Mathematics Tes...

The domain of the function \(f(x)=\sin ^{-1}\left(\frac{|x|+5}{x^{2}+1}\right)\) is \((-\infty,-a] \cup[a, \infty)\), Then \(a\) is equal to:

The differential equation of the family of curves \(y=c_1 e^x+c_2 e^{-x}\) is:

Find the coefficient of \(x^{2}\) in the expansion of \(\left(3 x+\frac{1}{x}\right)^{6}\) ?

If \(\sec ^{4} \theta-\sec ^{2} \theta=3\) then the value of \(\tan ^{4} \theta+\tan ^{2} \theta\) is:

The number of rectangles that you can find on a chess board is:

What is the coefficient of the middle term in the expansion of \(\left(1+4 x+4 x^{2}\right)^{5} ?\)

Form the differential equation for the family of circle with center \((0,0)\) and radius \(r\), where \(r\) is any constant.

If \(\sin \theta \cos \theta=k\), where \(0 \leq \theta \leq \frac{\pi}{2}\), then which one of the following is correct?

Find \(X\) if\(\mathrm{X}+\mathrm{Y}=\left[\begin{array}{ll}7 & 0 \\ 2 & 5\end{array}\right]\) and \(\mathrm{X}-\mathrm{Y}=\left[\begin{array}{ll}3 & 0 \\ 0 & 3\end{array}\right]\)

Find the area under the given curves and given lines:

\(y=x^{2}, x=1, x=2\) and \(x\)-axis