Form partial differential equation by eliminating arbitrary function 

z =  x + y + f(xy)

Eliminating arbitrary constants form partial differential equation from the 

z = ax + by

Solve the following partial differential equation 

(1).         pq + p + q = 0

(2).         pq = 1

Prove Green's theorem in a plane.

Using double integral find the area enclosed by the curve y= 2x² and y²=4x

Find the area bounded by the parabola y²= 4 - x and y² = 4 - 4x as a double integral and evaluate it.

Using double integration find the area of parallelogram whose vertices are A(1,0), B(3,1), C(2,2), D(0,1) .

Evaluate the area bounded by y = x and y = x²

Evaluate the area bounded by               y = 4x - x² and y = x

Find the area bounded by y² = 4 - x ,    y² = x

In an election between two candidates 68 votes declared invalid. Winning candidate got 52% of valid votes and gets elected by majority of 98 votes. Find the total votes.

(a) 2518

(b) 2450

(c) 3200

(d) 3280