Mathematics Tes...

12 points are marked on a circle. How many octagon can be formed joining these points.

If \(\alpha\) and \(\beta\) are the roots of the equation \(x^{2}-2 x+4=0\), then what is the value of \(\alpha^{3}+\beta^{3}\) ?

If${}^{15}{\mathrm{C}}_r{:}^{15}{\mathrm{C}}_{r-1}=11:5$the find the value of$r$.

If \(|\overrightarrow{\mathrm{a}}|=10,|\overrightarrow{\mathrm{b}}|=2\) and \(\overrightarrow{\mathrm{a}}. \overrightarrow{\mathrm{b}}=12\), then what is the value of \(|\overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{b}}| ?\)

If tan A - tan B = x and cot B - cot A = y, then what is the value of cot (A - B)?

There are 13 points in a plane of which 5 are collinear. Find the number of straight lines obtained by joining these points in pairs.

If \(\mathrm{A}+\mathrm{iB}=\frac{4+2 \mathrm{i}}{1-2 \mathrm{i}}\) where \(\mathrm{i}=\sqrt{-1}\), then what is the value of \(\mathrm{A} ?\)

What is the area of the rectangle having vertices \(\mathrm{A}, \mathrm{B}, \mathrm{C}\) and \(\mathrm{D}\) with position vectors \(-\hat{\mathrm{i}}+\frac{1}{2} \hat{\mathrm{j}}+4 \hat{\mathrm{k}}, \hat{\mathrm{i}}+\frac{1}{2} \hat{\mathrm{j}}+4 \hat{\mathrm{k}}, \hat{\mathrm{i}}-\frac{1}{2} \hat{\mathrm{j}}+4 \hat{\mathrm{k}}\) and \(-\hat{\mathrm{i}}-\frac{1}{2} \hat{\mathrm{j}}+4 \hat{\mathrm{k}}\)?

Let \(\mathrm{R}\) be the relation in the set \(\mathrm{N}\) given by \(\mathrm{R}=\{(a, b): a=b-2, b>6\} .\) Choose the correct answer.

The equations of normal to the curve \(3 x^{2}-y^{2}=8,\) such that it is parallel to the line \(x+3 y=4,\) is?