All wires have the same resistance $r$. The equivalent resistance between $A$ and $B$ is $R$ when the keys $K_1$ and $K_2$ are open. Now,if the keys are closed,what will be the new equivalent resistance?

Two wires are made of the same material and have the same volume. Wire $1$ has cross-sectional area $A$ and wire $2$ has cross-sectional area $3A$. If the length of wire $1$ increases by $\Delta x$ on applying force $F$,how much force is needed to stretch wire $2$ by the same amount $\Delta x$?

$A$ body of mass $m$ is moving in a circle of radius $r$ with a constant speed $v$. The force on the body is $\frac{mv^2}{r}$ and is directed towards the centre. What is the work done by this force in moving the body over half the circumference of the circle?

If a complex number $z$ satisfies $|z^2-1|=|z|^2+1$,then $z$ lies on

Let $Q$ be the set of all rational numbers in $[0,1]$ and $f:[0,1] \rightarrow [0,1]$ be defined by $f(x) = \begin{cases} x & \text{for } x \in Q \\ 1-x & \text{for } x \notin Q \end{cases}$. Then,the set $S = \{x \in [0,1] : (f \circ f)(x) = x\}$ is equal to

The solution of $\frac{dy}{dx} + 1 = e^{x+y}$ is