$A$ straight line passes through the point $A(3, 4)$ such that the portion of the line intercepted between the axes is bisected at $A$. Find the equation of the line.

When a current of $2\, A$ flows in a battery from negative to positive terminal,the potential difference across it is $12\, V$. If a current of $3\, A$ flows in the opposite direction,the potential difference across the terminals of the battery is $15\, V$. The $emf$ of the battery is ................ $V$.

$A$ particle $P$ is moving in a circle of radius $a$ with a uniform speed $v$. $C$ is the centre of the circle and $AB$ is a diameter. When passing through $B$,the angular velocity of $P$ about $A$ and $C$ are in the ratio:

$A$ potentiometer wire of length $1\,m$ is connected in series with a resistance of $490\,\Omega$ and a battery of $2\,V$. If the potential gradient is $0.2\,mV/cm$,then the resistance of the potentiometer wire is ............$\Omega$. (in $.9$)

$Taxa$ differs from $taxon$ due to being

If $\alpha = \frac{5}{2! 3} + \frac{5 \cdot 7}{3! 3^2} + \frac{5 \cdot 7 \cdot 9}{4! 3^3} + \ldots$,then $\alpha^2 + 4\alpha$ is equal to