Sets, Relations and Functions (KVPY Stream SB-SX (Class 12 & 1st Year BSC) Math): Questions 10 - 12 of 13

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Question number: 10

» Sets, Relations and Functions » Equivalence Relations

Appeared in Year: 2012

MCQ▾

Question

Let f: R ⟶ R be the function f(x)=(xa1)(xa2)+(xa2)(xa3)+(xa3)(xa1) with a1,a2,a3R . Then f(x)0 if and only if –

Choices

Choice (4) Response

a.

a1,a2,a3 are all positive and distinct

b.

a1,a2,a3 are all distinct

c.

At least two of a1,a2,a3 are equal

d.

a1=a2=a3

Question number: 11

» 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)

Question number: 12

» Sets, Relations and Functions » Functions and Composition

Appeared in Year: 2013

MCQ▾

Question

For given two functions,

P(x)=sinx and Q(x)=82xx2 .

Which of the following statement are true?

(i) Domain of Q((P(x))2)= Domain of Q(P(x))

(ii) Domain of P((Q(x))3)= Domain of Q(P(x))

(iii) Domain of Q(P(x))= Domain of Q(P(x))

(iv) Domain of Q(P(x))+P(Q(x))= Domain of P(Q(x)) (Model Paper)

Choices

Choice (4) Response

a.

Only (i) and (iv)

b.

Only (i)

c.

Only (i) and (ii)

d.

Only (iii) and (iv)

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