If the mean of the data $7, 8, 9, 7, 8, 7, \lambda, 8$ is $8$,then the variance of this data is

The equation of the common tangent of the parabolas $x^2 = 108y$ and $y^2 = 32x$ is

$A$ body projected vertically upwards crosses a point twice in its journey at a height $h$ just after $t_1$ and $t_2$ seconds. Maximum height reached by the body is

$A$ mass $m$,travelling at speed $V_0$ in a straight line from far away,is deflected when it passes near a black hole of mass $M$ which is at a perpendicular distance $R$ from the original line of flight. $a$,the distance of closest approach between the mass and the black hole,is given by the relation:

The voltage of an $ac$ source varies with time according to the equation $V = 100 \sin(100 \pi t) \cos(100 \pi t)$,where $t$ is in $seconds$ and $V$ is in $volts$. Then:

When a large bubble rises from the bottom of a lake to the surface, its radius doubles. If atmospheric pressure is equal to that of a column of water of height $H$, then the depth of the lake is: