Find the partial differential equation of eliminating f from z = xy + (x^{2}+y^{2}+z^{2})

Eliminate the arbitrary function f and g from z = f(x+iy) + g(x-iy) and form a partial differential equation.

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= 2x^{2} and y^{2}=4x

Find the area bounded by the parabola y^{2}= 4 - x and y^{2} = 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 = x^{2}

Evaluate the area bounded by y = 4x - x^{2} and y = x

Find the area bounded by y^{2} = 4 - x , y^{2} = 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

A shopkeeper allows 3 successive discounts of 50%, 40% and 20% respectively. Find equivalent discount?

(a) 66%

(b) 70%

(c) 60%

(d) 76%

A shopkeeper allows a discount of 10% on the marked price and gets a profit of 12%. Find the ratio of cost price and marked price.

(a) 45 : 56

(b) 40 : 113

(c) 45 : 59

(d) 48 : 51

Price of a diamond is directly proportional to the square of its weight. If the diamond break into 4 pieces by mistake, the ratio of their weight becomes 1 : 2 : 3 : 4, therefore loss will arise Rs 1,40,000. Find original price of the diamond?

(a) Rs 240000

(b) Rs 200000

(c) Rs 220000

(d) Rs 180000

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Geometry

Evaluate :

∫2xcos(x2 – 5).dx

If the sum of 14 terms of an A. P is 1050 its first term is 10 find 20th term ?

Diagonals of a quadrilateral 30 cm long and the perpendicular drawn from the opposite vertices are 5.6 and 7.4 cm find the area of the quadrilateral.with steps ?

Find the sum of the integers between 10 and 30 including 10 and 30 which are not divisible by 3.

A cyclic quadrilateral pqrs are where PS equals to PQ and angle SPQ is 70 degree find angle psq