21.

$$\begin{gathered} \mathrm{In} ∆\mathrm{ABC} \mathrm{if} \mathrm{x} = \tan \left(\frac{\mathrm{B} - \mathrm{C}}{2}\right)\tan \left(\frac{\mathrm{A}}{2}\right), \mathrm{y} = \tan \left(\frac{\mathrm{C} - \mathrm{A}}{2}\right)\tan \left(\frac{\mathrm{B}}{2}\right) \mathrm{and} \\ \mathrm{z} = \tan \left(\frac{\mathrm{A} - \mathrm{B}}{2}\right)\tan \left(\frac{\mathrm{C}}{2}\right), \mathrm{then} \left(\mathrm{x} + \mathrm{y}\hspace{0.17em}+ \mathrm{z}\right) = ? \end{gathered}$$

• xyz

• - xyz

• 2xyz

• $\frac{1}{2}\mathrm{xyz}$

ln $∆$ABC, if the sides a, b, c are in geometric progression and the largest angle exceeds the smallest angle by 60°, then cos(B) is equal to

• $\frac{\sqrt{13} + 1}{4}$

• $\frac{1 - \sqrt{13}}{4}$

• 1

• $\frac{\sqrt{13} - 1}{4}$

If the mean of 10 observations is 50 and the sum of the squares of the deviations of the observations from the mean is 250, then the coefficient of variation of those observations is

• 25

• 50

• 10

• 5

The variance of the first 50 even natural numbers is

• $\frac{833}{4}$

• 833

• 437

• $\frac{437}{4}$

A speaks truth in 75% of the cases and B in 80% of the cases. Then, the probability that their statements about an incident do not match, is

• $\frac{7}{20}$

• $\frac{3}{20}$

• $\frac{2}{7}$

• $\frac{5}{7}$

If the mean and variance of a binomial distribution are 4 and 2 respectively, then the probability of 2 successes of that binomial variate X, is

• $\frac{1}{2}$

• $\frac{37}{256}$

• $\frac{219}{256}$

• $\frac{7}{64}$

Equation of the locus of the centroid of the triangle whose vertices are (acos(k), asin(k)), [bsin(k), - bcos(k)) and (1, 0), where k is a parameter, is

• ${\left(1 - 3\mathrm{x}\right)}^2 + 9{\mathrm{y}}^2 = {\mathrm{a}}^2 + {\mathrm{b}}^2$

• ${\left(3\mathrm{x} - 1\right)}^2 + 9{\mathrm{y}}^2 = 2{\mathrm{a}}^2 + 2{\mathrm{b}}^2$

• ${\left(3\mathrm{x} + 1\right)}^2 + {\left(3\mathrm{y}\right)}^2 = 3{\mathrm{a}}^2 + 3{\mathrm{b}}^2$

• ${\left(3\mathrm{x} +\hspace{0.17em}1\right)}^2 + {\left(3\mathrm{y}\right)}^2 = 3{\mathrm{a}}^2 + 3{\mathrm{b}}^2$

If the coordinate axes are rotated through an angle $\frac{\mathrm{\pi }}{6}$ about the origin, then the transformed equation of $\sqrt{3}{\mathrm{x}}^2 - 4\mathrm{xy} + \sqrt{3}{\mathrm{y}}^2 = 0 \mathrm{is}$

• $\sqrt{3}{\mathrm{y}}^2 + \mathrm{xy} = 0$

• ${\mathrm{x}}^2 - {\mathrm{y}}^2 = 0$

• $\sqrt{3}{\mathrm{y}}^2 - \mathrm{xy} = 0$

If the lines x + 3y - 9 = 0, 4x + by - 2 = 0 and 2x - y - 4 = 0 are concurrent, then the equation of the line passing through the point (b, 0) and concurrent with the given lines, is

• 2x + y + 10 = 0

• 4x - 7y + 20 = 0

• x - y + 5 = 0

• x - 4y + 5 = 0

The distance from the origin to the image of (1, 1) with respect to the line x + y + 5 = 0 is

• $7\sqrt{2}$

• $3\sqrt{2}$

• $6\sqrt{2}$

• $4\sqrt{2}$