Mathematics Tes...

The complete solution of the equation \(\frac{\partial z}{\partial x} e^{y}=\frac{\partial z}{\partial y} e^{x}\) will be:

Find the values of \(k\) so the line \(\frac{2 x-2}{2 k}=\frac{4-y}{3}=\frac{\mathrm{z}+2}{-1}\) and \(\frac{\mathrm{x}-5}{1}=\frac{\mathrm{y}}{\mathrm{k}}=\frac{\mathrm{z}+6}{4}\) are at right angles.

If \(A=\left[\begin{array}{ll}1 & 2 \\ 2 & 1\end{array}\right], \mathrm{f}(\mathrm{x})=\mathrm{x}^{2}-2 \mathrm{x}-3\) then find the value of \(\mathrm{f}(\mathrm{A})\).

What is \((\vec{a}+\vec{b}) \times(\vec{a}-\vec{b})\) equal to?

If the mean of a set of observations \(x_{1}, x_{2}, x_{3}, \ldots, x_{10}\) is 50 , then the mean of \(x_{1}+5, x_{2}+10, x_{3}+15, \ldots, x_{10}+50\) is:

A straight line through \(\mathrm{P}(1,2)\) is such that its intercept between the axes is bisected at P. Its equation is:

Find the sum to \(n\) terms of the \(A.P.\), whose \(n^{\text {th }}\) term is \(5 n+1\)

Evaluate: \(\int \frac{\mathrm{dx}}{\mathrm{x}(\mathrm{x}+4)}\)

The equation \(\cos ^{2} \theta=\frac{(x+y)^{2}}{4 x y}\) is only possible when?

For a hyperbola \(\frac{x^{2}}{16}-\frac{y^{2}}{9}=1\) then equation of directrix is:

If \(\omega\) is the cube root of unity, then what is the value of\(\left|\begin{array}{ccc}1 & \omega & \omega^{2} \\ \omega & \omega^{2} & 1 \\ \omega^{2} & 1 & \omega\end{array}\right|\)

The probability that a contractor gets a plumbing contract is \(\frac{2}{3}\) and the probability that he will not get an electric contract is \(\frac{5}{9}\). If the probability of getting at least one contract is \(\frac{4}{5}\), then the probability that he will get both the contracts is: