What is the value of $x$ if $2x + 5 = 15$?

Given that,$a \alpha^2+2 b \alpha+c \neq 0$ and that the system of equations
$\begin{aligned} & (a \alpha+b) x+a y+b z=0 \\ & (b \alpha+c) x+b y+c z=0 \\ & (a \alpha+b) y+(b \alpha+c) z=0\end{aligned}$
has a non-trivial solution,then $a, b$ and $c$ lie in

$\int_0^\pi \frac{x \tan x}{\sec x+\tan x} d x=$

Two loops $P$ and $Q$ are made from a uniform wire. The radii of $P$ and $Q$ are $r_1$ and $r_2$ respectively,and their moments of inertia are $I_1$ and $I_2$ respectively. If $\frac{I_2}{I_1} = 4$,then $\frac{r_2}{r_1}$ equals:

From the top of a tower of height $40 \ m$,a ball is projected upwards with a speed of $20 \ m/s$ at an angle $30^{\circ}$ to the horizontal. The ball will hit the ground in time ......... $\sec$ (Take $g = 10 \ m/s^2$)

Which of the following is a characteristic test for the phenolic group?