For what distance is ray optics a good approximation when the aperture is 3 mm wide and the wavelength is 500 nm?

The dipole moment of a circular loop carrying a current I is m and the magnetic field at the centre of the loop is \( B_1 \). When the dipole moment is made three times by keeping the current I same, the magnetic field at the centre of the loop becomes \( B_2 \). The ratio of \( B_1 \) and \( B_2 \) is:

The ratio of speed of light in vacuum to the speed of light in a medium is :
Where \(\mu_{ r }=\) relative permeability of the medium,\(\epsilon_{ r }=\) relative permittivity of the medium

Time taken by sunlight to pass through a window of thickness 8 mm and refractive index \( \left( \frac{3}{2} \right) \) is :

The impact parameter for an \(\alpha\)-particle approaching a target nucleus is minimum when the scattering angle \(\theta\) is

In a diffraction pattern due to a narrow slit of width a, alternate dark and bright fringe pattern is obtained on a screen kept at distance D from the slit. Choose the correct option.
(A) The angular width of central maximum is given by 2D/a, linear width is given by 2D\lambda/a
(B) When the size of aperture, a is quite large, the diffraction effect is negligible,
(C) For light of smaller wavelength, angular width of central maximum increases, while linear width decreases,
(D) Angular width of central maximum does not decrease while linear width decreases on decreasing distance of screen from slit.
Choose the correct answer from the options given below:

An alternating current is given by \( i = i_1 \cos \omega t + i_2 \sin \omega t \). The rms current is given by :

A pair of dice is thrown, getting a total of 7 is considered a success. Then the probability of success in a single throw is:

Which of the following statements related to Wheatstone Bridge are correct?
(A).The bridge is most sensitive when all the four resistances are of the same order
(B). The internal resistance of the cell and the resistance of the galvanometer affect the null point
(C). It does not involve measurement of current and potential difference
(D).Resistances of ammeters and voltmeters do not affect the measurements
Choose the correct answer from the options given below:

Extinction of Steller's sea Cow and passenger pigeon is due to

Read the passage carefully and answer the questions
The chemical reactions proceed at different rates which depend on various factors like concentration, temperature, etc. Rate law is an expression which relates the rate of reaction with concentration of various reacting species in the reaction. For a first order reaction, the concentration of the reactant after time \(t\) is related with its initial concentration by the relation, \(C=C_0 e^{-k t}\). The rate constants for different orders have different expressions. For a first order reaction, \(k=\frac{2.303}{t} \log \frac{a}{a-x}\), where \(a\) is the initial concentration and \(x\) is the extent of reaction.
A reaction which is first order with respect to the reactant \(A\) has a rate constant of \(6 min^{-1}\). If the reaction is started with \([A]=5.0 mol L ^{-1}\) when would \([A]\) reach the value of \(0.05 mol L ^{-1}\)

What is the hybridisation of metal ion in \(\left[ Ni ( CO )_4\right]\) compound?

The sun maintains its shine because of the