KVPY Stream SB-SX (Class 12 & 1st Year BSC) Math: Questions 45 - 49 of 155

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Question number: 45

» Statistics and Probability » Probability of an Event

Appeared in Year: 2012

MCQ▾

Question

Let Sn=k=1n(k) denote the sum of the first n positive integers. The numbers S1, S2, S3, …, S99 are written on 99 cards. The probability of drawing a card with an even number written on it is –

Choices

Choice (4) Response
a.

49100

b.

12

c.

4999

d.

4899

Question number: 46

» Integral Calculus » Integration Using Trigonometric Identities

Appeared in Year: 2012

MCQ▾

Question

The value of the integral ππcos2x1+axdx , where a>0, is –

Choices

Choice (4) Response
a.

π2

b.

ax

c.

π

d.

2π

Question number: 47

» Sets, Relations and Functions » Equivalence Relations

Appeared in Year: 2012

MCQ▾

Question

Let n be a natural number and let ‘a’ be a real number. The number of zeros of x2n+1)earealnumber.Thenumberofzerosofn,thereforewecanwrite,urves(2n+1)x+a=0 in the interval [-1, 1] is

Choices

Choice (4) Response
a.

2 if a < 0

b.

At least three for every value of a

c.

2 if a > 0

d.

At most one for every value of a

Question number: 48

» 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: 49

» Integral Calculus » Evaluation of Simple Integrals

Appeared in Year: 2012

MCQ▾

Question

Let [x] and {x} are be the integer part and fractional part of a real number x respectively. The value of the integral, 05[x]{x}dx is –

Choices

Choice (4) Response
a.

5

b.

52

c.

35.5

d.

34.5

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