From a bag containing 4 white and 5 red balls, if 3 balls are drawn at random, then the mean of the number of red balls among the balls drawn, is

Let ' \(\mathrm{O}\) ' be the origin, \(\mathrm{A}\) and \(\mathrm{B}\) be two points with position vectors \(-3 \hat{i}-3 \hat{j}+4 \hat{k}\) and \(4 \hat{i}-4 \hat{j}-3 \hat{k}\) respectively. Let \(P\) be a point such that the line drawn through \(P\) parallel to \(\overrightarrow{\mathrm{OB}}\) meets \(\mathrm{OA}\) in \(\mathrm{L}\) and another line through \(\mathrm{P}\) parallel to \(\overrightarrow{\mathrm{OA}}\) meets \(\mathrm{OB}\) in \(\mathrm{M}\). If \(\mathrm{L}\) divides \(\mathrm{OA}\) in the ratio \(2: 3\) and \(\mathrm{M}\) divides \(\mathrm{OB}\) in the ratio \(3: 2\), then the distance from 0 to \(\mathrm{P}\) is

In \(\triangle \mathrm{ABC}, \frac{\mathrm{r}_1-\mathrm{r}}{\mathrm{a}}+\frac{\mathrm{r}_2-\mathrm{r}}{\mathrm{b}}=\)

If \(A\) and \(B\) are events of a random experiment such that \(P(A \cup B)=\frac{4}{5}, P(\bar{A} \cup \bar{B})=\frac{7}{10}\) and \(P(B)=\frac{2}{5}\), then \(P(A)\) equals

There exist \(\theta\) such that \(\mathrm{a}>|\sec \theta|\), then \(\int \frac{d x}{1+a \cos x}=\)

\(\left|\frac{1}{i^{2020}}+\frac{2}{i^{2021}}+\frac{3}{i^{2022}}+\frac{4}{i^{2023}}\right|\) is equal to

If $l$ and $m$ are the degree and the order respectively of the differential equation of the family of all circles in the $XY$ plane with radius $5$ units, then $2l+3m=$

The distance moved by a charged particle along the magnetic field (the component of velocity is parallel to the magnetic field) in one rotation is given by ( \(\mathrm{m}\) - mass of the particle, \(\mathrm{v}\) - velocity of the particle, \(\mathrm{q}\) charge of the particle, B - magnetic field)

Which of the following is not correct?

The differential equation formed by eliminating $a$ and $b$ from the equation $y=e^x(a\cos x+b\sin x)$ is

Compound ' \(A\) ' undergoes formation of cyanohydrins, which on hydrolysis gives lactic acid \(\left(\mathrm{CH}_3 \mathrm{CHOHCOOH}\right)\). Therefore, compound ' \(A\) ' is ____

The given circuit shows two capacitors connected to a battery. After the capacitors are completely charged, the battery is removed and the capacitors are connected with plates of opposite polarity together. Then the charge on \(2 \mathrm{C}\) and the energy lost in the process are respectively

The triangle formed by \(x^2-4 x y+y^2=0\) and \(x+y+4 \sqrt{6}=0\) is