NEST (National Entrance Screening Test-NISER) Mathematics: Questions 25 - 29 of 255

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Question 25

Appeared in Year: 2010

Question MCQ▾

Let P be an arbitrary point on the ellipse . Suppose F1 and F2 are the foci of the ellipse. The locus of the centroid of the triangle PF1F2 as P moves on the ellipse is –

Choices

Choice (4)Response

a.

An ellipse

b.

A circle

c.

A hyperbola

d.

A parabola

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Question 26

Appeared in Year: 2010

Question MCQ▾

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

Choices

Choice (4)Response

a.

b.

c.

d.

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Question 27

Appeared in Year: 2010

Question MCQ▾

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 is –

Choices

Choice (4)Response

a.

b.

c.

d.

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Question 28

Appeared in Year: 2010

Question MCQ▾

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.

4

d.

6

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Question 29

Appeared in Year: 2011

Question MCQ▾

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 real and distinct roots

b.

If then the equation has one real and two imaginary roots

c.

If then the equation has all real roots

d.

If then the equation has all real and distinct roots

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