In Young's double slit experiment using monochromatic light of wavelength \(\lambda\), the intensity of light at a point on the screen where path difference is \(\lambda\), is 'T' units. What is the intensity of light at a point where path difference is \(\frac{\lambda}{4}\) ?

A wire of length \( L \) meters, carrying a current \( I \) ampere is bent in the form of a circle. The magnitude of its magnetic moment, in SI units, is:

The energy equivalent of 5 g of substance is

Which of the following is not a significant characteristic of a pulse?

As the frequency of an ac circuit increases, the current first increases till it becomes maximum at resonance and then decreases. Which one of the following combinations of circuit elements are likely to comprise the circuit ?

Match List I with List - II.

List - I	List - II
(A) Interference experiment	(I) Maxwell
(B) Electromagnetic theory of light	(II) Christian Huygens
(C) Wave theory of light	(III) Isaac Newton
(D) Particle theory of light	(IV) Thomas Young

Choose the correct answer from the options given below :

The electric field and magnetic field of a plane electromagnetic wave propagating in vacuum are expressed as
\(E_x=E_0 \sin (k z-\omega t)\)
\(B_y=B_0 \sin (k z-\omega t)\)
Which of the following statements are correct?
(A). The wave is propagating along the z- direction.
(B). The electric field Ex and magnetic field By are perpendicular to each other and perpendicular to the z direction.
(C) The electric and magnetic fields Ex and By are perpendicular to each other, and parallel to the direction of propagation.
(D) k is related to the wave length À of the wave by the usual equation \(k = A / 2 Tt\)
Choose the correct answer from the options given below:

Which statements are true for X-ray ?
(A) The wavelength range of X-rays is about \( 10^{-8} \, \text{m} \) to \( 10^{-13} \, \text{m} \).
(B) X-rays can't affect a photographic film.
(C) X-rays can damage living tissues.
(D) We can generate X-rays by bombarding a metal target by high energy electrons.
(E) The wave length of X-rays is more then Microwave.
Choose the correct answer from the options given below :

The interval in which \(f(x)=\sin x-\cos x, 0 \leq x \leq 2 \pi\) is strictly decreasing is:

A current of 15 A in the primary coil of a circuit is reduced to zero at a uniform rate in \( 10^{-6} \, \text{s} \). If the coefficient of the Mutual Inductance is 4 H, what is the Induced emf in secondary coil?

The acute angle between the lines \(\vec{r}=(4 \hat{i}-\hat{j})+\lambda(2 \hat{i}+\hat{j}-3 \hat{k})\) and \(\frac{x-1}{1}=\frac{y+1}{-3}=\frac{z-2}{2}\) is

Read the passage carefully and answer the Questions
The concentration dependence of the rate of a reaction is called the differential rate equation. It is not always convenient to determine the instantaneous rate, as it is measured by calculating the slope of the tangent at point 't' in the concentration vs time plot. This makes it difficult to determine the rate and hence the order of the reaction. This difficulty is overcome by integrating the differential rate equation. This integrated rate equation gives a direct relation between concentrations at different times and the rate constant. The integrated rate equations are different for the reactions having different reaction orders.
A certain amount of \(N _2 O _5\) decomposes to half of its initial amount in 50 minutes.
If the decomposition is a first order reaction, the rate constant of the reaction is.

If \(e^y(x+2) = 10\), then \(\frac{d^2y}{dx^2}\) is equal to :