KVPY (Kishore Vaigyanik Protsahan Yojana) Stream SB-SX (Class 12 & 1st Year B.Sc.) Math: Questions 71 - 74 of 172

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Question number: 71

» Permutations and Combinations » Fundamental Principle of Counting

Appeared in Year: 2012

MCQ▾

Question

Three children, each accompanied by a guardian, seek admission in a school. The principal wants to interview all 6 persons one after the other subject to the condition that no child is interviewed before its guardian. In how many ways can this be done?

Choices

Choice (4) Response

a.

180

b.

90

c.

60

d.

120

Question number: 72

» 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

Question number: 73

» Sets, Relations and Functions » Equivalence Relations

Appeared in Year: 2012

MCQ▾

Question

Let f: R ⟶ R be the function with. Then if and only if –

Choices

Choice (4) Response

a.

are all positive and distinct

b.

are all distinct

c.

At least two of are equal

d.

Question number: 74

» Basic Mathematics » Arithmetic » Number Games

Appeared in Year: 2012

MCQ▾

Question

Suppose a1, a2, a3, …, a2012 are integers arranged on a circle. Each number is equal to the average of its two adjacent numbers. If the sum of all even indexed numbers is 3018, what is the sum of all numbers?

Choices

Choice (4) Response

a.

1509

b.

3018

c.

6036

d.

0

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