Download App

basic of algoritham — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSbasic of algoritham1 Mark
MCQ
The value of ${(0.05)^{{{\log }_{_{\sqrt {20} }}}(0.1 + 0.01 + 0.001 + ......)}}$ is
  • ✓
    $81$
  • B
    ${1 \over {81}}$
  • C
    $20$
  • D
    $0.05$
✓

Answer

Correct option: A.
$81$
a
(a) ${(0.05)^{{{\log }_{\sqrt {20} }}(0.1 + 0.01 + ......)}} = {\left( {{1 \over {20}}} \right)^{2{{\log }_{20}}\left( {{{0.1} \over {1 - 0.1}}} \right)}}$

$ = {20^{ - 2{{\log }_{20}}(1/9)}} = {20^{2{{\log }_{20}}9}} = {20^{{{\log }_{20}}{9^2}}} = {9^2} = 81$.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "MCQ" from basic of algoritham→basic of algoritham — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

$7^{2 n}+3^{n-1} \cdot 2^{3 n-3}$ is divisible by:
→
The line $x + y = 4$ divides the line joining the points $(-1, 1)$ and $(5, 7)$ in the ratio
→
To remove $xy$ term from the second degree equation $5x^2 + 8xy + 5y^2 + 3x + 2y + 5 = 0$, the coordinates axes are rotated through an angle $\theta$, then $\theta$ equals:-
→
$\mathop {\lim }\limits_{x \to 0} \frac{{{e^{\sin x}} - 1}}{x} = $
→
Among all cyclic quadrilaterals inscribed in a circle of radius $R$ with one of its angles equal to $120^{\circ}$. Consider the one with maximum possible area. Its area is
→
A set $S$ contains $7$ elements. A non-empty subset $A$ of $S$ and an element $x$ of $S$ are chosen at random. Then the probability that $x \in A$ is
→
A group of 1200 persons consisting of captains and soldiers is travelling in a train. For every 15 soldiers there is one captain. The number of captains in the group is:
→
Let ${x_1},\,{x_2},....,{x_n}$ be $n$ observations such that $\sum x_i^2 = 400$ and $\sum x_i^{} = 80$. Then a possible value of $n$ among the following is
→
Let $[t]$ denotes the greatest integer $\leq t$. If the constant term in the expansion of $\left(3 x^2-\frac{1}{2 x^5}\right)^7$ is $\alpha$, then $[\alpha]$ is equal to $............$.
→
If the paper of $4$ students can be checked by any one of $7$ teachers, then the probability that all the $4$ papers are checked by exactly $2$ teachers is
→