Class 12th

The decay of a proton to neutron is :

Three rays of light, red (R), green (G) and blue (B) are incident on the face PQ of a right angled prism PQR as shown in the figure. The refractive indices of material of the prism for red, green and blue wavelength are 1.27, 1.42 and 1.49 respectively. The colour of ray(s) emerging out of the face PR is

If x, y, z are in arithmetic progression with common difference d, x≠3d, and the determinant of the matrix [[3, 4√2, x], [4, 5√2, y], [5, k, z]] is zero, then the value of k² is:

Two tangents are drawn from a point P to the circle x² + y² - 2x - 4y + 4 = 0, such that the angle between these tangents is tan⁻¹(12/5), where tan⁻¹(12/5) ∈ (0,π). If the centre of the circle is denoted by C and these tangents touch the circle at points A and B, then the ratio of the areas of ΔPAB and ΔCAB is:

The time taken for the magnetic energy to reach 25% of its maximum value, when solenoid of resistance R, inductance L is connected to a battery, is:

A proton and an α-particle, having kinetic energy Kp and Kα respectively, enter into a magnetic field at right angles. The ratio of the radii of trajectory of proton to that of α-particle is 2 : 1. The ratio of Kp : Kα is

If the equation of plane passing through the mirror image of a point (2,3,1) with respect to line (x+1)/2 = (y-3)/1 = (z+2)/-1 and containing the line (x-2)/3 = (1-y)/2 = (z+1)/1 is, αx + βy + γz = 24 then α + β + γ is equal to:

The speed of electrons in a scanning electron microscope is 1*10⁷ m/s. If protons having the same speed are used instead of electrons, then the resolving power of scanning proton microscope will be changed by a factor of

Which of the following statements are correct?
(A) Electric monopoles do not exist whereas magnetic monopoles exist.
(B) Magnetic field lines due to a solenoid at its ends and outside can not be completely straight and confined.
(C) Magnetic field lines are completely confined within a toroid.
(D) Magnetic field lines inside bar magnet are not parallel.
(E) χ = -1 is the condition for a perfect diamagnetic material, where χ is its magnetic susceptibility.

Choose the correct answer from the options given below:

If the sides AB, BC and CA of triangle ABC have 3, 5 and 6 interior points respectively, then the total number of triangles that can be constructed using these points as vertices, is equal to: