KVPY (Kishore Vaigyanik Protsahan Yojana) Stream SBSX (Class 12 & 1st Year B.Sc.) Math: Questions 167  171 of 172
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Question number: 167
» Basic Mathematics » Arithmetic » Simplifying Expressions
Appeared in Year: 2016
Question
The Polynomial equation has,
Choices
Choice (4)  Response  

a.  three real roots for any , and exactly one real root for any 

b.  exactly one real root for any real 

c.  three real roots for any real 

d.  three real roots for any , and exactly one real root for any 

Question number: 168
» Trigonometry » Trigonometric Functions
Appeared in Year: 2016
Question
Let be a polynomial with real coefficients such that , for all . Consider the following statements:
(i) is an even function
(ii) can be expressed as a polynomial in
(iii) is a polynomial of even degree.
Then,
Choices
Choice (4)  Response  

a.  All are true 

b.  Only and are true 

c.  All are false 

d.  Only and are true 

Question number: 169
» Basic Mathematics » Algebra » Solutions to Equations
Appeared in Year: 2016
Question
The number of integers for which the equation has at least two distinct integer roots is –
Choices
Choice (4)  Response  

a.  2 

b.  4 

c.  1 

d.  3 

Question number: 170
» Integral Calculus » Determining Areas of Regions Bounded by Simple Curves
Appeared in Year: 2016
Question
The area of the region bounded by the curve and the axis, , is –
Choices
Choice (4)  Response  

a. 


b.  0 

c. 


d. 


Question number: 171
» Coordinate Geometry » Y Equals Mx Plus C to Be Tangent and Points of Tangency
Appeared in Year: 2016
Question
Suppose the tangent to the parabola at has slop . Then equals –
Choices
Choice (4)  Response  

a.  3 

b.  1 

c.  2 

d.  0 
