Mathematics Tes...

If $A=\left[\begin{array}{cc}1& 2\\ 2& 3\end{array}\right]$ and A² - kA - I₂ = o, where I₂: is the 2 × 2 identity matrix, then what is the value of k?

If \(x\) is positive, the first negative term in the expansion of \((1+x)^{27 / 5}\) is:

Let [x] denote the greatest integer function. What is the number of solutions of the equation x² - 4x + [x] = 0 in the interval [0, 2] ?

What is the solution to differential equation \(\frac{d x}{d y}+\frac{x}{y}=0\)?

Which of the following is equal to \(\tan ^{-1}\left(\frac{8 x \sqrt{x}}{1-16 x^{3}}\right)?\)

The solution to the differential equation dy = (1 + y²) dx is:

What is the number of ways that 4 boys and 3 girls can be seated so that boys and girls alternate?

If \(5 \times^{ n } P _{3}=4 \times^{( n +1)} P _{3}\), find \(n\)?

Given function \(f(x)=\left(\frac{e^{2 z}-1}{e^{2 z}+1}\right)\) is:

If \(\sin ^{-1} \frac{3}{x}+\sin ^{-1} \frac{9}{x}=\frac{\pi}{2}\) then what is the value of \(x\) ?