The magnetic flux through a coil of resistance \( 6 \text{ } \Omega \), perpendicular to its plane, is varying according to \( \phi = 6t^3 + 5t^2 + 4t - 6 \text{ Wb} \). What will be the induced current through the coil at \( t = 2 \text{ s} \)?

A charged particle moves along a circle under the action of constant electric and magnetic fields. Which of the following is possible?

Which of the following characteristics of electron determines the current in a conductor?

A charge q is moving with velocity \( \vec{v} \) in the presence of both electric field \( \vec{E} \) and magnetic field \( \vec{B} \). If velocity (\( \vec{v} \)), electric field (\( \vec{E} \)) and the magnetic field (\( \vec{B} \)) are mutually perpendicular. The charge will pass through the field undeflected if :

An equiconvex lens has a focal length of 20 cm and its radius of curvature is 30 cm. Its refractive index is

A 12 pF capacitor is connected to a 50 V battery. The electrostatic energy stored in the capacitor is

The necessary conditions for total internal reflection are
(A) Light must travel from denser to rarer medium.
(B) The angle of incidence in the denser medium must be less than the critical angle for the two media.
(C) Light must travel from rarer to denser medium.
(D) The angle of incidence in the denser medium must be greater than the critical angle for the two media.
Choose the correct answer from the options given below:

The derivative of \(f(\cot x)\) with respect to \(g(cosec x)\) at \(x=\frac{\pi}{4}\) (where \(\left.f^{\prime}(1)=2, g^{\prime}(\sqrt{2})=4\right)\) is:

Which of the following statements are correct?
(A) Inverse of a matrix, if it exists, is unique
(B) \((k A)^{\prime}=-k A^{\prime}\) (where \(k\) is any real number)
(C) For an invertible matrix \(A,\left(A^{-1}\right)^{-1}=A\)
(D) For an invertible matrix \(A,\left(A^{\prime}\right)^{-1}=\left(A^{-1}\right)^{\prime}\)
Choose the correct answer from the options given below :

Read the passage carefully and answer the Questions
According to Valence Bond theory, the metal atom or ion under the influence of ligands can use its ( \(n-1) d, n s, n p\) or \(n s, n p, n d\) orbitals for hybridisation to yield a set of equivalent orbitals of definite geometry such as octahedral, tetrahedral, square planar and so on. These hybridised orbitals are allowed to overlap with ligand orbitals that can donate electron pairs for bonding. While the VB theory, to a larger extent, explains the formation, structures and magnetic behaviour of coordination compounds, it suffers from the many shortcomings. The Crystal field theory (CFT) is an electrostatic model which considers the metal-ligand bond to be ionic arising purely from electrostatic interactions between the metal ion and the ligand. The five \(d\) orbitals in an isolated gaseous metal atom/ion have same energy, i.e., they are degenerate. This degeneracy is maintained if a spherically symmetrical field of negative charges surrounds the metal atom/ion. However, when this negative field is due to ligands in a complex, it becomes asymmetrical and the degeneracy of the \(d\) orbitals is lifted. It results in splitting of the \(d\) orbitals. The pattern of splitting depends upon the nature of the crystal field.
Select the incorrect statement about the Crystal field splitting in octahedral complexes.

Heavy water and __________ is one of the substance used as moderator in reactors.

Biogas is mixture of:

The method of producing thousands of plants through tissue culture is called as: