If the angles of dip at two places are $30^o$ and $45^o$ respectively,then the ratio of horizontal components of earth's magnetic field at the two places will be

In the sequence of sets $(1,2,3), (4,5,6), (7,8,9,10), \ldots$,the sum of elements in the $50^{th}$ set is

Water rises to a height $h$ in a capillary tube at the surface of the Earth. On the surface of the Moon,the height of the water column in the same capillary tube will be:

$A$ uniform rod of mass $m$ and length $l$ is moving with velocity $u$ in a direction perpendicular to its length. $A$ blow of impulse $J$ is given perpendicular to its length at a distance $\frac{l}{4}$ from its centre at point $P$ such that the instantaneous velocity of point $P$ becomes $2u$. Then the velocity of its centre of mass will be:

If the direction cosines of two lines are given by $l+m+n=0$ and $l^2-5m^2+n^2=0$,then the angle between them is

$\int_0^1 x^{3/2} \sqrt{1-x} \, dx$ is equal to