The principal amplitude of ${\left(\sin \left(40°\right) + \mathrm{icos}\left(40°\right)\right)}^5$ is

• $70°$

• $- 110°$

• $110°$

• $- 70°$

$\mathrm{If} \mathrm{}$ \mathrm{f}\left(\mathrm{x}\right) = \frac{\mathrm{x} - 1}{\mathrm{x} + 1}$\frac{\mathrm{}}{}$, then f(2x) is

• $\frac{\mathrm{f}\left(\mathrm{x}\right) + 1}{\mathrm{f}\left(\mathrm{x}\right) + 3}$

• $\frac{3\mathrm{f}\left(\mathrm{x}\right) + 1}{\mathrm{f}\left(\mathrm{x}\right) + 3}$

• $\frac{\mathrm{f}\left(\mathrm{x}\right) + 3}{\mathrm{f}\left(\mathrm{x}\right) + 1}$

• $\frac{\mathrm{f}\left(\mathrm{x}\right) + 3}{3\mathrm{f}\left(\mathrm{x}\right) + 1}$

If the distance between the plane Ax - 2 y + z = d and the plane containing the lines $\frac{\mathrm{x} - 1}{2} = \frac{\mathrm{y} - 2}{3} = \frac{\mathrm{z} - 3}{4}$ and $\frac{\mathrm{x} - 2}{3} = \frac{\mathrm{y} - 3}{4} = \frac{\mathrm{z} - 4}{5}$ is $\sqrt{6}$, then $\left|\mathrm{d}\right|$ is equal to

• 3

• 4

• 6

• 1

4.

If the lines $\frac{\mathrm{x} - 1}{2} = \frac{\mathrm{y} + 2}{3} = \frac{\mathrm{z} - 1}{4}$ and $\frac{\mathrm{x} - 3}{1} = \frac{\mathrm{y} - \mathrm{k}}{2} = \frac{\mathrm{z}}{1}$ intersect, then the value of k is

• 3/2

• 7/2

• - 2/7

• - 3/2

If A = {x : x² - 5x + 6 = 0}, B={2, 4}, C = {4, 5}, then A x (B ∩ C) is

• {(2, 4), (3, 4)}

• 
  {(4, 2), (4, 3)}

• {(2, 4), (3, 4), (4, 4)}

• {(2, 2), (3, 3), (4, 4), (5, 5)}

Let A and B be two non-empty sets having n elements in common. Then, the number of elements common to A x B and B x A is

• 2n

• n

• n²

• None of these

∼ (P ∨ q) v ( ∼ p ∧ q) is logically equivalent to

• - p

• p

• q

The foci of a hyperbola are (- 5, 18) and (10, 20) and it touches the Y-axis. The length of its transverse axis is

• 100

• $\raisebox{1ex}{$\sqrt{89}$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$

• $\sqrt{89}$

• $\sqrt{50}$

The locus of mid-point of the line segment joining the locus to a moving point on the parabola y² = 4ax is another parabola with directrix

• x = - a

• x = a

• x = 0

• x = a/2

The equation of the ellipse with its centre at (1, 2), one locus at (6, 2) and passing through (4, 6) is

• $\frac{{\left(\mathrm{x} - 1\right)}^2}{45} + \frac{{\displaystyle {\left(\mathrm{y} - 2\right)}^2}}{20} = 1$

• $\frac{{\left(\mathrm{x} - 1\right)}^2}{20} + \frac{{\displaystyle {\left(\mathrm{y} - 2\right)}^2}}{45} = 1$

• $\frac{{\left(\mathrm{x} + 1\right)}^2}{45} + \frac{{\displaystyle {\left(\mathrm{y} + 2\right)}^2}}{20} = 1$

• None of the above