KVPY (Kishore Vaigyanik Protsahan Yojana) Stream SBSX (Class 12 & 1st Year B.Sc.) Math: Questions 28  31 of 172
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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 

Question number: 31
» Basic Mathematics » Geometry » Advanced Therorems and Properties
Appeared in Year: 2010
Question
Let ABC be an equilateral triangle, let KLMN be a rectangle with K, L on BC, M on AC and N on AB. Suppose and the area of triangle BKN is 6. The area of the triangle ABC is –
Choices
Choice (4)  Response  

a.  54 

b.  108 

c.  48 

d.  Question does not provide sufficient data or is vague 
