Let S denote the set of 4-digit numbers abcd such that a > b > c > d and P […]

The number of elements in the set S = {x : x ∈ [0, 100] and ∫₀ˣ t² sin(x –

If the solution curve y = f(x) of the differential equation (x^2 – 4)y’ – 2xy + 2x(4 – x^2)^2

If the image of the point P(a, 2, a) in the line x/2 = (y+a)/1 = z/1 is Q and

The system of linear equations x + y + z = 6, 2x + 5y + az = 36, x

An equilateral triangle OAB is inscribed in the parabola y^2 = 4x with the vertex O at the vertex of

The area of the region enclosed between the circles x^2 + y^2 = 4 and x^2 + (y – 2)^2

Let a = i – 2j + 3k, b = 2i + j – k, c = λi + j

If f(x) = { (a|x| + x^2 – 2(sin|x|)(cos|x|))/x for x != 0, b for x = 0 } is

If the points of intersection of the ellipses x² + 2y² – 6x – 12y + 23 = 0 and