Q22) Evaluate

I =

dx       0  5 + 2cos x

Q23) Evaluate :

(tan x) dx

Q24) Find the value of 

3 (2x2 + 5x) dx 1

Q25) A population grows at the rate of 2% per year. How long does it take for the population to double itself.

Q26) Define the line of shortest distance between two skew lines. Find the shortest distance and the vector equation of the line of shortest distance between the lines given by 
= (3 + 8 + 3) + (3 - + )
and r = (-3 - 7 + 6) + (-3 + 2 + 4)

Q27) Find the Karl Pearson's coefficient of correlation between X and Y for the following data:

Also state whether Y increases or decreases with increase in X.

Q28) If 

A =

1  -2  0 2  1  3 0  -2  1

find A^-1. Using A^-1, solve the system of linear equations
x - 2y = 10
2x + y + 3z = 8
-2y + z = 7

Q29) Find the point on the curve y² = 4x which is nearest to the point (2, -8)

Q30) Draw a rough sketch of the region {(x, y) : y² 3x, 3x² + 3y² 16} and find the area enclosed by the region using method of integration.