A conducting wire of parabolic shape, initially y = x2, is moving with velocity $$v = {v_0}\widehat i$$ in a non-uniform magnetic field $$B = {B_0}\left( {1 + {{\left( {{y \over L}} \right)}^\beta }} \right)\widehat k$$, as shown in figure. If V0, B0, L and $$\beta $$ are positive constants and $$\Delta $$$$\phi $$ is the potential difference developed between the ends of the wire, then the correct statement(s) is/are
$$\left| {\Delta \phi } \right|$$ is proportional to the length of the wire projected on the y-axis.
2
JEE Advanced 2019 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-1
A thin convex lens is made of two materials with refractive indices n1 and n2, as shown in the figure. The radius of curvature of the left and right spherical surfaces are equal. f is the focal length of the lens when n1 = n2 = n. The focal length is f + $$\Delta $$f when n1 = n and n2 = n + $$\Delta $$n.
Assuming $$\Delta $$n << (n - 1) and 1 < n < 2, the correct statement(s) is/are
A
If $${{\Delta n} \over n} < 0$$ then $${{\Delta f} \over f}$$ > 0
B
For n = 1.5, $$\Delta $$n = 10-3 and f = 20 cm, the value of $$\left| {\Delta f} \right|$$ will be 0.02 cm (round off to 2nd decimal place).
The relation between $${{{\Delta f} \over f}}$$ and $${{{\Delta n} \over n}}$$ remains unchanged if both the convex surfaces are replaced by concave surfaces of the same radius of curvature.
3
JEE Advanced 2019 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-1
One mole of a monatomic ideal gas goes through a thermodynamic cycle, as shown in the volume versus temperature (V-T) diagram. The correct statement(s) is/are [R is the gas constant]
A
Work done in this thermodynamic cycle (1$$ \to $$2$$ \to $$3$$ \to $$4$$ \to $$1) is $$\left| W \right| = {1 \over 2}R{T_0}$$.
B
The ratio of heat transfer during processes 1$$ \to $$2 and 2$$ \to $$3 is $$\left| {{{{Q_{1 \to 2}}} \over {{Q_{2 \to 3}}}}} \right| = {5 \over 3}$$
C
The above thermodynamic cycle exhibits only isochoric and adiabatic processes.
D
The ratio of heat transfer during processes 1$$ \to $$2 and 3$$ \to $$4 is $$\left| {{{{Q_{1 \to 2}}} \over {{Q_{3 \to 4}}}}} \right| = {1 \over 2}$$
4
JEE Advanced 2019 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-1
In the circuit shown, initially there is no charge on the capacitors and keys S1 and S2 are open. The values of the capacitors are C1 = 10$$\mu $$F, C2 = 30$$\mu $$F and C3 = C4 = 80$$\mu $$F.
Which of the statement(s) is/are correct?
A
The key S1 is kept closed for long time such that capacitors are fully charged. Now, key S2 is closed, at this time, the instantaneous current across 30$$\Omega $$ resistor (between points P and Q) will be 0.2 A (round off to 1st decimal place).
B
If key S1 is kept closed for long time such that capacitors are fully charged, the voltage across the capacitor C1 will be 4V.
C
At time t = 0, the key S1 is closed, the instantaneous current in the closed circuit will be 25 mA.
D
If key S1 is kept closed for long time such that the capacitors are fully charged, the voltage difference between points P and Q will be 10 V.
