Power radiated by a black body at temperature $T_1$ is $P$ and it radiates maximum energy at a wavelength $\lambda_1$. If the temperature of the black body is changed from $T_1$ to $T_2$, it radiates maximum energy at a wavelength $\frac{\lambda_1}{2}$. The power radiated at $T_2$ is (in $P$)

Which of the following ions forms the most stable complex compound?

If $x_1$ and $x_2$ are the real roots of the equation $x^2-kx+c=0$,then the distance between the points $A(x_1, 0)$ and $B(x_2, 0)$ is

Two persons $A$ and $B$ are located in the $X-Y$ plane at the points $(0,0)$ and $(0,10)$ respectively. (The distances are measured in $MKS$ units). At time $t=0$,they start moving simultaneously with velocities $\overrightarrow{v}_A = 2\hat{j} \text{ m/s}$ and $\overrightarrow{v}_B = 2\hat{i} \text{ m/s}$ respectively. The time after which $A$ and $B$ are at their closest distance is

$5.6 \ L$ of helium gas at $STP$ is adiabatically compressed to $0.7 \ L$. Taking the initial temperature to be $T_1$,the work done in the process is

If $s$ and $p$ are respectively the sum and the product of the slopes of the lines $3x^2 - 2xy - 15y^2 = 0$,then $s:p$ is equal to