The length of an elastic string is $a \, m$ when the longitudinal tension is $4 \, N$ and $b \, m$ when the longitudinal tension is $5 \, N$. The length of the string in metres when the longitudinal tension is $9 \, N$ is

If $I$ is the identity matrix of order $2$ and $A = \begin{bmatrix} 1 & 1 \\ 0 & 1 \end{bmatrix}$,then for $n \geq 1$,mathematical induction gives

Two rings of radius $R$ and $nR$ made of the same material have a ratio of moment of inertia about an axis passing through their centers and perpendicular to their planes as $1:8$. The value of $n$ is (mass per unit length is constant).

The colour of the bead in the borax bead test is mainly due to the formation of:

Consider the statements given below regarding contraception and answer as directed thereafter:
$(1)$ Medical Termination of Pregnancy $(MTP)$ during the first trimester is generally safe.
$(2)$ Generally,chances of conception are nil until the mother breast-feeds the infant up to two years.
$(3)$ Intrauterine devices like Copper-$T$ are effective contraceptives.
$(4)$ Contraception pills may be taken up to one week after coitus to prevent conception.
Which two of the above statements are correct?

An $L-$shaped glass tube is just immersed in flowing water as shown. If the speed of the water current is $V$,then the height $h$ up to which water rises in the tube will be