Mathematics Tes...

Find the sum of the series whose nth term is \((2 n-1)^{2}\).

What is the value of the determinant \(\left|\begin{array}{ccc}\mathrm{i} & \mathrm{i}^{2} & \mathrm{i}^{3} \\ \mathrm{i}^{4} & \mathrm{i}^{6} & \mathrm{i}^{8} \\ \mathrm{i}^{9} & \mathrm{i}^{12} & \mathrm{i}^{15}\end{array}\right|\) where \(\mathrm{i}=\sqrt{-1} ?\)

If the roots of the equation \(3 a x^{2}+2 b x+c=0\) are in the ratio \(3: 2\), then which one of the following is correct?

Two coins are thrown at the same time. Find the probability of getting both heads.

Find the area of the region bounded by the parabola \(x^2=4 y, y=2\) and \(y=4\) and the \(y\)-axis in the first quadrant.

What is \(\int_{-a}^{a}\left(x^{2}+\sin x\right) d x\) equal to?

The solution of the differential equation \(\mathrm{dy}=\left(1+\mathrm{y}^{2}\right) \mathrm{dx}\) is?

The number of ways in which 5 boys and 4 girls to sit around a table so that all the boys sit together is:

If cot α and cot β are the roots of the equation x² - 5x + 4 = 0, then what is cot (α + β) equal to?

In the given figure, \(O\) is the centre of the circle, \(\angle A O B=\angle P O Q=30^{\circ}\) and \(\angle X O Y=\angle\) \(Z O W=40^{\circ}\). Also, \(X Y=4\) units and \(A B=3.5\) units. The value of \((A B+Z W+P Q+X Y)\) is: