The general solution of differential equation \(x d y-y d x=0\) represents

The differential equation satisfied by \(y=X \sin (6 t+5)+Y \cos (6 t+5)\) is (where \(X\) and \(Y\) are constants)

If \(z(2-i)=(3+i)\), then \(z^{38}=,(\) where \(z=x+\) iy \()\)

If the equation of the median through vertex \(A(3, k)\) of \(\triangle A B C\) with vertices \(\mathrm{B}(2,1)\) and \(\mathrm{C}(-4,5)\) is \(x+4 \mathrm{y}=\mathrm{p}\), then \(\mathrm{k}=\) where p and k are constants

The value of \(\int e^{x}\left[\frac{1+\sin x}{1+\cos x}\right] d x\) is

If \(\left(\cos ^{-1} x\right)^2-\left(\sin ^{-1} x\right)^2>0\), then

The value of \(\tan \left(\sin ^{-1}\left(\frac{3}{5}\right)+\tan ^{-1}\left(\frac{2}{3}\right)\right)\) is

Identify the correct statement regarding geometry and lone pair of electrons present in \(\mathrm{CH}_4\) and \(\mathrm{SiCl}_4\)

The resistance of conductivity cell filled with 0.1 M KCl solution is 100 ohm and conductivity is \(1.70 \times 10^{-4} \mathrm{~S} \mathrm{~cm}^{-1}\). What is the cell constant of the cell?

Which among the following salts undergoes hydrolysis?

If \(\overrightarrow{\mathbf{a}}+\overrightarrow{\mathbf{b}}+\overrightarrow{\mathbf{c}}=\overrightarrow{\mathbf{0}},|\overrightarrow{\mathbf{a}}|=3,|\overrightarrow{\mathbf{b}}|=5,|\overrightarrow{\mathbf{c}}|=7\), then the angle between \(\overrightarrow{\mathbf{a}}\) and \(\overrightarrow{\mathbf{b}}\) is

Which among the following compounds in used I Swartz reaction?

Let \(\quad \overline{\mathrm{a}}=\alpha \hat{\mathrm{i}}+3 \hat{\mathrm{j}}-\hat{\mathrm{k}}, \quad \overline{\mathrm{b}}=3 \hat{\mathrm{i}}-\beta \hat{\mathrm{j}}+4 \hat{\mathrm{k}} \quad\) and \(\overline{\mathrm{c}}=\hat{\mathrm{i}}+2 \hat{\mathrm{j}}-2 \hat{\mathrm{k}}\), where \(\alpha, \beta \in \mathbb{R}\), be three vectors. If the projection at \(\overline{\mathrm{a}}\) on \(\overline{\mathrm{c}}\) is \(\frac{10}{3}\) and \(\overline{\mathrm{b}} \times \overline{\mathrm{c}}=-6 \hat{\mathrm{i}}+10 \hat{\mathrm{j}}+7 \hat{\mathrm{k}}\), then the value of \(\alpha^2+\beta^2-\alpha \beta\) is equal to