercise 1-5 tenses on pages 241 ,242

6.Write the review of any motivational book you read in summer breaks in 100-150 words..

7 Do first three listening activities of BRAVIA.

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Physics • Do all the NCERT Exemplar questions of chapters completed in class

• Investigatory Project Report to be made on the topics allotted in class.

• Do following assignment in your holidays’ homework notebook.

SUBJECTIVE QUESTIONS

1. Write the characteristics of a standard unit.

2. Write difference between fundamental & derived unit with example.

3. Define the term one light year, astronomical unit & Parsec.

4. In the equation y = A sin (wt - kx), obtain the dimensional formula of w & k. Given x is distance & t is time.

5. Energy & young’s modulus have the same dimension comment.

6. The rotational K.E. of a body is given by ½ Iw2.

Use this equation to obtain the dimension of I. Where I=

Moment of inertia, w = angular velocity.

7. The value of Stefan’s constant is σ = 5.67 x 10-8

J/S / m2/ K

4. Find its value in cgs system.

8. How much larger than microsecond is a millisecond?

9. Why S.I is called rational system of units?

10. Find an expression for the maximum error when a physical quantity depends upon the product of two

physical quantities.

11. What is the difference between AU & A°?

12. What is random error? Explain with an example how this error can be estimated.

13. Explain law of conservation of linear momentum with example.

14. Explain law of conservation of angular momentum with example.

15. Why S.I is called coherent system of units?

16. Pressure may be defined as the linear momentum per unit volume. Is it correct? Check by the method of

dimensions.

17. Express one Parsec in terms of light year.

18. Write the difference between gravitational force, electromagnetic force, nuclear (strong &weak).

19. Write difference between fundamental & derived unit with example.

20. Define the term one light year, astronomical unit & Parsec.

21. What is absolute error? How is it calculated mathematically?

22. Find an expression for the maximum error when a physical quantity depends upon the powers of two

physical quantities.

23. Distinguish between accuracy and precision.

24. Draw velocity-time graph for the motion of a body moving with uniform positive acceleration.

25. Draw velocity-time graph for the motion of a body moving with uniform negative acceleration.

26. Describe in each case whether the motion is one, two or three dimensional

a. a moving car on a straight highway.

b. a piece of paper flying in air.

c. the earth revolving around the sun.

27. Distinguish between distance and displacement.

28. Can a body be said to be rest as well as in motion at the same time? Explain.

29. Distinguish between speed and velocity.

30. What is a velocity-time graph? Mention its use?

31. What do you understand by the non uniform motion? Explain variable velocity and instantaneous

velocity of an object in one dimensional motion.

32. What do slopes of position – time & velocity time graph of uniform accelerated motion represent?

33. Show that area under velocity time graph of a particle in uniform motion gives the displacement of the

particle in given time.

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34. Show that slope of displacement time graph is equal to velocity of uniform motion.

35. Derive the relation:-

S = u t + at2

Numericals 1. Subtract with due regard to significant figures :-

3.9 x 105 – 2.5 x 10

4.

2. A potential difference of V = 100 ± 2 volt, when applied across a resistance R gives a current of 10 ± 0.5

ampere. Calculate percentage error in R given by R = V/I.

3. Assuming that the frequency (ν) of a vibrating string depends upon the load (F) applied,

length of the string (l) and mass per unit length (m), prove that ν = .

4. Write the dimensions of a/b in the relation

P = , where P is pressure x is distance t is time.

5. In an experiment, the value of refractive index of glass was found to be 1.54, 1.53, 1.44, 1.54, 1.56 and

1.45 in successive measurements. Calculate (i) mean value of refractive index. (ii) Absolute error (iii)

relative error.

6. In the equation y = A sin (wt - kx), obtain the dimensional formula of w & k. Given x is distance & t is time.

7. Write the dimensions of a/b in the relation

P = , where P is pressure x is distance t is time.

8. If force, velocity & time are taken as fundamental quantities, what would be the dimensions of work.

9. A capacitor of capacitance C = (2.0 + 0.1) µ F is charged to a potential V = (20 + 0.5) volt calculate the

charge Q with error limits.

