1. Using Rolle's theorem, find the value of c for

.

2. Obtain the Maclaurin's series for e^x.

3. Evaluate:-

.

5. If x = cos t, y = sin t and

, find

.

6. Evaluate:-

.

7. Solve:

.

8. In a Poisson distribution, if P(X=2) = P(X=3) find P(X=5).
(Given e^-3 = 0.050).

9. Find the mean and variance for the probability density function

otherwise.

10. Simplify:-

.