The equation of the tangent at the vertex of the parabola x² + 4x + 2y = 0, is

• x = - 2

• x = 2

• y = - 2

• y = 2

The distance between the directrices of the ellipse $\frac{{\mathrm{x}}^2}{4} + \frac{{\mathrm{y}}^2}{9} = 1$ is

• $\frac{9}{\sqrt{5}}$

• $\frac{18}{\sqrt{5}}$

• $\frac{24}{\sqrt{5}}$

• None of these

The ratio in which yz-plane divides the line joining (2, 4, 5) and (3, 5, 7) is

• - 2 : 3

• 2 : 3

• 3 : 2

• - 3 : 2

14.

If a line makes angles $\mathrm{\alpha }, \mathrm{\beta }, \mathrm{\gamma }$ with x-axis, y-axis and z-axis respectively, then ${\sin }^2\left(\mathrm{\alpha }\right) + {\sin }^2\left(\mathrm{\beta }\right) + {\sin }^2\left(\mathrm{\gamma }\right)$ equals

• 1

• 2

• 3

• - 1

$\underset{\mathrm{x}\to 5}{\lim }\frac{\mathrm{x} - 5}{\left|\mathrm{x} - 5\right|}$ equals

• 2

• 0

• - 2

• None of these

$\underset{\mathrm{x}\to \frac{\mathrm{\pi }}{3}}{\lim }\frac{\sin \left(\frac{\mathrm{\pi }}{3} - \mathrm{x}\right)}{2\cos \left(\mathrm{x}\right) - 1}$ is equal to

• $\frac{1}{2}$

• $\frac{1}{\sqrt{3}}$

• $\frac{- 1}{\sqrt{3}}$

• $\frac{2}{\sqrt{3}}$

A man 2 m tall walks at a uniform speed of 5 km/h away from a lamp post 6 m high. The rate at which the length of his shadow increases, is

• 2.5km/h

• 5km/h

• 15km/h

• $\frac{5}{3} \mathrm{km}/\mathrm{h}$

Seven weddings occur in a week. What is the probability that they happen on the same day?

• $\frac{1}{7}$

• $\frac{1}{7^4}$

• $\frac{1}{7^6}$

• None of these

Two small squares on a chess board are chosen at random. Probability that they have a common side is

• $\frac{1}{3}$

• $\frac{1}{9}$

• $\frac{1}{15}$

• $\frac{1}{18}$

A die is thrown 7 times. What is the chance that an odd numberturns up exactly 4 times ?

• $\frac{35}{128}$

• $\frac{37}{128}$

• $\frac{4}{7}$

• $\frac{43}{128}$