CHAPTER

SETS
Q1. Let A and B be any two sets such that A B = A, then A B is equal to
(a) (b) B (c) A (d) None of these

Q2. If A = {x: x is a multiple of 4} and B = {x : x is a multiple of 6 } then A B consist of

multiples of
(a) 16 (b) 12 (c) 8 (d) 4

Q3. If * * + + then which of the following statement is incorrect?

(a)* + (b) ** ++ (c) * + (d)

Q4. Which of the following cannot be the number of elements in the power set of any finite
sets?
(a) 26 (b) 32 (c) 8 (d) 16

Q5. and are two sets such that ( ) and ( ) If ( )

( ) then is
(a) 5 (b) 10 (c) 20 (d) 15

Q6. Two sets A and B are such that n(A ) = 21 , n( A’ B’) = 9 , n( A B ) = 7 find n( A B)‘

Q7. If n( A) = 43 , n(B) = 51 and n(A ) = 75 , then find the value of n{ ( A ) ( B - A )}

Q8. Prove the following:

(A B) (A B’) = A
A – (A B) = A – B
(A B) – C = (A –C) (B-C)
A (B-C) = (A B) – (A C)

Q9. If every element of a set A is also an element of a set B, then set A is called a subset of
B and we write . Thus, A * +.
Moreover if ( ) , then set A will have a total of subsets.
Based on the above information, answer the following questions.
(i) How many subsets are possible for set * +?
(ii) Let * +. Is E a subset of * +? Justify your answer.
(iii) Write all those subsets of * +, which have exactly two elements.
(iv) Write all those subsets of * +, which have exactly one element.
(v) Write all the subsets of * +.

Q10. Write the following interval in Set builder form , )

Q11. Write the following set in roster form * +
Q12. Write the following sets in Roster form:
( ) { }
( ) * +

CHAPTER
RELATIONS AND FUNCTIONS

Q1. Which of the following relations is a function?

(a) R = {(4, 6) , (3, 9) , ( -11, 6) , ( 3 ,11)}
(b) R = {(1, 2) , (2, 4) , (2, 6) , ( 3 ,5)}
(c) R = {(2,1) , ( 4, 3) , (6, 5) , ( 8,7) , ( 10 , 9) }
(d) R = {(0,1) , ( 1, 3) , (2, 4) , ( 3 ,1) , ( 3, 5) }

Q2. If R= { (x, y) : x, y , x2 + y2 = 169 } ,then find domain of R

Q3. If ( ) and . / = 3, then

(a) f( ) ( ) (b) ( ) ( )
(c) f( ) ( ) (d) None of these

Q4. A relation in the set of natural numbers is defined as *( ) + the

range of relation is
(a) * + (b) * + (c) * + (d) * +

Q5. A relation R is defined from { 2,3,4,5} to { 3,6,7,10} by xRy x is relatively prime to y .

Then, domain of R is
(a) {2, 3, 5} (b) {3,5} (c) {2, 3, 4} (d) {2, 3, 4,5}

Q6. The domain of the function ( ) √ is

(a) , - (b) ( ) (c) ( ) (d) , -

Q7. Let A and B be finite sets such that n(A) = 3 . If the total number of relations that can be
defined from A to B is 4096, Then find n( B) ?

Q8. Write the values of x, for which the functions defined by f (x) = 3x 2 – 1 and g (x) = 3 + x
are equal.

Q9. Find x and y if (x+3, 5) = (6, 2x+y)

Q10. If f(x) = 2x2 +bx +c and f(0) = 3 and f( 2) = 1, then find the value of f(1)
Q11. Find the domain of the following functions:

(i) f(x) =
(ii) f(x) = √ √
(iii) f(x) =
√
(iv) f(x) =
√ | |

Q12. Find the range of the following function: f(x) = 1- | |

Q13. Find the range of the function ( ) √

Q14. Let R = {(x, x3): x is an even number less than 8}, Write R in roster form .

Q15. Find the domain of the function ( ) √ √

1
Q16. Find the domain of the function given by f(x) =
x  x  6
2

Q17. If * + and * +, then no. of functions defined from A to B is

(a) 64 (b) 81 (c) 4096 (d) 144

Q18. For the function ( ) , -, where [.] is greatest integer function, the range of ( ) is
(a) (b) (c) , ) (d)

Q19. Draw the graph of the function defined by ( ) {

Also, find its range.

Q20. Let * + * + and *( ) +

Is the relation a function? If so, find its range.

Q21. Find the range of the function f(x) =

Q22. A relation in the set of natural numbers is defined as *( ) +.

Find
(i) in roster form (ii) Domain of (iii) Range of

Q23. Find the domain and range of ( ) √

Q24. Find the range of ( )

Q25. Define Signum function and Draw its graph. Also write its domain and range.
 ( )( )
Q26. The domain of the function ( ) √ is
( )
(a) , ) , ) (b) ( ) , ) (c) , - , ) (d) none of these

Q27. Let * + and * is prime less than 5}. Find and

CHAPTER
TRIGONOMETRIC FUNCTIONS

Q1. The valueof cot( ) ( ) is

(a) -1 (b) 0 (c) 1 (d) Not defined
Q2. The value of cot(1215 ) is
(a) 1 (b) – 1 (c) √ (d) - √

Q3. A value of satisfying √ is

(a) (b) (c) (d)

Q4. is equal to
(a) (b) (c) (d)

Q5. If tanα = is equal to

( ) (b) (c) (d)

Q6. The perimeter of a certain sector of a circle is equal to the length of the arc of a semi-
circle having the same radius .Express the angles of a sector in degrees.

Q7. A horse is tied to a post by a rope 30 m long.If the horse moves along the circumference
of a circle always keeping the rope tight ,find how far it will have gone when the rope has
traced an angle of 1050

Q8. Show that sin 1500 cos 1200 + cos 3300 sin 6600 = -1

Q9. Draw the graph of

Q10. Prove that sin20

 2   4 
Q11. If x cos  y cos    z cos   , then find the value of .
 3   3 

Q12. If sin ( ) ( )
Cos2( ) ( ) = 1 -2a2 -2b2
Q13. Show that

Q14. Prove that √ √

Q15. Prove that:

Q16. If , then prove that

Q17. Prove that: . / . /

( )
Q18. If ( )

Q19. If ( ) prove that ( )

Q20. Prove that:

Q21. Ashu visited hill station with his father during vacations. There he saw a railway train
travelling on a circular curve of 1500 metres radius at the rate of 66 km/hr.
(i) Find the angle (in radians) by which it turned in 10 seconds.
(ii) Find the degree measure of the angle turned by railway train in 10 seconds.
(iii) How much degree will train turn in 20 seconds?
(iv) If train changes its speed to 60km/hr then what angle (in radians) will train turn in 10
seconds?

Q22. If . / and . / then λ =

(a) (b) (c) 1 (d) None of these

Q23. If , then value of ( ) is

(a) (b) (c) (d)

Statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct
answer out of the following choices.

(a) Both (A) and (R) are true and (R) is the correct explanation of (A)
(b) Both (A) and (R) are true and (R) is not the correct explanation of (A)
(c) (A) is true, but (R) is false.
(d) (A) is false, but (R) is correct
√
Q24. Assertion (A):
√

Reason (R): ( )