A monochromatic source emitting light of wavelength 300 nm has a power output of 33 W.
Calculate the number of photons emitted by this source in 2 minutes. (\( h = 6.62 \times 10^{-34} \text{ J s} \))

It is observed that only 25% of a given radioactive sample is left undecayed after 16 days. What is the decay constant of the sample in \(\text{day}^{-1}\)?

A circular loop of 20 turns carries a current of 5.0 A. If the magnetic field at the centre of the loop is 1.57 mT, the radius of the loop would be :

A radioactive isotope has half-life of ' \(K\) ' years. How long will it take, so that activity reduces to \(6 . 2 5 \%\) of its original value?

The instantaneous power supplied to a capacitor is given by\(P_c=i_m \cos (\omega t) v_m \sin (\omega t)\).
The average power over a complete cycle would be:

The generalised communication system will have following essential components in sequence in a block diagram.
(A) Transmitter
(B) Channel
(C) Receiver
(D) Information source
(E) User of information
Choose the correct answer from the options given below :

Two charges \( q_1 = 4 \times 10^{-7} \text{ C} \) and \( q_2 = -6 \times 10^{-7} \text{ C} \) are located 3 m apart. At what point on the line joining the two charges is the electric potential zero? (Consider potential zero at infinity.)

With the rise in temperature, the electrical resistance

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 comple: 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 \(\Delta_0\) 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 paring 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 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?

Two solenoids of the same length and the same cross-sectional area have 400 turns and 250 turns, respectively. The ratio of self-inductance of the two solenoids, respectively, is

The probability that X can take the values \(x_i\) has the following form:
\(P\left(X=x_i\right)=\left\{\begin{array}{ll}0.2 & \text { if } x_i=0 \\ k x_i & \text { if } x_i=1 \text { or } 2 \\ k\left(5-x_i\right) & \text { if } x_i=3 \\ 0 & \text { otherwise }\end{array}\right.\)
The value of P(X = 2) is:

Match List - I with List - II.

List – I	List – II
(A) Glycosidic linkage	(I) Monomeric units of nucleic acid
(B) Peptide linkage	(II) Sugar-heterocyclic base combination
(C) Nucleotide	(III) Linkage between two amino acid units
(D) Nucleoside	(IV) Linkage between two mono saccharide units

Choose the correct answer from the options given below :

Match List-I with List-II

List-I (Electric Field)	List-II (Expression)
(A) Field due to an infinitely long straight uniformly charged wire	(I) \(\sigma\left(2 \varepsilon_0\right)^{-1}\)
(B) Field due to a uniformly charged thin spherical shell (inside the shell)	(II)\(q\left(4 \pi \varepsilon_0 r^2\right)^{-1}\)
(C) Field due to a uniformly charged infinite plane sheet	(III) \(\lambda\left(2 \pi \varepsilon_0 r\right)^{-1}\)
(D) Field due to a uniformly charged thin spherical shell (outside the shell)	(IV) zero

Choose the correct answer from the options given below: