Mathematics Tes...

The mean of \(8\) observations is \(25\). The \(7\) observations are \(30, 24, 27, 22, 18, 26, 32\). What is the \(8\)th observation?

The variance of the first \(20\) natural numbers is:

What is \(\int \frac{\mathrm{dx}}{\mathrm{x}\left(\mathrm{x}^{7}-1\right)}\) equal to?

What is the rate of change of \(\sqrt{\mathrm{x}^{2}+48}\) relative to \(\mathrm{x}^{2}\) at \(\mathrm{x}=4 ?\)

If tan^-1 2, tan^-1 3 are two angles of a triangle, then what is the third angle?

Evaluate:

\(2(\sec A-\cos A)^{2}+2(\operatorname{cosec} A-\sin A)^{2}-2(\cot A-\tan A)^{2}-2\)

If \(\overrightarrow{\mathrm{a}}=\hat{\mathrm{i}}+2 \hat{\mathrm{j}}-3 \hat{\mathrm{k}}, \overrightarrow{\mathrm{b}}=3 \hat{\mathrm{i}}-\hat{\mathrm{j}}+2 \hat{\mathrm{k}}\) then the angle between \(\vec{a}+\vec{b}, \vec{a}-\vec{b}\) is:

A medicine is known to be \(50 \%\) effective to cure a patient. If the medicine is given to \(4\) patients, what is the probability that at least one patient is cured by this medicine?

The solution of the differential equation \(\frac{d y}{d x}=y\left(1-3 x^{2}\right)\) is:

What is the most probable number of successes in \(10\) trials with probability of success \(\frac{2}{3}\)?