$A$ 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......$\%$

The perimeter of a $\triangle ABC$ is $6$ times the arithmetic mean of the sine of its angles. If its side $BC$ is of unit length,then $\angle A=$

The image of the point $(1, 2, -1)$ on the plane containing the line $\frac{x+1}{-3}=\frac{y-3}{2}=\frac{z+2}{1}$ and the point $(0, 7, -7)$ is:

If the standard deviation of the numbers $-1, 0, 1, k$ is $\sqrt{5}$ where $k > 0,$ then $k$ is equal to

The curve $f(x) = e^x \sin x$ is defined in the interval $[0, 2\pi]$. The value of $x$ for which the slope of the tangent drawn to the curve at $x$ is maximum,is

Four resistors $A, B, C$ and $D$ form a Wheatstone bridge as shown in the figure. The bridge is balanced when $C = 100 \Omega$. If $A$ and $B$ are interchanged,the bridge balances for $C = 121 \Omega$. The value of $D$ is (in $\Omega$)