The eccentricity of ellipse $\frac{{\mathrm{x}}^2}{16} + \frac{{\mathrm{y}}^2}{9} = 1$ is

• $\frac{7}{16}$

• $\frac{5}{4}$

• $\frac{\sqrt{7}}{4}$

• $\frac{\sqrt{7}}{2}$

The products of lengths of perpendiculars from any point of hyperbola x² - y² = 8 to its asymptotes, is

• 2

• 3

• 4

• 8

The equation 16x² + y² + 8xy - 74x - 78y + 212 = 0 represents

• a circle

• a parabola

• an ellipse

• a hyperbola

Equation of curve in polar coordinates is $\frac{\mathrm{l}}{\mathrm{r}} = 2{\sin }^2\left(\frac{\mathrm{\theta }}{2}\right)$ represents

• a straight line

• a parabola

• a circle

• an ellipse

$\underset{\mathrm{x}\to \infty }{\lim }{\left(\frac{\mathrm{x} + \mathrm{a}}{\mathrm{x} + \mathrm{b}}\right)}^{\mathrm{a} + \mathrm{b}}$ is equal to

• 1

• 1^{b - a}

• e^{a - b}

• e^b

$\underset{\mathrm{x}\to 0}{\lim }\left(\frac{\mathrm{x} . {10}^{\mathrm{x}} - \mathrm{x}}{1 - \cos \left(\mathrm{x}\right)}\right)$ is equal to

• $\log \left(10\right)$

• $2\log \left(10\right)$

• $3\log \left(10\right)$

• $4\log \left(10\right)$

27.

If y_k is the kth derivative of y with respect to 'x', and y = cos(sin(x)), then ${\mathrm{y}}_1\sin \left(\mathrm{x}\right) + {\mathrm{y}}_2\cos \left(\mathrm{x}\right)$ is equal to

• ${\mathrm{ysin}}^3\left(\mathrm{x}\right)$

• $- {\mathrm{ysin}}^3\left(\mathrm{x}\right)$

• ${\mathrm{ycos}}^3\left(\mathrm{x}\right)$

• $- {\mathrm{ycos}}^3\left(\mathrm{x}\right)$

$\tan \left(\mathrm{\theta }\right) + \cot \left(\mathrm{\theta }\right) = 2$ = 2, then $\sin \left(\mathrm{\theta }\right)$ is equal to

• $\frac{1}{\sqrt{2}}$

• $\frac{1}{\sqrt{3}}$

• $\frac{1}{2}$

• 1

f(x) = (20 - x⁴)^1/4 for 0 < x < $\sqrt{5}$, then $\mathrm{f}\left(\mathrm{f}\left(\frac{1}{2}\right)\right)$ is equal to

• 2^{- 4}

• 2^{- 3}

• 2^{- 2}

• 2^{- 1}

$\frac{\sqrt{8 + \sqrt{28}} + \sqrt{8 - \sqrt{28}}}{\sqrt{8 + \sqrt{28}} - \sqrt{8 - \sqrt{28}}}$ is equal to

• 2

• 7

• $\sqrt{7}$

• $\sqrt{2}$