The escape velocity is \(11.2 \mathrm{~km} / \mathrm{s}\). If a body is to be projected in a direction making an angle \(60^{\circ}\) to the vertical, then the escape velocity is

In the figure shown above, a cell of negligible internal resistance and emf 22 V is connected to a network of resistors. If the power dissipated in the whole circuit is \(\dfrac{x}{10 R}\), then the value of \(x\) is:

For a series \(L-C-R\) circuit at resonance, the statement which is not true ?

Identify the wrong statement in the following. Coulomb's law correctly describes the electric force that

The reverse current in the semiconductor diode changes from \(20 \mu \mathrm{A}\) to \(40 \mu \mathrm{A}\) when the reverse potential is changed from \(10 \mathrm{~V}\) to \(15 \mathrm{~V}\), then the reverse resistance of the junction diode will be :

An ideal gas is taken via path \(A B C A\) as shown in figure.



The network done in the whole cycle is

Which of the following is a wrong statement?

Choose the correct metal/ ion from the brackets which ..........
A. has chemical reactivity similar to that of the first few members of the Lanthanoids \((\mathrm{Zn}, \mathrm{Ca}, \mathrm{Fe}, \mathrm{Cu})\).
B. has stable \(4 \mathrm{f}^7\) electronic configuration, but acts as a strong reducing agent and converts to \(\mathrm{M}^{3+}\) state. \(\left(\mathrm{Eu}^{2+}, \mathrm{Ce}^{2+}, \mathrm{Pr}^{2+}, \mathrm{Dy}^{2+}\right)\)
C. is a colorless ion \(\left(\mathrm{Tm}^{3+}, \mathrm{Lu}^{3+}, \mathrm{Gd}^{3+}, \mathrm{Sm}^{3+}\right)\).
D. shows stable +2 oxidation state and is diamagnetic \((\mathrm{Ce}, \mathrm{Sm}, \mathrm{Ho}, \mathrm{Yb})\)

The ratio in which the line \(3 x+4 y+2=0\) divides the distance between the lines \(3 x+4 y+5=0\) and \(3 x+4 y-5=0\) is

Choose the group of ions / molecules in which none of the species undergo Disproportionation reaction.

If the position vector of a point \(A\) is \(\vec{a}+2 \vec{b}\) and \(\vec{a}\) divides \(A B\) in the ratio \(2: 3\), then the position vector of \(B\) is

The line \(\dfrac{x-2}{3}=\dfrac{y-3}{4}=\dfrac{z-4}{5}\) is parallel to the plane

\(\int e^x\left(1+\tan x+\tan ^2 x\right) d x \text { is equal to }\)