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

A candidate scores 25% and fails by 30 marks, while another candidate who scores 50% marks, gets 20 marks more than the minimum required marks to pass the examination. Find the maximum marks for the examination.

(a) 200

(b) 120

(c) 300

(d) 350

Two trains are running at the speed 40 km/hr and 20 km/hr respectively in the same direction. The fast train completely passes a man sitting in the slow train in 5 seconds. The length of the fast train is

(a) 23 1⁄9 m

(b) 27 m

(c) 27 7⁄9 m

(d) 23 m