The equation of bisectors of the angles between the lines $\left|\mathrm{x}\right| = \left|\mathrm{y}\right|$ are

• $\mathrm{y} = \pm \mathrm{x} \mathrm{and} \mathrm{x} = 0$

• $\mathrm{x} = \frac{1}{2} \mathrm{and} \mathrm{y} = \frac{1}{2}$

• y = 0 and x = 0

• None of the above

The equation of the pair of straight lines parallel to x-axis and touching the circle x² + y²- 6x - 4y -12 = 0 is

• y² - 4y - 21 = 0

• y² + 4y - 21 = 0

• y² - 4y + 21 = 0

• y² + 4y + 21 = 0

If the lines 3x - 4y - 7 = 0 and 2x - 3y - 5 = 0 are two diameters of a circle of area 49$\mathrm{\pi }$ sq unit, then equation of the circle is

• x² + y² + 2x - 2y - 62 = 0

• x² + y² - 2x + 2y - 62 = 0

• x² + y² - 2x + 2y - 47 = 0

• x² + y² + 2x - 2y - 47 = 0

The locus of middle point of chords of hyperbola 3x² - 2y² + 4x - 6y = 0 parallel to y = 2x is

• 3x - 4y = 4

• 3x - 4x + 4 = 0

• 4x - 3y = 3

• 3x - 4y = 2

If $\left|\mathrm{z} + 4\right| \le 3$, then the greatest and the least value of $\left|\mathrm{z} + 1\right|$ are

• 6, - 6

• 6, 0

• 7, 2

• 0, - 1

The real part of ${\left(1 - \cos \left(\mathrm{\theta }\right) + 2\mathrm{isin}\left(\mathrm{\theta }\right)\right)}^{- 1}$

• $\frac{1}{3 + 5\cos \left(\mathrm{\theta }\right)}$

• $\frac{1}{5 - 3\cos \left(\mathrm{\theta }\right)}$

• $\frac{1}{3 - 5\cos \left(\mathrm{\theta }\right)}$

• $\frac{1}{5 + 3\cos \left(\mathrm{\theta }\right)}$

The value of $\sin \left(36°\right)\sin \left(72°\right)\sin \left(108°\right)\sin \left(144°\right)$ is equal to

• $\frac{1}{4}$

• $\frac{1}{16}$

• $\frac{3}{4}$

• $\frac{5}{16}$

8.

If $\sin \left(\mathrm{A}\right) = \frac{1}{\sqrt{10}} \mathrm{and} \sin \left(\mathrm{B}\right) = \frac{1}{\sqrt{5}}$ where A and B are positive acute angles, then A + B is equal to 

• $\mathrm{\pi }$

• $\frac{\mathrm{\pi }}{2}$

• $\frac{\mathrm{\pi }}{3}$

• $\frac{\mathrm{\pi }}{4}$

$\frac{d^{\mathrm{n}}}{d{\mathrm{x}}^{\mathrm{n}}}\left(\log \left(\mathrm{x}\right)\right)$ is equal to

• $\frac{\left(\mathrm{n} - 1\right)!}{{\mathrm{X}}^{\mathrm{n}}}$

• $\frac{\mathrm{n} !}{{\mathrm{X}}^{\mathrm{n}}}$

• $\frac{\left(\mathrm{n} - 2\right)!}{{\mathrm{X}}^{\mathrm{n}}}$

• ${\left(- 1\right)}^{\mathrm{n} - 1}\frac{\left(\mathrm{n} - 1\right)!}{{\mathrm{X}}^{\mathrm{n}}}$

The larger of 99⁵⁰ + 100⁵⁰ and 101⁵⁰ is

• 99⁵⁰ + 100⁵⁰

• both are equal

• 101⁵⁰

• None of the above