The number of angular and radial nodes of $4d$ orbital respectively are

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

$A$ circle with center at $(2,4)$ is such that the line $x+y+2=0$ cuts a chord of length $6$. The radius of the circle is

The position of a particle is given by $\overrightarrow {r} = (\hat i + 2\hat j - \hat k)$ and its momentum is given by $\overrightarrow {P} = (3\hat i + 4\hat j - 2\hat k)$. The angular momentum is perpendicular to:

If $m \begin{bmatrix} -3 & 4 \end{bmatrix} + n \begin{bmatrix} 4 & -3 \end{bmatrix} = \begin{bmatrix} 10 & -11 \end{bmatrix}$,then $3m + 7n$ is equal to

Two particles $A$ and $B$,initially at rest,move towards each other under a mutual force of attraction. At an instance when the speed of $A$ is $v$ and the speed of $B$ is $2v$,the speed of the centre of mass $(CM)$ is: