KVPY Stream SBSX (Class 12 & 1st Year B.Sc.) Math: Questions 91  94 of 172
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Question number: 91
» Integral Calculus » Integral as Limit of a Sum
Appeared in Year: 2014
Question
For a real number let denote the largest integer less than or equal to and . Let be a positive integer. Then is equal to –
Choices
Choice (4)  Response  

a.  0 

b. 


c.  1 

d. 


Question number: 92
» Basic Mathematics » Algebra » Solutions to Equations
Appeared in Year: 2014
Question
The under of integers for which has three real roots is –
Choices
Choice (4)  Response  

a. 


b.  55 

c.  1 

d.  25 

Question number: 93
» Basic Mathematics » Arithmetic » Number Games
Appeared in Year: 2014
Question
For each positive integer , let . Then the number of elements is for which is:
Choices
Choice (4)  Response  

a.  9 

b.  11 

c.  12 

d.  10 

Question number: 94
» Coordinate Geometry » Parallel and Perpendicular Lines
Appeared in Year: 2013
Question
Let be unit vectors in the plane, one each in the interior of the four quadrants. Which of the following statements is necessarily true? (Model Paper)
Choices
Choice (4)  Response  

a. 


b.  There exist with such is in the first quadrant 

c.  There exist with such that 

d.  There exist with such that 
