Question

One bag contains 3 red and 5 black balls. Another bag contains 6 red and 4 black balls. A ball is transferred from first bag to the second bag and then a ball is drawn from the second bag. Find the probability that the ball drawn is red.

Form the differential equation of all circles which is tough the x-axis at the origin.

The radius r of a right circular cylinder is increasing uniformly at the rate of 0.3 cm/s and its height h is decreasing at the rate of 0.4 cm/s. When r = 3.5 cm and h = 7 cm, find the rate of change of the curved surface area of the cylinder. $[\mathrm{Use}\:\pi=\:\frac{22}{7}\:]$

Find the area of the parallelogram whose diagonals are represented by the vectors $\stackrel{\rightarrow}{a}\$ = $2{\hat{i}}-3{\hat{j}}+4{\hat{k}}$ and ${\vec{b}}=2{\hat{i}}-{\hat{j}}+2{\hat{k}}$

If A and B are square matrices of order 3 such that |A| = –1, |B| = 3, then find the value of |2AB|.

If A = $\begin{vmatrix}2 & 3 & -1 \\ 4 & 1 & 0 \\ 3 & 3 & 2\end{vmatrix}$ , find $M_{12}\times M_{21}+C_{21}\times C_{12}$ when $M_{i j}$ is called minor and $C_{i j}$ is called co-factors of A.

Find : $\textstyle\int$$\frac{d x}{\sqrt{3-2\,x-x^{2}}}$