The volume of the solid generated by revolving about the y-axis bounded by the parabola y = x2 and x = y2 is 1) (2/15) π 2) (24/5) π 3) 3π/10 4) (5/24) π Solution: (1) (2/15) π... View Article
If A is the area of the region bounded by the curve y = √3x + 4, x-axis and the lines x = – 1 and x = 4 and B is the area bounded by curve y2 = 3x + 4, x-axis and the lines x = – 1 and x = 4, then A : B = 1) 1 : 1 2) 2 : 1 3) 1 : 2 4) None of these Solution: (1) 1 : 1 y = √3x + 4 y2 = 3 [x + (4 / 3)] A = ∫-14 √3x + 4 dx Let 3x + 4... View Article
The area cut off by the latus rectum from the parabola y2 = 4ax is 1) (8/3) a sq units 2) (8/3) √a sq units 3) (3/8) a2 sq unit 4) (8/3) a2 sq unit Solution: (4) (8/3) a2 sq unit... View Article
The area (in sq units) bounded by the curves y2 = 4x and x2 = 4y in the plane is 1) 8/3 2) 16/3 3) 32/3 4) 64/3 Solution: (2) 16/3... View Article
The area of the region bounded by the curve 9x2 + 4y2 – 36 = 0 is 1) 9Ï€ sq units 2) 4Ï€ sq units 3) 36Ï€ sq units 4) 6Ï€ sq units Solution: (4) 6Ï€ sq units... View Article
Area bounded by the curves y = x2 and y = 2 – x2 is 1) 8/3 sq units 2) 3/8 sq unit 3) 3/2 sq units 4) None of these Solution: (1) 8/3 sq units... View Article
The area enclosed between the curve y = loge (x + e) and the coordinate axes is 1) 4 sq units 2) 3 sq units 3) 2 sq units 4) 1 sq units Solution: (4) 1 sq units Required area = ∫1-e0 loge (x + e) dx =... View Article
The area bounded by the curves y = (x – 1)2, y = (x + 1)2 and y = 1/4 is 1) 1/3 sq unit 2) 2/3 sq units 3) 1/4 sq units 4) 1/5 sq units Solution: (1) 1/3 sq unit... View Article
The area enclosed within the curve |x| + |y| = 1 is 1) 1 sq unit 2) 2√2 sq units 3) √2 sq units 4) 2 sq units Solution: (4) 2 sq units... View Article
Area bounded by the curve y = loge x, x = 0, y ≤ 0 and x-axis is 1) 1 sq units 2) 1/2 sq unit 3) 2 sq units 4) None of these Solution: (1) 1 sq unit... View Article
The area bounded by y = log x, x-axis and ordinates x = 1, x = 2 is 1) (1 / 2) (log x)2 2) log (2/e) 3) log (4/e) 4) log 4 Solution: (3) log (4/e)... View Article
The area (in sq unit)bounded by the parabola y2 = 4ax and the line x = a and x = 4a is 1) 35a2 / 3 2) 4a2 / 3 3) 7a2 / 3 4) 56a2 / 3 Solution: (4) 56a2 / 3... View Article
The area (in sq units) enclosed between the curves y = x and y = 2x – x2 is 1) 1/2 2) 1/6 3) 1/3 4) 1/4 Solution: (2) â…™... View Article
The area (in sq units)bounded by the curves y = 3x and y = x2 is 1) 10 2) 5 3) 4.5 4) 9 Solution: (3) 4.5... View Article
The area (in sq unit) of the region enclosed by the curves y = x2 and y = x3 and the ordinates x = 1, x = 2 is 1) 17/12 2) 11/6 3) 13/3 4) 1 Solution: (1) 17/12... View Article
Area bounded by y2 = x, y = 0, x = 1, x = 4 is 1) (14 / 3) sq units 2) (3 / 28) sq units 3) (8 / 3) sq units 4) (4 / 3) sq units Solution: (1) (14 / 3) sq units... View Article
The area of the smaller segment cut off from the circle x2 + y2 = 9 by x = 1 is 1) [(1 / 2) (9 sec-1 3 - √8)] sq units 2) (9 sec-1 3 - √8) sq units 3) (√8 - 9 sec-1 3) sq unit 4) None of these Solution: (2) (9... View Article
Area bounded by the curve y2 = 16x and line y = mx is 2/3, then m is equal to 1) 3 2) 4 3) 1 4) 2 Solution: (2) 4... View Article
The area bounded by the parabola y2 = 8x and its latus rectum is 1) 16/3 sq units 2) 32/3 sq units 3) 8/3 sq units 4) 64/3 sq units 5) 4/3 sq units Solution: (2) 32/3 sq units... View Article
If f (x) is a non – negative continuous function such that the area bounded by the curve y = f (x), x-axis and the coordinates x = Ï€ / 4 and x = β > (Ï€ / 4) is (β sin β + (Ï€ / 4) cos β + √2β). Then f (Ï€ / 2) = 1) (1 - (π / 4) + √2) 2) (1 - (π / 4) - √2) 3) ((π / 4) - √2 + 1) 4) ((π / 4) + √2 - 1) Solution: (1) (1 - (Ï€ / 4) + √2)... View Article
