The electric field intensity at the mid point of a dipole with charge \( \pm q \) and dipole length \( 2a \) is:

A cell of emf 2.2 V gives a current of 0.2 A through a resistance of 9 \(\Omega\). The internal resistance of the cell will be:

The frequency of a photon whose energy is 66.3 eV would be
(Given \( h = 6.63 \times 10^{-34} \text{ Js} \))

According to the Biot- Savart law, the magnetic field due to a current element is
(A) inversely proportional to the square of the distance from the current element to the point of interest.
(B) produced by a vector source.
(C) perpendicular to the plane containing the displacement vector and the current element.
(D) non-zero at any point in the direction of the current element.
Choose the correct answer from the options given below:

A resistor develops 200 J of thermal energy in 5 s when a current of 2 A is passed through it. If the current is measured to 5 A, what will be the energy developed in 12 s ?

What would be the amount of energy released if 1 g of a substance is converted to energy? (Given, speed of light in vacuum \(=3 \times 10^8 m s ^{-1}\) )

A sinusoidal voltage with peak value 220 V and variable frequency is applied to a series LCR circuit in which \( R = 10 \, \Omega \), \( L = 4 \, \text{mH} \), and \( C = 100 \, \text{mF} \). Consider the following:
(A) Resonant angular frequency \(\left(w_o\right)=50 rad / s\)
(B) Resonant frequency \(\left(v_o\right)=25 / n Hz\)
(C) Resonant frequency \(\left(v_o\right)=50 / n Hz\)
(D) The rms current at resonance is 15.5 A
Choose the correct answer from the options given below:

A \( 25 \, \mu\text{F} \) capacitor, a 0.10 H inductor and a \( 25 \, \Omega \) resistor are connected in series with an ac source of emf \( \epsilon = 310 \sin 314t \). What is the frequency of AC source ?

If \(y=\log \left[\frac{x^2}{e^2}\right]\) then value of \(\frac{d^2 y}{d x^2}\) is :

The brain size of the Neanderthal man was:

The values of \(\lambda\) for which the system of equation \(x+2 y+z=14,-x+y+z=10, x+\lambda y+z=2\) has unique solution is :

Among the following statements on the nitration of aromatic compounds, the false one is:

Read the passage carefully and answer the Questions In the formation of coordination complexes, if the inner \(d\) orbital \((n-1) d\) is used in hybridisation, the complex, is called an inner orbital or low spin or spin paired complex. And if it uses outer \(d\) orbital ( \(n d\) ) in hybridisation (like \(s p^3 d^2\) ), it is called outer orbital or high spin or spin free complex. The degeneracy of the \(d\) orbitals has been removed due to ligand electron-metal electron repulsions in the complex. This splitting of the degenerate levels due to the presence of ligands in a definite geometry is termed as crystal field splitting. For coordination complexes, the magnetic moment is determined by the number of unpaired electrons and is calculated by using the 'spin-only' formula, \(\mu=\sqrt{n(n+2)}\) where \(n\) is the number of unpaired electrons and \(\mu\) is the magnetic moment in units of Bohr magneton (BM). The coordination compounds are of great importance. These compounds are widely present in the mineral, plant and animal worlds and are known to play many important functions in the area of analytical chemistry, metallurgy, biological systems, industry and medicine.
\(\left[ Co \left( NH _3\right)_6\right]^{3+}\) and \(\left[ Ni \left( NH _3\right)_6\right]^{2+}\) respectively are