11.

If $\frac{\left(\mathrm{x} + 1\right)}{\left(2\mathrm{x} - 1\right)\left(3\mathrm{x} + 1\right)} = \frac{\mathrm{A}}{\left(2\mathrm{x} - 1\right)} + \frac{\mathrm{B}}{\left(3\mathrm{x} +\hspace{0.17em}1\right)}$, then 16A + 9B is equal to

• 4

• 5

• 6

• 8

The value of the series ${\mathrm{xlog}}_{\mathrm{e}}\left(\mathrm{a}\right) + \frac{{\mathrm{x}}^3}{3!}{\left({\log }_{\mathrm{e}}\left(\mathrm{a}\right)\right)}^3$ + $\frac{{\mathrm{x}}^5}{5!}{\left({\log }_{\mathrm{e}}\left(\mathrm{a}\right)\right)}^5$ + ... is

• $\cosh \left({\mathrm{xlog}}_{\mathrm{e}}\left(\mathrm{a}\right)\right)$

• $\coth \left({\mathrm{xlog}}_{\mathrm{e}}\left(\mathrm{a}\right)\right)$

• $\sinh \left({\mathrm{xlog}}_{\mathrm{e}}\left(\mathrm{a}\right)\right)$

• $\tanh \left({\mathrm{xlog}}_{\mathrm{e}}\left(\mathrm{a}\right)\right)$

Coefficient of x¹⁰ in the expansion of (2 + 3x)e^{- x} is

• $\frac{- 26}{\left(10\right)!}$

• $\frac{- 28}{\left(10\right)!}$

• $\frac{- 30}{\left(10\right)!}$

• $\frac{- 32}{\left(10\right)!}$

The set of all solutions of the inequation ${\mathrm{x}}^2 - 2\mathrm{x} + 5 \le 0$ in R is

• $\mathrm{R} - \left(- \infty , - 5\right)$

• $\mathrm{R} - \left(5, \infty \right)$

• $\mathrm{\varphi }$

• $\mathrm{R} - \left(- \infty , - 4\right)$

If (x - 2) is a common factor of the expressions x² + ax + b and x² + cx + d, then, $\frac{\mathrm{b} - \mathrm{d}}{\mathrm{c} - \mathrm{a}}$ is equal to

• - 2

• - 1

• 1

• 2

If the roots of the equation 4x³ - 12x² + 11x + k = 0 are in arithmetic progression, then k is equal to

• - 3

• 1

• 2

• 3

If f(x) is apolynomial ofdegreen with rational coefficients and 1 + 2i , $2 - \sqrt{3}$ and 5 are three roots of f(x) = 0 , then the least value of n is

• 5

• 4

• 3

• 6

If z₁, z₂ are two complex numbers satisfying $\left|\frac{{\mathrm{z}}_1 - 3{\mathrm{z}}_2}{3 - {\mathrm{z}}_1\overline{{\mathrm{z}}_2}}\right| = 1, \left|{\mathrm{z}}_1\right| \ne 3$, then $\left|{\mathrm{z}}_2\right|$ is equal to

• 1

• 2

• 3

• 4

The value of $\sum _{\mathrm{n} = 0}^{\infty }{\left(\frac{2\mathrm{i}}{3}\right)}^{\mathrm{n}}$ is

• $\frac{9 + 6\mathrm{i}}{13}$

• $\frac{9 - 6\mathrm{i}}{13}$

• 9 + 6i

• 9 - 6i

If ${\mathrm{x}}_{\mathrm{n}} = \cos \left(\frac{\mathrm{\pi }}{2^{\mathrm{n}}}\right) + \mathrm{isin}\left(\frac{\mathrm{\pi }}{2^{\mathrm{n}}}\right)$, then $\prod _{\mathrm{n} = 1}^{\infty }$xⁿ is equal to

• - 1

• 1

• $\frac{1}{\sqrt{2}}$

• - 3