KVPY Stream SBSX (Class 12 & 1st Year B.Sc.) Math: Questions 73  76 of 172
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Question number: 73
» Sets, Relations and Functions » Equivalence Relations
Appeared in Year: 2012
Question
Let f: R ⟶ R be the function with . Then if and only if –
Choices
Choice (4)  Response  

a.  are all positive and distinct 

b.  are all distinct 

c.  At least two of are equal 

d. 


Question number: 74
» Basic Mathematics » Arithmetic » Number Games
Appeared in Year: 2012
Question
Suppose a_{1}, a_{2}, a_{3}, …, a_{2012} are integers arranged on a circle. Each number is equal to the average of its two adjacent numbers. If the sum of all even indexed numbers is 3018, what is the sum of all numbers?
Choices
Choice (4)  Response  

a.  1509 

b.  3018 

c.  6036 

d.  0 

Question number: 75
» Complex Numbers and Quadratic Equations » Nature of Roots
Appeared in Year: 2012
Question
Suppose a, b, c are real numbers, and each of the equations and has two distinct real roots. Then the equation has –
Choices
Choice (4)  Response  

a.  Two equal roots 

b.  No real roots 

c.  One positive and one negative root 

d.  Two distinct positive real roots 

Question number: 76
» Basic Mathematics » Algebra » Simplifying Expressions
Appeared in Year: 2012
Question
The maximum value M of , as x varies over real, satisfies –
Choices
Choice (4)  Response  

a. 


b.  9 < M < 25 

c. 


d. 

