Mathematics Tes...

The solution of differential equation dy = (4+y²)dx is

The general solution y(x) of the differential equation 

\(\frac{{dy}}{{dx}}=\frac{{x} \sqrt{1-{y}^{2}}}{{y} \sqrt{1-{x}^{2}}}\)

What is the value of \(\sin ^{-1} \frac{4}{5}+\sec ^{-1} \frac{5}{4}-\frac{\pi}{2} ?\)

If \(\sin \left(\tan ^{-1} \frac{1}{10}+\cot ^{-1} x\right)=1\) then, find the value of \(x\).

\(\frac{{d}}{{dx}}\left(\frac{{x}^{4}+{x}^{2}+1}{{x}^{2}-{x}+1}\right)={ax}+{b}\), what is the value of \(a\) and \(b ?\)

A line, with the slope greater than one, passes through the point \(A(4,3)\) and intersects the line \(x-y-2=0\) at the point \(B\). If the length of the line segment \(A B\) is \(\frac{\sqrt{29}}{3}\), then \(B\) also lies on the line:

If \(z^{2}+z+1=0\), where \(z\) is a complex number, then the value of \(\left(z+\frac{1}{z}\right)^{2}+\left(z^{2}+\frac{1}{z^{2}}\right)^{2}+\left(z^{3}+\frac{1}{z^{3}}\right)^{2}+\ldots .+\left(z^{6}+\frac{1}{z^{6}}\right)^{2}\) is:

Let a vertical tower \(A B\) have its end \(A\) on the level ground. Let \(C\) be the mid-point of \(A B\) and \(P\) be a point on the ground such that \(AP =2 AB\). If \(\angle BPC =\beta\), then \(\tan \beta\) is equal to: