A short bar magnet of magnetic moment \(m =0.45 J / T\) is placed in a uniform magnetic field of 0.22 T . If the bar is free to rotate in the plane of the field, what is the potential energy of the magnet in stable and unstable equilibrium respectively?

Two identical capacitors are joined in parallel, charged to a potential V and then separated and connected in series, i.e., negative plate of first is connected to positive plate of second :

The self-inductance (L) of a long solenoid on doubling its number of turns and length, keeping other factors constant, will become

Which of the following statements are correct?
(A) In a p-n junction diode, accumulation of electric charge of the opposite type on two sides of the junction produces an electric field and a potential barrier,
(B) the potential barrier opposes the movement of the majority charge carriers across the junction.
(C) In the reverse biased p-n junction, the width of the depletion layer decreases.
(D) In forward bias of a p-n junction, the potential barrier increases.
Choose the correct answer from the options given below:

Match List-I with List-II for the band gap energy for different materials

List-I (Substances)	List-II (Band gap Energy)
(A) Germanium	(I) 1.1 eV
(B) Silicon	(II) 0.7 eV
(C) Insulator	(III) Zero
(D) metal	(IV) 5 eV

Choose the correct answer from the options given below:

Which of the following statements are correct?
(A) In an ac circuit containing only resistance, power consumption is \( I^2 R \).
(B) In an LCR circuit, there is resonance at zero phase difference between \( X_C \) and \( X_L \) and the power consumption is \( I(\omega X_C + \omega X_L)^{1/2} \).
(C) In an LCR circuit, at resonance, impedance is minimum.
(D) In an LCR circuit, there is resonance at zero phase difference between \( X_C \) and \( X_L \) and the power consumption is zero.
Choose the correct answer from the options given below:

The ratio of total energy to the kinetic energy of an electron in a Bohr orbit of the hydrogen atom is

If \(f(x)=|2 x+5|\), then \(f(x)\) is :

In order to fabricate n-type semiconductor, the impurity elements used are

The value of \(\left|\begin{array}{lll}2^x & 1 & 6^x \\ 4^x & 1 & 3^x \\ 2^x & 1 & 6^x\end{array}\right|\), where \(x \neq 0 ;\) is:

A copper wire of area of cross-section \( 2 \times 10^{-6} \, \text{m}^2 \) and electron density \( 10^{28} \, \text{m}^{-3} \) carries a current of 1.6 A. Time taken by an electron to drift from one end of a 1.0 m long wire to its other end will be

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 complez 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 \(\Delta_0\) and pairing energy, \(P\) (energy required for electron pairing in a single orbital) determine the formation of low spin ( \(\Delta_0>P\) ) or high spin ( \(\Delta_0<P\) ) complex. In tetrahedral coordination entity formation, the \(d\)-orbital splitting is inverted and is smaller as compared to the octabedral 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 relations is correct for the splitting of \(d\) orbitals in octahedral and tetrahedral crystal fields, considering same metal, the same ligands and metal-ligand distances?

The unit's digit of \(13^{13}\) is :