The events $A$ and $B$ have probabilities $0.25$ and $0.50$,respectively. The probability that both $A$ and $B$ occur simultaneously is $0.14$. Then,the probability that neither $A$ nor $B$ occurs is:

If $Q$ denotes the set of all rational numbers and $f\left(\frac{p}{q}\right)=\sqrt{p^2-q^2}$ for any $\frac{p}{q} \in Q$,then observe the following statements.
$I$. $f\left(\frac{p}{q}\right)$ is real for each $\frac{p}{q} \in Q$
$II$. $f\left(\frac{p}{q}\right)$ is a complex number for each $\frac{p}{q} \in Q$.
Which of the following is correct?

The figure shows the variation of the gravitational acceleration $a_g$ of four planets with the radial distance $r$ from the centre of the planet for $r \geq$ radius of the planet. Plots $1$ and $2$ coincide for $r \geq R_2$,and plots $3$ and $4$ coincide for $r \geq R_4$. The sequence of the planets in the descending order of their densities is:

$A$ variable plane is at a constant distance $h$ from the origin and meets the coordinate axes in $A, B, C$. The locus of the centroid of $\triangle ABC$ is

If $a \neq 0, b \neq 0, c \neq 0, a \times b = 0$ and $b \times c = 0$, then $a \times c$ is equal to

In the following arrangement,$y = 1.0 \, mm$,$d = 0.24 \, mm$,and $D = 1.2 \, m$. The work function of the material of the emitter is $2.2 \, eV$. The stopping potential $V$ needed to stop the photocurrent will be....$V$