Basic MathematicsGeometry (KVPY Stream SBSX (Class 12 & 1st Year B.Sc.) Math): Questions 10  12 of 24
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Question number: 10
» 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: 11
» 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: 12
» Basic Mathematics » Geometry » Triangle and Properties
Appeared in Year: 2013
Question
In a triangle , let G denote its centroid and let M, N be points in the interiors of the segments , respectively, such that are collinear. If denotes the ratio of the area of triangle to the area of then, (Model Paper)
Choices
Choice (4)  Response  

a. 


b. 


c. 


d. 

