If five G.M.’s are inserted between 486 and 2/3 then fourth G.M. … - Vidyadip

Question

If five $G.M.’s$ are inserted between $486$ and $2/3$ then fourth $G.M.$ will be

✓

Answer

b
(b) Let ${G_1},{G_2},{G_3},{G_4},{G_5}$ be the $G.M.’s$ are inserted between $486$ and $2/3$.

So total terms are $7$.

${T_n} = a{r^{n - 1}}$

==> $2/3 = 486$${(r)^6}$

$ \Rightarrow r = 1/3$

Hence $4^{th}$ $G.M.$ will be,

${T_5} = a{r^4} = 486\,{(1/3)^4} = 6$.

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

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

The gradient of the line joining the points on the curve $y = {x^2} + 2x$ whose abscissa are $1$ and $3$, is

If in a geometric progression $\left\{ {{a_n}} \right\},\;{a_1} = 3,\;{a_n} = 96$ and ${S_n} = 189$ then the value of $n$ is

A man standing on a railway platform noticed that a train took $21\, s$ to cross the platform (this means the time elapsed from the moment the engine enters the platform till the last compartment leaves the platform) which is $88\,m$ long, and that it took $9 s$ to pass him. Assuming that the train was moving with uniform speed, what is the length of the train in meters?

Let $P ( x )= x ^{2}+ bx + c$ be a quadratic polynomial with real coefficients such that $\int_{0}^{1} P ( x ) dx =1$ and $P ( x )$ leaves remainder $5$ when it is divided by $(x-2)$. Then the value of $9(b+c)$ is equal to:

Consider two G.Ps. $2,2^{2}, 2^{3}, \ldots$ and $4,4^{2}, 4^{3}, \ldots$ of $60$ and $n$ terms respectively. If the geometric mean of all the $60+n$ terms is $(2)^{\frac{225}{8}}$, then $\sum_{ k =1}^{ n } k (n- k )$ is equal to.

If $\Delta (x) = \left| {\,\begin{array}{*{20}{c}}{{x^n}}&{\sin x}&{\cos x}\\{n!}&{\sin \frac{{n\pi }}{2}}&{\cos \frac{{n\pi }}{2}}\\a&{{a^2}}&{{a^3}}\end{array}\,} \right|,$ then the value of $\frac{{{d^n}}}{{d{x^n}}}[\Delta (x)]$ at $x = 0$ is

The area of the region $A\,\{ \,(x,y)\,\,:\,\,0\,\, \le \,y\, \le \,x\,\left| x \right|\, + \,1$ and $ - \,1\, \le \,x\, \le \,1\,\} $ in sq. units, is

The value of the determinant $\left| {\,\begin{array}{*{20}{c}}{31}&{37}&{92}\\{31}&{58}&{71}\\{31}&{105}&{24}\end{array}\,} \right|$ is

If $f(0) = 2,$ then $\mathop {\lim }\limits_{x \to 0} \frac{{\int\limits_0^x {\left( {tf(x) + xf(t)} \right)dt} }}{{{x^2}}}$ is equal to -

Let $f(x) = \left\{ \begin{array}{l}{x^2} + k,\;\;\;\;{\rm{when}}\;\;x \ge 0\\ - {x^2} - k,\;\;{\rm{when\,\, }}x < 0\end{array} \right.$. If the function $f(x)$ be continuous at $x = 0$, then $k =$