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Maths:

solve by logarithmic differentiation.

Find the determinants of .

A bag contains 5 red marbles and 3 black marbles. Three marbles are drawn one by one without replacement. What is the probability that at least on of the three marbles drawn be black, if the first marble is red?

Is the function f defined by f(x)= continuous at x=0 or x=1 or x=2 ?

Evaluate

If P(A)=0.8, P(B)=0.5 and P(B/A)=0.4. Find (i) P(A intersection B). (ii) P(A given B). (iii)P(A union B).

If Z= then find the value of 3Z+Z+8I.

Maximize Z= -x+2y, subject to the constraints: x>2, x+y>5 ,y>0

Differentiate the function with respect to

Explain why the experiment of tossing a coin three times is said to have a binomial distribution.

Write a unit vector perpendicular to both the vectors and

In a dice game, a player pays a stake of Re.1 for each throw of a die. She receives Rs.5 if the die shows a 3 , Rs.2 if the die shows a 1 or 6 and nothing otherwise. What is the player’s expected profit per throw over a long series of throws?

Find the inverse of

A green and a blue dice are rolled. Find the conditional probability of obtaining a sum greater than 5, given that the blue die resulted in a 2.

Find the area of the region bounded by y^2=9x, x=2, x=4 and the y-axis in the first quadrant.

Evaluate

If x +y = , then write the value of y.

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