NTA JEE Main 9th January 2019 Shift 1

Temperature difference of 120$$^{\circ}$$C is maintained between two ends of a uniform rod $$AB$$ of length $$2L$$. Another bent rod $$PQ$$, of same cross-section as $$AB$$ and length $$\frac{3L}{2}$$, is connected across $$AB$$ (See figure). In steady state, temperature difference between $$P$$ and $$Q$$ will be close to:

A gas can be taken from A to B via two different processes ACB and ADB.

When path ACB is used 60 J of heat flows into the system and 30 J of work is done by the system. If the path ADB is used then work done by the system is 10 J, the heat flows into the system in the path ADB is:

A mixture of 2 moles of helium gas (atomic mass = 4u), and 1 mole of argon gas (atomic mass = 40 u) is kept at 300 K in a container. The ratio of their rms speeds $$\frac{v_{rms}(helium)}{v_{rms}(argon)}$$, is close to:

Three charges $$+Q$$, $$q$$, $$+Q$$ are placed respectively, at distance, $$0$$, $$d/2$$ and $$d$$ from the origin, on the $$x$$-axis. If the net force experienced by $$+Q$$, placed at $$x = 0$$, is zero, then value of $$q$$ is:

For a uniformly charged ring of radius $$R$$, the electric field on its axis has the largest magnitude at a distance $$h$$ from its centre. Then value of $$h$$ is:

A parallel plate capacitor is made of two square plates of side $$a$$, separated by a distance $$d$$ ($$d \ll a$$). The lower triangular portion filled with a dielectric of dielectric constant $$K$$, as shown in the figure. Capacitance of this capacitor is:

When the switch $$S$$, in the circuit shown, is closed, then the value of current $$i$$ will be:

Drift speed of electrons, when 1.5 A current flows in a copper wire of cross section 5 mm$$^2$$ is $$v_d$$. If the electron density in copper is $$9 \times 10^{28}$$ m$$^{-3}$$, the value of $$v_d$$ in mm s$$^{-1}$$ is close to (Take charge of an electron to be $$= 1.6 \times 10^{-19}$$ C)

Mobility of electrons in a semiconductor is defined as the ratio of their drift velocity to the applied electric field. If, for an N-type semiconductor, the density of electrons is $$10^{19}$$ m$$^{-3}$$ and their mobility is 1.6 m$$^2$$ V$$^{-1}$$ s$$^{-1}$$, then the resistivity of the semiconductor (since it is an N-type semiconductor contribution of holes is ignored) is close to:

A resistance is shown in the figure. Its value and tolerance are given respectively by: