KVPY Stream-SA (Class 11) Math: Questions 29 - 33 of 251

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Question number: 29

» Basic Mathematics » Geometry » Triangle and Properties

Appeared in Year: 2009

MCQ▾

Question

In a right triangle ABC, the incircle touches the hypotenuse AC at D. If AD = 10 and DC = 3 and the sides AB, BC and AC are integer, the inradius of ABC is

Choices

Choice (4) Response

a.

4

b.

5

c.

2

d.

3

Question number: 30

» Sequence and Series » Arithmetico - Geometric Progression

Appeared in Year: 2012

MCQ▾

Question

If a, b, c, d are positive real numbers such that, a3=a+b4=a+b+c5=a+b+c+d6 , then ab+2c+3d is

Choices

Choice (4) Response

a.

1

b.

12

c.

2

d.

All of the above

Question number: 31

» Sets, Relations and Functions » Equivalence Relations

Appeared in Year: 2014

MCQ▾

Question

Let a, b, c be non-zero real numbers such that a + b + c = 0; let q=a2+b2+c2 and r=a4+b4+c4 Then.

Choices

Choice (4) Response

a.

q2<2r always

b.

q2=2r always

c.

q22r can take both positive and negative value

d.

q2>2r always

Question number: 32

» Basic Mathematics » Geometry » Advanced Therorems and Properties

Appeared in Year: 2012

MCQ▾

Question

In the figure, AKHF, FKDE and HBCK are unit squares; AD and BF intersect in X. Then the ratio of the areas of triangles AXF and ABF is.

 Figure made up of three squares

Figure Made Up of Three Squares

In figure AKHF, FKDE and HBCK are unit squares; AD and BF intersect in X.

Choices

Choice (4) Response

a.

14

b.

18

c.

15

d.

16

Question number: 33

» Sequence and Series » Sum Upto N Terms of Special Series

Appeared in Year: 2010

MCQ▾

Question

The number of positive integers n in the set {1, 2, 3, …, 100} for which the number

12+22+32++n21+2+3++n is an integer is

Choices

Choice (4) Response

a.

4

b.

6

c.

7

d.

14

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