Class 12th

Choose the correct option relating wavelengths of different parts of electromagnetic wave spectrum:

A small bar magnet placed with its axis at ${30}^{\circ }$ with an external field of $0.06\mathrm{T}$ experiences a torque of $0.018\mathrm{N}\mathrm{m}$ . The minimum work required to rotate it from its stable to unstable equilibrium position is:

A beam of plane polarized light of large cross-sectional area and uniform intensity of $3.3{\mathrm{W}\mathrm{m}}^{-2}$ falls normally on a polarizer (cross sectional area $3*{10}^{-4}{\mathrm{m}}^2$ ) which rotates about its axis with an angular speed of $31.4\mathrm{r}\mathrm{a}\mathrm{d}/\mathrm{s}$ . The energy of light passing through the polariser per revolution, is close to:

Let the mirror image of a circle c₁ : x² + y² – 2x – 6y + a = 0 in line y = x + 1 be c₂ : 5x² + 5y² + 10gx + 10fy + 38 = 0.  If r is the radius of circle c₂, then a + 6r² is equal to………….

A telegraph line of length 100km has a capacity of $0.01\mu F/km$  and it carries an alternating current at 0.5 kilo cycle per second. If minimum impedance is required, then the value of the inductance that need to be introduced in series is _________mH. (if π = $\sqrt[]{10}$ )

The specific heat of water $=4200\mathrm{J}{\mathrm{k}\mathrm{g}}^{-1}{\mathrm{K}}^{-1}$ and the latent heat of ice $=3.4*{10}^5\mathrm{J}{\mathrm{k}\mathrm{g}}^{-1}$ . 100 grams of ice at $0^{\circ }\mathrm{C}$ is placed in $200\mathrm{g}$ of water at ${25}^{\circ }\mathrm{C}$ . The amount of ice that will melt as the temperature of water reaches $0^{\circ }\mathrm{C}$ is close to (in grams):

Let S = {4, 6, 9} and T = {9, 10, 11,…., 1000}.

If A = $\left\{a_1+a_2+...+a_k:k\in N,a_1,a_2,a_3,.....,a_k\in S\right\},$ then the sum of all the elements in the set T – A is equal to…………….

If $\frac{1}{2*3*4}+\frac{1}{3*4*5}+\frac{1}{4*5*6}+...+\frac{1}{100*101*102}=\frac{k}{101},$ then 34 k is equal to………….

A singly ionized magnesium atom (A = 24) ion is accelerated to kinetic energy 5 ke V, and is projected perpendicularly into a magnetic field B of the magnitude 0.5 T. The radius of path formed will be ________cm.

Let p and p + 2 be prime numbers and let

$\Delta =\left|\begin{array}{ccc}\hfill p!\hfill & \hfill \left(p+1\right)!\hfill & \hfill \left(p+2\right)!\hfill \\ \hfill \left(p+1\right)!\hfill & \hfill \left(p+2\right)!\hfill & \hfill \left(p+3\right)!\hfill \\ \hfill \left(p+2\right)!\hfill & \hfill \left(p+3\right)!\hfill & \hfill \left(p+4\right)!\hfill \end{array}\right|$

Then the sum, of the maximum values of and , such that p and (p + 2) divide $\Delta ,$ is………….