KVPY Stream SB-SX (Class 12 & 1st Year B.Sc.) Math: Questions 140 - 144 of 172

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Question number: 140

» Matrices and Determinants » Evaluation of Determinants

Appeared in Year: 2015

MCQ▾

Question

The remainder when the determinant,

201420142015201520162016201720172018201820192019202020202021202120222022

is divided by 5 is –

Choices

Choice (4) Response

a.

1

b.

3

c.

4

d.

2

Question number: 141

» Trigonometry » Trigonometric Identities and Equations

Appeared in Year: 2015

MCQ▾

Question

The number of real numbers λ for which the equality

sin(λα)sinαcos(λα)cosα=λ1

Holds for all real α which are not integral multiple of π2 is –

Choices

Choice (4) Response

a.

Infinite

b.

3

c.

2

d.

1

Question number: 142

» Coordinate Geometry » Parabola

Appeared in Year: 2015

MCQ▾

Question

The number of ordered pairs (x,y) of real numbers that satisfy the simulation equations x+y2=x2+y=12 is –

Choices

Choice (4) Response

a.

4

b.

0

c.

2

d.

1

Question number: 143

» Basic Mathematics » Arithmetic » Number Games

Appeared in Year: 2015

MCQ▾

Question

Suppose a,b,c are positive integers such that 2a+4b+8c=328 . Then a+2b+3cabc is equal to –

Choices

Choice (4) Response

a.

58

b.

1724

c.

56

d.

12

Question number: 144

» Integral Calculus » Fundamental Integrals Involving Functions

Appeared in Year: 2015

MCQ▾

Question

Let f:RR be a continuous function satisfying,

f(x)+0xtf(t)dt+x2=0,

For all xR . Then –

Choices

Choice (4) Response

a.

limxf(x)=2

b.

f(x) is an odd function

c.

limxf(x)=2

d.

f(x) has more than 1 point in common with the x axis

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