Mathematics Tes...

If n^th terms of two A.P.’s are 3n + 8 and 7n + 15, then the ratio of their 12^th terms will be:

Find the modulus of the complex number \(\frac{1+{i}}{1+\sqrt{3} {i}}\).

In the given figure, \(\mathrm{X}\) is the centre of the circle, \(\mathrm{XM} \perp \mathrm{AB}, \mathrm{XM}=3\) units and \(\mathrm{MB}=3\) units. What is the length of AM?

Find \(X\), if \(Y=\left[\begin{array}{ll}3 & 2 \\ 1 & 4\end{array}\right]\) and \(2 X+Y=\left[\begin{array}{cc}1 & 0 \\ -3 & 2\end{array}\right]\).

\(\left|\begin{array}{ccc}1+i & 1-i & 1 \\ 1-i & i & 1+i \\ i & 1+i & 1-i\end{array}\right|\) is a :

Find the angle between the pair of lines given by

\(\vec{r}=3 \hat{i}+2 \hat{j}-4 \hat{k}+\lambda(\hat{i}+2 \hat{j}+2 \hat{k}) \) and

\(\vec{r}=5 \hat{i}-2 \hat{j}+\mu(3 \hat{i}+2 \hat{j}+6 \hat{k})\)

The sides \(a, b, c\) (taken in order) of a \(\triangle A B C\) are in A.P. If \(\cos \alpha=\frac{\mathrm{a}}{\mathrm{b}+\mathrm{c}}, \cos \beta=\frac{\mathrm{b}}{\mathrm{c}+\mathrm{a}}\) \(\cos \gamma=\frac{\mathrm{c}}{\mathrm{a}+\mathrm{b}}\), then \(\tan ^{2} \frac{\alpha}{2}+\tan ^{2} \frac{\gamma}{2}\) is equal to:

If (2 - i) (x - iy) = 3 + 4i then 5x is:

In a simultaneous throw of two dice, what is the probability of getting a total of \(7\)?

What is the general solution of the differential equation x² dy + y² dx = 0 ?

Where c is the constant of integration.