The value of $\tan \left(9°\right) - \tan \left(27°\right) - \tan \left(63°°\right) + \tan \left(31°\right)$ is

• 3

• 2

• 8

• 4

The number of terms in the series 105 + 103 + 101 + ... + 49 + 47 is

• 28

• 30

• 25

• 22

13.

If the variance oftwo variables x and y are respectively 9 and 16 and covariance is 8, then the coefficient of correlation between x and y will be

• $\frac{2}{3}$

• $\frac{8}{3\sqrt{2}}$

• $\frac{9}{8\sqrt{2}}$

• $\frac{2}{9}$

If the points (k, 2 - 2k), (- k + 1, 2k) and (- 4 - k, 6 - 2) are collinear, then k is equal to

• - 1

• $\frac{1}{3}$

• 1

• $- \frac{1}{2}$

If ${\log }_{{10}^4}\left(\mathrm{x}\right) = \mathrm{y}, \mathrm{then} {\log }_{{10}^8}\left({\mathrm{x}}^4\right)$ is equal to

• $\frac{2}{3}\mathrm{y}$

• 3y

• 4y

• 2y

The largest term in the expansion of (3 + 2x)⁵⁰ where x = $\frac{1}{5}$, is

• 7th

• 5th

• 8th

• 49th

If $\mathrm{x} = {\mathrm{acos}}^3\left(\mathrm{t}\right) \mathrm{and} \mathrm{y} = {\mathrm{asin}}^3\left(\mathrm{t}\right)$, then ${\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)}_{\mathrm{t} = \raisebox{1ex}{$\mathrm{\pi }$}\!\left/ \!\raisebox{-1ex}{$4$}\right.}$ is equal to

• 1

• - 1

• 0

• $\infty$

The anti-derivative F of f defined by f(x) = 4x³ - 6x² + 2x + 5, F(0) = 5, is

• x⁴ - 2x³ + x² + 5x

• 12x² - 12x + 2

• 16x⁴ - 18x³ + 4x² + 5x

• x⁴ - 2x³ + x² + 5x + 5

Scanner is

• an input device

• an output device

• a memory device

• None of the above

The geometric mean of roots of the equation x² - 18x + 81 = 0 is

• 18

• 6

• 9

• 3