Download App

STD 11 - 8. sequence and series — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 11 - 8. sequence and series4 Marks
MCQ
If ${a_1},{a_2},....{a_n}$ are positive real numbers whose product is a fixed number $c$, then the minimum value of ${a_1} + {a_2} + ...$ $ + {a_{n - 1}} + 2{a_n}$ is
  • ✓
    $n{(2c)^{1/n}}$
  • B
    $(n + 1)\,{c^{1/n}}$
  • C
    $2n{c^{1/n}}$
  • D
    $(n + 1){(2c)^{1/n}}$
✓

Answer

Correct option: A.
$n{(2c)^{1/n}}$
a
(a) $A.M.$ $ \ge $ $G.M. $

==> $\frac{{{a_1} + {a_2} + .... + {a_{n - 1}} + 2{a_n}}}{n} \ge {({a_1}.{a_{2,}}...{a_{n - 1}}2{a_n})^{\frac{1}{n}}} \ge {(2c)^{\frac{1}{n}}}$

Minimum value of ${a_1} + {a_2} + ...... + {a_{n - 1}} + 2{a_n} = n{(2c)^{1/n}}$.

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

Integers $1,2,3, \ldots \ldots, n,(n \geq 3)$ are written on a black board and an integer $k (1 < k < n )$ is erased. The average of the remaining numbers is $16$ . Then $n + k$ is
→
The equation of the ellipse whose vertices are $( \pm 5,\;0)$ and foci are $( \pm 4,\;0)$ is
→
In a geometric progression consisting of positive terms, each term equals the sum of the next two terms. Then the common ratio of its progression is equals
→
A continuous function $f: R \rightarrow R$ satisfies the equation $f(x)=x+\int_0^x f(t) d t$. Which of the following options true?
→
If one of the diameters of the circle $x^2+y^2-10 x+$ $4 y+13=0$ is a chord of another circle $C,$ whose center is the point of intersection of the lines $2 x+$ $3 y=12$ and $3 x-2 y=5$, then the radius of the circle $\mathrm{C}$ is
→
If $f(x) = ({\log _{\cot x}}\tan x){({\log _{\tan x}}\cot x)^{ - 1}},$ then $f'(2) = $
→
The number of ways, $16$ identical cubes, of which $11$ are blue and rest are red, can be placed in a row so that between any two red cubes there should be at least $2$ blue cubes, is
→
Let $A =\left[ a _{ i }\right]$ be a matrix of order $3 \times 3$, with $a _{ ij }=(\sqrt{2})^{ i + j }$. If the sum of all the elements in the third row of $A ^2$ is $\alpha+\beta \sqrt{2}, \alpha, \beta \in Z$, then $\alpha+\beta$ is equal to
→
Let $f :(0, \infty) \rightarrow(0, \infty)$ be a differentiable function such that $f(1)= e$ and $\lim \limits_{t \rightarrow x} \frac{t^{2} f^{2}(x)-x^{2} f^{2}(t)}{t-x}=0$ If $f ( x )=1,$ then $x$ is equal to
→
Let $f(x)$ be a polynomial function of the second degree. If $f(1) = f( - 1)$ and ${a_1},{a_2},{a_3}$ are in $A.P.$ then $f'({a_1})$, $f'({a_2})$, $f'({a_3})$ are in
→