$AlCl_3$ is:

$A$ curve satisfying the initial condition,$y(1) = 0,$ satisfies the differential equation,$x \frac{dy}{dx} = y - x^2.$ The area bounded by the curve and the $x$-axis is

Which one of the following statements is not correct?

The resistance of a wire is $R$. It is bent at the middle by $180^{\circ}$ and both the ends are twisted together to make a shorter wire. The resistance of the new wire is

In an experiment with a beam balance,an unknown mass $m$ is balanced by two known masses of $16\,kg$ and $4\,kg$ as shown in the figure. The value of the unknown mass $m$ is ......... $kg$.

When a wave travels in a medium,the particle displacement is given by: $y = a \sin 2\pi (bt - cx)$,where $a, b$,and $c$ are constants. The maximum particle velocity will be twice the wave velocity if