21.

If a, b, c are in GP (a> 1, b > 1, c > 1), then for any real number x (with x > 0, x  1), are in

• GP

• AP

• HP

• GP but not in HP

A line through the point A(2, 0) which makes an angle of 30° with the positive direction of x-axis is rotated about A in clockwise direction through an angle 15°. Then, the equation of the straight line in the new position is

• $\left(2 - \sqrt{3}\right)\mathrm{x} + \mathrm{y} - 4 + 2\sqrt{3} = 0$

• $\left(2 - \sqrt{3}\right)\mathrm{x} - \mathrm{y} - 4 + 2\sqrt{3} = 0$

• $\left(2 - \sqrt{3}\right)\mathrm{x} - \mathrm{y} + 4 + 2\sqrt{3} = 0$

• $\left(2 - \sqrt{3}\right)\mathrm{x} + \mathrm{y} + 4 + 2\sqrt{3} = 0$

The equation $\sqrt{3}\sin \left(\mathrm{x}\right) + \cos \left(\mathrm{x}\right)$ = 4 has

• only one solution

• two solutions

• infinitely many solutions

• no solution

The modulus of $\frac{1 - \mathrm{i}}{3 + \mathrm{i}} + \frac{4\mathrm{i}}{5}$ is

• $\sqrt{5}$ unit

• $\frac{\sqrt{11}}{5}$ unit

• $\frac{\sqrt{5}}{5}$ unit

• $\frac{\sqrt{12}}{5}$

The equation of the tangent to the conic x² - y² - 8x + 2y + 11 = 0 at (2, 1) is

• x + 2 = 0

• 2x + 1 = 0

• x + y + 1 = 0

• x - 2 = 0

A and B are two independent events such that P(A $\cup$ B') = 0.8, and P(A) = 0.3. Then, P(B) is

• $\frac{2}{7}$

• $\frac{2}{3}$

• $\frac{3}{8}$

• $\frac{1}{8}$

The total number of tangents through the point ( 3, 5) that can be drawn to the ellipses 3x² + 5y² = 32 and 25x + 9y² = 450 is

• 0

• 2

• 3

• 4

The value of $\underset{\mathrm{n}\to \infty }{\lim }\left[\frac{\mathrm{n}}{{\mathrm{n}}^2 + 1^2} + \frac{{\displaystyle \mathrm{n}}}{{\displaystyle {\mathrm{n}}^2 + 2^2}} + ... + \frac{{\displaystyle \mathrm{n}}}{{\displaystyle {\mathrm{n}}^2 + {\mathrm{n}}^2}}\right]$ is

• $\frac{\mathrm{\pi }}{4}$

• $\log \left(2\right)$

• 0

• 1

A particle is moving in a straight line. At time t, the distance between the particle from its starting point is given by x = t - 6t² + t³. Its acceleration will be zero at

• t = 1 unit time

• t = 2 unit time

• t = 3 unit time

• t = 4 unit time

Three numbers are chosen at random from 1 to 20. The probability that they are consecutive is

• $\frac{1}{190}$

• $\frac{1}{120}$

• $\frac{3}{190}$

• $\frac{5}{190}$