Two cells of emf 2 V and 4 V and internal resistance of \( 0.5 \text{ } \Omega \) each are connected with an external resistor of resistance \( 3 \text{ } \Omega \) as shown in the figure. The terminal potential difference of 2 V cell is:

Arrange the following in the decreasing order of their wavelengths.
(A) microwaves
(B) ultraviolet rays
(C) infrared rays
(D) gamma rays
Choose the correct answer from the options given below:

A short solenoid of radius a and \( n_{1} \) number of turns per unit length and length L is kept coaxially inside a very long solenoid of radius b and \( n_{2} \) number of turns per unit length. What is the mutual inductance of the system.

When an electron of hydrogen atom is raised from the ground state to an excited state.

The energy required to remove an electron from the inner most orbit of the hydrogen atom to a distance far away from its nucleus is

What is the force between two small charged spheres having charges of \( 4 \times 10^{-7} \text{ C} \) and \( 6 \times 10^{-7} \text{ C} \) placed 60 cm apart in air ?

dentify the correct statements.
(A) Photographic plates are sensitive to infrared waves.
(B) Infra-red waves are invisible but can cast shadows like visible light.
(C) Photographic plates are sensitive to ultraviolet rays.
(D) Infrared photons have more energy than photons of visible light.
Choose the correct answer from the options given below:

The half life for radioactive decay of C-14 is 5730 years.
A sample of tree had only 80% of C-14 left.
Estimate the age of the tree.
(log 5 = 0.698) (log 4 = 0.602)

A medicinal plant growing in different Himalayan ranges shows different potency and concentration of the active chemical (reserpine) that the plant produces. Identify the plant:

If \(A\) is a square matrix of order 2 , then \(|\operatorname{adj} A|\) is equal to:

If \(\vec{a}=2 \hat{i}-\hat{j}+3 \hat{k}\) and \(\vec{b}=2 \hat{i}+2 \hat{j}+\hat{k}\) then
Match List-I with List-II

List-I	List-II
(A) Projection of \(\vec{a}\) on \(\vec{b}\) is	(I) \(-7 \hat{i}+4 \hat{j}+6 \hat{k}\)
(B) \(\vec{a} \times \vec{b}\) is	(II) \(\frac{1}{\sqrt{101}}(-7 \hat{i}+4 \hat{j}+6 \hat{k})\)
(C) Unit vector along \(\vec{a}+\vec{b}\) is	(III) \(\frac{5}{3}\)
(D) Unit vector perpendicular to both \(\vec{a}\) and \(\vec{b}\) is	(IV) \(\frac{1}{\sqrt{33}}(4 \hat{i}+\hat{j}+4 \hat{k})\)

Choose the correct answer from the options given below :

Answer the question on basis of passage given below :
Transition metals form a large number of complexes or coordination compounds in which the metal atoms are bound to a number of anions or neutral molecules. The valence bond theory explain the formation, magnetic behaviour and geometrical shapes while the crystal field theory explains the effect of different crystal fields on the degeneracy of d-orbitals energies of the central metal atom/ion. This provides for the quantitative estimation of orbital separation energies, magnetic moments and spectral and stability parameters.
Amongst the following ions which should have the highest magnetic moment value?

The area of the region bounded by the curves \(y=x^2+2, y=-x, x=0\) and x = 1 is :