### CSIR JUNE 2011 PART C QUESTION 62 SOLUTION

Which of the following subsets of $\Bbb R$ are convex.
1) $\{(x,y) : \mid x\mid \le 5, \mid y \mid \le 10\}$,
2) $\{(x,y):x^2 + y^2 = 1\}$,
3)$\{(x,y) : y \ge x^2\}$,
4) $\{(x,y) : y \le x^2\}$.
Solution:
A subset $A$ of $\Bbb R^2$ is said to be convex if the line segment joining any two points of $A$ lies entirely in $A$. The given sets are
option 1

option 2
option 3
option 4
From the images (shaded regions), we see that the sets which are given in option (1) and (3) are convex.
### NBHM 2020 PART A Question 4 Solution $$\int_{-\infty}^{\infty}(1+2x^4)e^{-x^2} dx$$
Evaluate : $$\int_{-\infty}^{\infty}(1+2x^4)e^{-x^2} dx$$ Solution : \int_{-\infty}^{\infty}(1+2x^4)e^{-x^2} dx = \int_{-\infty}^{\inft...