Mathematics Tes...

The equation of the plane passing through the line of intersection of the planes x + y + z = 1, 2x +3y + 4 z =7, and perpendicular to the plane x - 5y + 3z = 5 is given by:

Find the area between the curve \(y=\sin x\) and lines \(x=-\frac{\pi}{3}\) to \(x=\frac{\pi}{3}\).

Consider the following L.P.P. Maximize \(Z=3 x+2 y\) Subject to the constraints:

\(\mathrm{x}+2 \mathrm{y} \leq 10 \)

\(3 \mathrm{x}+\mathrm{y} \leq 15 \)

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

Find the maximum value of \(Z\).

Find distance between the parallel lines \(p(x+y)+q=0\) and \(p(x+y)-r=0\)?

For a distribution of student’s height, the quartiles are \(60.125, 61.345, 62.688\). The absolute measure of skewness is:

Find the value of \(\int \frac{\mathrm{dx}}{1+\mathrm{e}^{-\mathrm{x}}}\), where \(c\) is the constant of integration.

The base of an equilateral triangle is along the line given by \(3 x+4 y=9\). If \(a\) vertex of the triangle is \((1,2)\), then the length of a side of the triangle is:

The differential coefficient of \(\log _{10} x\) with respect to \(\log _{x} 10\) is:

Let \(S(K)=1+3+5 \ldots+(2 K-1)=3+\mathrm{K}^2\). Then which of the following is true