From a point on the level ground,the angle of elevation of the top of a pole is $30^{\circ}$. On moving $20 \ m$ nearer to the pole,the angle of elevation becomes $45^{\circ}$. The height of the pole (in metres) is:

The element having the electronic configuration $[Kr] 4d^{10} 4f^{14} 5s^2 5p^6 5d^2 6s^2$ belongs to

Let $x+y=k$ be a normal to the parabola $y^2=12x$. If $p$ is the length of the perpendicular from the focus of the parabola onto this normal,then $4k-2p^2$ is equal to

If $\int \frac{x-\sin x}{1+\cos x} dx = x \tan \left(\frac{x}{2}\right) + p \log \left|\sec \left(\frac{x}{2}\right)\right| + C$, then $p$ is equal to

Two resistances of $400\,\Omega$ and $800\,\Omega$ are connected in series with a $6\,V$ battery of negligible internal resistance. $A$ voltmeter of resistance $10,000\,\Omega$ is used to measure the potential difference across the $400\,\Omega$ resistor. The error in the measurement of potential difference (in volts) is approximately:

Among $TiF_6^{2-}, CoF_6^{3-}, Cu_2Cl_2$ and $NiCl_4^{2-}$,the colourless species are: