1
JEE Main 2018 (Offline)
+4
-1
In an a.c. circuit, the instantaneous e.m.f. and current are given by
e = 100 sin 30 t
i = 20 sin $$\left( {30t - {\pi \over 4}} \right)$$
In one cycle of a.c., the average power consumed by the circuit and the wattless current are, respectively
A
50, 0
B
50, 10
C
$${{1000} \over {\sqrt 2 }},10$$
D
$${{50} \over {\sqrt 2 }}$$
2
JEE Main 2018 (Offline)
+4
-1
For an RLC circuit driven with voltage of amplitude vm and frequency $${\omega _0}$$ = $${1 \over {\sqrt {LC} }}$$ the current exhibits resonance. The quality factor, Q is given by :
A
$${{CR} \over {{\omega _0}}}$$
B
$${{{\omega _0}L} \over R}$$
C
$${{{\omega _0}R} \over L}$$
D
$${R \over {\left( {{\omega _0}C} \right)}}$$
3
JEE Main 2018 (Offline)
+4
-1
An EM wave from air enters a medium. The electric fields are
$$\overrightarrow {{E_1}}$$ = $${E_{01}}\widehat x\cos \left[ {2\pi v\left( {{z \over c} - t} \right)} \right]$$ in air and $$\overrightarrow {{E_2}}$$ = $${E_{02}}\widehat x\cos \left[ {k\left( {2z - ct} \right)} \right]$$ in medium, where the wave number k and frequency $$\nu$$ refer to their values in air. The medium is non-magnetic. If $${\varepsilon _{{r_1}}}$$ and $${\varepsilon _{{r_2}}}$$ refer to relative permittivities of air and medium respectively, which of the following options is correct ?
A
$${{{\varepsilon _{{r_1}}}} \over {{\varepsilon _{{r_2}}}}} = 4$$
B
$${{{\varepsilon _{{r_1}}}} \over {{\varepsilon _{{r_2}}}}} = 2$$
C
$${{{\varepsilon _{{r_1}}}} \over {{\varepsilon _{{r_2}}}}} = {1 \over 4}$$
D
$${{{\varepsilon _{{r_1}}}} \over {{\varepsilon _{{r_2}}}}} = {1 \over 2}$$
4
JEE Main 2018 (Online) 15th April Evening Slot
+4
-1

A copper rod of mass m slides under gravity on two smooth parallel rails, with separation l and set at an angle of $$\theta$$ with the horizontal. At the bottom rails are joined by a resistance R. There is a uniform magnetic field B normal to the plane of the rails, as shown in the igure. The terminal speed of the copper rod is :
A
$${{mg\,R\,\tan \,\theta } \over {{B^2}\,{l^2}}}$$
B
$${{mg\,R\,\cot \,\theta } \over {{B^2}\,{l^2}}}$$
C
$${{mg\,R\,\sin \,\theta } \over {{B^2}\,{l^2}}}$$
D
$${{mg\,R\,\cos \,\theta } \over {{B^2}\,{l^2}}}$$
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