NTA JEE Main 19th April 2014 Online

The figure shows a circular area of radius R where a uniform magnetic field $$\vec{B}$$ is going into the plane of the paper and increasing in magnitude at a constant rate. In that case, which of the following graphs, drawn schematically, correctly shows the variation of the induced electric field E(r)?

If microwaves, X-rays, infrared, gamma rays, ultraviolet, radio waves and visible parts of the electromagnetic spectrum are denoted respectively by M, X, I, G, U, R and V the following is the arrangement in ascending order of the wavelength:

The diameter of the objective lens of the microscope makes an angle $$\beta$$ at the focus of the microscope. Further, the medium between the object and the lens is the oil of the refractive index n. Then the resolving power of the microscope:

A ray of light is incident from a denser to a rarer medium. The critical angle for total internal reflection is $$\theta_{iC}$$ and Brewster's angle of incidence is $$\theta_{iB}$$, such that $$\frac{\sin\theta_{iC}}{\sin\theta_{iB}} = \eta = 1.28$$. The relative refractive index of the two media is:

In Young's double-slit experiment, the distance between the two identical slits is 6.1 times larger than the slit width. Then the number of intensity maxima observed within the central maximum of the single-slit diffraction pattern is:

Match List-I (Experiment performed) with List-II (Phenomena discovered/associated) and select the correct option from the options given below the lists.

List-I:                                                                  List-II:
(a) Davisson and Germer experiment                    (i) Wave nature of electrons
(b) Millikan's oil drop experiment                         (ii) Charge of an electron
(c) Rutherford experiment                                   (iii) Quantisation of energy levels
(d) Franck-Hertz experiment                               (iv) Existence of the nucleus

A piece of wood from a recently cut tree shows 20 decays per minute. A wooden piece of the same size placed in a museum (obtained from a tree cut many years back) shows 2 decays per minute. If the half-life of C$$^{14}$$ is 5730 years, then the age of the wooden piece placed in the museum is approximately: [This question was awarded a bonus and proper correction was made to avoid that]

Given, A and B are input terminals. Logic 1 is > 5 V, Logic 0 is < 1 V. Which logic gate operation, the following circuit does?

Note: This question was awarded a bonus. C option changed.

Long-range radio transmission is possible when the radio waves are reflected from the ionosphere. For this to happen the frequency of the radio waves must be in the range:

In an experiment to determine the gravitational acceleration g of a place with the help of a simple pendulum, the measured time period squared is plotted against the string length of the pendulum in the figure. What is the value of g at the place?