Mathematics Tes...

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

If \(A=\left[\begin{array}{ll}i & 0 \\ 0 & i\end{array}\right], n \in N\), then \(A^{4 n}\) equals:

Find the integer value of \(\mathrm{k}\) for which the equation \(\mathrm{x}^{2}-5(\mathrm{k}-1) \mathrm{x}+(8 \mathrm{k}+1)=0\) has equal roots.

Two dice are thrown simultaneously. The probability of getting a sum of \(9\) is:

For what value of \(\alpha \in R\) the system of equation: \(x+2 y+z=3,2 x+4 y+2 z=6\) and \(\alpha x+ \alpha y+ \alpha z=3\alpha\) has infinitely many solutions.

If \(\frac{x \operatorname{cosec}^2 30^{\circ} \sec ^2 45^{\circ}}{8 \cos ^2 45^{\circ} \sin ^2 60^{\circ}}=\tan ^2 60^{\circ}-\tan ^2\) \(30^{\circ}\), then \(x=\)

The value of \((\sqrt{-6} \times \sqrt{-6})\) is:

Let \(\vec{a}=\hat{i}+\hat{j}+\hat{k}, \vec{b}=\hat{i}-\hat{j}+\hat{k}\) and \(\vec{c}=\hat{i}-\hat{j}-\hat{k}\) be three vectors. A vector \(\vec{v}\) in the plane of \(\vec{a}\) and \(\vec{b}\), whose projection on \(\vec{c}\) is \(\frac{1}{\sqrt{3}}\), is given by;

In binomial expansion of \((a-b)^{n}, n \geq 5\), the sum of the \(5^{\text {th }}\) and \(6^{\text {th }}\) terms is zero. Then \(\frac{a}{b}\) is equal to: