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

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

The minimum value of 4 tan²θ + 9 cot²θ is equal to

(a) 0

(b) 5

(c) 12

(d) 13