Mathematics Tes...

If \(f(x)=\left|\begin{array}{ccc}a & -1 & 0 \\ a x & a & -1 \\ a x^{2} & a x & a\end{array}\right|,\) then \(f(2 x)-f(x)\) is not divisible by

Find the area of the triangle whose vertices are \((1,-1),(-4,0)\) and \((-2,-3)\).

The solution of the equation x² dy/dx = x² + xy + y² is

The equation x³ – 3x + [a] = 0, will have three real and distinct roots if –

(where [ ] denotes the greatest integer function)

Let function f : R → R be defined by f(x) = cos x for x∈ R. Then f is

If g(x) satisfies the conditions of Rolle’s theorem in [1, 2] and g′(x) = f(x), then\(\int_{1}^{2} f(x) d x\)is equal to

If the latus rectum of a hyperbola through one focus, subtends 60 ° angle at the other focus, then its eccentricity is

At a point, the addition of two active force is 18 N. If the magnitude of resultant is 12 N and meet at the right angle. Then, the magnitude of forces are:

Find the range of f(x) = x² + x + 2/x² + x + 1.

If tan^-1 (x - 1) + tan^-1 x + tan^-1 (x + 1) = tan^-1 3x, then x is equal to