Sets, Relations and Functions-Equivalence Relations (KVPY Stream SB-SX (Class 12 & 1st Year BSC) Math): Questions 1 - 2 of 2

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Question number: 1

» Sets, Relations and Functions » Equivalence Relations

Appeared in Year: 2012

MCQ▾

Question

Let n be a natural number and let ‘a’ be a real number. The number of zeros of x2n+1)earealnumber.Thenumberofzerosofn,thereforewecanwrite,urves(2n+1)x+a=0 in the interval [-1, 1] is

Choices

Choice (4) Response

a.

2 if a < 0

b.

At least three for every value of a

c.

2 if a > 0

d.

At most one for every value of a

Question number: 2

» 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

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