Three identical charges are placed at the vertices of an equilateral triangle. The force experienced by each charge, (if $k=1 / 4 \pi \varepsilon_0$ ) is

$\int_0^{\pi / 2} \sin ^8 x \cos ^2 x \, dx$ is equal to

If $f:[2,3] \rightarrow R$ is defined by $f(x)=x^3+3x-2$, then the range of $f(x)$ is contained in the interval

Given below are two statements: one is labelled as Assertion $A$ and the other is labelled as Reason $R$:
Assertion $A$: Size of $Bk^{3+}$ ion is less than $Np^{3+}$ ion.
Reason $R$: The above is a consequence of the lanthanoid contraction.
In the light of the above statements,choose the correct answer from the options given below:

An aircraft executes a horizontal loop with a speed of $150 \, m/s$ with its wings banked at an angle of $12^\circ$. The radius of the loop is .......... $km$. $(g = 10 \, m/s^2)$

The distance of the point $(1, 1, 9)$ from the point of intersection of the line $\frac{x-3}{1} = \frac{y-4}{2} = \frac{z-5}{2}$ and the plane $x+y+z=17$ is