KVPY Stream SB-SX (Class 12 & 1st Year B.Sc.) Math: Questions 149 - 154 of 172

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Question number: 149

» Basic Mathematics » Arithmetic » Number Games

Appeared in Year: 2015

MCQ▾

Question

The largest perfect square that divides 2014320133+2012320113++2313 is –

Choices

Choice (4) Response

a.

10072

b.

20142

c.

22

d.

12

Question number: 150

» Integral Calculus » Properties of Definite Integrals

Appeared in Year: 2015

MCQ▾

Question

If p(x) is a cubic polynomial with p(1)=3 , p(0)=2 and p(1)=4 , then

11p(x)dxis

Choices

Choice (4) Response

a.

3

b.

2

c.

5

d.

4

Question number: 151

» Sets, Relations and Functions » Domain, Range

Appeared in Year: 2015

MCQ▾

Question

Let f(x)=αx22+1x ; where, α is a real constant. The smallest α for which f(x)0 for all x>0 is –

Choices

Choice (4) Response

a.

2333

b.

2433

c.

2233

d.

2533

Question number: 152

» Limits & Continuity » Real Valued Functions

Appeared in Year: 2015

MCQ▾

Question

Let a>0 be a real number. Then the limit

limx2ax+a3x(a2+a)a3xax2

is –

Choices

Choice (4) Response

a.

a2+a2

b.

23(1a)

c.

43a

d.

2loga

Question number: 153

» Basic Mathematics » Arithmetic » Simplifying Expressions

Appeared in Year: 2015

MCQ▾

Question

Let x=(50+7)13(507)13 . Then –

Choices

Choice (4) Response

a.

x=3

b.

x=2

c.

x is a rational number, but not an integer

d.

x is an irrational number

Question number: 154

» Vector Algebra » Scalar and Vector Products

Appeared in Year: 2015

MCQ▾

Question

Let a=6i^3j^6k^ and d=i^+j^+k^ . Suppose that a=b+c where b is parallel to d and c is perpendicular to d . Then c is –

Choices

Choice (4) Response

a.

7i^2j^5k^

b.

3i^+6j^9k^

c.

4i^5j^+k^

d.

5i^4j^k^

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