Statements

Let p: I m not feeling well q: I will go to doctor Given statement :- its contrapositive If I will not go to the doctor then i am feeling well.

The contrapositive of statement is Here, p : you are born in India. q : you are citizen of India. So, contrapositive of above statement is " If you are not a citizen of India, then you are not born in India".

The correct answer is 9.
$5^{99}=5^4.5^{95}$
$=625{\left[5^5\right]}^{19}$
$=625[3125{]}^{19}$
$=625[3124+1{]}^{19}$
$=625[11k\times 19+1]$
$=625\times 11k\times 19+625$
$=11k_1+616+9$
$=11\left(k_2\right)+9$
Remainder $=9$

$\underset{1}{\overset{2}{\int }}{x}^2{e}^{\left[x^3\right]+1}dx$
$x^3=t$
$3x^{2}dx=dt$
$=\frac{e}{3}\underset{1}{\overset{8}{\int }}{e}^{[t]}dt$
$=\frac{e}{3}\left\{\underset{1}{\overset{2}{\int }}edt+{\int }_2^3{e}^{2}dt+\dots \dots ..+\underset{7}{\overset{8}{\int }}{e}^{7}dt\right\}$
$=\frac{e}{3}\left(e+e^2+\dots \dots \dots +e^7\right)$
$=\frac{e^2}{3}\left(1+e+\dots \dots \dots +e^6\right)=\frac{e^2}{3}\frac{\left(e^7-1\right)}{(e-1)}$
$\frac{3(e-1)}{e}\underset{1}{\overset{2}{\int }}{x}^2\times e^{[x]+\left[x^3\right]}dx=\frac{3}{e}(e-1)\times \frac{e^2}{3}\frac{\left(e^7-1\right)}{(e-1)}$ $=e\left(e^7-1\right)$
$=e^8-e$