Mathematics Tes...

∫ (2x¹² + 5x⁹) / (x⁵ + x³ + 1)³ dx is equal to

Let , Q,R and S be four points on the ellipse 9x² + 4y² = 36. Let PQ and RS be mutually perpendicular and pass through the origin. If  where p and q are coprime, then p + q is equal to :

T is a point on the tangent to a parabola y² = 4ax at its point P. TL and TN are the perpendiculars on the focal radius SP and the directrix of the parabola respectively. Then

If the roots of the equation 2x² − (a³ + 1)x + (a² − 2a) = 0 are of opposite signs, then the set of possible value of a is

The general solution of sin²θ sec θ + √3 tan θ = 0 is

The fundamental period of the function f(x) = e^{4{x}+3}, where {⋅} denotes the fractional part function is

In the figure, AB, DE and GF are parallel to each other and AD, BG and EF are parallel to each other. If CD : CE = CG : CB = 2 : 1, then the value of area (△AEG): area (ΔABD) is equal to

Let p, q, r be three statements, then (p → (q → r)) ↔ ((p ∧ q) → r), is a

Tangent and normal are drawn at P (16, 16) on the parabola y² = 16x, which intersect the axis of the parabola at A and B, respectively. If C is the centre of the circle through the points P, A and B and ∠CPB = θ, then value of tan θ is

The number of values of k for which the system of linear equations (k + 2)x + 10y = k and kx + (k + 3)y = k - 1 has no solution is