KV NO.2 DELHI CANTT

SUMMER BREAK HOLIDAY HOME WORK

SESSION 2017-18

CLASS 12

ENGLISH 1. Read all chapter of the Novel and Write chapter wise summary.

2. Write three Notices.

3. Make Notes of 2 Passages from CBSE Qn. Papers of last 5 years.

Or

Make notes of Lessons 1 & 2 of Flamingo.

4. Prepare for 1st term test All syllabus covered from the month April to June 2017

MATHS

RELATION AND FUNCTIONS (20 Questions)

Q.1. If A = {1, 2, 3, 4, 5}, write the relation a R b such that a + b = 8, a ,b A. Write the

domain, range& co-domain.

Q.2. Define a relation on the set N ofnatura lnumbersbyR={(x,y):y= x+7, xisanatural

numberlessthan4;x, yN}.Write down the domain and the range.

Q.3. Let R be the relation in the set N given by R = {(a,b)| a = b 2 , b > 6}

Whether the relation is reflexive or not ?justify your answer.

Q.4. Show that the relation R in the set N given by R = {(a , b)| a is divisible by b , a , b

N}

is reflexive and transitive but not symmetric.

Q5 Let R be the relation in the set N given by R = {(a ,b)| a > b} Show that the relation is

neither reflexive nor symmetric but transitive.

Q6 Let R be the relation on R defined as (a , b) R iff 1+ ab > 0 a,b R.

a. aShow that R is symmetric.

b. Show that R is reflexive.

c. Show that R is not transitive.

Q7 Check whether the relation R is reflexive, symmetric and transitive.

R = { (x ,y)| x 3y = 0} on A ={1,2,3.13,14}.

Q8 If f(x) = , then find f(1/x).

Q9 Show that the function f: NN given by f(x) = 2x is one-one but not onto.

Q10 Show that the signum function f: RR given by:

is neither one-one nor onto.

Q11 Let A = {-1, 0, 1} and B = {0 , 1}. State whether the function f : A B defined by f(x)

= x2

is bijective .

Q12 Let f(x) = , x -1,then find f-1(x)

Q13 If f(x) = e2x and g(x) = log x , x > 0, find

(a) (f + g)(x) (b) (f .g)(x) (c) f o g ( x ) (d) g o f (x ).

Q14 If f(x) = , then show that (a) = f(x) (b) =

Q15 Let * be the binary operation on N given by a*b = LCM of a &b . Find 3*5.

22 xx

0xif,1

0xif,0

0xif,1

)x(f

1x

1x

1x

1x

x

1f

x

1f

)x(f

1

Q16 Let *be the binary on N given by a*b =HCF of a ,b , a,b N. Find 20*16.

Q17 Let * be a binary operation on the set Q of rational numbers defined as a * b = .

Write the identity of *, if any.

Q18 If a binary operation * on the set of integer Z , is defined by a * b = a + 3b2

Then find the value of 2 * 4.

Q19 Let A = {1,2,3}, B = {4,5,6,7} and let f = {(1 , 4),(2 , 5), (3 , 6)} be a function from A to

B. State whether f is one-one or not.

Q20 If f: RR is defined by f(x) = . Find f -1

INVERSE TRIGONOMETRIC FUNCTIONS (20 Questions)

Write the principal value of the following:

5. Evaluate 6. Find x if

7. Evaluate 8 . Evaluate

9. Evaluate 10 Evaluate. 10

11 Find the principal value of

12 Evaluate

13 Express in simplest form: sin-1[3x 4x3] 14 Evaluate: sin(cot-1x)

15 For =

2

1sin 1 , find the value of

16 Evaluate: 1(3) 1(2)

17 Express in simplest form: 1 [cos

1sin ]

18 Evaluate: [

3 1 (

1

2)]

5

ab

2

5x3

2

3cos.1 1

2

1sin.2 1

3tan.3 1

2

1cos.4 1

]acotacot[tan 11 2

xeccos2sec 11

3

2sinsin

3

2coscos 11

5

4sinsin 1

6

7coscos 1

6

7 tan tan 1

19 Find the Principal value of 1 (2

3) + 1 (

7

6)

20 Evaluate: 1 [ (

4)]

MATRICES (20 QUESTIONS)

1. If a matrix has 5 elements, what are the possible orders it can have?

2. Construct a 3 2 matrix whose elements are given by aij = |i 3j |

3. If A = , B = , then find A 2 B.

4. If A = and B = , write the order of AB and BA.

5 Find the co-factor of a12 in A = 6 For the following matrices A and B, verify (AB)T = BTAT,

where A = , B = 7 Give example of matrices A & B such that AB = O, but BA O, where O is a zero matrix and

A, B are both non zero matrices. 8 If B is skew symmetric matrix, write whether the matrix (ABAT) is

Symmetric or skew symmetric.

