One line of the pair of lines $x^2+xy-2y^2=0$ is perpendicular to one line of the pair of lines $3y^2-5xy-2x^2=0$. If the combined equation of the two lines other than those two perpendicular lines is $ax^2+2hxy+by^2=0$,then $a+2h+b=$

$A$ small sphere oscillates simple harmonically in a watch glass whose radius of curvature is $1.6 \ m$. The period of oscillation of the sphere in seconds is (acceleration due to gravity,$g = 10 \ m/s^2$). (in $\pi$)

An inductive circuit contains a resistance of $10\,\Omega$ and an inductance of $2.0\,H$. If an $AC$ voltage of $120\,V$ and frequency $60\,Hz$ is applied to this circuit,the current would be nearly ................$A$.

$A$ spherical iron ball of $10 \; cm$ radius is coated with a layer of ice of uniform thickness that melts at a rate of $50 \; cm^{3}/min$. When the thickness of ice is $5 \; cm$,the rate (in $cm/min$) at which the thickness of ice decreases is:

Sertoli cells are regulated by the pituitary hormone known as:

When an air bubble of radius $r$ rises from the bottom to the surface of a lake, its radius becomes $\frac{5r}{4}$. If the atmospheric pressure is equal to the pressure exerted by a $10 \ m$ height of water column, and the temperature remains constant while surface tension is neglected, what is the depth of the lake (in $m$)?