Download App

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

CBSE BoardEnglish MediumSTD 11 ScienceMathsSTD 11 - 12. limits1 Mark
MCQ
$\lim _{x \rightarrow \frac{\pi}{2}}\left(\frac{\int_{x^3}^{(\pi / 2)^3}\left(\sin \left(2 t^{1 / 3}\right)+\cos \left(t^{1 / 3}\right)\right) d t}{\left(x-\frac{\pi}{2}\right)^2}\right)$ is equal to:
  • ✓
     $\frac{9 \pi^2}{8}$
  • B
    $\frac{11 \pi^2}{10}$
  • C
     $\frac{3 \pi^2}{2}$
  • D
     $\frac{5 \pi^2}{9}$
✓

Answer

Correct option: A.
 $\frac{9 \pi^2}{8}$
a
$ \lim _{x \rightarrow \frac{\pi}{2}} \frac{0-\{\sin (2 x)+\cos (x)\} \cdot 3 x^2}{2\left(x-\frac{\pi}{2}\right)} $

$ =\lim _{x \rightarrow \frac{\pi}{2}} \frac{-\{2 \sin x \cos x+\cos x\} 3 x^2}{2\left(x-\frac{\pi}{2}\right)} $

$ =\lim _{x \rightarrow \frac{\pi}{2}}\left\{\frac{2 \sin x \sin \left(\frac{\pi}{2}-x\right)}{2\left(x-\frac{\pi}{2}\right)}+\frac{\sin \left(\frac{\pi}{2}-x\right)}{2\left(\frac{\pi}{2}-x\right)}\right\} 3 x^2 $

$ =\left(1(1)+\frac{1}{2}\right) 3\left(\frac{\pi}{2}\right)^2 $

$ =\frac{9 \pi^2}{8}$

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

The remainder when $(2023)^{2023}$ is divided by $35$ is $..........$.
→
$\mathop {\lim }\limits_{\theta \to 0} \frac{{4\theta (\tan \theta - 2\theta \tan \theta )}}{{{{(1 - \cos 2\theta )}^2}}}$ is
→
The orthocentre of the triangle with vertices $(-2, -6)$, $(-2, 4)$ and $(1, 3)$ is
→
The odds against a certain event is $5 : 2$ and the odds in favour of another event is $6 : 5$. If both the events are independent, then the probability that at least one of the events will happen is
→
If $2^{10}+2^{9 \cdot} \cdot 3^{1}+2^{8 \cdot 3^{2}+\ldots+2 \cdot 3^{9}+3^{10}}=S-2^{11}$ then $S$ is equal to
→
The points $\left( {\frac{a}{{\sqrt 3 }},a} \right),\;\left( {\frac{{2a}}{{\sqrt 3 }},\,2a} \right),\;\left( {\frac{a}{{\sqrt 3 }},\,3a} \right)$ are the vertices of
→
If $l,m,n$ are real and $l \ne m$, then the roots of the equation $(l - m){x^2} - 5(l + m)x - 2(l - m) = 0$are
→
If $\mathrm{P}(6,1)$ be the orthocentre of the triangle whose vertices are $A(5,-2), B(8,3)$ and $C(h, k)$, then the point $C$ lies on the circle.
→
The coefficient of $x^{4}$ is the expansion of $\left(1+\mathrm{x}+\mathrm{x}^{2}\right)^{10}$ is
→
The distance between two parallel lines $3x + 4y - 8 = 0$ and $3x + 4y - 3 = 0$, is given by
→