Mathematics Tes...

The function \(f: R \rightarrow[-1,1]\) defined by \(f(x)=\frac{|x|}{1+|x|}, x \in R\) is

Combine terms: 12a + 26b -4b – 16a.

Find the differential equation of the family of ellipse such that its centre is on the origin

If Area occupied by the curves with equation given below is A then Value of A/2 is-

Equation \(1:(x-5)^{2}+y^{2}=25\)

Equation \(2: y^{2}=9 x\)

If \(y=\tan ^{-1}\left(\frac{\sin x}{1+\cos x}\right),\) then \(\frac{d y}{d x}=\)

The number of values of k for which the system of equations (k + 1) x + 8y = 4k and
kx + (k + 3)y = 3k - 1 has infinitely many solutions is

The eccentricity of an ellipse with its centre at the origin is 1/2. If one of the directrix is x = 4, then the equation of the ellipse is

The value of \(\int_{0}^{1} \mathrm{x}(1-\mathrm{x})^{99} \mathrm{dx}\) is