Compound $B$ is ?

Water is conveyed through a uniform tube of $8 \text{ cm}$ in diameter and $3140 \text{ m}$ in length at the rate of $2 \times 10^{-3} \text{ m}^3/\text{s}$. The pressure required to maintain the flow is (Viscosity of water $= 10^{-3} \text{ SI units}$):

Two bodies $A$ and $B$ of equal mass are suspended from two separate massless springs of force constant $k_{1}$ and $k_{2}$ respectively. The bodies oscillate vertically such that their maximum velocities are equal. The ratio of the amplitudes of body $A$ to that of body $B$ is

$A$ particle is performing simple harmonic motion along the $x$-axis with an amplitude of $4\, cm$ and a time period of $1.2\, s$. The minimum time taken by the particle to move from $x = 2\, cm$ to $x = +4\, cm$ and back again is given by .... $s$.

$A$ man wants to reach a certain destination. One-sixth of the total distance is muddy while half the distance is tar road. For the remaining distance,he takes a boat. His speed of travelling in mud,in water,and on tar road is in the ratio $3:4:5$. The ratio of the durations he requires to cross the patch of mud,stream,and tar road is

If $\int \frac{\sin^8 x - \cos^8 x}{1 - 2 \sin^2 x \cos^2 x} dx = A \sin 2x + B$, then $A$ is equal to