KVPY Stream-SA (Class 11) Math: Questions 52 - 54 of 251

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Question number: 52

» Basic Mathematics » Geometry » Circle and Properties

Appeared in Year: 2012

MCQ▾

Question

A circle is drawn in a sector of a larger circle of radius, r, as shown in the adjacent figure. The smaller circle is tangent to the two bounding radii and the arc of the sector. The radius of the small circle is.

A circle in a sector of a larger circle of radius r

A Circle in a Sector of a Larger Circle of Radius R

Figure shows a circle in a sector of a larger circle of radius r. The smaller circle is tangent to the boundary radii and the arc of the sector.

Choices

Choice (4) Response

a.

r2

b.

r2

c.

23r5

d.

r3

Question number: 53

» Complex Numbers and Quadratic Equations » Formation of Quadratic Equations With Given Roots

Appeared in Year: 2014

MCQ▾

Question

Let p(x)=x25x+a and q(x)=x23x+b , where a and b are positive integers. Suppose hcf(p(x),q(x))=x1 and k(x)=lcm(p(x),q(x)) . If the coefficient of the highest degree term of k (x) is 1, the sum of the roots of (x1)+k(x) is

Choices

Choice (4) Response

a.

6

b.

5

c.

4

d.

7

Question number: 54

» Basic Mathematics » Geometry » Advanced Therorems and Properties

Appeared in Year: 2014

MCQ▾

Question

Suppose S1 and S2 are two unequal circles; AB and CD are the direct common tangents to these circles. A transverse common tangent PQ cuts AB in R and CD in S. If AB = 10, then RS is

Two unequal circles with three tangents

Two Unequal Circles With Three Tangents

In figure two unequal circles with two tangents are shown. AB and CD are the direct common tangents to these circles. And a transverse common tangent PQ cut AB in R and CD in S.

Choices

Choice (4) Response

a.

9

b.

8

c.

11

d.

10

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