KVPY Stream SB-SX (Class 12 & 1st Year BSC) Math: Questions 99 - 102 of 155

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Question number: 99

» Statistics and Probability » Probability of an Event

Appeared in Year: 2013

MCQ▾

Question

In a tournament with five teams, each team plays against every other team exactly once. Each game is won by one of the playing teams and the winning team scores one point, while the losing team scores zero. Which of the following is NOT necessarily true? (Model Paper)

Choices

Choice (4) Response
a.

There are at least two teams which have at most two points each.

b.

There are at least two teams which have at least two points each

c.

There are at most three terms which have at least three points each

d.

There are at most four terms which have at most two points each.

Question number: 100

» Integral Calculus » Fundamental Integrals Involving Functions

Appeared in Year: 2014

MCQ▾

Question

A continuous function f:RR satisfies the equation,

f(x)=x+0xf(t)dt.

Which of the following options is true?

Choices

Choice (4) Response
a.

f(x+y)=f(x)f(y)

b.

f(x+y)=f(x)+f(y)+f(x)f(y)

c.

f(x+y)=f(x)+f(y)

d.

f(x+y)=f(xy)

Question number: 101

» Integral Calculus » Evaluation of Definite Integrals

Appeared in Year: 2014

MCQ▾

Question

Let, In=0π2xncosxdx Where, n is a non-negative integer. Then,

n=2(Inn!+In2(n2)!)=_.

Choices

Choice (4) Response
a.

eπ21π2

b.

eπ2

c.

eπ21

d.

eπ2π2

Question number: 102

» Statistics and Probability » Addition Theorem

Appeared in Year: 2014

MCQ▾

Question

Two person A and B throw a (fair) die (six – faced cube with faces numbered from 1 to 6) alternately, starting with A. The first person to get an outcome different from the previous one by the opponent wins. The probability that B wins is:

Choices

Choice (4) Response
a.

89

b.

67

c.

56

d.

78

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