10. Write down the number of significant figures in the following

i. 52.38 N ii. 34.000 m iii. 4200 kg iv. 0.02340 N/m

11. Subtract 5.5 x 105 from 6.6 x 10

7 with due regard to significant figures.

12. A physical quantity x is calculated from the relation x =

If percentage error in a, b, c, d are 1%, 2%, 3% , 5%. What is percentage error in X.

13. A body travels uniformly a distance of (5.6 + 0.5) m in a time of (3.1 + 0.2) sec. calculate percentage error

in velocity.

14. Distinguish between accuracy and precision.

15. Derive by the method of dimensions, an, expression for the volume of a liquid flowing out per

second through a narrow pipe. Assume that the rate of flow of liquid depends on (i) the coefficient of

viscosity ‘ ’ of the liquid (ii) the radius ‘r’ of the pipe and (iii) the pressure gradient [P/L] along the pipe.

16. The period of vibration of a tuning fork depends on the length L of its prong, density d and

Young’s modulus Y of its material. Deduce an expression for the period of vibration on the basis of

dimensions.

17. The period of oscillation of a simple pendulum is T = 2 , Measured value of L is 20.0 cm known to 1

mm accuracy and time for 100 oscillations of the pendulum is found to be 90 s using a wristwatch of 1 s

resolution. What is the accuracy in the determination of g?

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18. For the estimation of Young’s modulus Y = for the specimen of wire, following observations were

recorded L = 2.890, M = 3.00, d = 0.082, g = 9.81, l = 0.087. Calculate the maximum percentage error in

the value of Y and mention which physical quantity causes maximum error.

19. If two resistors of resistances R1 = (4 0.5) and R2 = (16 0.5) are connected (i) in series and (ii) in

parallel; find the equivalent resistance in each case with limits of percentage errors.

20. The SI unit of energy is J = kg m2s

-2, that of speed v is ms

-1 and of acceleration a is ms

-2. Which of the

formulae for kinetic energy (K) given below can you rule out on the basis of dimensional arguments ( m

stands for the mass of the body).

a. K = m2v

3 b. K = ½ mv

2 c. K = ma d. K = mv

2 e. K = ½ mv

2 + ma

21. The escape velocity from the surface of earth is given by v= , where M is mass and R is radius of

earth. Check the correctness of the formulae.

22. Check by the method of dimensions, the formula v= , where v is velocity of longitudinal waves, λ is

wavelength of wave, K is coefficient of volume elasticity and d is density of the medium.

23. Two roads have lengths measured as (1.8 ± 0.2) m and (2.3 ± 0.1) m. Calculate their combined length with

in error limits.

24. A potential difference of V = (20 ± 1) volt is applied across a resistance of (8 ± 2) ohm. Calculate the

current with error limits.

25. The radius of a sphere is measured to be (2.1 ± 0.5) cm. Calculate its surface area with error limits.

26. A physical quantity x is calculated from x = . Calculate % error in x, when % error in measuring a,b,c are

4,2 and 3 respectively.

27. Assuming that the mass m of the largest stone that can be moved by a flowing river depends upon v (the

velocity), d(the density water) and on g (the acceleration due to gravity), show that m varies with sixth

power of the velocity of flow.

28. Show dimensionally that the centripetal force, acting on a particle of mass m, moving in a circle of radius r

with a uniform speed v rotations per seconds is 4π2 2mr.

29. A gas bubble from an explosion under water, oscillates with a period T proportional to Paρb

Ec where P is

the static pressure, ρ is the density of water and E is the total energy of the explosion. Find the values of

a, b and c.

Multiple choice Questions 1. What is the % error in measurement of time period ‘T’ of a pendulum if maximum error in the

measurement of ‘ℓ’ & ‘g’ are 2% & 4% respectively? (when T = 2π )

a. 6% b. 3% c. 4% d. 5%

2. The length of rod is (11.05 0.05) cm. What is the total length of two such rods?

a. (22.1 0.05) cm b.(22.10 0.05) cm c. (22.1 d.(22.10 0.10)cm

3. If energy E, velocity v and time T are chosen as fundamental quantities then dimension of surface

tension will be represented as:-

a. EV-1

T-1

b. EV-1

T-2

c. EV-2

T-2

d. E2V

-1T

-3

4. A dimensionless quantity

a. may have a unit b. never has a unit

c . always has a unit d. do not exist

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5. One astronomical unit (A U) is:

a. 108 m b. 10

-10 m c. 10

-15 m d. 1.5 x 10

11 m

6. The dimensions of RC, where R is resistance & C is capacitance are same as that of

a. Inverse time b. time c. square of time d. square root of time

7. Dimensions of ‘ohm’ are same as that:

(where h is Planck’s constant & e is charge)

a. b. c. d.

