Mathematics Test - 11

The area of an expanding rectangle is increasing at the rate of 48 cm2/sec. The length of the rectangle is always equal to the square of the breadth. At the instant when the breadth is 4.5 cm, The length is increasing at the rate of-

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 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-

If the fourth term of  is equal to 200 and x > 1, then x is equal to-

The equation of the smallest circle passing through the intersection of the line x + y = 1 and the circle x² + y² = 9 is-

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

If tanθ = tan 30^∘ ⋅ tan 60^∘ and θ is an acute angle,then 2θ is equal to:

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 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-