31.

The degree of the differential equation ${\left[1 + {\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)}^2\right]}^2 = \frac{{\mathrm{d}}^2\mathrm{y}}{{\mathrm{dx}}^2}$ is

• 3

• 2

• 1

• 4

$\int \frac{\cos \left(2\mathrm{x}\right) - \cos \left(2\mathrm{\theta }\right)}{\cos \left(\mathrm{x}\right) - \cos \left(\mathrm{\theta }\right)}\mathrm{dx}$ is equal to

• $2\left(\sin \left(\mathrm{x}\right) + \mathrm{xcos}\left(\mathrm{\theta }\right)\right)$

• $2\left(\sin \left(\mathrm{x}\right) - \mathrm{xcos}\left(\mathrm{\theta }\right)\right)$

• $2\left(\sin \left(\mathrm{x}\right) + 2\mathrm{xcos}\left(\mathrm{\theta }\right)\right)$

• $2\left(\sin \left(\mathrm{x}\right) - 2\mathrm{xcos}\left(\mathrm{\theta }\right)\right)$

If a $= 2\hat{\mathrm{i}} + \mathrm{\lambda }\hat{\mathrm{j}} + \hat{\mathrm{k}}$ and b = $\hat{\mathrm{i}} + 2\hat{\mathrm{j}} + 3\hat{\mathrm{k}}$ are orthogonal, then value of $\mathrm{\lambda }$ is

• 3/2

• 1

• 0

• - 5/2

If a, b, c are unit vectors such that a + b + c = 0, then the value of a · b + b · c + c · a is equal to

• 3/2

• 1

• 3

• - 3/2

The plane 2x - 3y + 6z - 11 = 0 makes an angle sin^-1($\mathrm{\alpha }$) with X-axis, the value of $\mathrm{\alpha }$ is equal to

• $\frac{\sqrt{2}}{3}$

• $\frac{2}{7}$

• $\frac{\sqrt{3}}{2}$

• $\frac{3}{7}$

${\int }_{0.2}^{3.5}\left[\mathrm{x}\right]\mathrm{dx}$ is equal to

• 3.5

• 4

• 4.5

• 3

The perpendicular distance of the point P(6, 7, 8) from XY-plane is

• 6

• 7

• 5

• 8

The integrating factor of the differential equation $\mathrm{x} . \frac{\mathrm{dy}}{\mathrm{dx}} + 2\mathrm{y} = {\mathrm{x}}^2 \mathrm{is} \left(\mathrm{x} \ne 0\right)$

• x

• $\log \left|\mathrm{x}\right|$

• x²

• ${\mathrm{e}}^{\log \left(\mathrm{x}\right)}$

${\int }_0^{\raisebox{1ex}{$\mathrm{\pi }$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}\frac{{\tan }^7\left(\mathrm{x}\right)}{{\cot }^7\left(\mathrm{x}\right) + {\tan }^7\left(\mathrm{x}\right)}\mathrm{dx}$ is equal to

• $\frac{\mathrm{\pi }}{4}$

• $\frac{\mathrm{\pi }}{2}$

• $\frac{\mathrm{\pi }}{6}$

• $\frac{\mathrm{\pi }}{3}$

Reflexion of the point $\left(\mathrm{\alpha }, \mathrm{\beta }, \mathrm{\gamma }\right)$ in XY-plane is

• $\left(0, 0, \mathrm{\gamma }\right)$

• $\left(- \mathrm{\alpha }, - \mathrm{\beta }, \mathrm{\gamma }\right)$

• $\left(\mathrm{\alpha }, \mathrm{\beta }, - \mathrm{\gamma }\right)$

• $\left(\mathrm{\alpha }, \mathrm{\beta }, 0\right)$