MCQ
જો $A = \left[ {\begin{array}{{}{c}}1&1\\1&1\end{array}} \right]$ તો ${A^{10}} = .........$
- ✓$512A$
- B$1024A$
- C$10A$
- D$299A$
${A^2} = \left[ {\begin{array}{{}{c}}1&1\\1&1\end{array}} \right]\left[ {\begin{array}{{}{c}}1&1\\1&1\end{array}} \right] = \left[ {\begin{array}{{}{c}}{1 + 1}&{1 + 1}\\{1 + 1}&{1 + 1}\end{array}} \right] = \left[ {\begin{array}{{}{c}}2&2\\2&2\end{array}} \right]$
આ જ રીતે ${A^3} = \left[ {\begin{array}{{}{c}}4&4\\4&4\end{array}} \right]=\left[ {\begin{array}{{}{c}}{{2^2}}&{{2^2}}\\{{2^2}}&{{2^2}}\end{array}} \right]$
$\therefore$ ${A^{10}} = \left[ {\begin{array}{{}{c}}{{2^9}}&{{2^9}}\\{{2^9}}&{{2^9}}\end{array}} \right] = 512\left[ {\begin{array}{{}{c}}1&1\\1&1\end{array}} \right] = 512A$
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
$ \mathrm{L}_1: \overrightarrow{\mathrm{r}}=(2+\lambda) \hat{\mathrm{i}}+(1-3 \lambda) \hat{\mathrm{j}}+(3+4 \lambda) \hat{\mathrm{k}}, \lambda \in \mathbb{R} $
$ \mathrm{L}_2: \overrightarrow{\mathrm{r}}=2(1+\mu) \hat{\mathrm{i}}+3(1+\mu) \hat{\mathrm{j}}+(5+\mu) \hat{k}, \mu \in \mathbb{R}$
વચ્ચેનું ન્યૂનતમ અંતર $\frac{m}{\sqrt{n}}$ હોય, જ્યાં $\operatorname{gcd}(m, n)=1$, તો $m+n$ નું મૂલ્ય ........... છે.