$A$ $500 \,\mu F$ capacitor is charged at a steady rate of $100\, \mu C/s$. The potential difference across the capacitor will be $10\, V$ after an interval of.....$s$.

The position vectors of $P$ and $Q$ are respectively $\overrightarrow{a}$ and $\overrightarrow{b}$. If $R$ is a point such that $\overrightarrow{PR}=5 \overrightarrow{PQ}$, then the position vector of $R$ is

If $x-y+1=0$ meets the circle $x^2+y^2+y-1=0$ at $A$ and $B$,then the equation of the circle with $AB$ as diameter is

The rate of steady volume flow of water through a capillary tube of length $l$ and radius $r$ under a pressure difference of $P$ is $V$. This tube is connected with another tube of the same length but half the radius in series. Then the rate of steady volume flow through them is (The pressure difference across the combination is $P$).

$A$ carrier signal $60 \sin(2\pi \times 10^6 t)$ is used to modulate an audio signal $15 \sin(300\pi t)$. The depth of modulation is .........$\%$.

If the lines $x^2+2xy-35y^2-4x+44y-12=0$ and $5x+\lambda y-8=0$ are concurrent,then $\lambda$ equals