9 A = and I = , find a and b so that A2 + aI = bA

10 Find the co-factor of a23 in A =

11 Find the adjoint of the matrix A =

12 If A = , write A-1 in terms of A 13 Verify A(adjA) = (adjA) A = I if

1. A = 14 Verify A(adjA) = (adjA) A = I if

A = 15 If A is square matrix satisfying A2 = I, then what is the inverse of A ?

16 For what value of k , the matrix A = is not invertible ?

17 If A = , show that A2 5A 14I = 0. Hence find A-1

18 Evaluate

19 What is the value of , where I is identity matrix of order 3? 20. If A is non singular matrix of order 3 and = 3, then find

DETERMINANTS (20 questions)

1 If A = , find A-1 and hence solve the following system of equations: 2x 3y + 5z = 11, 3x + 2y 4z = - 5, x + y 2z = - 3

2. Using matrices, solve the following system of equations:

a. x + 2y - 3z = - 4 2x + 3y + 2z = 2 3x - 3y 4z = 11 b. 4x + 3y + 2z = 60 x + 2y + 3z = 45 6x + 2y + 3z = 70

3. Find the product AB, where A = , B = and use it to solve the equations x y = 3, 2x + 3y + 4z = 17, y + 2z = 7 4. Using matrices, solve the following system of equations:

- + = 4

+ - = 0

+ + = 2 5. Using elementary transformations, find the inverse of the matrix

6 Using properties of determinants, solve the following for x :

= 0

7 Using properties of determinants, solve the following for x :

= 0 8 Using properties of determinants, solve the following for x :

= 0 9 If a, b, c, are positive and unequal, show that the following determinant is negative:

= 10 prove that

11 prove that

11 prove that

12 prove that

13 prove that

= 2abc( a + b + c)3

222

2

2

2

cba1

1ccbca

bc1bab

acab1a

abc3cba

baaccb

accbba

cba333

0

baabba

accaac

cbbccb

22

22

22

3

22

22

22

)cabcab(

ababbaba

accacaca

bccbcbbc

14 If p, q, r are not in G.P and .

15 If a, b, c are real numbers, and

Show that either a + b +c = 0 or a = b = c.

16 Using properties of determinants, prove that :

17 Using properties of determinants, prove that :

18 Using properties of determinants, prove that :

19 .Express A = as the sum of a symmetric and a skew-symmetric matrix.

20 Let A = , prove by mathematical induction that : .

NOTE :- SOLVE ALL EXAMPLES OF NCERT EXEMPLAR IN YOUR HOME WORK COPY

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ba1

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2

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cba1

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542

354

323

31

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POLITICAL SCIENCE

1. Read newspaper daily and collect some information related to your subject. Write

your comment also.

2. Prepare 25 short question from each below chapters

1. Era of cold war

2. End of bipolarity

3. U.S hegemony in world politics

4. Revise and learn all the chapters which are taught in the class.

GEOGRAPHY

1. Five year CBSE answers for chapter 1-4 ( world) and chapter 1-5 ( India )

2. Collect census 2011 data on indian population

3. Collect HDI 2016 data for all category . Rank top 5 and least 5 countries

4. Collect data for various crops according to countries and states of

India and rank top 5 and least 5 according to production

5. Collect data for various minerals according to various countries

and indian state and rank top 6 and least 5

7 learn all the chapters reached in class from NCERT

8. Draw all the map for which data is collected

HISTORY

1. Make a question bank from chapters 1 to 15.

2. Very short answer questions, 1 question from (each) chapter.

3. Short answer questions, 3 questions from (each)chapter.

4. Long answer questions, 2 questions from (each) chapter.

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