Area (in sq units ) bounded by the curves y = ex, y = e-x and the straight line x = 1 is 1) e + (1 / e) 2) e + (1 / e) + 2 3) e + (1 / e) - 2 4) e - (1 / e) + 2 5) e - (1 / e) Solution: (3) e + (1 / e) - 2... 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) â…“ The given two curves are parabola y = x2 and y2 = x. The point of intersection of these two... 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 / 2]12 = (m / 2) [3] (3m / 2) = 6 m = 4... 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 units... 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 units 4) [3 - (π / 4)] sq units Solution: (2) [2 - (Ï€ / 2)]... 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) 4π sq units... 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 units... 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] / 2 Solution: (1) [π3 - 8] / 4... 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) â…“... View Article
The area of the region described by A = {(x, y) : x2 + y2 ≤ 1 and y2 ≤ 1 – x} is 1) (Ï€ / 2) + (4 / 3) 2) (Ï€ / 2) - (4 / 3) 3) (Ï€ / 2) - (2 / 3) 4) (Ï€ / 2) + (2 / 3) Solution: (1) (Ï€ / 2) + (4 / 3)... 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 y + 3 = 0 Solution: (2) x-axis at the origin... 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.... View Article
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 bisector of the joining... 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) = √42 + 32 = 5... View Article
The circle x2 + y2 + 4x – 4y + 4 = 0 touches 1) x-axis 2) y-axis 3) x- axis and y-axis 4) None of these Solution: (3) x-axis and y-axis The centre is (−2, 2) and the radius is... View Article
If a circle passes through the point (0, 0), (a, 0), (0, b),then its centre is 1) (a, b) 2) (b, a) 3) (a / 2, b / 2) 4) (b / 2, - a / 2) Solution: (3) (a / 2, b / 2)... View Article
The area of the circle whose centre is at (1, 2) and which passes through the point (4, 6) is 1) 5Ï€ 2) 10Ï€ 3) 25Ï€ 4) None of these Solution: (3) 25Ï€... View Article
The equation of the circle which touches both the axis and whose radius is a, is 1) x2 + y2 - 2ax - 2ay + a2 = 0 2) x2 + y2 + ax + ay - a2 = 0 3) x2 + y2 + 2ax + 2ay - a2 = 0 4) x2 + y2 - ax - ay + a2 = 0 Solution:... View Article
The equation of the smallest circle passing through the intersection of the line x + y =1 and the circle x2 + y2 = 9 is 1) x2 + y2 + x + y – 8 = 0 2) x2 + y2 – x – y – 8 = 0 3) x2 + y2 – x + y – 8 = 0 4) none of these Solution: (2) x2 + y2 – x – y – 8 = 0... View Article
Lines are drawn to the point P(–2, –3) to meet the circle x2 + y2 – 2x – 10y + 1 = 0. The length of the line segment PA, A being the point on the circle where the line meets the circle at coincident points, is 1) 16 2) 4√3 3) 48 4) None of these Solution: (2) 4√3... View Article
