Mathematics Tes...

If \(\left|\begin{array}{cc}x & 2 \\ 18 & x\end{array}\right|=\left|\begin{array}{cc}6 & 2 \\ 3 x & 6\end{array}\right|\), then \(x\) is equal to:

If \(x d y=y d x+y^2 d y, y>0\) and \(y(1)=1\), then what is \(y(-3)\) equal to:

Find the area under the curve \(y=\cos x\) in the interval \(0

The solution of the inequality \(\frac{3(x-2)}5 \geq \frac{5(2-x)}3\) is:

A company produces two types of goods, \(A\) and \(B\), that require gold and silver. Each unit of type \(A\) requires \(3 \mathrm{gm}\) of silver and \(1 \mathrm{gm}\) of gold while that of type \(B\) requires \(1 \mathrm{gm}\) of silver and \(2 \mathrm{gm}\) of gold. The company can produce \(9 \mathrm{gm}\) of silver and \(8 \mathrm{gm}\) of gold. If each unit of type \(A\) brings a profit of Rs 40 and that of type \(B\) Rs 50. What is the maximum profit?

Find the equation of the line perpendicular to the line \(x-3 y+5=0\) and passes through the point \((2,-4)\).

Find\(\cot ^{-1} \frac{1}{3}-2 \tan ^{-1} \frac{2}{3}\).

If \(A=\left(\begin{array}{cc}\frac{1}{\sqrt{5}} & \frac{2}{\sqrt{5}} \\ -\frac{2}{\sqrt{5}} & \frac{1}{\sqrt{5}}\end{array}\right), B=\left(\begin{array}{cc}1 & 0 \\ i & 1\end{array}\right), \mathrm{i}=\sqrt{-1}\), and \(Q=A^T B A\), then the inverse of the matrix \(\mathrm{AQ}^{2021} \mathrm{~A}^{\mathrm{T}}\) is equal to:

Using principle of mathematical induction, prove that for all \(n \in N, n(n+\) 1) \((n+5)\) is: