Download App

STD 11 - 12. limits — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsSTD 11 - 12. limits1 Mark
MCQ
$\mathop {\lim }\limits_{n \to \infty } \left( {\frac{{{{\left( {n + 1} \right)}^{1/3}}}}{{{n^{4/3}}}} + \frac{{{{\left( {n + 2} \right)}^{1/3}}}}{{{n^{4/3}}}} + .... + \frac{{{{\left( {2n} \right)}^{1/3}}}}{{{n^{4/3}}}}} \right)$ is equal to
  • ✓
    $\frac{3}{4}{\left( 2 \right)^{4/3}} - \frac{3}{4}$
  • B
    $\frac{4}{3}{\left( 2 \right)^{3/4}}$
  • C
    $\frac{3}{4}{\left( 2 \right)^{4/3}} - \frac{4}{3}$
  • D
    $\frac{4}{3}{\left( 2 \right)^{4/3}}$
✓

Answer

Correct option: A.
$\frac{3}{4}{\left( 2 \right)^{4/3}} - \frac{3}{4}$
a
$\mathop {\lim }\limits_{n \to \infty } \sum\limits_{r = 1}^n {\frac{1}{n}} {\left( {\frac{{n + r}}{n}} \right)^{1/3}}$

$ = \int\limits_0^1 {{{\left( {1 + x} \right)}^{1/3}}} dx = \frac{3}{4}\left( {{2^{4/3}} - 1} \right)$

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 "M.C.Q (1 Marks)" from STD 11 - 12. limits→STD 11 - 12. limits — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

If the value of $\lim _{x \rightarrow 0}(2-\cos x \sqrt{\cos 2 x})^{\left(\frac{x+2}{x^{2}}\right)}$ is equal to $e^{a}$, then $a$ is equal to $.....$
→
If slope of a line is positive then its inclination is:
→
The first $3$ terms in the expansion of ${(1 + ax)^n}$ $(n \ne 0)$ are $1, 6x$ and $16x^2$. Then the value of $a$ and $n$ are respectively
→
Equations of the two straight lines passing through the point $(3, 2)$ and making an angle of ${45^o}$ with the line $x - 2y = 3,$ are
→
If ​$\cos\text{x}=-\frac{1}{2}$ and $0<\text{x}<2\pi,$ then the solutions are:
→
Find the sum of series $6^3+ 7^3+…..…..+ 20^3$.
→
If $\sin x=\frac{-2 \sqrt{6}}{5}$ and $x$ lies in quadrant III, then $\cot x$ ?
→
Let $\alpha ,\beta $ be the roots of ${x^2} + (3 - \lambda )x - \lambda = 0.$ The value of $\lambda $ for which ${\alpha ^2} + {\beta ^2}$ is minimum, is
→
$\lim _{x \rightarrow \frac{\pi}{2}}\left(\frac{\int_{x^3}^{(\pi / 2)^3}\left(\sin \left(2 t^{1 / 3}\right)+\cos \left(t^{1 / 3}\right)\right) d t}{\left(x-\frac{\pi}{2}\right)^2}\right)$ is equal to:
→
${C_0} - {C_1} + {C_2} - {C_3} + ..... + {( - 1)^n}{C_n}$ is equal to
→