# 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

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

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

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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