The value of `e^(2mi cot^-1 p)((p i+1)/(p i-1))^m` is equal to `(p > 0)`

Find the value of 'p' for which the qudratic equations have equal roots: (3p +1) c^(2) + 2 ( p+1) c+ p=0.

If I=int(1)/(2p)sqrt((p-1)/(p+1))dp=f(p)+c, then f(p) is equal to

Show that e^(2mi theta)((i cot theta+1)/(i cot theta-1))^(m)=1

If alpha , beta are the roots of the quadratic equation (p^2 + p + 1) x^2 + (p - 1) x + p^2 = 0 such that unity lies between the roots then the set of values of p is (i) O/ (ii) p in (-infty,-1) cup (0,infty) (iii) p in (-1,infty) (iv) (-1,1)

The random variable X can take only the values 0, 1, 2. Given that P(X = 0) = P(X = 1) = p and that E(X^(2)) = E(X) , find the value of p.

Let E_(1) and E_(2) be two events such that P(E_(1))=0.3, P(E_(1) uu E_(2))=0.4 and P(E_(2))=x . Find the value of x such that (i) E_(1) and E_(2) are mutually exclusive, (ii) E_(1) and E_(2) are independent.