#### 1. RELATIONS AND FUNCTIONS

10th Standard EM

Reg.No. :
•
•
•
•
•
•

MATHEMATICS

Time : 00:10:00 Hrs
Total Marks : 15

15 x 1 = 15
1. If n(A x B) =6 and A={1,3} then n(B) is

(a)

1

(b)

2

(c)

3

(d)

6

2. A={a,b,p}, B={2,3}, C={p,q,r,s} then n[(A U C) x B] is

(a)

8

(b)

20

(c)

12

(d)

16

3. If A={1,2}, B={1,2,3,4}, C={5,6} and D={5,6,7,8} then state which of the following statement is true..

(a)

(A x C) ⊂ (B x D)

(b)

(B x D) ⊂ (A x C)

(c)

(A x B) ⊂ (A x D)

(d)

(D x A) ⊂ (B x A)

4. If there are 1024 relations from a set A = {1, 2, 3, 4, 5} to a set B, then the number of elements in B is

(a)

3

(b)

2

(c)

4

(d)

8

5. The range of the relation R ={(x,x2) |x is a prime number less than 13} is

(a)

{2,3,5,7}

(b)

{2,3,5,7,11}

(c)

{4,9,25,49,121}

(d)

{1,4,9,25,49,121}

6. If the ordered pairs (a+2,4) and (5,2a+b) are equal then (a,b) is

(a)

(2,-2)

(b)

(5,1)

(c)

(2,)

(d)

(3,-2)

7. Let n(A)= m and n(B) = n then the total number of non-empty relations that can be defined from A to B is

(a)

mn

(b)

nm

(c)

2mn-1

(d)

2mn

8. If {(a,8),(6,b)}represents an identity function, then the value of a and b are respectively

(a)

(8,6)

(b)

(8,8)

(c)

(6,8)

(d)

(6,6)

9. Let A={1,2,3,4} and B={4,8,9,10}. A function f: A ⟶ B given by f={(1,4), (2,8), (3,9), (4,10)} is a

(a)

Many-one function

(b)

Identity function

(c)

One-to-one function

(d)

Into function

10. If f(x)=2x2 and g(x)=$\frac{1}{3x}$, then f o g is

(a)

$\\ \frac { 3 }{ 2x^{ 2 } }$

(b)

$\\ \frac { 2 }{ 3x^{ 2 } }$

(c)

$\\ \frac { 2 }{ 9x^{ 2 } }$

(d)

$\\ \frac { 1 }{ 6x^{ 2 } }$

11. If f: A ⟶ B is a bijective function and if n(B) =8, then n(A) is equal to

(a)

7

(b)

49

(c)

1

(d)

14

12. Let f and g be two functions given by
f={(0,1), (2,0), (3,-4), (4,2), (5,7)}
g={(0,2), (1,0), (2,4), (-4,2), (7,0)} then the  range of f o g is

(a)

{0,2,3,4,5}

(b)

{–4,1,0,2,7}

(c)

{1,2,3,4,5}

(d)

{0,1,2}

13. Let f(x) = $\sqrt { 1+x^{ 2 } }$ then

(a)

f(xy) = f(x).f(y)

(b)

f(xy) ≥ f(x).f(y)

(c)

f(xy) ≤ f(x).f(y)

(d)

None of these

14. If g={(1,1), (2,3), (3,5), (4,7)} is a function givrn by g(x)=αx+β then the values of α and β are

(a)

(-1,2)

(b)

(2,-1)

(c)

(-1,-2)

(d)

(1,2)

15. f(x) = (x+1)3 - (x-1)3 represents a function which is

(a)

linear

(b)

cubic

(c)

reciprocal

(d)