In how many ways can $3$ letters be posted in $4$ letter-boxes,if all the letters are not posted in the same letter-box?

The cubic equation whose roots are thrice to each of the roots of $x^3+2 x^2-4 x+1=0$ is

Vegetative propagation in $Pistia$ occurs by:

$A$ curve passes through the point $\left(1, \frac{\pi}{6}\right)$. Let the slope of the curve at each point $(x, y)$ be $\frac{y}{x}+\sec \left(\frac{y}{x}\right)$,where $x>0$. Then,the equation of the curve is:

If $(2,-1,3)$ is the foot of the perpendicular drawn from the origin to the plane,then the equation of the plane is

If the slope of one of the pair of lines represented by $2x^2 + 3xy + Ky^2 = 0$ is $2$,then the angle between the pair of lines is