KVPY (Kishore Vaigyanik Protsahan Yojana) Stream SBSX (Class 12 & 1st Year B.Sc.) Math: Questions 110  112 of 172
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Question number: 110
» Basic Mathematics » Geometry » Advanced Therorems and Properties
Appeared in Year: 2013
Question
Let be a non – constant polynomial with real coefficients such that and for all real . Which of the following statements is NOT necessarily true? (Model Paper)
Choices
Choice (4)  Response  

a.  The coefficient of the highest degree term in is negative 

b.  has at least two real roots 

c.  If then 

d.  At least one of the coefficients of is bigger than . 

Question number: 111
» Basic Mathematics » Geometry » Advanced Therorems and Properties
Appeared in Year: 2014
Question
Let be the circle in the XY – plane. For each , let be the line passing through and . Note that intersects C in two points, one of which is . Let be the other point. As varies between and , the collection of points sweeps out an arc on C. The angle subtended by this are at is:
Choices
Choice (4)  Response  

a. 


b. 


c. 


d. 


Question number: 112
» Basic Mathematics » Arithmetic » Number Games
Appeared in Year: 2014
Question
If is a positive integer and is a cube root of unity, the number of possible values of
is –
Choices
Choice (4)  Response  

a.  6 

b.  4 

c.  2 

d.  3 
