KVPY Stream SB-SX (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

MCQ▾

Question

Let V1 be the volume of a given right circular cone with O as the centre of the base and A as its apex. Let V2 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 V2V1 is –

Choices

Choice (4) Response
a.

49

b.

827

c.

325

d.

427

Question number: 28

» Basic Mathematics » Arithmetic » Simplifying Expressions

Appeared in Year: 2010

MCQ▾

Question

Let I, ω and ω2 be the cube roots of unity. The lest possible degree of a polynomial, with real coefficients, having 2 ω2, 3 + 4 ω, 3 + 4 ω2 and 5 – ω – ω2 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

MCQ▾

Question

Consider the cubic equation x3+ax2+bx+c=0 , where a, b, c are real numbers. Which of the following statements is correct?

Choices

Choice (4) Response
a.

If a22b>0, then the equation has all real and distinct roots

b.

If 4a327b2>, then the equation has real and distinct roots

c.

If a22b<0, then the equation has one real and two imaginary roots

d.

If a22b0, then the equation has all real roots

Question number: 30

» Basic Mathematics » Geometry » Advanced Therorems and Properties

Appeared in Year: 2011

MCQ▾

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 2xy+4=0 . Then the area of the rectangle is –

Choices

Choice (4) Response
a.

210

b.

25

c.

16

d.

20

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