$A$ transformer is used to light a $140 \, W, 24 \, V$ lamp from a $240 \, V \, AC$ mains. The current in the main cable is $0.7 \, A$. The efficiency of the transformer is......$\%$

$A$ person moves $30\, m$ north and then $20\, m$ towards east and finally $30\sqrt{2}\, m$ in south-west direction. The displacement of the person from the origin will be

$A$ body of mass $M$ at rest explodes into three pieces,two of which of mass $M/4$ each are thrown off in perpendicular directions with velocities of $3 \ m/s$ and $4 \ m/s$ respectively. The third piece will be thrown off with a velocity of.......... $m/s$.

$A$ real value of $x$ will satisfy the equation $\left( \frac{3 - 4ix}{3 + 4ix} \right) = \alpha - i\beta$ (where $\alpha, \beta$ are real),if

If $f: R \rightarrow R$ is defined by $f(x) = [\frac{x}{5}]$ for $x \in R$,where $[y]$ denotes the greatest integer not exceeding $y$,then $\{f(x) : |x| < 71\}$ is equal to

Each pair forms an ideal solution except: