A spherical conductor placed in vacuum has capacitance of \( 3.14 \times 10^{-9} \, \text{F} \). Its radius will be:

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

Two sitar strings A and B playing a note are slightly out of tune and produce beats of frequency 5 Hz. The tension in string B is slightly increased and beat frequency becomes 3 Hz. What is the original frequency of B if frequency of A is 427 Hz?

The instantaneous current from a a.c source is I = 10sin 314t The frequency of the source would be

Which of the following is a transducer ?
(A) Loudspeaker
(B) Amplifier
(C) Rectifier
(D) Microphone
Choose the correct answer from the options given below :

The internal resistance of primary cell is \( 3 \Omega \). It generates a current of \( 0.3 \text{ A} \) in an external resistance of \( 22 \Omega \). The rate at which chemical energy is consumed in providing the current is:

A 0.5 m long solenoid has 500 turns and has a flux density of \( 2.52 \times 10^{-3} \text{ T} \) at its centre.
The current flowing in the solenoid would be (given, \( \mu_0 = 4\pi \times 10^{-7} \text{ Hm}^{-1} \))

If a line makes angles \(\frac{2 \pi}{3}\) and \(\frac{\pi}{3}\) with positive direction of \(x\)-axis and \(y\)-axis respectively,
then the acute angle made by the line with positive \(z\)-axis is:

Which one of the following genetic law is responsible for 3:1 expression of the phenotypic ratio in F2 generation?

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 \(\Delta_{\circ}\) 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 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.
What will be the crystal field splitting energy for tetrahedral \(\left[ CoCl _4\right]^{2-}\) if its value for octahedral \(\left[ CoCl _6\right]^{4-}\) is \(18,000 cm^{-1}\) ?

If \(\vec{a}, \vec{b}\) and \(\vec{c}\) are three unit vectors such that \(\vec{a}+2 \vec{b}-3 \vec{c}=\overrightarrow{0}\), then the value of \(2 \vec{a} \cdot \vec{b}-6 \vec{b} \cdot \vec{c}-3 \vec{c} \cdot \vec{a}\) is

If \(A^2-A+I=0\), then \(A^{-1}\) is equal to :

The amine which will not undergo benzoylation in alkaline medium is