KVPY Stream SB-SX (Class 12 & 1st Year B.Sc.) Math: Questions 26 - 29 of 172

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Question number: 26

» Vector Algebra » Scalar and Vector Triple Product

Appeared in Year: 2010

MCQ▾

Question

Let Equation be vectors in R3 and Equation be a unit vector in the xy-plane. Then the maximum possible value of Equation is –

Choices

Choice (4) Response

a.

Equation

b.

Equation

c.

Equation

d.

Equation

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 Equation is –

Choices

Choice (4) Response

a.

Equation

b.

Equation

c.

Equation

d.

Equation

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 Equation , where a, b, c are real numbers. Which of the following statements is correct?

Choices

Choice (4) Response

a.

If Equation then the equation has all real and distinct roots

b.

If Equation then the equation has real and distinct roots

c.

If Equation then the equation has one real and two imaginary roots

d.

If Equation then the equation has all real roots

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