Which of the following sets are convex? - Vidyadip

MCQ

Which of the following sets are convex?

A
$\{(\text{x},\text{y}):\text{x}^2+\text{y}^2\geq1\}$
B
$\{(\text{x},\text{y}):\text{y}^2\geq\text{x}\}$
C
$\{(\text{x},\text{y}):3\text{x}^2+4\text{y}^2\geq5\}$
✓
$\{(\text{x},\text{y}):\text{y}\geq2,\text{y}\leq4\}$

✓

Answer

Correct option: D.

$\{(\text{x},\text{y}):\text{y}\geq2,\text{y}\leq4\}$

is the region between two parallel lines, so any line segment joining any two points in it lies in it.
Hence, it is a convex set.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from Linear Programming→Linear Programming — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

If $f(x) = x^5 - 5x^4 + 5x^3 - 10$ has local maximum and minimum at $x = p$ and $x = q$ , respectively, then $(p, q)$ equals

$\frac{d}{d x}\left[\sin ^{-1} x-\sin ^{-1} \sqrt{x}\right]$ is equal to

The general solution of ${y^2}\,dx + ({x^2} - xy + {y^2})\,\,dy = 0$ is

If $\frac{d}{{dx}}f(x) = x\cos x + \sin x$ and $f(0) = 2$, then $f(x) = $

The probability that a randomly selected $2$ digit number belongs to the set $\left(n \in N:\left(2^{n}-2\right)\right.$ is a multiple of $3\, )$ is equal to:

Let $f(x)$ be $a$ quadratic expression which is positive for all real $x$ . If $g(x) = f(x) + f' (x) + f'' (x)$, then for any real $x$, which one is correct .

$\int \limits_{6}^{16} \frac{\log _{\mathrm{e}} x^{2}}{\log _{e} x^{2}+\log _{e}\left(x^{2}-44 x+484\right)} d x$ is equal to:

$\int_{}^{} {\frac{{dx}}{{\sin x + \sqrt 3 \cos x}}} = $

If $\text{f(x)}=\begin{cases}\frac{1}{1+\text{e}^{\frac{1}{\text{x}}}},&\text{x}\neq0\\0,&\text{x}=0\end{cases}$ then $f(x)$ is :

$\int_{}^{} {{{\left( {x + \frac{1}{x}} \right)}^3}} dx = $