In class XII, suppose \(5 \% \) of boys and \(0.25\%\) of girls are physically fit for a game.
A fit student is selected at random from this class having same number of boys and girls.
If the probability that the selected student is a girl is \(\frac{m}{n}\), \(\operatorname{gcd}(m, n)=1\), then \(m+n\) is equal to

Let \(R\) be the relation in the set \(\{1,2,3\}\) given by \(R=\{(1,1),(2,2),(3,3),(1,2),(2,3)\}\). Choose the correct answer.

The solution of the differential equation xdy - ydx = 0 represents

The maximum value of the objective function \(Z=10 x+15 y\) of an L.P.P, whjected to the constraints
\(2 x+4 y \leq 8,\)
\(3 x+y \leq 6\)
\(-x-y \geq-4\)
\(x \geq 0, y \geq 0\) is :

The value of k for which \(k \frac{d y}{d x}=\sqrt{x}-\frac{1}{\sqrt{x}}\), where \(y=\sqrt{x}+\frac{1}{\sqrt{x}}\); is :

\(\int\left(x+\frac{1}{x}\right)^2 d x\) equals :

\(\lim _{x \rightarrow \infty}\left(\frac{x+7}{x+1}\right)^x\) is equal to:

A parallel plate air capacitor has a capacitance C. When it is half filled with a dielectric of dielectric constant 5, the percentage increase in the capacitance will be

The value of \(\int_0^{\pi / 2} \frac{\tan ^7 x}{\cot ^7 x+\tan ^7 x} d x\) is

Match List I with List II

LIST I	LIST II
A. Wheat	I. Perisperm
B. Black pepper	II. Polyembryony
C. Cashew	III. Albuminous seed
D. Citrus	IV. False fruits

Choose the correct answer from the options given below:

A circular coil of 20 turns and radius 10 cm is placed in a uniform magnetic field of 0.10 T normal to the plane of the coil. If the current in the coil is 5 A . The total torque on the coil is :

The distance between the line \(\vec{r}=2 \hat{i}+2 \hat{j}-3 \hat{k}+\lambda(\hat{i}+\hat{j}+4 \hat{k})\) and the plane \(\vec{r} \cdot(\hat{i}-5 \hat{j}+\hat{k})-4=0\) is:

Three identical resistors are connected first in series to an electrical voltage V. Let I be the total current flowing in the circuit. These resistors are disconnected and again connected in parallel with the same source. Which of the following statements are true?
(A) The potential difference across each resistor is V/3 in series connection
(B) The potential difference across all three resistors in parallel connection is 3V
(C) The current flowing in each resistor in series connection is the same as I
(D) The current flowing through each resistor in parallel combination is equal to 31
Choose the correct answer from the options given below: