NTA JEE Main 11th April 2014 Online

A hot body, obeying Newton's law of cooling is cooling down from its peak value 80°C to an ambient temperature of 30°C. It takes 5 minutes in cooling down from 80°C to 40°C. How much time will it take to cool down from 62°C to 32°C? (Given ln 2 = 0.693, ln 5 = 1.609)

During an adiabatic compression, 830 J of work is done on 2 moles of a diatomic ideal gas to reduce its volume by 50%. The change in its temperature is nearly: (R = 8.3 JK$$^{-1}$$ mol$$^{-1}$$)

An ideal monoatomic gas is confined in a cylinder by a spring loaded piston of cross section $$8.0 \times 10^{-3}$$ m$$^2$$. Initially the gas is at 300 K and occupies a volume of $$2.4 \times 10^{-3}$$ m$$^3$$ and the spring is in its relaxed state as shown in figure. The gas is heated by a small heater until the piston moves out slowly by 0.1 m. The force constant of the spring is 8000 N/m and the atmospheric pressure is $$1.0 \times 10^5$$ N/m$$^2$$. The cylinder and the piston are thermally insulated. The piston and the spring are massless and there is no friction between the piston and the cylinder. The final temperature of the gas will be:(Neglect the heat loss through the lead wires of the heater. The heat capacity of the heater coil is also negligible).

The angular frequency of the damped oscillator is given by, $$\omega = \sqrt{\left(\frac{k}{m} - \frac{r^2}{4m^2}\right)}$$ where k is the spring constant, m is the mass of the oscillator and r is the damping constant. If the ratio $$\frac{r^2}{mk}$$ is 8%, the change in time period compared to the undamped oscillator is approximately as follows:

Two factories are sounding their sirens at 800 Hz. A man goes from one factory to other at a speed of 2 m/s. The velocity of sound is 320 m/s. The number of beats heard by the person in one second will be:

A cone of base radius R and height h is located in a uniform electric field $$\vec{E}$$ parallel to its base. The electric flux entering the cone is:

A parallel plate capacitor is made of two plates of length l, width w and separated by distance d. A dielectric slab (dielectric constant K) that fits exactly between the plates is held near the edge of the plates. It is pulled into the capacitor by a force $$F = -\frac{\partial U}{\partial x}$$ where U is the energy of the capacitor when dielectric is inside the capacitor up to distance x (See figure). If the charge on the capacitor is Q then the force on the dielectric when it is near the edge is:

In the circuit shown, current (in A) through 50 V and 30 V batteries are, respectively:

In the circuit diagrams (A, B, C and D) shown below, R is a high resistance and S is a resistance of the order of galvanometer resistance G. The correct circuit, corresponding to the half deflection method for finding the resistance and figure of merit of the galvanometer, is the circuit labelled as:

(a)

(b)

(c)

(d)

Three identical bars A, B and C are made of different magnetic materials. When kept in a uniform magnetic field, the field lines around them look as follows:

Make the correspondence of these bars with their material being diamagnetic (D), ferromagnetic (F) and paramagnetic (P):