If the angular velocity of a disc depends on the angle rotated $\theta$ as $\omega = \theta^2 + 2\theta$,then its angular acceleration $\alpha$ at $\theta = 1 \ rad$ is ......... $rad/sec^2$.

In the following circuit,$PN$-junction diodes $D_1, D_2$,and $D_3$ are ideal. For the following potentials of $A$ and $B$,the correct increasing order of resistance between $A$ and $B$ will be:
$(i) -10 \ V, -5 \ V$
$(ii) -5 \ V, -10 \ V$
$(iii) -4 \ V, -12 \ V$

An infinite number of electric charges each equal to $5 \text{ nC}$ (magnitude) are placed along the $X$-axis at $x=1 \text{ cm}, x=2 \text{ cm}, x=4 \text{ cm}, x=8 \text{ cm} \dots$ and so on. In this setup, if the consecutive charges have opposite signs, then the electric field in $\text{N/C}$ at $x=0$ is: $\left(\frac{1}{4 \pi \varepsilon_0}=9 \times 10^9 \text{ N} \cdot \text{m}^2/\text{C}^2\right)$

The lines $x-y-2=0$,$x+y-4=0$ and $x+3y=6$ meet at a common point:

$A$ current-carrying coil is placed with its axis perpendicular to the $N-S$ direction. Let the horizontal component of the earth's magnetic field be $H_0$ and the magnetic field inside the loop be $H$. If a magnet is suspended inside the loop,it makes an angle $\theta$ with $H$. Then $\theta =$

Two electric charges of $9 \mu C$ and $-3 \mu C$ are placed $0.16 \ m$ apart in air. There will be a point $P$ on the line joining the two charges and in between them where the electric potential is zero. The distance of $P$ from the $9 \mu C$ charge is (in $m$)