KVPY Stream SB-SX (Class 12 & 1st Year B.Sc.) Math: Questions 6 - 10 of 172

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Question number: 6

» Coordinate Geometry » Locus and Its Equation

Appeared in Year: 2011

MCQ▾

Question

All the points (x, y) in the plane satisfying the equation x2+2xsin(xy)+1=0 lie on –

Choices

Choice (4) Response

a.

a pair of straight lines

b.

a parabola

c.

a family of hyperbolas

d.

an ellipse

Question number: 7

» Basic Mathematics » Arithmetic » Simplifying Expressions

Appeared in Year: 2011

MCQ▾

Question

Suppose logab+logba=c. The smallest possible integer value of c for all a, b > 1 is –

Choices

Choice (4) Response

a.

2

b.

3

c.

1

d.

4

Question number: 8

» Basic Mathematics » Arithmetic » Simplifying Expressions

Appeared in Year: 2011

MCQ▾

Question

The value of

limn(14n21+14n24++14n2n2)

is –

Choices

Choice (4) Response

a.

14

b.

π6

c.

π4

d.

π12

Question number: 9

» Binomial Theorem » Simple Applications

Appeared in Year: 2011

MCQ▾

Question

If f(x)=(2011+x)n, where x is a real variable and n is a positive integer, then the value of, f(0)+f(0)+f(0)2++fn1(0)(n1)! is –

Choices

Choice (4) Response

a.

(2012)n

b.

n(2011)n

c.

(2011)n

d.

(2012)n1

Question number: 10

» Sets, Relations and Functions » Union, Intersection and Complement of Sets

Appeared in Year: 2010

MCQ▾

Question

Consider the region A={(x,y) x2+y2100} and B={(x,y) sin(x+y)>0} in the plane. Then the area of the region AB is

Choices

Choice (4) Response

a.

100

b.

100π

c.

50π

d.

10 π

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