KVPY Stream SB-SX (Class 12 & 1st Year BSC) Math: Questions 69 - 72 of 155

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Question number: 69

» Sets, Relations and Functions » Types of Relations

Appeared in Year: 2012

MCQ▾

Question

Let S={1,2,3,,n} and A={(a,b) 1a,bn}=S×S . A subset B of A is said to be a good subset if (x,x)B for every xS . Then the number of good subsets of A is –

Choices

Choice (4) Response

a.

2n2

b.

22n

c.

1

d.

2n1

Question number: 70

» Integral Calculus » Evaluation of Simple Integrals

Appeared in Year: 2012

MCQ▾

Question

The value 20122012(sin(x3)+x5+1)dx is

Choices

Choice (4) Response

a.

4024

b.

0

c.

2012

d.

2013

Question number: 71

» Permutations and Combinations » Fundamental Principle of Counting

Appeared in Year: 2012

MCQ▾

Question

Three children, each accompanied by a guardian, seek admission in a school. The principal wants to interview all 6 persons one after the other subject to the condition that no child is interviewed before its guardian. In how many ways can this be done?

Choices

Choice (4) Response

a.

180

b.

90

c.

60

d.

120

Question number: 72

» Integral Calculus » Integration Using Trigonometric Identities

Appeared in Year: 2013

MCQ▾

Question

For x, t ∈ R let,

pt(x)=(sint)x2(2cost)x+sint

be a family of quadratic polynomials in x with variable coefficients. Let

A(t)=01pt(x)dx.

Which of the following statements are true?

(i) A(t)<0 for all t.

(ii) A(t) has infinitely many critical points.

(iii) A(t)=0 for infinitely many t

(iv) A(t)<0 for all t.

Choices

Choice (4) Response

a.

(i) and (ii) only

b.

(iii) and (iv) only

c.

(ii) and (iii) only

d.

(iv) and (i) only

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