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Range of Quadratic Expression

Which of the ...

Question

Which of the following sets are convex ?

A

{(x, y) : y² ≥ x}

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B

{(x, y) : 3x² + 4y² ≥ 5}

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C

{(x, y) : y ≤ 2. y ≤ 4}

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D

{(x, y) : x² + y² ≥ 1}

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Solution

The correct option is C
{(x, y) : y ≤ 2. y ≤ 4}

{(x, y) : y ≤ 2. y ≤ 4}

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Similar questions

Q. Which of the following sets are convex?
(a) {(x, y) : x² + y²≥ 1}
(b) {(x, y) : y² ≥ x}
(c) {(x, y) : 3x² + 4y² ≥ 5}
(d) {(x, y) : y ≥ 2, y ≤ 4}

Q. Which of the following is not a convex set?
(a) {(x, y) : 2x + 5y < 7}
(b) {(x, y) : x² + y² ≤ 4}
(c) {x :|x| = 5}
(d) {(x, y) : 3x² + 2y² ≤ 6}

Q. Solve the following equations:

\frac{\sqrt{x} - \sqrt{y}}{\sqrt{x} + \sqrt{y}} + \frac{\sqrt{x} + \sqrt{y}}{\sqrt{x} - \sqrt{y}} = \frac{17}{4}

x^{2} + y^{2} = 706

x, y, z

be positive integers such that

H C F (x, y, z) = 1

x^{2} + y^{2} = 2 z^{2}

. Which of the following statements are true?
I.

4

x

4

y

3

x + y

3

x - y

5

z (x^{2} - y^{2})

.

Q. Solve the following equations for

(x + y)

\sqrt{x + y} + \sqrt{x - y} = 4

x^{2} - y^{2} = 9

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