8. Which one of the following has dimensions of pressure?

a. b. c. d.

9. If C represents capacitance, R represents resistance then the unit of CR2 are:-

a. Henry b. c. d.

10. Add (3.8×10-6

) to (4.2×10-5

) with due regard to significant figures.

a. 4.6 × 10-5

b. 4.6 × 10-6

c. 4.85 × 10-5

d. 4.580 × 10-5

11. The area enclosed by a circle of diameter 1.06 m with correct number of significant figure is :

a. 0.88 m2 b. 0.883 m

2 c. 1.88 m

2 d. 0.88202 m

2

12. Subtract 2.6×104 from 3.9×10

5 with due regard to significant figures.

a. 3.64 × 105 b. 3.7 × 10

5 c. 3.6 × 10

5 d. 3.65 × 10

6.

13. The correct number of significant figures in 0.0006032 is

a. seven b. six c. eight d. four

14. Which of the following pair have same dimension

a .Torque & work b. Angular momentum& Linear momentum

c. Energy & young’s modulus d. Energy & volume

15. A quantity x = 0 r where 0 is permittivity of free space

L = length , = potential difference , t = time interval.The dimensional formula for X is same as that

of

a. resistance b. charge c. voltage d. current

16. The physical quantity which has the dimensional formula as that of is

a. Force b. power c. pressure d. acceleration

17. Which of the following have the same dimensions of as v2/r? Where v is speed of the particle describing

the circular path of radius r?

a. Acceleration b. momentum c. Force d. impulse

18. The frequency of vibration of mass M suspended from a spring of spring constant K is given by

relation.

f = C Mx k

y

The value of x and y are:

a. x = , y = b. x = , y =

c. x = , y = d.x = , y =

19. A thermal physical quality is measured in calorie per gram, its dimensional formula will be:-

a. M L0T

-2 b. M

2 L

2 T

0 c. M

2LT

-2 d. M

0 L

2T

-2

20. The density of the material of a cube is measured by measuring its mass and length to its side. It the

maximum errors in the measurements of mass and length are 3% & 2% respectively, the maximum

error in the measurement of density is:

a. 1% b. 5% c. 9% d.7%

21. What are the dimensions of in length?

a. -2 b. 0 c. 2 d. None of these

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22. The dimensional formula for strain is same as that for:-

a. Stress b. modulus of Rigidity

c. thrust d. angle of twist

23. Dimensions of are:

a. A-1

b. A-2

c. A d. A2

24. The dimensional formula for Planck’s constant h is:

a. ML2T

--2 b. ML

2T

-1 c. M

-1L

2T

-2 d. ML

2T

+1

25. (Mean value-measured value) gives

a. Absolute error b. relative error c. gross error d. random error

CHEMISTRY UNIT I:

SOME BASIC CONCEPTS OF CHEMISTRY

Q1. Account for the following:

a) In the combustion of methane in air, methane is limiting reagent.

b) Molality is preferred over molarity in expressing the concentration of a solution.

c) It is necessary to balance a chemical equation.

d) Air is sometime considered as a heterogenous mixture.

Q2. When two substances A and B are mixed together in a pestel and mortar, a large amount of heat is

evolved and a new substance C is formed . C has the properties different from A and B. Is C an element, a

compound or a mixture?

Q3. How many moles and how many grams of sodium chloride(NaCl) are present in 250cm3 of a 0.5M NaCl

solution?

Q4.If 6.3 gram of NaHCO3 is added to 15 gram of CH3COOH solution, the residue is found to be 18gram. What

is the mass of CO2 released in the reaction?

