Basic Mathematics (KVPY Stream SBSX (Class 12 & 1st Year B.Sc.) Math): Questions 50  54 of 57
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Question number: 50
» Basic Mathematics » Geometry » Circle and Properties
Appeared in Year: 2015
Question
Among all sectors of a fixed perimeter, choose the one with maximum area. Then the angle at the centre of this sector (i. e. , the angle between the bounding radii) is –
Choices
Choice (4)  Response  

a. 


b. 


c. 


d.  2 

Question number: 51
» Basic Mathematics » Geometry » Advanced Therorems and Properties
Appeared in Year: 2015
Question
A mirror in the first quadrant is in the shape of a hyperbola whose equation is . A light source in the second quadrant emits a beam of light that hits the mirror at the points . If the reflected ray is parallel to the axis, the slope of the incident beam is –
Choices
Choice (4)  Response  

a. 


b. 


c.  2 

d. 


Question number: 52
» Basic Mathematics » Arithmetic » Number Games
Appeared in Year: 2015
Question
The largest perfect square that divides is –
Choices
Choice (4)  Response  

a. 


b. 


c. 


d. 


Question number: 53
» Basic Mathematics » Arithmetic » Simplifying Expressions
Appeared in Year: 2015
Question
Let . Then –
Choices
Choice (4)  Response  

a. 


b. 


c.  is a rational number, but not an integer 

d.  is an irrational number 

Question number: 54
» Basic Mathematics » Geometry » Advanced Therorems and Properties
Appeared in Year: 2016
Question
In a circle with centre , suppose are three points on its circumference such that is the mid – point of minor arc . Suppose when ,
If is doubled to , then the ratio is –
Choices
Choice (4)  Response  

a. 


b. 


c. 


d. 

