﻿ A mapping f : N ➔ N, where N is the set of natural numbers is defined asf(n) = n2 for n oddf(n) = 2n + 1, for n evenfor n ∈ N. Then f is | Relations and Functions

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Relations and Functions

Multiple Choice Questions

11.

The number of real roots of equation loge(x) + ex = 0 is

• 0

• 1

• 2

• 3

12.

Let the number of elements of the sets A and B be p and q, respectively. Then, the number of relations from the set A to the set B is

• 2p + q

• 2pq

• p + q

• pq

13.

Eleven apples are distributed among a girl and a boy, Then, which one of the following statements is true ?

• atleast one of them will receive 7 apples

• the girl receives atleast 4 apples or the boy receives atleast 9 apples

• the girl receives atleast 5 apples or the boy receives atleast 8 apples

• the girl receives atleast 4 apples or the boy receives atleast 8 apples

14.

The domain of definition of the function

15.

The function f(x) =  satisfies the equation

• f(x + 2) - 2f(x + 1) + f(x) = 0

• f(x) + f(x + 1) = f{x(x + 1)}

• f(x) + f(y) =

• f(x + y) = f(x)f(y)

16.

The range of the function f (x) =  is given by

17.

If , then the value of x is

• 32

• 125

• 625

• 25

18.A mapping f : N ➔ N, where N is the set of natural numbers is defined asf(n) = n2 for n oddf(n) = 2n + 1, for n evenfor n ∈ N. Then f issurjective but not injective injective but not surjective bijective neither injective nor surjective

B.

injective but not surjective

and for two odd functions

Thus, f(n) is injective but not surjective.

19.

A function f: A $\to$ B, where A = {x: } and B = {y: } is defined by the rule y = f(x) = 1 + x2 Which of the following statement is true ?

• f is injective but not surjective

• f is surjective but not injective

• f is both injective and surjective

• f is neither injective nor surjective

20.

The equation ex - x - 1 = 0 has, apart from x = 0

• one other real root

• two real roots

• no other real root

• infinite number of real roots