If $x$ is a solution of the equation $\sqrt{2x+1} - \sqrt{2x-1} = 1$ for $x \geq \frac{1}{2}$,then $\sqrt{4x^2-1}$ is equal to:

Consider the fourteen lines in the plane given by $y=x+r$ and $y=-x+r$,where $r \in \{0, 1, 2, 3, 4, 5, 6\}$. The number of squares formed by these lines,whose sides are of length $\sqrt{2}$,is:

If $(p \wedge \sim q) \wedge (p \wedge r) \to \sim p \vee q$ is false,then the truth values of $p, q$ and $r$ are respectively

In ruby laser,the stimulated emission is due to transition from

$A$ parallel plate capacitor has plate area $A$ and separation $d$. It is charged to a potential difference $V_0$. The charging battery is disconnected and the plates are pulled apart to $3$ times the initial separation. The work required to separate the plates is

Let $A$ and $B$ be independent events with $P(A)=0.3$ and $P(B)=0.4$. Find $P(A | B)$.