Mathematics Tes...

If \(\overrightarrow{O A}=\vec{a}\) and \(\overrightarrow{O B}=\vec{b}\), then \(\overrightarrow{B A}\) is:

Find the value of \(\theta\) for which \(z=\frac{3-2 i \sin \theta}{2-i \sin \theta}\) is purely real.

Find the are bounded between the curve \(\mathrm{y}=\mathrm{x}^{2}\) and \(\mathrm{y}=\mathrm{x}^{3}\)

What is value of \(\int_{\frac{-\pi}{2}}^{\frac{\pi}{2}} \mathrm{x}^{5} \sin ^{4} \mathrm{xdx}\)?

Order and degree of the differential equation${\left[1+{\left(\frac{dy}{dx}\right)}^3\right]}^{\frac{7}{3}}=7\frac{d^{2}y}{d{x}^2}$are respectively-

If \({x}+{iy}=\frac{3+4 {i}}{2-{i}}\) where \({i}=\sqrt{-1}\), then what is the value of y?

A box contains \(3\) white and \(2\) black balls. Two balls are drawn at random one after the other. If the balls are not replaced, what is the probability that both the balls are black?

The argument of the complex number \(\frac{1-\mathrm{i}}{1+\mathrm{i}},\) where \(\mathrm{i}=\sqrt{-1},\) is

Find the standard deviation of \(\{7,13,15,11,4\}\).