If $u=\log \left(x^3+y^3+z^3-3 x y z\right)$,then $(x+y+z)(u_x+u_y+u_z)$ is equal to

The number of radial nodes of $3s$ and $2p$ orbitals respectively are

If $4$ moles of an ideal monoatomic gas at temperature $400 ~K$ is mixed with $2$ moles of another ideal monoatomic gas at temperature $700 ~K$,the temperature of the mixture is

Let $P(6, 3)$ be a point on the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$. If the normal at point $P$ intersects the $x$-axis at $(9, 0)$,then the eccentricity of the hyperbola is:

The contrapositive of the statement "If two numbers are not equal,then their squares are not equal" is

If the circle $x^2+y^2+8x-4y+c=0$ touches the circle $x^2+y^2+2x+4y-11=0$ externally and cuts the circle $x^2+y^2-6x+8y+k=0$ orthogonally,then $k$ is equal to