Mathematics Tes...

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

Let a function \(f: \mathrm{R} \rightarrow \mathrm{R}\) satisfy the equation \(f(\mathrm{x}+\mathrm{y})=f(\mathrm{x})+f(\mathrm{y})\) for all \(\mathrm{x}, \mathrm{y} .\) If the function \(f(\mathrm{x})\) is continuous at \(x=0,\) then

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 \(\mathrm{i}=\sqrt{-1} ?\)

The mean of a distribution is \(22\) and the standard deviation is \(10\). What is the value of variance coefficient?

Equation of hyperbola whose latus rectum is 6 and eccentricity is 2:

Find the conjugate of \(\left(i-i^{2}\right)^{3}\)

If \(\cos ^{-1}\left(\frac{p}{a}\right)+\cos ^{-1}\left(\frac{q}{b}\right)=\alpha\), then \(\frac{p^{2}}{a^{2}}+k \cos \alpha+\frac{q^{2}}{b^{2}}=\sin ^{2} \alpha\) where \(k\) is equal to:

If \(f(x)=\left\{\begin{array}{ll}\frac{\sin 3 x}{e^{2 x}-1}, & x \neq 0 \\ k-2, & x=0\end{array}\right.\) is continuous at \(x=0\), then \(k=?\)

If \(\overrightarrow{\mathrm{a}}=4 \hat{\mathrm{i}}+6 \hat{\mathrm{j}}\) and \(\overrightarrow{\mathrm{b}}=3 \hat{\mathrm{j}}+4 \hat{\mathrm{k}}\), then the vector form of the component of \(\overrightarrow{\mathrm{a}}\) along \(\overrightarrow{\mathrm{b}}\) is:

Using principle of mathematical induction, prove that for all \(n \in N, \frac{n^{5}}{5}+\frac{n^{3}}{3}+\frac{7 n}{15}\) is a: