MCQ
${(\sqrt 2 + 1)^6} - {(\sqrt 2 - 1)^6} = $
- A$101$
- B$70\sqrt 2 $
- ✓$140\sqrt 2 $
- D$120\sqrt 2 $
$ = 2\,{[^n}{C_1}{x^{n - 1}}a + {\,^n}{C_3}{x^{n - 3}}{a^3} + {\,^n}{C_5}{x^{n - 5}}{a^5} + ......]$
${(\sqrt 2 + 1)^6} - {(\sqrt 2 - 1)^6}$
$ = 2\,{[^6}{C_1}{(\sqrt 2 )^5}{(1)^1} + {\,^6}{C_3}{(\sqrt 2 )^3}{(1)^3} + {\,^6}{C_5}{(\sqrt 2 )^1}{(1)^5}]$
$\,\,\,{(\sqrt 2 + 1)^6} - {(\sqrt 2 - 1)^6} = 2[6 \times 4\sqrt 2 + 20 \times 2\sqrt 2 + 6\sqrt 2 ]$
$=2[24\sqrt 2 + 40\sqrt 2 + 6\sqrt 2 ] = 140\sqrt 2 $.
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
| List $I$ | List $II$ |
| $P.$ For each $z_k$ there exists a $z_j$ such that $z_k \cdot z_j=1$ | $1.$ True |
| $Q.$ There exists a $k \in\{1,2, \ldots ., 9\}$ such that $z_{1 .} . z=z_k$ has no solution $z$ in the set of complex numbers. | $2.$ False |
| $R.$ $\frac{\left|1-z_1\right|\left|1-z_2\right| \ldots . .\left|1-z_9\right|}{10}$ equals | $3.$ $1$ |
| $S.$ $1-\sum_{k=1}^9 \cos \left(\frac{2 k \pi}{10}\right)$ equals | $4.$ $2$ |
Codes: $ \quad P \quad Q \quad R \quad S$