KVPY Stream SB-SX (Class 12 & 1st Year BSC) Math: Questions 84 - 87 of 172

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Question number: 84

» 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 . The smallest positive integer n for which the integer 1n[x][x]dx exceed 60 is –

Choices

Choice (4) Response

a.

9

b.

10

c.

8

d.

[6023]

Question number: 85

» Basic Mathematics » Algebra » Solutions to Equations

Appeared in Year: 2014

MCQ▾

Question

Suppose a parabola y=ax2+bx+c has two x intercepts one positive and one negative, and its vertex is (2,2) . Then which of the following is true –

Choices

Choice (4) Response

a.

ab>0

b.

bc>0

c.

ca>0

d.

a+b+c>0

Question number: 86

» Limits & Continuity » Trigonometric Functions

Appeared in Year: 2014

MCQ▾

Question

Let f:[0,π]R be defined as,

f(x)={sinx,ifxisirrationalandx[0,π]tan2x,ifxisrationalandx[o,π]

The number of points in [0,π] at which the function f is continuous is –

Choices

Choice (4) Response

a.

4

b.

2

c.

0

d.

6

Question number: 87

» Sequence and Series » Sum Upto N Terms of Special Series

Appeared in Year: 2014

MCQ▾

Question

Let n3 be an integer. For a permutation σ=(a1,a2,,an) of (1, 2,n) we let fσ(x)=anXn1+an1++a2x+a1 . Let Sσ be the sum of the roots of fσ(x)=0 and let S denote the sum over all permutation σ of (1, 2,,n) of the number Sσ . Then

Choices

Choice (4) Response

a.

S<n!

b.

n!<S<0

c.

0<S<n!

d.

n!<S

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