$A$ calcite crystal is placed over a dot on a piece of paper and rotated. On seeing through the calcite,one will see:

$A$ circle passes through the point $(3, 4)$ and cuts the circle $x^2 + y^2 = a^2$ orthogonally. The locus of its centre is a straight line. If the distance of this straight line from the origin is $25$,then $a^2$ is equal to

The voltage gain of a transistor in common emitter configuration is $160$. The resistances in base and collector sides of the circuit are $1 \text{ k}\Omega$ and $4 \text{ k}\Omega$ respectively. If the change in base current is $100 \mu A$, then the change in output current is:

If the coefficient of $x$ in the expansion of $\left(x^2+\frac{k}{x}\right)^5$ is $270$,then $k$ is equal to

Two identical balls $A$ and $B$ are released from the positions shown in the figure. They collide elastically on the horizontal portion $MN$. The ratio of the heights attained by $A$ and $B$ after the collision will be: (neglect friction)

Which of the following statements is incorrect?