Q5. 3.0 gram of H2 reacts with 29.0 gram of O2 to form H2O

i. Which is the limiting reactant?

ii. Calculate the maximum amount of H2O that can be formed.

iii. Calculate the amount of the reactant left unreacted.

Q6. (i) A compound (molecular mass=246g/mol) contains following elements:

Element % composition Relative no. of atoms

Element

% composition Relative no. of atoms

A

9.76 0.406

B

13.01 0.406

C

26.01 1.625

D

51.22 2.846

From the data find out:

a. Atomic masses of the element A,B,C and D.

b. Simple atomic ratio of each element.

c. Empirical formula.

d. Molecular formula of the compound.

UNIT II: STRUCTURE OF ATOM

Q7. An electron is in one of the 4p orbital. Give the possible values of n, l and m for the electron.

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Q8. Can we apply uncertainty principle to a stationary electron?

Q9. When is the energy of electron regarded as zero?

Q10. Which of the following sets of orbital’s are degenerate and why?

(i) 1s, 2s and 3s in Mg atom. (ii) 2px, 2py and 2pz in carbon atom.

Q11. How many nodes are present in 3p orbital?

Q12. What will happen to the wavelength associated with a moving particle if its velocity is

Reduced to half?

Q13. How many electrons are present in all sub shells (fully filled) n+l=5?

Q14. What is Zeeman Effect and Stark effect?

Q15. Light of wavelength 4000 Ao falls on the surface of cesium. Calculate the energy of the

Photoelectron emitted. The critical wavelength for photoelectric effect in cesium is

6600 Ao.

Q16. Calculate the frequency and the wavelength of the radiations in nm emitted when an electron in the

hydrogen atoms jumps from third orbit to the ground state. In which region of electromagnetic spectrum will this

line lie?

Q17.To which orbits the electron in the hydrogen atom will jump on absorbing 12.1eV of energy?

Q18.a) what observations in scattering experiment led Rutherford to make following conclusions:

i. The most of the space in an atom is empty.

ii. The whole of the mass of the atom is present in the centre of the nucleus.

iii. Nucleus has positive charge.

b) What is the value of orbital angular momentum for an electron in 2s orbital?

c) How many electrons in an atom may have n=4 and ms=+1/2?

UNIT III: PERIODIC CLASSIFICATION OF ELEMENTS

Q19.Which among I,I+,I- has smallest size?

Q20.To which block the elements with atomic numbers 28 and 32 belong?

Q21.Among alkali metals which element do you expect to be least electronegative and why?

Q22.The element 108 has not yet been discovered. What is its IUPAC name and symbol?

Q23 .Give the general electronic configuration of s-block and p-block elements.

Q24.All transition elements are d-block elements, but all d-block elements are not transition element. Explain with

example.

Q25.Give reasons

i. Halogen acts as a good oxidizing agent.

ii. Electron gain enthalpy of noble gas is almost zero.

Q26.The increasing order of reactivity among group 1 elements is Li˂ Na˂ K˂ Rb ˂ Cs whereas that among group

17 elements is F ˃ Cl ˃ Br ˃I. Explain.

Q27 Arrange the element N, P, O and S in order of increasing first ionization enthalpy and increasing non-metallic

character. Give reason for the arrangement assigned.

Q28. i. Justify the given statement with suitable example “The properties of the elements are a periodic function of

their atomic numbers”.

iii. Discuss the factors which determine the magnitude and sign of electron gain enthalpy and are the trends of

its variation in the periodic table.

Q.29 Make a table of electronic configuration of all the elements and learn their atomic

numbers.

30. Draw the spectrum of electromagnetic radiation and visible spectrum in your

notebooks so as to elaborate their significance.

31. 1 Prepare a project report containing at least 10 pages related with environmental chemistry.

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MATHS

Note : (i) Do all the assignments in Holidays Homework Notebook.

(ii) Make a project on Relation & function and types of function.

(iii) Make a project on venn diagram related to properties of sets .

(iv) Plot the graphs of sin x, sin 2x, 2sinx and sin 2 x , using same coordinate axes

(v) Prepare chapter 1 to 5 for unit test .

