The values of p for which the difference between the roots of the equation x² + px + 8 = 0 is 2, are

• $\pm 2$

• $\pm 4$

• $\pm 6$

• $\pm 8$

20 persons are invited for a party. In how many different ways can they and the host be seated at circular table, if the two particular persons are to be seated on either side of the host?

• 20!

• 2(18!)

• 18!

• None of these

The area of the smaller segment cut off from the circle x² + y² = 9 by x = 1 is

• $\frac{1}{2}\left(9{\sec }^{-1}\left(3 - \sqrt{8}\right)\right)$

• $\left(9{\sec }^{-1}\left(3 - \sqrt{8}\right)\right)$ sq unit

• $\left(\sqrt{8} - 9{\sec }^{-1}\left(3 \right)\right)$

• None of the above

The distance travelled by a motor car in t seconds after the brakes are applied is s feet, wheres = 22t - 12t². The distance travelled by the car before it stops, is

• 10.08 ft

• 10ft

• 11ft

• 11.5ft

45.

$\underset{\mathrm{x}\to 0}{\lim }\frac{\left(1 - \cos \left(2\mathrm{x}\right)\right)\sin \left(5\mathrm{x}\right)}{{\mathrm{x}}^2\sin \left(3\mathrm{x}\right)}$ equals

• $\frac{10}{3}$

• $\frac{3}{10}$

• $\frac{6}{5}$

• $\frac{5}{6}$

If $\cos \left(\mathrm{\theta } - \mathrm{\alpha }\right) = \mathrm{a}, \cos \left(\mathrm{\theta } - \mathrm{\beta }\right) = \mathrm{b}$, then

${\sin }^2\left(\mathrm{\alpha } - \mathrm{\beta }\right) + 2\mathrm{abcos}\left(\mathrm{\alpha } - \mathrm{\beta }\right)$ is equal to

• a² + b²

• a² - b²

• b² - a²

• - a² - b²

For any two complex numbers z₁ and z₂ and any real numbers a and b, ${\left|\left({\mathrm{az}}_1 - {\mathrm{az}}_2\right)\right|}^2 + {\left|\left({\mathrm{bz}}_1 + {\mathrm{az}}_2\right)\right|}^2$ is equal to

• $\left({\mathrm{a}}^2 + {\mathrm{b}}^2\right)\left(\left|{\mathrm{z}}_1\right| + \left|{\mathrm{z}}_2\right|\right)$

• $\left({\mathrm{a}}^2 + {\mathrm{b}}^2\right)\left({\left|{\mathrm{z}}_1\right|}^2 + {\left|{\mathrm{z}}_2\right|}^2\right)$

• $\left({\mathrm{a}}^2 + {\mathrm{b}}^2\right)\left({\left|{\mathrm{z}}_1\right|}^2 - {\left|{\mathrm{z}}_2\right|}^2\right)$

• None of these

If w ($\left(\ne 1\right)$ )is a cube root of unity and (1 + w²)ⁿ = (1 + w⁴)ⁿ, then the least positive value of n is

• 2

• 3

• 5

• 6

The harmonic mean of the roots of the equation

$\left(5 + \sqrt{2}\right){\mathrm{x}}^2 - \left(4 + \sqrt{5}\right)\mathrm{x} + 8 + 2\sqrt{5} = 0$ is

• 2

• 4

• 6

• 8

If in the expansion of (1 + x)^m (1 - x)ⁿ, the coefficient of x and x² are 3 and - 6 respectively, then m is

• 6

• 9

• 12

• 24