KVPY Stream SBSX (Class 12 & 1st Year BSC) Math: Questions 27  30 of 155
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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. 

Question number: 28
» Basic Mathematics » Arithmetic » Simplifying Expressions
Appeared in Year: 2010
Question
Let I, ω and ω^{2} be the cube roots of unity. The lest possible degree of a polynomial, with real coefficients, having 2 ω^{2}, 3 + 4 ω, 3 + 4 ω^{2} and 5 – ω – ω^{2} as roots is –
Choices
Choice (4)  Response  

a.  8  
b.  5  
c.  6  
d.  4 
Question number: 29
» Complex Numbers and Quadratic Equations » Nature of Roots
Appeared in Year: 2011
Question
Consider the cubic equation , where a, b, c are real numbers. Which of the following statements is correct?
Choices
Choice (4)  Response  

a.  If then the equation has all real and distinct roots  
b.  If then the equation has real and distinct roots  
c.  If then the equation has one real and two imaginary roots  
d.  If then the equation has all real roots 
Question number: 30
» Basic Mathematics » Geometry » Advanced Therorems and Properties
Appeared in Year: 2011
Question
In a rectangle ABCD, the coordinates of A and B are (1, 2) and (3, 6) respectively and some diameter of the circumscribing circle of ABCD has equation . Then the area of the rectangle is –
Choices
Choice (4)  Response  

a. 
 
b. 
 
c.  16  
d.  20 