The bond angles of $NH_3$,$NH_4^+$,and $NH_2^-$ are in the order :-

If $\frac{dy}{dx} + 2x \tan(x-y) = 1$,then $\sin(x-y)$ is equal to

Beats are produced by two waves given by $y_1 = a \sin(2000 \pi t)$ and $y_2 = a \sin(2008 \pi t)$. The number of beats heard per second is

If $e^{f(x)}=\frac{10+x}{10-x}, x \in(-10,10)$ and $f(x)=k f\left(\frac{200 x}{100+x^2}\right)$,then $k$ is equal to

An elevator weighing $6000\, kg$ is pulled upward by a cable with an acceleration of $5\, m/s^2$. Taking $g$ to be $10\, m/s^2$,then the tension in the cable is ........... $N$.

The locus of the centre of a circle which always passes through the fixed points $(a, 0)$ and $(-a, 0)$ is