ASSIGNMENT

Sets Q.No. Sums Answer

1 Write the following sets in the roaster form.

(i) A = {x | x is a positive integer less than 10 and x2 – 1 is an odd number}

(ii) C = {x : 2x + 7x – 8 = 0, x ∈ R} (iii) A = {x : x ∈ R, 2x + 11 =

15}

(iv) B = {x | 2x = x, x ∈ R} (v) C = {x | x is a positive

factor of a prime number p}

(vi) D = {t | t 3 = t, t ∈ R} (vii) E = {w | 3

2

+−

w

w = 3, w ∈

R}

(viii) F = {x | 65 24 +− xx = 0, x ∈ R}

2 In a class of 60 students, 25 students play cricket and 20 students play tennis,

and 10 students play both the games. Find the number of students who play

neither?

3 From 50 students taking examinations in Mathematics, Physics and Chemistry,

each of the student has passed in at least one of the subject, 37 passed

Mathematics, 24 Physics and 43 Chemistry. At most 19 passed Mathematics and

Physics, at most 29 Mathematics and Chemistry and at most 20 Physics and

Chemistry. What is the largest possible number that could have passed all three

examination?

14

4 Out of 100 students; 15 passed in English, 12 passed in Mathematics, 8 in

Science, 6 in English and Mathematics, 7 in Mathematics and Science; 4 in

English and Science; 4 in all the three. Find how many passed (i) in English and

Mathematics but not in Science (ii) in Mathematics and Science but not in

English (iii) in Mathematics only (iv) in more than one subject only

2,3,3,9

5 In a survey of 200 students of a school, it was found that 120 study

Mathematics, 90 study Physics and 70 study Chemistry, 40 study Mathematics

and Physics, 30 study Physics and Chemistry, 50 study Chemistry and

Mathematics and 20 none of these subjects. Find the number of students who

study all the three subjects

20

6 In a town of 10,000 families it was found that 40% families buy newspaper A,

20% families buy newspaper B, 10% families buy newspaper C, 5% families

buy A and B, 3% buy B and C and 4% buy A and C. If 2% families buy all the

3300,4000

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three newspapers. Find (a) The number of families which buy newspaper A

only. (b) The number of families which buy none of A, B and C

7 In a group of 50 students, the number of students studying French, English,

Sanskrit were found to be as follows: French = 17, English = 13, Sanskrit = 15

French and English = 09, English and Sanskrit = 4 French and Sanskrit = 5,

English, French and Sanskrit = 3. Find the number of students who study (i)

French only (v) French and Sanskrit but not English (ii) English only (vi)

French and English but not Sanskrit (iii) Sanskrit only (vii) at least one of the

three languages (iv) English and Sanskrit but not French (viii) none of the three

languages.

6,3,9,1,2,6,30,20

8 Draw the Venn diagrams to illustrate the following relationship among sets E, M

and U, where E is the set of students studying English in a school, M is the set of

students studying Mathematics in the same school, U is the set of all students in

that school.

i. All the students who study Mathematics study English, but some students who

study English do not study Mathematics.

ii. There is no student who studies both Mathematics and English.

iii. Some of the students study Mathematics but do not study English, some

study English but do not study Mathematics, and some study both.

iv. Not all students study Mathematics, but every students studying English

studies Mathematics

Relations & Functions

1 If P = {x : x < 3, x ∈ N}, Q = {x : x ≤ 2, x ∈ W}. Find (P ∪ Q) × (P ∩ Q), where W is the set

of whole numbers.

2 If A = {x : x ∈ W, x < 2} B = {x : x ∈ N, 1 < x < 5} C = {3, 5} find (i) A × (B ∩ C) (ii) A

× (B ∪ C)

3 Redefine the function which is given by

(i) f (x) = xx ++− 11 , – 2 ≤ x ≤ 2 (ii) f (x) = xx ++− 22 , – 3 ≤ x ≤ 3

Ans.(i)

≤≤

<≤−

−<≤−−

=

21,2

11,2

12,2

)(

xx

x

xx

xf (ii)

