Basic MathematicsGeometry (KVPY (Kishore Vaigyanik Protsahan Yojana) StreamSA (Class 11) Math): Questions 29  34 of 64
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Question number: 29
» Basic Mathematics » Geometry » Quadrilateral and Properties
Question
Let ABCD be a square of side length 1. Let P, Q, R, S be points in the interiors of the sides AD, BC, AB, CD, respectively, such that PQ and RS intersect at right angles. If then RS equals –
Choices
Choice (4)  Response  

a. 


b. 


c. 


d. 


Question number: 30
» Basic Mathematics » Geometry » Polygons With More Than 4 Sides
Question
In the figure given below, if the areas of the two regions are equal then which of the following is true?
Choices
Choice (4)  Response  

a.  x = y 

b.  x = 3y 

c.  x = 2y 

d.  2x = y 

Question number: 31
» Basic Mathematics » Geometry » Advanced Therorems and Properties
Question
A square ABCD is inscribed in a circle of radius 3. Two tangents to a circle at points A and B on the circle intersect at a point E. If AE = 4 then find the length of the sides of square.
Choices
Choice (4)  Response  

a.  24 

b.  12 

c. 


d. 


Question number: 32
» Basic Mathematics » Geometry » Triangle and Properties
Question
Let P be an interior point of a triangle ABC. Let Q and R be the reflections of P in AB and AC, respectively. If Q, A, R are collinear then ∠A equals 
Choices
Choice (4)  Response  

a.  90^{0} 

b.  60^{0} 

c.  30^{0} 

d.  120^{0} 

Question number: 33
» Basic Mathematics » Geometry » Quadrilateral and Properties
Question
The area of a rectangular PQRS is 36. Points M and N are on the side RS, such that PM = QN = 5. Find the length of MN. (Lengths of sides of the rectangular are integer)
Choices
Choice (4)  Response  

a.  5 

b.  3 

c.  4 

d.  2 

Question number: 34
» Basic Mathematics » Geometry » Circle and Properties
Question
Suppose P is a point on the circle with centre O and radius 2; R is a point outside the circle such that in triangle PRO, ∠POR = 4^{0}. Let S be the point where the segment PS intersects the given circle. If PS = SR, then measure of ∠SRP equals,
Choices
Choice (4)  Response  

a.  46^{0} 

b.  88^{0} 

c.  44^{0} 

d.  48^{0} 
