Class 12th

Which of the following is true for y(x) that satisfies the differential equation dy/dx = xy - 1 + x - y; y(0) = 0:

A loop of flexible wire of irregular shape carrying current is placed in an external magnetic field. Identify the effect of the field on the wire.

Imagine that the electron in a hydrogen atom is replaced by a muon (µ). The mass of muon particle is 207 times that of an electron and charge is equal to the charge is of an electron. The ionization potential of this hydrogen atom will be :

The atomic hydrogen emits a line spectrum consisting of various series. Which series of hydrogen atomic spectra is lying in the visible region?

A radioactive sample disintegrates via two independent decay processes having half lives T?/?¹? and T?/?²? respectively. The effective half-life, T?/? of the nuclei is:

The standard enthalpies of formation of Al₂O₃ and CaO are –1675 kJ mol⁻¹ and -635 kJ mol⁻¹ respectively.
For the reaction 3CaO + 2Al → 3Ca + Al₂O₃ the standard reaction enthalpy ΔᵣH° = _______ kJ.
(Round off to the nearest integer).

A plane electromagnetic wave of frequency 100 MHz is traveling in vacuum along the x-direction. At a particular point in space and time, B = 2.0 * 10? k? T. (where, k? is unit vector along z-direction) What is E at this point? (speed of light c = 3 x 10? m/s)

15 mL of aqueous solution of Fe²⁺ in acidic medium completely reacted with 20 ml of 0.03 M aqueous Cr₂O₇^2-. The molarity of the Fe²⁺ solution is _______ *10^-2 M (Round off to the nearest integer).

Match List-I with List-II

Choose the most appropriate answer from the options given below :

Four identical long solenoids A, B, C and D are connected to each other as shown in the figure. If the magnetic field at the centre of A is 3T, the field at the centre of C would be: (Assume that the magnetic field is confined within the volume of respective solenoid).