1
MHT CET 2021 21th September Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $$y = {\tan ^{ - 1}}\left\{ {{{a\cos x - b\sin x} \over {b\cos x + a\sin x}}} \right\}$$, then $${{dy} \over {dx}}$$

A
$${1 \over {1 + {x^2}}}$$
B
$${1 \over {\sqrt {1 - {x^2}} }}$$
C
$$ - 1$$
D
None of these
2
MHT CET 2021 21th September Evening Shift
MCQ (Single Correct Answer)
+1
-0

Under isothermal conditions, two soap bubbles of radii '$$r_1$$' and '$$r_2$$' combine to form a single soap bubble of radius '$$R$$'. The surface tension of soap solution is ( $$P=$$ outside pressure)

A
$$\frac{P\left(R^3+r_1^3+r_2^3\right)}{4\left(r_1^2-r_2^2+R^2\right)}$$
B
$$\frac{P^2+r_1^2+r_2^2}{4\left(r_1^2+r_2^2+R^2\right)}$$
C
$$\frac{P\left(R^3-r_1^3-r_2^3\right)}{4\left(r_1^2+r_2^2-R^2\right)}$$
D
$$\frac{P\left(R^2-r_1^2-r_2^2\right)}{4\left(r_1^3+r_2^3-R^3\right)}$$
3
MHT CET 2021 21th September Evening Shift
MCQ (Single Correct Answer)
+1
-0

Two identical parallel plate air capacitors are connected in series to a battery of emf '$$\mathrm{V}$$'. If one of the capacitor is inserted in liquid of dielectric constant '$$\mathrm{K}$$' then, potential difference of the other capacitor will become

A
$$\frac{\mathrm{K}-1}{\mathrm{KV}}$$
B
$$\frac{\mathrm{K}+1}{\mathrm{KV}}$$
C
$$\left(\frac{\mathrm{KV}}{\mathrm{K}+1}\right)$$
D
$$\frac{\mathrm{KV}}{\mathrm{K}-1}$$
4
MHT CET 2021 21th September Evening Shift
MCQ (Single Correct Answer)
+1
-0

In LCR series resonant circuit, at resonance, voltage across 'L' and 'C' will cancel each other because they are

A
90$$^\circ$$ out of phase
B
90$$^\circ$$ in phase
C
180$$^\circ$$ in phase
D
180$$^\circ$$ out of phase
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