Match the column I with column II

A-P B-R C-P D-R

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A-P B-Q C-P,S D-R

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A-Q B-Q C-S D-Q

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A-Q B-Q C-Q,R D-P

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Solution

The correct option is A
A-P B-R C-P D-R

$C_{1} = C, C_{2} = 2 C, C_{3} = 3 C, C_{4} = 4 C$

Let q be the charge on $C_{1}$ . So charge on $C_{2} = q .$

Let $q_{3}$ be charge on $C_{3}$ and $q_{4}$ on $C_{4} .$

So, $q = q_{3} + q_{4}$

And the potential drop across $C_{3}$ and $C_{4}$ is the same.

So, $\frac{q_{3}}{3 C} = \frac{q_{4}}{4 C}$

Solving we get, $q_{3} = \frac{3 q}{7}$

and $q_{4} = \frac{4 q}{7}$

Now by calculating potential drop as q/C and potential energy as $q^{2} / 2 C$ (for charge q and capacitance C),

We find that maximum potential difference is across $C_{1}$ , minimum across $C_{3}$ and $C_{4}$ . And potential energy is maximum for $C_{1}$ and minimum for $C_{3}$ .

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Similar questions

Q. Match the following

List I	List II
I. $\int_{- 1}^{1} x \| x \| d x$	(a) $\frac{π}{2}$
II. $\int_{0}^{\frac{π}{2}} (1 + log (\frac{4 + 3 sin x}{4 + 3 cos x})) d x$	(b) $\int_{0}^{\frac{a}{2}} f (x) d x$
III. $\int_{0}^{a} f (x) d x$	(c) $\int_{0}^{a} [f (x) + f (- x)] d x$
IV. $\int_{- a}^{a} f (x) d x$	(d) $0$
	(e) $\int_{0}^{a} f (a - x) d x$

Q. Observe the following Lists

List-I	List-II
$A) \int_{0}^{a} f (x) d x$	1) $\int_{0}^{a} f (a + x) d x$
B) $\int_{- a}^{a} f (x) d x$	2) $\int_{0}^{a} f (a - x) d x$
C) $\int_{0}^{2 a} f (x) d x$	3) 0, if $f (x)$ is odd
D) $\int_{0}^{n a} f (x) d x$	4) $0$ , if $f (2 a - x)$ $= - f (x)$
	5) $(n - 1) \int_{0}^{a} f (x) d x$ , if period of f(x) is $a$ .
	6) $\int_{0}^{a} f (x) d x$ , if period of $f (x)$ is $a$ .

Match the statements of Column I with values of Column II
$\begin{matrix} C o l u m n I & C o l u m n I I (A) \int \frac{e^{2 x} - 2 e^{x}}{e^{2 x} + 1} d x = A l n (e^{2 x} + 1) + B t a n^{- 1} (e^{x}) + c & (p) A = - \frac{1}{2}, B = - \frac{1}{4} (B) \int \sqrt{x + \sqrt{x^{2} + 2}} d x = A {x + \sqrt{x^{2} + 2}}^{\frac{3}{2}} + \frac{B}{\sqrt{x + \sqrt{x^{2} + 2}}} + c & (q) A = \frac{1}{2}, B = - 2 (C) \int \frac{c o s 8 x - c o s 7 x}{1 + 2 c o s 5 x} d x = A s i n 3 x + B s i n 2 x + c & (r) A = \frac{1}{3}, B = - 2 (D) \int \frac{l n x}{x^{3}} d x = A \frac{l n x}{x^{2}} + \frac{B}{x^{2}} + c & (s) A = \frac{1}{3}, B = - \frac{1}{2} \end{matrix}$

Q. Integrate:

\int (a^{x} + x^{a} + a^{a}) d x

I = \int \sqrt{\frac{a + x}{a - x}} d x

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