NTA JEE Main 9th April 2016 Online

200 g water is heated from 40°C to 60°C. Ignoring the slight expansion of water, the change in its internal energy is close to (Given specific heat of water = 4184 J kg$$^{-1}$$ K$$^{-1}$$):

Two particles are performing simple harmonic motion in a straight line about the same equilibrium point. The amplitude and time period for both particles are same and equal to A and T, respectively. At time $$t = 0$$ one particle has displacement A while the other one has displacement $$-\frac{A}{2}$$ and they are moving towards each other. If they cross each other at time t, then t is:

Two engines pass each other moving in opposite directions with uniform speed of 30 m/s. One of them is blowing a whistle of frequency 540 Hz. Calculate the frequency heard by driver of second engine before they pass each other. Speed of sound is 330 m/sec:

The potential (in volts) of a charge distribution is given by
$$V(z) = 30 - 5z^2$$ for $$|z| \leq 1$$ m
$$V(z) = 35 - 10|z|$$ for $$|z| \geq 1$$ m.
$$V(z)$$ does not depend on x and y. If this potential is generated by a constant charge per unit volume $$\rho_0$$ (in units of $$\epsilon_0$$) which is spread over a certain region, then choose the correct statement.

Three capacitors each of 4 $$\mu$$F are to be connected in such a way that the effective capacitance is 6 $$\mu$$F. This can be done by connecting them

In the circuit shown, the resistance r is a variable resistance. If for $$r = fR$$, the heat generation in r is maximum then the value of f is

To know the resistance $$G$$ of a galvanometer by half deflection method, a battery of emf $$V_E$$ and resistance $$R$$ is used to deflect the galvanometer by angle $$\theta$$. If a shunt of resistance $$S$$ is needed to get half deflection the $$G$$, $$R$$ and $$S$$ are related by the equation:

A 50 $$\Omega$$ resistance is connected to a battery of 5 V. A galvanometer of resistance 100 $$\Omega$$ is to be used as an ammeter to measure current through the resistance, for this a resistance $$r_S$$ is connected to the galvanometer. Which of the following connections should be employed if the measured current is with in 1% of the current without the ammeter in the circuit?

A magnetic dipole is acted upon by two magnetic fields which are inclined to each other at an angle of 75°. One of the fields has a magnitude of 15 mT. The dipole attains stable equilibrium at an angle of 30° with this field. The magnitude of the other field (in mT) is close to

A series $$LR$$ circuit is connected to a voltage source with $$V(t) = V_0\sin(\omega t)$$. After a very large time, current $$I(t)$$ behaves as $$(t_0 \gg \frac{L}{R})$$: