Sets, Relations and Functions-Functions and Composition (KVPY Stream SB-SX (Class 12 & 1st Year B.Sc.) Math): Questions 1 - 5 of 7

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Question number: 1

» Sets, Relations and Functions » Functions and Composition

Appeared in Year: 2012

MCQ▾

Question

Let a, b, c, d be numbers in the set {1, 2, 3, 4, 5, 6} such that the curves y=2x3+ax+b and y=2x3+cx+d have no point in common. The maximum possible value of (ac)2+bd is

Choices

Choice (4) Response

a.

36

b.

5

c.

30

d.

0

Question number: 2

» Sets, Relations and Functions » Functions and Composition

Appeared in Year: 2012

MCQ▾

Question

Let f(x)=x+1x1 for all x1 . Let f1(x)=f(x) , f2(x)=f(f(x)) and generally fn(x)=f(fn1(x)) for n > 1.

Let, P=f1(2)f2(3)f3(4)f4(5) which of the following is a multiple of P

Choices

Choice (4) Response

a.

125

b.

375

c.

250

d.

147

Question number: 3

» Sets, Relations and Functions » Functions and Composition

Appeared in Year: 2014

MCQ▾

Question

Consider the function f(x)={ . Then f(f(x)) is discontinuous –

Choices

Choice (4) Response

a.

At exactly one value of x

b.

At exactly three value of x

c.

At all real numbers

d.

At exactly two value of x

Question number: 4

» Sets, Relations and Functions » Functions and Composition

Appeared in Year: 2012

MCQ▾

Question

The mid-point of the domain of the function f(x)=42x+5 for real x is –

Choices

Choice (4) Response

a.

14

b.

25

c.

32

d.

23

Question number: 5

» Sets, Relations and Functions » Functions and Composition

Appeared in Year: 2013

MCQ▾

Question

Let f(x)=2xx2 and g(x)=cosx . Which of the following statements are true?

(i) Domain of f((g(x))2) = Domain of f(g(x))

(ii) Domain of f(g(x))+g(f(x)) = Domain of g(f(x))

(iii) Domain of f(g(x)) = Domain of g(f(x))

(iv) Domain of g((f(x))3) = Domain of f(g(x))

Choices

Choice (4) Response

a.

Only (i) and (iv)

b.

Only (i)

c.

Only (iii) and (v)

d.

Only (i) and (ii)

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