Q2) Find the work done by the force = + 2 + , acting on a particle, if the particle is displaced from the point with position vector 2 + + to the point with position vector 3 + 2 + 4.

Q4) For the matrices A and B, verify that (AB' ) = A'B' where 

A =

1  3 2  4

B =

1  4 2  5

Q7) Two dice are thrown together. What is the probability that the sum of the numbers on the two faces is divisible by 3 or by 4?

Q8) Evaluate

cot 2x - cosec 2x           x

Q10) Verify Rolle's theorem for the following f(x) in the interval |-3, -2|:
f(x) = x² + 5x + 6

Section B

x + 4    2x       2x 2x       x + 4    2x  2x       2x     x + 4

= (5x + 4)(4 - x)2

Q20) Find the equation of the plane passing through point(-1, 2, 1) and perpendicular to the line joining the points (-3, 1, 2) and (2, 3, 4) find also the perpendicular distance of the origin from the plane.

Q25) Solve the differential equation 
cos x[1 + cos y]dx - sin y[1 + sin x]dy = 0

Q27) Evaluate

State the property of definite integrals which you have used.

Q28) Evaluate 

dx     x(x3 + 1)

Q33) Solve the differential equation
x² dy + y(x + y) dx = 0, given that y = 1 when x = 1