Mathematics Tes...

For what values of 'a', f(x) = –x³ + 4ax² + 2x – 5 is decreasing for all x :-

If one of the root of the equation x² + xf(a) + a=0 is the cube of the other for all x ∈ R then f(x)

Let ƒ : (–10, 10) → R be an even function. If n be the number of values of x for which  then value of n is

Let f(x) = [2x³ – 5]; then number of points in (1, 2) where the function is discontinuous are (where [.] → G.I.F.)

The angle of elevation of the top of a mobile tower from three points P, Q and R (on a straight line through the foot of the tower) are α, β and γ respectively. If all three points are lie on same side of foot of tower and α : β : γ = 1 : 2 : 3 and PQ = ℓ, then height of tower is -

Write contrapositve of conditional statement "If x = 2 or y = 6 then x + 4y ≠ 22" is :-

The integral is equal to

(where c is a constant of integration)

The differential equation satisfied by the system of parabolas y² = 4a(x + a) is :

Let f : [–3, 1] → R be given as

If the area bounded by y = f(x) and x-axis is A, then the value of 6A is equal to ______.