Mathematics Tes...

Evaluate: \(\left|\begin{array}{ccc}0 & a & -b \\ -a & 0 & -c \\ b & c & 0\end{array}\right|\)

The solution of the differential equation \(\frac{d y}{d x}=\sec \left(\frac{y}{x}\right)+\frac{y}{x}\) is:

Jobs arrive at a facility at an average rate of \(5\) in an \(8\) hour shift. The arrival of the jobs follows Poisson distribution. The average service time of a job on the facility is \(40\) minutes. The service time follows exponential distribution. Idle time (in hours) at the facility per shift will be _______.

Given Data set is \(1, 0, 2, 3, 1, 1, 15, 1, 3\).

Find the value of Variance and Standard mean deviation for the given data set?

Find slope of the tangent to the curve \(2 x^{3}+3 y=2 y^{3}+3 x\) at \(p(x, y)\).

Find the sum of the series 3 + 9 + 27 + 81 + ..... + 6561.

Find the values of \(k\) so the line \(\frac{x-2}{2 k}=\frac{y-3}{3}=\frac{z+2}{-1}\) and \(\frac{x-2}{8}=\frac{y-3}{6}=\frac{z+2}{-2}\) are parallel.

Let \(\mathrm{z}_1\) and \(\mathrm{z}_2\) be two complex number such that \(\mathrm{z}_1+\mathrm{z}_2=5\) and \(z_1^3+z_2^3=20+15 i\). Then \(\left|z_1^4+z_2^4\right|\) equals-

Using principle of mathematical induction, prove that for all \(n \in N, \frac{n^{5}}{5}+\frac{n^{3}}{3}+\frac{7 n}{15}\) is a:

Evaluate \(\underset{{{x \rightarrow 0}}}{\lim} \frac{x \tan x}{1-\cos x}\)