Basic Mathematics (KVPY (Kishore Vaigyanik Protsahan Yojana) StreamSA (Class 11) Math): Questions 77  81 of 164
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Question number: 77
» Basic Mathematics » Geometry » Advanced Therorems and Properties
Question
Let ABCD be a square of side length 1, and a circle of radius r, passing through B and C, and touching AD. The radius of r is –
Choices
Choice (4)  Response  

a. 


b. 


c. 


d. 


Question number: 78
» Basic Mathematics » Geometry » Triangle and Properties
Question
In a triangle ABC, points X and Y are on AB and AC, respectively, such that XY is parallel to BC. Which of the two following equalities always hold? (Here [PQR] denotes the area of triangle PQR) –
(I) [BCX] = [BCY]
(II)
Choices
Choice (4)  Response  

a.  (II) 

b.  Neither (I) nor (II) 

c.  (I) 

d.  Both a. and c. are correct 

Question number: 79
» Basic Mathematics » Geometry » Advanced Therorems and Properties
Question
A triangular corner is cut from a rectangular piece of paper and the resulting pentagon has sides 5,6, 8,9, 12 in some order. The ratio of the area of the pentagon to the area of the rectangle is –
Choices
Choice (4)  Response  

a. 


b. 


c. 


d. 


Question number: 80
» Basic Mathematics » Geometry » Advanced Therorems and Properties
Question
In the figure given below, a rectangle of perimeter 76 units is divided into 7 congruent rectangles:
What is the perimeter of each of the smaller rectangles?
Choices
Choice (4)  Response  

a.  32 

b.  38 

c.  28 

d.  19 

Question number: 81
» Basic Mathematics » Geometry » Triangle and Properties
Question
In a right triangle ABC, the incircle touches the hypotenuse AC at D. If AD = 2 and DC = 3, the inradius of ABC is,
Choices
Choice (4)  Response  

a.  1 

b.  2 

c.  3 

d.  4 
