21.

A point is in motion along the curve 12y = x³. The x-coordinate, changes faster than y-coordinate, if

• $\mathrm{x} \in \left[- 2, \infty \right]$

• $\mathrm{x} \in \left[- \infty , 2\right] \cup \left[2, \infty \right]$

The coefficient of x⁴ in the expansion of (1 + x + x² + x³)¹¹ is

• 990

• 605

• 810

• None of these

Which of the following is correct?

• 2 + 3i > 1 + 4i

• 6 + 2i > 3 + 3i

• 5 + 8i > 5 + 7i

• None of these

${\left[\frac{- 1 + \sqrt{\left(- 3\right)}}{2}\right]}^{3\mathrm{n}} + {\left[\frac{- 1 - \sqrt{\left(- 3\right)}}{2}\right]}^{3\mathrm{n}}$ is equal to

• 0

• 1

• 2

• 3

If y = sin²(x)cos²(x), then y_n is equal to

• $\left(\frac{4^{\mathrm{n}}}{8}\right) . \cos \left(4\mathrm{x} + \frac{\mathrm{n\pi }}{2}\right)$

• $\left({\left(- 1\right)}^{\mathrm{n}} \frac{4^{\mathrm{n}}}{8}\right) . \cos \left(4\mathrm{x} + \frac{\mathrm{n\pi }}{2}\right)$

• $\left(- \frac{4^{\mathrm{n}}}{8}\right) . \cos \left(4\mathrm{x} + \frac{\mathrm{n\pi }}{2}\right)$

• None of the above

If A is any non-zero square matrix of order n, then A (adj A) is equal to

• I

• $\left|\mathrm{A}\right|$I

• ${\left|\mathrm{A}\right|}^{\mathrm{n}}$I

• None of these

If A = $\left[\begin{array}{ccc}2& 3& 1\\ 0& - 1& 5\end{array}\right]$ and B = $\left[\begin{array}{ccc}1& 2& - 6\\ 0& - 1& 3\end{array}\right]$, then 3A - 4B is equal to

• $\left[\begin{array}{ccc}2& 1& 27\\ 0& 1& 3\end{array}\right]$

• $\left[\begin{array}{ccc}2& 1& 27\\ 0& 1& 3\end{array}\right]$

• $\left[\begin{array}{ccc}3& 5& - 5\\ 0& - 2& 8\end{array}\right]$

• None of these

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

• $\log \left(2\right)$

• $\frac{1}{2}\log \left(2\right)$

• $2\log \left(2\right)$

• None of these

Let f(2) = 4 and f'(2)= 1. Then, $\underset{\mathrm{x}\to 2}{\lim }\frac{\mathrm{xf}\left(2\right) - 2\mathrm{f}\left(\mathrm{x}\right)}{\mathrm{x} - 2}$ is given by

• 2

• - 2

• - 4

• 3

$\mathrm{If} \mathrm{y} = {\log }_{\sin \left(\mathrm{x}\right)}\left(\tan \left(\mathrm{x}\right)\right), \mathrm{then} {\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)}_{\raisebox{1ex}{$\mathrm{\pi }$}\!\left/ \!\raisebox{-1ex}{$4$}\right.}$ is equal to

• $\frac{4}{\log \left(2\right)}$

• $- 4\log \left(2\right)$

• $- \frac{4}{\log \left(2\right)}$

• None of these