1
JEE Main 2022 (Online) 25th July Evening Shift
Numerical
+4
-1
Change Language

Let $$x = \sin (2{\tan ^{ - 1}}\alpha )$$ and $$y = \sin \left( {{1 \over 2}{{\tan }^{ - 1}}{4 \over 3}} \right)$$. If $$S = \{ a \in R:{y^2} = 1 - x\} $$, then $$\sum\limits_{\alpha \in S}^{} {16{\alpha ^3}} $$ is equal to _______________.

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2
JEE Main 2022 (Online) 25th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language

In AM modulation, a signal is modulated on a carrier wave such that maximum and minimum amplitudes are found to be 6 V and 2 V respectively. The modulation index is :

A
100%
B
80%
C
60%
D
50%
3
JEE Main 2022 (Online) 25th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The electric current in a circular coil of 2 turns produces a magnetic induction B1 at its centre. The coil is unwound and in rewound into a circular coil of 5 tuns and the same current produces a magnetic induction B2 at its centre. The ratio of $${{{B_2}} \over {{B_1}}}$$ is

A
$${5 \over 2}$$
B
$${25 \over 4}$$
C
$${5 \over 4}$$
D
$${25 \over 2}$$
4
JEE Main 2022 (Online) 25th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

A drop of liquid of density $$\rho$$ is floating half immersed in a liquid of density $${\sigma}$$ and surface tension $$7.5 \times 10^{-4}$$ Ncm$$-$$1. The radius of drop in $$\mathrm{cm}$$ will be :

(g = 10 ms$$-$$2)

A
$$ \frac{15}{\sqrt{(2 \rho-\sigma)}} $$
B
$$\frac{15}{\sqrt{(\rho-\sigma)}}$$
C
$$\frac{3}{2 \sqrt{(\rho-\sigma)}}$$
D
$$\frac{3}{20 \sqrt{(2 \rho-\sigma)}}$$
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