If $\frac{x}{(x - 1)(x^2 + 1)^2} = \frac{1}{4}\left[ \frac{1}{(x - 1)} - \frac{x + 1}{x^2 + 1} \right] + y$,then $y =$

$A$ conducting rod $PQ$ of length $5\,m$ oriented as shown in the figure is moving with a velocity $\vec{v} = (2\,m/s)\hat{i}$ without any rotation in a uniform magnetic field $\vec{B} = (3\hat{j} + 4\hat{k})\,T$. The induced $EMF$ in the rod is........$V$.

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

The coefficient of $x^{10}$ in the expansion of $(2+3x)e^{-x}$ is

$A$ prism of refractive index $\mu$ and angle $A$ is placed in the minimum deviation position. If the angle of minimum deviation is $A$,then the value of $A$ in terms of $\mu$ is :

$A$ $1 ~N$ pendulum bob is held at an angle $\theta$ from the vertical by a $2 ~N$ horizontal force $F$ as shown in the figure. The tension in the string supporting the pendulum bob (in newton) is