The derivative of

A biased coin with probability $$p$$, (0$$< p < $$1) of showing head is tossed until a head appears for the first time. If the probability that the number of tosses required is odd is $$\displaystyle \frac{7}{11}$$  then $$p$$ =

The name written on the card is the name of a boy.

1) $$\displaystyle \frac{4}{7}$$
2) $$\displaystyle \frac{3}{7}$$
3) $$\displaystyle \frac{4}{11}$$
4) $$\displaystyle \frac{2}{3}$$

If  xÖ(1 + y) +  yÖ(1 + y) = 0, then  dy / dx is :

If $$ A = \begin{bmatrix} a & x \\ y & a \end{bmatrix} $$ and if $$xy=1$$ , then $$ \text{det} (AA^T) $$ is equal to :

1) $$ a^2 - 1$$
2) $$ (a^2+1)^2 $$
3) $$ 1 - a^2 $$
4) $$ (a^2 - 1)^2 $$

An urn contains $$6$$ white and $$4$$ black balls. A fair die whose faces are numbered from $$1$$ to $$6$$ is rolled and number of balls equal to that of the number appearing on the die is drawn from the urn at random. The probability that all those are white is

1) $$\displaystyle \frac{1}{5}$$
2) $$\displaystyle \frac{2}{5}$$
3) $$\displaystyle \frac{3}{5}$$
4) $$\displaystyle \frac{4}{5}$$

The solution of differential equation siny (dy/dx) = cosy(1 – xcosy) is-

1) cos y = (x + 1) – ce^x
2) sec y = (x + 1) – ce^x
3) sec y = (x–1) – ce^x
4) None

If the foci of an ellipse are (± √5, 0) and its eccentricity is √5/3, then the equation of the ellipse is

1) 9x² + 4y² = 36
2) 4x² + 9y² = 36
3) 36x² + 9y² = 4
4) 9x² + 36y² = 4

If ,  where  , then α -β is equal to :
 

If P(E) denotes the probability of an event E, then E is called certain event if:

1) P(E) = 0
2) P(E) = 1
3)  P(E) is either 0 or 1
4) P(E)=1 / 2

If f(x) =     then the derivative of f(x) on the interval [0, 7] is  

1) 1
2) -1
3) 0
4) Does not exist