Integral Calculus (KVPY (Kishore Vaigyanik Protsahan Yojana) Stream SB-SX (Class 12 & 1st Year B.Sc.) Math): Questions 1 - 7 of 20

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Question number: 1

» Integral Calculus » Evaluation of Definite Integrals

Appeared in Year: 2010

MCQ▾

Question

Let, where n is non-negative integer. Then is equal to –

Choices

Choice (4) Response

a.

b.

c.

d.

Question number: 2

» Integral Calculus » Integration Using Trigonometric Identities

Appeared in Year: 2012

MCQ▾

Question

The value of the integral, where is –

Choices

Choice (4) Response

a.

b.

c.

d.

Question number: 3

» 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, is –

Choices

Choice (4) Response

a.

5

b.

c.

35.5

d.

34.5

Question number: 4

» Integral Calculus » Integration Using Trigonometric Identities

Appeared in Year: 2012

MCQ▾

Question

The value is –

Choices

Choice (4) Response

a.

b.

c.

d.

Question number: 5

» Integral Calculus » Integral as Limit of a Sum

Appeared in Year: 2012

MCQ▾

Question

Consider,

Choices

Choice (4) Response

a.

b.

c.

d.

Question number: 6

» Integral Calculus » Evaluation of Simple Integrals

Appeared in Year: 2012

MCQ▾

Question

The value is

Choices

Choice (4) Response

a.

4024

b.

0

c.

2012

d.

2013

Question number: 7

» Integral Calculus » Integration Using Trigonometric Identities

Appeared in Year: 2013

MCQ▾

Question

For x, t ∈ R let,

be a family of quadratic polynomials in x with variable coefficients. Let

Which of the following statements are true?

(i) for all t.

(ii) has infinitely many critical points.

(iii) for infinitely many t

(iv) for all t.

Choices

Choice (4) Response

a.

(i) and (ii) only

b.

(iii) and (iv) only

c.

(ii) and (iii) only

d.

(iv) and (i) only

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