A light wave has a frequency of \( 4 \times 10^{14} \, \text{Hz} \). Find the difference in its wavelengths in alcohol of refractive index 1.35 and glass of refractive index 1.5 :

A cell of emf 3 V and internal resistance 0.1 \(\Omega\) is connected to a 3.9 \(\Omega\) external resistance. What will be the potential difference across the terminals of the cell ?

Arrange the following in the increasing order of their energy gap between their conduction and valence bands:
(A) Si
(B) C (diamond)
(C) Ge
(D) Sn
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A transformer has 1000 turns in the primary and 2000 turns in its secondary winding. The primary voltage is 200 V and the load across the secondary is \(100 \Omega\). If the transformer is assumed to be ideal, then the value of current in the primary is

Two circular coils of diameter 10 cm and 20 cm, carrying equal currents have the same number of turns. The ratio of magnetic fields produced at the center of coils, respectively will be

At some instant, the current in the circuit shown below is 1 A, and it is decreasing at a rate of \( 10^2 \text{ A/s} \). The value of the potential difference \( (V_P - V_Q) \) at that instant is:

A 200 turns closely wound circular coil of radius 10 cm carries a current of 3.5 A. The magnetic moment of the coil is

The structures present in human sperm are-
(A). Nucleus
(B). Zona pellucida
(C). Acrosome
(D). Mitochondria
Choose the correct answer from the options given below:

In a concave mirror, an object is placed at a distance \( x \) from the focus and the image is formed at a distance \( y \) from the focus. What is the focal length of the mirror?

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 \(18,000 cm^{-1}\) ?

Ammonia is manufactured by:
\(N _2(g)+3 H _2(g) \rightleftharpoons 2 NH _3(g) \quad \Delta H=-46.1 kJ / mol\)
The various steps involved are:
(A) Condensation of mixture of gases
(B) Passing the gaseous mixture over catalyst
(C) Compression of the mixture of gases
(D) Recirculation of the gaseous mixture
Choose the correct answer from the options given below :

Which of the following is not a sexually transmitted disease?

Which of the following are correct?
(A) For a square matrix \(A\), if \(A^3=I\), then \(A^{-1}=A^2\).
(B) The determinant of only a square matrix can be defined.
(C) If \(A\) is a square matrix of order 3 , then the number of minors of the matrix \(A\) is 3 .
(D) If \(A\) and \(B\) are two non-singular matrices of the same order, then \((A B)^{-1}=B^{-1} A^{-1}\).
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