21.

The value of $\cos \left(15°\right) - \sin \left(15°\right)$ is

• 0

• $\frac{1}{\sqrt{2}}$

• $- \frac{1}{\sqrt{2}}$

• $\frac{1}{2\sqrt{2}}$

The period of the function f(x) = $\cos \left(4\mathrm{x}\right) + \tan \left(3\mathrm{x}\right)$ is

• $\mathrm{\pi }$

• $\frac{\mathrm{\pi }}{2}$

• $\frac{\mathrm{\pi }}{3}$

• $\frac{\mathrm{\pi }}{4}$

4 boys and 2 girls occupy seats in a row at random. Then the probability that the two girls occupy seats side by side is

• $\frac{1}{2}$

• $\frac{1}{4}$

• $\frac{1}{3}$

• $\frac{1}{6}$

A coin is tossed again and again. If tail appears on first three tosses, then the chance that head appears on fourth toss is

• $\frac{1}{16}$

• $\frac{1}{2}$

• $\frac{1}{8}$

• $\frac{1}{4}$

The coefficient of xⁿ in the expansion of $\frac{{\mathrm{e}}^{7\mathrm{x}} + {\mathrm{e}}^{\mathrm{x}}}{{\mathrm{e}}^{3\mathrm{x}}}$ is

• $\frac{4^{\mathrm{n} - 1} - {\left(- 2\right)}^{\mathrm{n} - 1}}{\mathrm{n}!}$

• $\frac{4^{\mathrm{n} - 1} - 2^{\mathrm{n} - 1}}{\mathrm{n}!}$

• $\frac{4^{\mathrm{n}} - 2^{\mathrm{n}}}{\mathrm{n}!}$

• $\frac{4^{\mathrm{n}} + {\left(- 2\right)}^{\mathrm{n}}}{\mathrm{n}!}$

The sum of the series $\frac{1}{1 . 2} - \frac{1}{2 . 3} + \frac{1}{3 . 4} - ... \infty$

• $2{\log }_{\mathrm{e}}\left(2\right) + 1$

• $2{\log }_{\mathrm{e}}\left(2\right)$

• $2{\log }_{\mathrm{e}}\left(2\right) - 1$

• ${\log }_{\mathrm{e}}\left(2\right) - 1$

The number (101)¹⁰⁰ - 1 is divisible by

• 10⁴

• 10⁶

• 10⁸

• 10¹²

If A and B are coefficients of xⁿ in the expansions of (1 + x)²ⁿ and (1+ x)^{2n - 1} respectively, then A /B is equal to

• 4

• 2

• 9

• 6

If n > 1 is an integer and x $\ne$ 0, then (1 + x)ⁿ - nx - 1 is divisible by

• nx³

• n³x

• x

• nx

If ${}^{\mathrm{n}}\mathrm{C}_4, {}^{\mathrm{n}}\mathrm{C}_5 \mathrm{and} {}^{\mathrm{n}}\mathrm{C}_6$ are in AP, then n is

• 7 or 14

• 7

• 14

• 14 or 21