KVPY Stream SB-SX (Class 12 & 1st Year BSC) Math: Questions 40 - 44 of 155

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Question number: 40

» Matrices and Determinants » Area of Triangles Using Determinants

Appeared in Year: 2011

MCQ▾

Question

Let A=(4, 0),B=(0, 12) be two points in the plane. The locus of a point C such that the area of triangle ABC is 18 sq. units is –

Choices

Choice (4) Response

a.

(y+3x12)2=81

b.

(y+3x81)2=14

c.

(y+3x+12)2=81

d.

(y+3x+81)2=12

Question number: 41

» Trigonometry » Trigonometric Identities and Equations

Appeared in Year: 2012

MCQ▾

Question

The value of tan810tan630tan270+tan90 is –

Choices

Choice (4) Response

a.

0

b.

3

c.

2

d.

4

Question number: 42

» Basic Mathematics » Geometry » Advanced Therorems and Properties

Appeared in Year: 2012

MCQ▾

Question

Let h be the orthocenter of an acute – angled triangle ABC and O be its circumcenter. Then HA+HB+HC ,

Choices

Choice (4) Response

a.

Is equal to HO

b.

Is equal to 2HO

c.

Is equal to 3HO

d.

Is not a scalar multiple of HO in general

Question number: 43

» Trigonometry » Trigonometric Identities and Equations

Appeared in Year: 2012

MCQ▾

Question

Let f(x)=sin(xa)+sin(x+a)cos(xa)cos(x+a), then –

Choices

Choice (4) Response

a.

f is strictly increasing function

b.

f is strictly decreasing function

c.

f(x+2π)=f(x) but f(x+α)f(x) for any 0<α<2π

d.

f is a constant function:

Question number: 44

» Basic Mathematics » Algebra » Solutions to Equations

Appeared in Year: 2012

MCQ▾

Question

In the real number system, the equation x+34x1+x+86x1=1 has –

Choices

Choice (4) Response

a.

No solution

b.

Exactly two distinct solutions

c.

Infinitely many solutions

d.

Exactly four distinct solutions

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