Mathematics Tes...

The solution of the differential equation \(x \frac{d y}{d x}+2 y=x^{2}(x \neq 0)\) with \(y(1)=1\), is:

If\(A=\left[\begin{array}{lll}1 & 0 & 0 \\ 1 & 0 & 1 \\ 0 & 1 & 0\end{array}\right]\) satisfies \(A^{n}=A^{n-2}+A^{2}-I\) for \(n \geq 3\), then the value of\(\left|A^{50}\right|\) equal:

Let \(f: R-\left\{-\frac{4}{3}\right\} \rightarrow R\) be a function as \(f(x)=\frac{4 x}{3 x+4}\). The inverse of \(f\) is map \(g:\) Range \(f \rightarrow R-\left\{-\frac{4}{3}\right\}\) given by:

What is \(\tan \left\{2 \tan ^{-1}\left(\frac{1}{3}\right)\right\}\) equal to?

A bag contains 5 black and 3 white balls. Two balls are drawn at random one after the other without replacement. What is the probability that both are white?

What is the number of different messages that can be represented by three a’s and two b’s?

The value of \(\int(x-1) e^{-x} d x\) is equal to:

If \(A=\left[\begin{array}{cc}1 & -1 \\ -1 & 1\end{array}\right]\), then the expression \(A^{3}-2 A^{2}\) is:

What is the equation of the straight line parallel to \(3 x+2 y+1=0\) and passing through the point \((-1,-2) ?\)

Find the degree of the differential equation\(y=x \frac{d y}{d x}+\left(\frac{d y}{d x}\right)^{-1}\).