$A$ marine cartilaginous fish that can produce electric current is

$A$ person lives in a high-rise building at a height of $30 \, m$ on the bank of a river. Across the river is a well-lit tower of height $60 \, m$. When the person looks through a polarizer at an appropriate angle at the light from the top of the tower reflecting from the river surface,he finds the intensity of light is least. If the refractive index of water is $\frac{4}{3}$,the width of the river is......$m$.

Two towers $A$ and $B$,each of height $20 \ m$,are situated a distance $200 \ m$ apart. $A$ body is thrown horizontally from the top of tower $A$ with a velocity $20 \ ms^{-1}$ towards tower $B$ and hits the ground at point $P$. Another body is thrown horizontally from the top of tower $B$ with a velocity $30 \ ms^{-1}$ towards tower $A$ and hits the ground at point $Q$. If a car starting from rest from point $P$ reaches point $Q$ in $10 \ s$,the acceleration of the car is . . . . . . . (Acceleration due to gravity $g = 10 \ ms^{-2}$) (in $ms^{-2}$)

If $3 \cos x \neq 2 \sin x$,then the general solution of $\sin^2 x - \cos 2x = 2 - \sin 2x$ is

The work done by a force $\vec F = (-6x^3 \hat i) \text{ N}$,in displacing a particle from $x = 4 \text{ m}$ to $x = -2 \text{ m}$ is .............. $J$.

$A$ body executes simple harmonic motion under the action of a force $F_1$ with a time period $T_1 = \frac{4}{5} \ s$. If the force is changed to $F_2$,it executes $SHM$ with a time period $T_2 = \frac{3}{5} \ s$. If both the forces $F_1$ and $F_2$ act simultaneously in the same direction on the body,what is its new time period in seconds?