Mathematics Tes...

Maximise, \(Z=x+y\), subject to \(x-y \leq-1, ~-x+y \leq 0,~\text{and}~ x, y \leq 0\).

What is the product of the perpendiculars drawn from the points \(\left(\pm \sqrt{a^{2}-b^{2}}, 0\right)\) upon the line \(b x \cos \alpha+\) ay \(\sin \alpha=a b\)?

If \(\sin ^{-1} x+\sin ^{-1} y=\frac{5 \pi}{6}\), then what is the value of \(\cos ^{-1} x+\cos ^{-1} y\)?

Find \(2 X-Y\) matrix such as \(X+Y=\left[\begin{array}{ll}7 & 5 \\ 3 & 4\end{array}\right]\) and \(X-Y=\left[\begin{array}{cc}1 & -3 \\ 3 & 0\end{array}\right]\).

If the distances of \(\mathrm{P}(x, y)\) from \(\mathrm{A}(4,1)\) and \(\mathrm{B}(-1,4)\) are equal, then which of the following is true?

If the position vectors of \(\mathrm{A}\) and \(\mathrm{B}\) are \(\vec{a}\) and \(\vec{b}\) respectively, then the position vector of mid-point of \(\mathrm{AB}\) is:

The radius of a circle is changing at the rate of \(\frac{ dr }{ dt }=0.01\) m/sec. The rate of change of its area \(\frac{ dA }{ dt }\), when the radius of the circle is \(4\) m, is:

Find the area bounded by the curve \(\mathrm{y}=\sin \mathrm{x}\) between \(\mathrm{x}=0\) and \(\mathrm{x}=2 \pi\).

Find graphically, the maximum value of \(\mathrm{z}=2 \mathrm{x}+5 \mathrm{y}\), subject to constraints given below:

\(2 \mathrm{x}+4 \mathrm{y} \leq 8 \)

\(3 \mathrm{x}+\mathrm{y} \leq 6 \)

\(\mathrm{x}+\mathrm{y} \leq 4 \)

\(\mathrm{x} \geq 0, \mathrm{y} \geq 0\)

Let \(f: R \rightarrow R\) be defined by \(f(x)=2 x+6\) which is a bijective mapping then \(f^{-1}(x)\) is given by: