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The area enclosed between the curves y = x³ and y = √x is

1) 5/3 2) 5/4 3) 5/12 4) 12/5 Solution: (3) 5/12 \(\begin{array}{l}\begin{array}{l} \text { Area of shaded region }=\int_{0}^{1}\left(\sqrt{x}-x^{3}\right) d... View Article

The area (in sq units) of the region bounded by x = – 1, x = 2, y = x² + 1 and y = 2x – 2 is

1) 10 2) 7 3) 8 4) 9 Solution: (4) 9 \(\begin{array}{l}\begin{array}{l} \int_{-1}^{2}\left(x^{2}+1\right)-(2 x-2) d x\\ =\int_{-1}^{2} x^{2}-2 x+3 d... View Article

Area bounded by the curve x = 0 and x + 2|y| = 1 is

1) 1/4 2) 1/2 3) 1 4) 2 Solution: (2) ½ \(\begin{array}{l}\begin{array}{l} \text { Area of bounded region } =... View Article

Area (in sq units ) bounded by the curves y = e^x, y = e^-x and the straight line x = 1 is

1) e + (1 / e) 2) e + (1 / e) + 2 3) e + (1 / e)... View Article

The area of the region bounded by two parabolas y = x² and x = y² is

1) 1/4 2) 1/3 3) 4 4) 3 Solution: (2) ⅓ The given two curves are parabola y = x2... View Article

The area of the region bounded by the lines y = mx, x = 1, x = 2 and x-axis is 6 sq units, then m is equal to

1) 3 2) 1 3) 2 4) 4 Solution: (4) 4 Area enclosed = ∫12 mx dx = m [x2... View Article

The area of the region bounded by 1 – y² = |x| and |x| + |y| = 1 is

1) 1/3 sq units 2) 2/3 sq units 3) 4/3 sq units 4) 1 sq units Solution: (2) 2/3 sq... View Article

The area enclosed by the curves |y + x| ≤ 1, |y – x|≤ 1 and 2x² + 2y² = 1 is

1) [2 + (π / 2)] sq units 2) [2 – (π / 2)] sq units 3) [3 + (π / 2)] sq... View Article

The area bounded by y = x|sin x| and x-axis between x = 0, x = 2π is

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

The area bounded y = xe^|x| and line |x| = 1, y = 0 is

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

The area in the first quadrant between x² + y² = π² and y = sin x is

1) [π3 – 8] / 4 2) π3 / 4 3) [π3 – 16] / 4 4) [π3 – 8]... View Article

The area bounded by the curves y = -√-x and x = – √-y, where x, y ≤ 0, is

1) 1/3 2) 1/4 3) 1/5 4) ½ Solution: (1) ⅓ \(\begin{array}{l}\therefore \text { Required area } =\int_{-1}^{1}-x d x-\int_{-1}^{0}-x^{2}... View Article

The area of the region described by A = {(x, y) : x² + y² ≤ 1 and y² ≤ 1 – x} is

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

The circle x² + y² + 6y = 0 touches

1) y-axis at the origin 2) x-axis at the origin 3) x-axis at the point (3, 0) 4) the line... View Article

The number of circles touching the line y – x = 0 and the y-axis is

1) Zero 2) One 3) Two 4) Infinite Solution: (4) Infinite Infinite, as there is a family of co-axial circles.

The number of a circle having a radius of 5 and passing through the points (–2, 0) and (4, 0) is

1) One 2) Two 3) Four 4) Infinite Solution: (2) Two Two, a centre of each lying on the perpendicular... View Article

A circle touches the y-axis at the point (0, 4) and cuts the x-axis in a chord of length 6 units. The radius of the circle is

1) 3 2) 4 3) 5 4) 6 Solution: (3) 5 O’ is centre and from the figure, radius (r)... View Article

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