Mathematics Tes...

If the line 3x + 2y = 13divides the area enclosed by the curve, 9x²+4y²−18x−16y−11=0 into two parts then the ratio of the larger area to the smaller area is

The equation of a circle C₁ is x²+y²−4x−2y−11=0. A circle C₂ of radius 1 unit rolls on the outside of the circle C₁ touching it externally. The locus of the centre of C₂ has the equation

The function f(x) = x³+ λx²+ 5x + sin 2x will be an invertible function if λ belongs to the set -

If the tangent and the normal to x² - y² = 4 at a point cut off intercepts a₁ , a₂ on the x-axis respectively and b₁ , b₂ on the y-axis respectively then the value of a₁a₂ + b₁b₂ is

A line makes angles of 45° and 60° with the positive directions of x and y axes respectively. An angle, which the line can make with the positive direction of z-axis is:

The co-ordinates of the point which divides the line segment joining the points (5,4, 2) and (−1,−2, 4) in the ratio 2 : 3 externally is

The third vertex of the triangle whose centroid is (7,−2, 5) and whose other two vertices are (2, 6, −4) and (4,−2, 3) is

The vertices of a triangle are A(x₁, x₁ tan α), B (x₂, x₂ tan β) and C(x₃, x₃tan γ) . If the circumcentre of ΔABC coincides with the origin and H (a,b) be its orthocentre, then a/b is equal to: (Here α, β and γ are acute angles)