Integral Calculus (KVPY (Kishore Vaigyanik Protsahan Yojana) Stream SB-SX (Class 12 & 1st Year B.Sc.) Math): Questions 6 - 9 of 20

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Question number: 6

» Integral Calculus » Evaluation of Simple Integrals

Appeared in Year: 2012

MCQ▾

Question

The value Equation 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,

Equation

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

Equation

Which of the following statements are true?

(i) Equation for all t.

(ii) Equation has infinitely many critical points.

(iii) Equation for infinitely many t

(iv) Equation 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

Question number: 8

» Integral Calculus » Integral as Limit of a Sum

Appeared in Year: 2014

MCQ▾

Question

For a real number Equation let Equation denote the largest integer less than or equal to Equation . The smallest positive integer Equation for which the integer Equation exceed 60 is –

Choices

Choice (4) Response

a.

9

b.

10

c.

8

d.

Equation

Question number: 9

» Integral Calculus » Integration Using Trigonometric Identities

Appeared in Year: 2013

MCQ▾

Question

A function Equation is defined as,

Equation

It is a family of quadratic polynomials in Equation with variable coefficients. And also function,

Equation Which of the following statements are true?

(i) Equation

(ii) Equation has infinitely many critical points.

(iii) Equation (Model Paper)

Choices

Choice (4) Response

a.

(iii) and (i) only

b.

(i) and (ii) only

c.

(iii) only

d.

(ii) and (iii) only

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