≤≤

<≤−

−<≤−−

=

32,2

22,4

23,2

)(

xx

x

xx

xf

4 Find the domain of each of the following functions given by

(i) f (x) = 5

1

−x (ii) =)(xf

x

x

−28

3 (iii) =)(xf x|x| (iv) =)(xf

1

32

3

−+−

x

xx

Ans. (5,∞ ) (ii) R- {28} (iii)R (iv) R- {-1,1}

5 Find the range of the following functions given by

(i ) f (x) = 22

3

x− (ii) f (x) = 1 – | x−2| (iii) f (x) = | x−3| (iv) f (x) = 1 + 3 cos2x (Hint : – 1

≤ cos 2x ≤ 1 ⇒ – 3 ≤ 3 cos 2x ≤ 3 ⇒ –2 ≤ 1 + 3cos 2x ≤ 4) (v) f (x) = 5

1

−x

Ans. (i) [3/2,∞ ) (ii) (-∞ ,1) (iii) [0,∞ ) (iv) [-2,4] (v) R+

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6 If f (x) =

1

1

+−

x

x, then show that (i) f (1/x) = -f(x) (ii) f (-1/x) = -1/f(x)

7 Let f (x) = x and g (x) = x be two functions defined in the domain R +∪ {0}.

Find (i) (f + g) (x) (ii) (f – g) (x) (iii) (fg)(x) (iv) (f/g)( x )

8 If f (x) = y =

acx

bax

−−

, then prove that f (y) = x

Trigonometry 1 Find the value of tan (x+y), given that cot x =1/2 ,x ϵ(π,3π/2) and sec y =-5/3 , y ϵ(π,2π)

2 If tan a = ,

3 Find the value of (i) 3 cosec 20° – sec 20° [4] (ii) Find the value of tan 22°30′.

12

1

+

4 If θ lies in the second quadrant, then show that

θθ

θθ

sin1

sin1

sin1

sin1

−+

++−

= −2secθ

5 8 Prove that : cos 10⁰ cos 30⁰ cos 50⁰ cos 70⁰ = 3/16

6 (i) The value of sin 20° sin 40° sin 60° sin 80° is …………..3/ 16

(ii) The value of cos 5

8cos

5

4cos

5

2cos

5

ππππ is ……… . -1/16

(iii) The value of the expression8

7cos

8

5cos

8

3cos

8cos 4444 ππππ

+++ …………..3/2

(iv ) The value of

+

+

+

+8

7cos1

8

5cos1

8

3cos1

8cos1

ππππ …………… 1/8

7 (i) If 3 tan (θ – 15°) = tan (θ + 15°), 0° < θ < 90°, then θ = _________ π/4

(ii) If tan x = b/ a , then find the value of ba

ba

ba

ba

+−

+−+

x

x

2cos

cos2

8 (i) If a cos θ + b sin θ = m and a sin θ – b cos θ = n, then show that a 2 + b 2 = m 2 + n 2

(ii) If tanθ + sinθ = m and tanθ – sinθ = n, then prove that m 2 – n 2 = 4sinθ tanθ

[Hint: m + n = 2tanθ, m – n = 2 sinθ, then use m 2 – n 2 = (m + n) (m – n)]

9 Prove that (i)

θθ

θθ

2tan

8tan

14sec

18sec=

−−

(ii)A

A

cos

sin1

1secA -tanA

1-secAtanA +=

+

(iii) sin 4A = 4sinA cos3A – 4 cosA sin3A. (iv) cosθ cosθ/2 – cos3θcos9θ/2 = sin 7θ sin 8θ

(v ) 2sin β2 +4cos(α+ β) sin α sin β + cos 2 (α + β) = cos 2α (vi)

(vii) = 4 cos2x.cos4x (viii)

10

(i) If tan (A + B) = p, tan (A – B) = q, then show that tan2A = pq

qp

−+

1 [Hint: Use 2A = (A + B) +

(A – B)]

(ii) If cos (α + β) = 4/5 and sin (α – β) = 5/13 , where α lie between 0 and 4 π , find the value of

tan2α

(iii) If cosα + cosβ = 0 = sinα + sinβ, then prove that cos 2α + cos 2β = – 2cos (α + β).

