NTA JEE Main 6th April 2014 Offline

The pressure that has to be applied to the ends of a steel wire of length 10 cm to keep its length constant when its temperature is raised by 100 °C is: (For steel, Young's modulus is $$2 \times 10^{11}$$ N m$$^{-2}$$ and coefficient of thermal expansion is $$1.1 \times 10^{-5}$$ K$$^{-1}$$)

Three rods of Copper, Brass and Steel are welded together to form a Y-shaped structure. Area of cross-section of each rod is 4 cm$$^2$$. End of copper rod is maintained at 100 °C. Where as ends of brass and steel are kept at 0 °C. Lengths of the copper, brass and steel rods are 46, 13 and 12 cms respectively. The rods are thermally insulated from surroundings except at ends. Thermal conductivities of copper, brass and steel are 0.92, 0.26 and 0.12 CGS units respectively. Rate of heat flow through copper rod is:

One mole of diatomic ideal gas undergoes a cyclic process ABC as shown in figure. The process BC is adiabatic. The temperatures at A, B and C are 400 K, 800 K and 600 K respectively. Choose the correct statement:

A particle moves with simple harmonic motion in a straight line. In first $$\tau$$ s, after starting from rest it travels a distance a, and in next $$\tau$$ s it travels 2a, in same direction, then:

A pipe of length 85 cm is closed from one end. Find the number of possible natural oscillations of air column in the pipe whose frequencies lie below 1250 Hz. The velocity of sound in air is 340 m/s.

Assume that an electric field $$\vec{E} = 30x^2\hat{i}$$ exists in space. Then the potential difference $$V_A - V_O$$, where $$V_O$$ is the potential at the origin and $$V_A$$ the potential at x = 2 m is:

A parallel plate capacitor is made of two circular plates separated by a distance of 5 mm and with a dielectric of dielectric constant 2.2 between them. When the electric field in the dielectric is $$3 \times 10^4$$ V/m, the charge density of the positive plate will be close to:

In a large building, there are 15 bulbs of 40 W, 5 bulbs of 100 W, 5 fans of 80 W and 1 heater of 1 kW. The voltage of the electric mains is 220 V. The minimum capacity of the main fuse of the building will be:

The coercivity of a small magnet, where the ferromagnet gets demagnetised is $$3 \times 10^3$$ A/m. The current required to be passed in a solenoid of length 10 cm and number of turns 100, so that the magnet gets demagnetised when inside the solenoid is:

A conductor lies along the z-axis at $$-1.5 \leq z < 1.5$$ m and carries a fixed current of 10.0 A in $$-\hat{a}_z$$ direction (see figure). For a field $$\vec{B} = 3.0 \times 10^{-4} e^{-0.2x} \hat{a}_y$$ T, find the power required to move the conductor at constant speed to x = 2.0 m, y = 0 m in $$5 \times 10^{-3}$$ s. Assume parallel motion along the x-axis.