The angle of elevation of the Sun, when the shadow of the pole is $\sqrt{3}$ times the height of the pole, is

• 60°

• 45°

• 15°

• 30°

The curves x = y² and xy = k cut at right angles, if k² is equal to

• 1

• 0

• $\frac{1}{8}$

• 8

If $\mathrm{\alpha } \mathrm{and} \mathrm{\beta }$ are the rooots of ax² + bx + c = 0, then $\underset{\mathrm{x}\to \mathrm{\alpha }}{\lim }\frac{1 - \cos \left({\mathrm{ax}}^2 + \mathrm{bx} + \mathrm{c}\right)}{{\left(\mathrm{x} - \mathrm{\alpha }\right)}^2}$ is equal to

• $\frac{{\mathrm{a}}^2}{2}{\left(\mathrm{\alpha } - \mathrm{\beta }\right)}^2$

• $- \frac{{\mathrm{a}}^2}{2}{\left(\mathrm{\alpha } - \mathrm{\beta }\right)}^2$

• 0

• 1

The square root of 2i is

• 1 + i

• 1 - i

• $\sqrt{2}\mathrm{i}$

• $- \sqrt{2}$

5.

The locus of z given by $\left|\frac{\mathrm{z} - 1}{\mathrm{z} +\hspace{0.17em}1}\right|$ = 1 is

• a parabola

• an ellipse

• a circle

• a straight line

If $\sin \left(\mathrm{\theta }\right) \frac{\sqrt{3}}{2}$, then the general value of $\mathrm{\theta }$ is

• $\mathrm{n\pi } + {\left(- 1\right)}^{\mathrm{n}}\frac{\mathrm{\pi }}{3}$

• $2\mathrm{n\pi } \pm \frac{\mathrm{\pi }}{6}$

• $2\mathrm{n\pi } \pm \frac{\mathrm{\pi }}{3}$

• $\mathrm{n\pi } + {\left(- 1\right)}^{\mathrm{n}}\frac{\mathrm{\pi }}{6}$

The root ofthe equation 2x - log₁₀(x) = 7 is between

• 3 and 3.5

• 2 and 3

• 3.5 nad 4

• None of these

The coefficient of correlation between x and y is 0.8, whereas the regression coefficient of y on x is 0.2, then the
regression coefficient of x on y will be

• - 3.2

• 3.2

• 4

• 0.16

If sin(x + y) = log(x + y), then $\frac{\mathrm{dy}}{\mathrm{dx}}$ is equal to

• - 1

• 1

• 2

• - 2

A conic section represents a circle, if its eccentricity e is

• e < 0

• e > 0

• e = 0

• None of these