KVPY Stream SB-SX (Class 12 & 1st Year B.Sc.) Math: Questions 117 - 120 of 172

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Question number: 117

» Limits & Continuity » Continuity

Appeared in Year: 2013

MCQ▾

Question

For real x with 10x10 define f(x)=10x2[t]dt , where for a real number r we denote by [r] the largest integer less than or equal to r . The number of points of discontinuity of f in the interval (10, 10) is – (Model Paper)

Choices

Choice (4) Response

a.

18

b.

10

c.

0

d.

19

Question number: 118

» Integral Calculus » Fundamental Theorem of Calculus

Appeared in Year: 2013

MCQ▾

Question

For a real number x let [x] denote the largest integer less than or equal to x and {x}=x[x] . The smallest possible integer value of n for which 1n[x]{x}dx exceeds 2013 is – (Model Paper)

Choices

Choice (4) Response

a.

90

b.

64

c.

63

d.

91

Question number: 119

» Sets, Relations and Functions » Functions and Composition

Appeared in Year: 2013

MCQ▾

Question

For given two functions,

P(x)=sinx and Q(x)=82xx2 .

Which of the following statement are true?

(i) Domain of Q((P(x))2)= Domain of Q(P(x))

(ii) Domain of P((Q(x))3)= Domain of Q(P(x))

(iii) Domain of Q(P(x))= Domain of Q(P(x))

(iv) Domain of Q(P(x))+P(Q(x))= Domain of P(Q(x)) (Model Paper)

Choices

Choice (4) Response

a.

Only (i) and (iv)

b.

Only (i)

c.

Only (i) and (ii)

d.

Only (iii) and (iv)

Question number: 120

» Coordinate Geometry » Equations of a Line

Appeared in Year: 2013

MCQ▾

Question

If a,b are positive real numbers such that the lines ax+9y=5 and 4x+by=3 are parallel, then the least possible value of a+b is – (Model Paper)

Choices

Choice (4) Response

a.

6

b.

13

c.

12

d.

8

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