XINM-11

[Hint: (cosα + cosβ) 2 – (sinα + sinβ) 2 = 0]

11 Find the general solution of the equation

(i) cotθ + tanθ = 2 cosecθ, (ii) 2sin2θ = 3cosθ, where 0 ≤ θ ≤ 2π,

(iii) secx cos5x + 1 = 0, where 0 < x ≤ π/2 , (iv) 5cos 2 θ + 7sin 2 θ – 6 = 0

(v) sinx – 3sin2x + sin3x = cosx – 3cos2x + cos3x (vi) sinθ + cosθ = 1,

(vii) 3 cos θ + sin θ = 2 Ans . (i) 2nπ ± π/3 (ii) 2nπ ± 7π/4 (iii) 2nπ

± π/3 (iv) nπ ± π/4 (v) Ans nπ/2 ± π/8 (vi ) = mπ + (-1)n π/4 – π/4 (vii) θ = 2mπ + 5π/12 and θ

= 2mπ – π/12

12

If ( )( ) ba

ba

yx

yx

−+

=−+

sin

sin, then show that

b

a

y

x=

tan

tan [Hint: Use Componendo and Dividendo].

13 If m sin θ = n sin (θ + 2α), then prove that tan (θ + α) cot α =

nm

nm

−+

14 If cos (θ + φ) = m cos (θ – φ), then prove that tanθ=

m

m

+−

1

1cotφ

15

If , Prove that (i) (ii)

16 If 0 x 2 and x lies in the IInd quadrant such that sin x = Find the values of cos , sin

P.M. I. 1

Using P.M.I, prove that : )4942()76)(16(

1.......................

25.19

1

19.13

1

13.7

1

+=

++++++

n

n

nn, nεN.

2 Prove the following by using the principle of mathematical induction for all n∈N:

n

n

n 2

1

2

11.........................

24

11

23

11

22

11

+=

−

−

−

− for all natural number n ≥2

3 Using principle of mathematical induction, prove the following for all n N∈ , 1332 3.27 −−+ nnn is divisible by 25.

4 Prove the rule of exponents ( ) nnnbaab = by using principle of mathematical induction for

every natural number.

5 Using principle of mathematical induction, prove that (i) nn −3 is divisible by 6, for each

natural number n ≥2 . (ii) ( )52 +nn is divisible by 6, for each natural number n.

6 Using principle of mathematical induction, prove that 2n + 1 < 2n , for all natural numbers

n 3≥

7 Using P.M. I. For all Nx∈ : prove that

15

7

35

35 nnn++ is a natural number.

Complex Numbers 1 (i) If (1+2i) (2 +3i) (3+4i) = a+ib , prove that a

2 +b

2 = 1625

(ii) Prove that ( )( )( )( ) 41111 4 +=−−+−−+++ xixixixix

2 Let

1 i zz a i b and w

z i

−= + =

−. If w 1,= then show that z is purely real.

XINM-12

3 If

1 b a ia b i 1, then show that: b a i.

1 b a i

+ ++ = = +

+ −

4 If

1

1

+−

z

z is a purely imaginary number (z ≠ – 1), then find the value of z . Ans. 1

5 Evaluate ( )∑

=

++13

1

1

n

nn ii , where n∈N. -1+ i

6 Find the square root of i341+ , (ii) -21+20i

7 Prove that ( ) ( ) 620342034 2

12

1

=−−+−+

8 Find the modulus and argument of the following:(i) i344 + (ii)

i

i

31

21

−+

. (iii) (i25

)3

9 Solve : ( ) ( )( ) 1327522 =−−−+− xxxx

10 In Argand’s plane, the point corresponding to

( )( )( )i

ii

+

+−

3

131lies in ……………IV quadrant.

11 Find the values of x and y for which the following equation is

true:( )( )

( )( )

ii

iyi

i

ixi=

−+−

++−+

3

32

3

21

Music

1. Make a collage/ chart showing different types of Indian musical instruments and their origin.

2. Make a PPT on short description of Raga Bhairvi & Bihag and insert music related to these talas in your slides.

Physical Education 1. a) Make a Report file on ‘Components of Physical Fitness’ using A3 sheets. (Roll No 1 to 20)

b) Make a report on component of health related fitness on A3 sheet (Roll No 21 onwards)

2. Calculate your BMI & Waist Hip Ratio and mention it on last page of your file.