1
JEE Main 2023 (Online) 24th January Evening Shift
+4
-1 A metallic rod of length 'L' is rotated with an angular speed of '$$\omega$$' normal to a uniform magnetic field 'B' about an axis passing through one end of rod as shown in figure. The induced emf will be : A
$$\mathrm{\frac{1}{2}B^2L^2\omega}$$
B
$$\mathrm{\frac{1}{2}BL^2\omega}$$
C
$$\mathrm{\frac{1}{4}BL^2\omega}$$
D
$$\mathrm{\frac{1}{4}B^2L\omega}$$
2
JEE Main 2023 (Online) 24th January Morning Shift
+4
-1 A conducting circular loop of radius $$\frac{10}{\sqrt\pi}$$ cm is placed perpendicular to a uniform magnetic field of 0.5 T. The magnetic field is decreased to zero in 0.5 s at a steady rate. The induced emf in the circular loop at 0.25 s is :

A
emf = 10 mV
B
emf = 5 mV
C
emf = 100 mV
D
emf = 1 mV
3
JEE Main 2022 (Online) 27th July Evening Shift
+4
-1 A series LCR circuit has $$\mathrm{L}=0.01\, \mathrm{H}, \mathrm{R}=10\, \Omega$$ and $$\mathrm{C}=1 \mu \mathrm{F}$$ and it is connected to ac voltage of amplitude $$\left(\mathrm{V}_{\mathrm{m}}\right) 50 \mathrm{~V}$$. At frequency $$60 \%$$ lower than resonant frequency, the amplitude of current will be approximately :

A
466 mA
B
312 mA
C
238 mA
D
196 mA
4
JEE Main 2022 (Online) 26th July Morning Shift
+4
-1 In a series $$L R$$ circuit $$X_{L}=R$$ and power factor of the circuit is $$P_{1}$$. When capacitor with capacitance $$C$$ such that $$X_{L}=X_{C}$$ is put in series, the power factor becomes $$P_{2}$$. The ratio $$\frac{P_{1}}{P_{2}}$$ is:

A
$$\frac{1}{2}$$
B
$$\frac{1}{\sqrt{2}}$$
C
$$\frac{\sqrt{3}}{\sqrt{2}}$$
D
2 : 1
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