KVPY Stream SB-SX (Class 12 & 1st Year BSC) Math: Questions 91 - 94 of 155

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Question number: 91

» Integral Calculus » Integral as Limit of a Sum

Appeared in Year: 2014

MCQ▾

Question

For a real number x let [x] denote the largest integer less than or equal to x and {x}=x[x] . Let n be a positive integer. Then 0ncos(2π[x]{x})dx is equal to –

Choices

Choice (4) Response
a.

0

b.

2n1

c.

1

d.

n

Question number: 92

» Basic Mathematics » Algebra » Solutions to Equations

Appeared in Year: 2014

MCQ▾

Question

The under of integers n for which 3x225x+n=0 has three real roots is –

Choices

Choice (4) Response
a.

Infinite

b.

55

c.

1

d.

25

Question number: 93

» Basic Mathematics » Arithmetic » Number Games

Appeared in Year: 2014

MCQ▾

Question

For each positive integer n , let An=max{(nr) 0r<n} . Then the number of elements n is {1, 2,3,20} for which 1.9AnAn12 is:

Choices

Choice (4) Response
a.

9

b.

11

c.

12

d.

10

Question number: 94

» Coordinate Geometry » Parallel and Perpendicular Lines

Appeared in Year: 2013

MCQ▾

Question

Let v1,v2,v3,v4 be unit vectors in the xy plane, one each in the interior of the four quadrants. Which of the following statements is necessarily true? (Model Paper)

Choices

Choice (4) Response
a.

v1+v2+v3+v4=0

b.

There exist i,j with 1i<j4 such vi+vj is in the first quadrant

c.

There exist i,j with 1i<j4 such that vivj<0

d.

There exist i,j with 1i<j4 such that vivj>0

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