Mathematics Tes...

The area bounded by the curve y = ln(x) and the line y = 0, y = ln(3) and x = 0 is equal to:

The values of ‘a’ for which one root of the equation x² – (a + 1) x + a² + a – 8 = 0 exceeds 2 and the other is lesser than 2, are given by:

If the surface area of a sphere of radius r is increasing uniformly at the rate 8 cm²/s, then the rate of change of its volume is:

The probability of a man hitting a target is 2/5 . He fires at the target k times (k, a given number). Then the minimum k, so that the probability of hitting the target at least once is more than 7/10 , is :

Equation of the line passing through the points of intersection of the parabola x² = 8y and the ellipse x³ + y² = 1 is:

The sum of the series: 1 + 1/1+2 + 1/1+2+3+...up to 10 terms, is:

A value of x for which sin(cot⁻¹( 1+x)) = cos (tan⁻¹x), is:

If a and c are positive real numbers and the ellipse x²/4c² + y²/c² = 1 has four distinct points in common with the circle x² + y² = 9a², then

The number of integral values of k for which the equation 7cosx + 5sinx = 2k + 1 has a solution is

A light ray emerging from the point source placed at P(1, 3) is reflected at a point Q in the axis of x. If the reflected ray passes through the point R(6, 7), then the abscissa of Q is: