Mathematics Tes...

The area (in sq. units) of the region A = {(x, y) : (x - 1) [x] ≤ y ≤ 2 √x, 0 ≤ x ≤ 2}, where [t] denotes the greatest integer function, is

The maximum and minimum value of f(x) = ab sin x + b  cos x + c lie in the interval (assuming |a| < 1, b > 0)

A given right circular cone has a volume p, and the largest right circular cylinder that can be inscribed in the cone has a volume q. Then p : q is

An object is moving in clockwise direction around the unit circle x² + y² = 1. As it passes through the point (1/2, √3/2), its y-coordinate is decreasing at the rate of 3 units per second. The rate at which the x-coordinate changes at this point is (in units per second)

The tangent to the curve y = e^x drawn at the point (c, e^c) intersects the line joining the points (c – 1, e^c–1) and (c + 1, e^{c + 1})

The abscissa of the point on the curve 9y² = x³, the normal at which cuts off equal intercepts on the coordinate axes is

What is the maximum value of 16 sin θ - 12 sin² θ?

f(x) = sin^p θ cos^q θ, (p, q > 0, 0 < θ < π/2) has a point of maxima at