A and B toss coin alternately till one of them gets a head and wins the game. If A starts first, find the probability the B will win the game.

Two cards are drawn successively with replacement from a well shuffled pack of 52 cards. Find the probability distribution of number of jacks.

Evaluate : $\int \frac{2\text{x}{\dot{\text{tan}}}^{-1}x}{1+{\text{x}}^4}\text{ dx}$

Using properties of determinants, prove the following $\left|\begin{array}{ccc}3a& -a+b& -a+c\\ a-b& 3b& c-a\\ a-c& b-c& 3c\end{array}\right|=3\left(a+b+c\right)\left(ab+bc+ca\right)$

Evaluate : $\int \frac{{\text{x}}^2+1}{{\left(\text{x}+1\right)}^2}\text{dx}$

Evaluate : $\int \frac{\text{dx}}{{\text{x}}^3+{\text{x}}^2+\text{x}+1}$

Solve the following differentia equation: $\left({\text{y}}^2-{\text{x}}^2\right)\text{dy}=3\text{x ydx}$

Solving the following differentia equation: $\text{s i n x}\frac{\text{dy}}{\text{dx}}+\text{cos x}\dot{\text{y}}=\cos x{\dot{\text{sin}}}^2\text{x}$

Verify that $\text{y}=\text{A c o s x}-\text{B s i nx}$ is solution of the differential equation. $\frac{{\text{d}}^{2\text{y}}}{{\text{dx}}^2}+\text{y}=0$

Express the matrix as $A=\left[\begin{array}{ccc}1& 3& 5\\ -6& 8& 3\\ -4& 6& 5\end{array}\right]$ the sum of a symmetric and a skew-symmetric matrix