From the point $(-1, 2)$,tangents are drawn to the parabola $y^2 = 4x$. Find the area of the triangle formed by the chord of contact and the tangents. (in $sqrt{2}$)

The coefficient of $x^k$ in the expansion of $\frac{1-2x-x^2}{e^{-x}}$ is

The point $(3,2)$ undergoes the following three transformations in the order given:
$(i)$ Reflection about the line $y=x$.
(ii) Translation by the distance $1$ unit in the positive direction of $x$-axis.
(iii) Rotation by an angle $\frac{\pi}{4}$ about the origin in the anti-clockwise direction.
Then,the final position of the point is:

The magnetic induction and the intensity of the magnetic field inside an iron core of an electromagnet are $1 \ Wb \ m^{-2}$ and $150 \ A \ m^{-1}$,respectively. The relative permeability of iron is $\left(\mu_0 = 4 \pi \times 10^{-7} \ H \ m^{-1}\right)$.

The total charge induced in a conducting loop when it is moved in a magnetic field depends on

Light waves producing interference have their amplitudes in the ratio $3:2$. The intensity ratio of maximum and minimum of interference fringes is