A parallel plate capacitor of capacitance 2 \( \mu F \) has energy \( 10 \times 10^{-5} \, J \). The potential difference and the charge on the capacitor are:

Match List-I with List-II

List-I (Series)	List-II (Values of \( n_1 \) and \( n_2 \) in Bohr's formula)
(A) Lyman	(I) \( n_1=4, n_2 \geq 5 \)
(B) Balmer	(II) \( n_1=3, n_2 \geq 4 \)
(C) Paschen	(III) \( n_1=2, n_2 \geq 3 \)
(D) Brackett	(IV) \( n_1=1, n_2 \geq 2 \)

Choose the correct answer from the options given below:

The power factor of an RL circuit is \( \frac{1}{2} \). If the frequency of a.c. is doubled, the power factor will be :

A common emitter amplifier has a current gain 75. The collector resistance is 4 \( k\Omega \) and the input resistance is 500 \( \Omega \). The voltage gain of amplifier is:

A steady current flows in a conductor of non-uniform cross-section. The physical quantity which remains constant along the length is :

Identify the incorrect statement(s) from the following in the context of an electric current flowing through a conductor.
(A) The electrons suffer collisions with heavy fixed ions in the conductor
(B) The resistance of the given conductor depends on its temperature
(C) Resistance and resistivity both depend on the dimensions of the conductor
(D) When a potential difference V is applied across the conductor then V= IR
Choose the correct answer from the options given below:

A parallel plate capacitor made of circular plates each of radius 10.0 cm has a capacitance 200 pF . The capacitor is connected to a 200 V ac supply with an angular frequency of \(200 rad / s\). The amplitude of the current is :

Let \(X\) and \(Y\) be any two invertible square matrices of order \(n\). Then which of the statements are true?
(A) \((A B)^{-1}=A^{-1} B^{-1}\)
(B) \((A B)^{-1}=B^{-1} A^{-1}\)
(C) \((A B)^T=A^T B^T\), where \(A^T\) denotes transpose of A
(D) \((A B)^T=B^T A^T\), where \(A^T\) denotes transpose of A
Choose the correct answer from the options given below :

Which of the following statements are correct?
(A) In ideal solutions, the enthalpy of mixing of the pure components to form the solution is zero.
(B) The volume of the solution is equal to the sum of the volumes of the two components.
(C) In binary ideal solutions, attractive forces between A-A and B-B are nearly equal to those between A-B.
(D) In negative Raoult's law deviation, attractions between A-B are weaker than those of A-A and B-B attractions.
Choose the correct answer from the options given below:

In an intrinsic semiconductor, the relation between the number of holes \( (n_h) \) and conduction electrons \( (n_e) \) will be:

The time required for a 50 Hz alternating current to reach the peak value starting from zero

Read the passage carefully and answer the questions:
The degeneracy of the \(d\) orbitals has been removed due to ligand electron-metal electron repulsions in the octahedral complex to yield three orbitals of lower energy, \(t_{2 g}\) set and two orbitals of higher energy, \(e_g\) set. This splitting of the degenerate levels due to the presence of ligands in a definite geometry is termed as crystal field splitting and the energy separation is denoted by \(\Delta_0\). Thus energy of the two \(e_g\) orbitals will increase by \((3 / 5) \Delta_0\) and that of three \(t_{2 g}\) will decrease by \((2 / 5) \Delta_0\). The crystal field splitting \(\Delta_{\circ}\) depends upon the field produced by the ligand and charge on the metal ion. Some ligands are able to produce strong fields, in which case the splitting will be large, whereas others produce weak fields and consequently result in small splitting of \(d\) orbitals. Relative magnitude of crystal field splitting energy \(\Delta_{\circ}\) and pairing energy, \(P\) (energy required for electron pairing in a single orbital) determine the formation of low spin ( \(\Delta_{\circ}>P\) ) or high spin ( \(\Delta_{\circ}<P\) ) complex. In tetrahedral coordination entity formation, the \(d\)-orbital splitting is inverted and is smaller as compared to the octahedral field splitting. The crystal field theory attributes the colour of the complex to \(d-d\) transition of the electron. The colour of the coordination compounds depends on the crystal field splitting. In the absence of ligand, crystal field splitting does not occur and hence the substance is colourless.
Which of the following complex is not expected to be coloured?

Assuming \(\text{[NiCl}_4\text{]}^{2-}\) as Complex-A and \(\text{[Ni(CO)}_4\text{]}\) as Complex-B, choose the correct statement.
(Atomic number of Ni = 28)