The voltage of an $AC$ source varies with time according to the equation $V = 100 \sin(100\pi t) \cos(100\pi t)$,where $t$ is in seconds and $V$ is in volts. Then:

If $\int \frac{\sin x}{\cos x(1+\cos x)} d x=f(x)+c$,then $f(x)$ is equal to

An ideal transformer has $500$ and $5000$ turns in primary and secondary windings respectively. If the primary voltage is connected to a $6\,V$ battery, then the secondary voltage is.......$V$.

In the given circuit,the readings of voltmeters $V_1$ and $V_2$ are $300 \, V$ each. The readings of voltmeter $V_3$ and ammeter $A$ are respectively:

If $2 x^2-3 x y+y^2+x+2 y-8=0$,then $\frac{d y}{d x}$ is equal to

$A$ bullet of mass $10\,g$ moving horizontally with a velocity of $400\,m/s$ strikes a wooden block of mass $2\,kg$ which is suspended by a light inextensible string of length $5\,m$. As a result,the centre of gravity of the block is found to rise a vertical distance of $10\,cm$. The speed of the bullet after it emerges out horizontally from the block will be ............... $m/s$.