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 |
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. |
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. |
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 |
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 |