If f(x) + f(1/(1-x)) = x for all x ≠ 0, 1, find the value of f(2).

Evaluate: lim (x→0) [x^2 sin(1/x)]

If 'a' and 'b' are roots of the equation x^2 - 3x + 2 = 0, then find the value of a^3 + b^3.

Find the area of the region bounded by the curves y = x^2 and y = x.

If A = [[1, 2], [3, 4]], then find |adj(A)|.

The number of solutions of the equation sin x + cos x = 2 in [0, 2π] is:

If the lines x + y = 1 and x - y = 3 are two diameters of a circle, then the center of the circle is:

If ∫ f(x) dx = g(x), then ∫ f(x)g'(x) dx is equal to:

Find the value of ∑(r=1 to n) r * nCr

The number of integral values of 'a' for which the quadratic equation x^2 + a x + a + 1 = 0 has integral roots is: