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
The number of feet of normals from the point (7, –4) to the circle x2 + y2 = 5 is 1) 1 2) 2 3) 3 4) 4 Solution: (2) 2... View Article
A foot of the normal from the point (4, 3) to a circle is (2, 1) and a diameter of the circle has the equation 2x – y = 2. Then the equation of the circle is 1) x2 + y2 + 2x – 1 = 0 2) x2 + y2 – 2x – 1 = 0 3) x2 + y2 – 2y – 1 = 0 4) none of these Solution: (2) x2 + y2 – 2x – 1 = 0... View Article
If (2, 4) is a point interior to the circle x2 + y2 – 6x – 10y + λ = 0 and the circle does not cut the axes at any point, then λ belongs to the interval 1) (25, 32) 2) (9, 32) 3) (32, + ∞) 4) None of these Solution: (1) (25, 32)... View Article
Let f(x, y) = 0 be the equation of a circle. If f (0, λ) = 0 has equal roots λ = 2, 2 and f (λ,0) = 0 has roots λ = 4/5, 5, then the centre of the circle is 1) (2, 29 / 10) 2) (29 / 10, 2) 3) (- 2, 29 / 10) 4) none of these Solution: (2) (29 / 10, 2)... View Article
A region in the xy-plane is bounded by the curve x2 + y2 = 25 and the line y = 0. If the point (p, p +1) lies in term of the region, then 1) p ∈ (–1, 3) 2) p ∈ (– ∞, – 1) ∪ (3, ∞) 3) p ∈ (– 4, 3) 4) p ∈ (– ∞, – 1) Solution: (1) p ∈ (–1, 3)... View Article
A line meets the co-ordinate axes an A and B. A circle is circumscribed about the ∆ ABO. If p and q are the distances of the tangents to the circle at the origin from points A and B respectively, then the diameter of the circle is 1) q (p + q) 2) p + q 3) p (p + q) 4) p (p – q) Solution: (2) p + q... View Article
The equation of the circumcircle of an equilateral triangle is x2 + y2 + 2gx + 2fy + c = 0 and one vertex of the triangle is (1, 1). The equation of incircle of the triangle is 1) 4 (x2 + y2) = g2 + f2 2) 4 (x2 + y2) + 8gx + 8fy = (1 – g) (1 + 3g) + (1 – f) (1 + 3f) 3) 4 (x2 + y2) + 8gx + 8fy = g2 + f2 4) none of... View Article