$A$ particle is executing simple harmonic motion with an amplitude $A$ and time period $T$. The displacement of the particle after $2T$ time from its initial position is

The refracting angle of a prism is $A$ and the refractive index of the material of the prism is $\cot (A / 2)$. The angle of minimum deviation of the prism is

If in a $\triangle ABC$,$r_1 < r_2 < r_3$,then:

If the angular momentum of a rotating body is increased by $200\ \%$,then its kinetic energy of rotation will be increased by .......... $\%$

Wires $A$ and $B$ have resistivities $\rho_A$ and $\rho_B$,where $\rho_B = 2 \rho_A$,and have lengths $l_A$ and $l_B$. If the diameter of wire $B$ is twice that of $A$ and the two wires have the same resistance,then the ratio $\frac{l_B}{l_A}$ is:

The set of values of $x$ for which the inequalities $x^2-3x-10 < 0$ and $10x-x^2-16 > 0$ hold simultaneously,is