KVPY Stream SB-SX (Class 12 & 1st Year BSC) Math: Questions 73 - 76 of 155

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Question number: 73

» Sets, Relations and Functions » Equivalence Relations

Appeared in Year: 2012

MCQ▾

Question

Let f: R ⟶ R be the function f(x)=(xa1)(xa2)+(xa2)(xa3)+(xa3)(xa1) with a1,a2,a3R . Then f(x)0 if and only if –

Choices

Choice (4) Response

a.

a1,a2,a3 are all positive and distinct

b.

a1,a2,a3 are all distinct

c.

At least two of a1,a2,a3 are equal

d.

a1=a2=a3

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

Question number: 75

» Complex Numbers and Quadratic Equations » Nature of Roots

Appeared in Year: 2012

MCQ▾

Question

Suppose a, b, c are real numbers, and each of the equations x2+2ax+b2=0 and x2+2bx+c2=0 has two distinct real roots. Then the equation x2+2cx+a2=0 has –

Choices

Choice (4) Response

a.

Two equal roots

b.

No real roots

c.

One positive and one negative root

d.

Two distinct positive real roots

Question number: 76

» Basic Mathematics » Algebra » Simplifying Expressions

Appeared in Year: 2012

MCQ▾

Question

The maximum value M of 3x+5x9x+15x25x , as x varies over real, satisfies –

Choices

Choice (4) Response

a.

3<M<5

b.

9 < M < 25

c.

0<M<2

d.

5<M<9

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