KVPY Stream SB-SX (Class 12 & 1st Year B.Sc.) Math: Questions 31 - 34 of 172

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Question number: 31

» Basic Mathematics » Geometry » Advanced Therorems and Properties

Appeared in Year: 2010

MCQ▾

Question

Let ABC be an equilateral triangle, let KLMN be a rectangle with K, L on BC, M on AC and N on AB. Suppose ANNB=2 and the area of triangle BKN is 6. The area of the triangle ABC is –

Choices

Choice (4) Response

a.

54

b.

108

c.

48

d.

Question does not provide sufficient data or is vague

Question number: 32

» Trigonometry » Trigonometric Functions

Appeared in Year: 2011

MCQ▾

Question

Let f(x)=cos5x+Acos4x+Bcos3x+Ccos2x+Dcosx+E, and T=f(0)f(π5)+f(2π5)f(3π5)++f(8π5)f(9π5). Then T,

Choices

Choice (4) Response

a.

Is independent of A, B, C, D, E

b.

Depends on A, B, C, D, E

c.

Depend on B, D but independent of A, C, E

d.

Depends on A, C, E but independent of B and D

Question number: 33

» Integral Calculus » Evaluation of Definite Integrals

Appeared in Year: 2010

MCQ▾

Question

Let In=01(logx)ndx , where n is non-negative integer. Then I2011+2011I2010 is equal to –

Choices

Choice (4) Response

a.

I100+100I99

b.

I1000+999I998

c.

I890+890I889

d.

I53+54I52

Question number: 34

» Basic Mathematics » Arithmetic » Simplifying Expressions

Appeared in Year: 2011

MCQ▾

Question

Let [x] denote the largest integer not exceeding x and {x}=x[x] . Then 02012ecos(π{x})ecos(π{x})+ecos(π{x})dx is equal to –

Choices

Choice (4) Response

a.

2012x

b.

0

c.

2012

d.

1006

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