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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 \(\begin{array}{l}\begin{array}{l} \mathbf{V}=\int_{0}^{1} \pi \mathbf{x}^{2} \mathbf{d}... 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 :... 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... 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 \(\begin{array}{l}\text {For the point of intersection, solve } y^{2}=4... View Article

The area of the region bounded by the curve 9x² + 4y² – 36 = 0 is

1) 9π sq units 2) 4π sq units 3) 36π sq units 4) 6π sq units Solution: (4) 6π sq... 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... View Article

The area enclosed between the curve y = log_e (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... 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... 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... View Article

Area bounded by the curve y = log_e 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... 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) \(\begin{array}{l}\begin{array}{l}... 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 /... 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) ⅙ \(\begin{array}{l}\begin{array}{l} \text { Shaded Area }=\int_{0}^{1}\left\{\left(2 x-x^{2}\right)-x\right\} d x... 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 \(\begin{array}{l}y=3 x \text \ and \ y=x^{2} \ in... 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 \(\begin{array}{l}\text { The given curves are } \mathrm{y}=\mathrm{x}^{3} \... 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... 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)... 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 \(\begin{array}{l}\text { Intersection points of both the curves are... 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... 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 = π / 4 and x = β > (π / 4) is (β sin β + (π / 4) cos β + √2β). Then f (π / 2) =

1) (1 – (π / 4) + √2) 2) (1 – (π / 4) – √2) 3) ((π / 4) – √2 +... View Article

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