KVPY StreamSA (Class 11) Math: Questions 52  54 of 265
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Question number: 52
» Basic Mathematics » Geometry » Circle and Properties
Appeared in Year: 2012
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.
Choices
Choice (4)  Response  

a. 


b. 


c. 


d. 


Question number: 53
» Complex Numbers and Quadratic Equations » Formation of Quadratic Equations With Given Roots
Appeared in Year: 2014
Question
Let and , where a and b are positive integers. Suppose and. If the coefficient of the highest degree term of k (x) is 1, the sum of the roots of 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
Question
Suppose S_{1} and S_{2} 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
Choices
Choice (4)  Response  

a.  9 

b.  8 

c.  11 

d.  10 
