KVPY (Kishore Vaigyanik Protsahan Yojana) Stream SBSX (Class 12 & 1st Year B.Sc.) Math: Questions 23  27 of 172
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Question number: 23
» Sequence and Series » Geometric Progressions
Appeared in Year: 2010
Question
The number of natural numbers n in the interval [500, 2010] for which the polynomial divides the polynomial is –
Choices
Choice (4)  Response  

a.  1006 

b.  503 

c.  100 

d.  0 

Question number: 24
» Vector Algebra » Scalar and Vector Products
Appeared in Year: 2011
Question
Let be three vectors in the xyz space such that. If A, B, C are points with position vectors respectively, then the number of possible of the centroid of triangle ABC is –
Choices
Choice (4)  Response  

a.  1 

b.  6 

c.  3 

d.  2 

Question number: 25
» Coordinate Geometry » Ellipse
Appeared in Year: 2010
Question
Let P be an arbitrary point on the ellipse. Suppose F_{1} and F_{2} are the foci of the ellipse. The locus of the centroid of the triangle PF_{1}F_{2} as P moves on the ellipse is –
Choices
Choice (4)  Response  

a.  A hyperbola 

b.  A circle 

c.  A parabola 

d.  An ellipse 

Question number: 26
» Vector Algebra » Scalar and Vector Triple Product
Appeared in Year: 2010
Question
Let be vectors in R^{3} and be a unit vector in the xyplane. Then the maximum possible value of is –
Choices
Choice (4)  Response  

a. 


b. 


c. 


d. 


Question number: 27
» Three Dimensional Geometry » Ratios and Direction Cosines
Appeared in Year: 2010
Question
Let V_{1} be the volume of a given right circular cone with O as the centre of the base and A as its apex. Let V_{2} be the maximum volume of the right circular cone inscribed in the given cone whose apex is O and whose base is parallel to the base of the given cone. Then the ratio is –
Choices
Choice (4)  Response  

a. 


b. 


c. 


d. 

