The period of ${\sin }^4\left(\mathrm{x}\right) + {\cos }^4\left(\mathrm{x}\right)$ is

• $\frac{{\mathrm{\pi }}^4}{2}$

• $\frac{{\mathrm{\pi }}^2}{2}$

• $\frac{\mathrm{\pi }}{4}$

• $\frac{\mathrm{\pi }}{2}$

12.

The number of subsets of {1, 2, 3, . . . , 9} containing at least one odd number is

• 324

• 396

• 496

• 512

$\frac{\cos \left(\mathrm{x}\right)}{\cos \left(\mathrm{x} - 2\mathrm{y}\right)} = \mathrm{\lambda } \Rightarrow \tan \left(\mathrm{x} - \mathrm{y}\right)\tan \left(\mathrm{y}\right)$ is equal to

• $\frac{1 + \mathrm{\lambda }}{1 - \mathrm{\lambda }}$

• $\frac{1 - \mathrm{\lambda }}{1 + \mathrm{\lambda }}$

• $\frac{\mathrm{\lambda }}{1 + \mathrm{\lambda }}$

• $\frac{\mathrm{\lambda }}{1 + \mathrm{\lambda }}$

p points are chosen on each of the three coplanar lines. The maximum number of triangles formed with vertices at these points is

• ${\mathrm{p}}^3 + 3{\mathrm{p}}^2$

• $\frac{1}{2}\left({\mathrm{p}}^3 +\hspace{0.17em}\mathrm{p}\right)$

• $\frac{{\mathrm{p}}^2}{2}\left(5\mathrm{p} - 3\right)$

• ${\mathrm{p}}^2\left(4\mathrm{p} - 3\right)$

$\cos \left(\mathrm{A}\right)\cos \left(2\mathrm{A}\right)\cos \left(4\mathrm{A}\right) ... \cos \left(2^{\mathrm{n} - 1}\mathrm{A}\right)$ equals

• $\frac{\sin \left(2^{\mathrm{n}}\mathrm{A}\right)}{2^{\mathrm{n}}\sin \left(\mathrm{A}\right)}$

• $\frac{2^{\mathrm{n}}\sin \left(2^{\mathrm{n}}\mathrm{A}\right)}{\sin \left(\mathrm{A}\right)}$

• $\frac{2^{\mathrm{n}}\sin \left(2^{\mathrm{n}}\mathrm{A}\right)}{\sin \left(2^{\mathrm{n}}\mathrm{A}\right)}$

• $\frac{\sin \left(\mathrm{A}\right)}{2^{\mathrm{n}}\sin \left(2^{\mathrm{n}}\mathrm{A}\right)}$

The coefficient of x²⁴ in the expansion of (1 + x²)¹²(1 + x¹²)(1 + x²⁴) is

• ${}_{12}\mathrm{C}_6$

• ${}_{12}\mathrm{C}_6 + 2$

• ${}_{12}\mathrm{C}_6 + 4$

• ${}_{12}\mathrm{C}_6 +\hspace{0.17em}6$

If 3cos(x) $\ne$ sin x, then the general solution of sin²(x) - cos(2x) = 2 - sin(2x) is

• $\mathrm{n\pi } + {\left(- 1\right)}^{\mathrm{n}}\frac{\mathrm{\pi }}{2}, \mathrm{n} \in \mathrm{Z}$

• $\frac{\mathrm{n\pi }}{2}, \mathrm{n} \in \mathrm{Z}$

• $\left(4\mathrm{n} \pm 1\right)\frac{\mathrm{\pi }}{2}, \mathrm{n} \in \mathrm{Z}$

• $\left(2\mathrm{n} - 1\right)\mathrm{\pi }, \mathrm{n} \in \mathrm{Z}$

If x is numerically so small so that x and higher powers of x can be neglected, then ${\left(1 + \frac{2\mathrm{x}}{3}\right)}^{\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}{\left(32 +\hspace{0.17em}5\mathrm{x}\right)}^{\raisebox{1ex}{$- 1$}\!\left/ \!\raisebox{-1ex}{$5$}\right.} \mathrm{is} \mathrm{approximately} \mathrm{equal} \mathrm{to}$

• $\frac{32 + 31\mathrm{x}}{64}$

• $\frac{31 + 32\mathrm{x}}{64}$

• $\frac{31 - 32\mathrm{x}}{64}$

• $\frac{1 - 2 x}{64}$

For $\left|\mathrm{x}\right| < 1$, the constant term in the expansion of $\frac{1}{{\left(\mathrm{x} - 1\right)}^2\left(\mathrm{x} - 2\right)} \mathrm{is}$

• 2

• 1

• 0

• $- \frac{1}{2}$

$$\begin{gathered} \frac{1}{{\mathrm{e}}^{3\mathrm{x}}}\left({\mathrm{e}}^{\mathrm{x}} + {\mathrm{e}}^{5\mathrm{x}}\right) = {\mathrm{a}}_0 + {\mathrm{a}}_1\mathrm{x} + {\mathrm{a}}_2{\mathrm{x}}^2 + . . \\ \Rightarrow 2{\mathrm{a}}_1 + 2^3{\mathrm{a}}_3 + 2^5{\mathrm{a}}_5 + . . . = ? \end{gathered}$$

• e

• e ^{- 1}

• 1

• 0