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

f(n) = n2 for n odd

f(n) = 2n + 1, for n even

for n ∈ N. Then f is

• surjective but not injective

• injective but not surjective

• bijective

• neither injective nor 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 = 0one other real root two real roots no other real root infinite number of real roots

C.

no other real root

On equating the various powers of x, we get

x2 = 0, x3 = 0, ..., xn = 0

Hence, x = 0 is only one real root of given equation.