Download App

5. continuity and differentiation — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths5. continuity and differentiation1 Mark
MCQ
If the function $f(x)=\left\{\begin{array}{cc}\frac{72^x-9^x-8^x+1}{\sqrt{2}-\sqrt{1+\cos x}} & , x \neq 0 \\ a \log _e 2 \log _e 3 & , x=0\end{array}\right.$ is continuous at $x=0$, then the value of $a^2$ is equal to
  • A
    $968$
  • ✓
    $1152$
  • C
    $746$
  • D
    $1250$
✓

Answer

Correct option: B.
$1152$
b
$ \lim _{x \rightarrow 0} f(x)=a \ln 2 \ln 3 $

$ \lim _{n \rightarrow 0} \frac{72^x-9^x-8^x+1}{\sqrt{2}-\sqrt{1+\cos x}}=\lim _{x \rightarrow 0} \frac{\left(8^x-1\right)\left(9^x-1\right)}{\sqrt{2}-\sqrt{1+\cos x}} $

$ \lim _{n \rightarrow 0}\left(\frac{8^x-1}{x}\right)\left(\frac{9^x-1}{x}\right)\left(\frac{x^2}{1-\cos x}\right)(\sqrt{2}+\sqrt{1+\cos x}) $

$ \therefore \ln 8 \times \ln 9 \times 2 \times 2 \sqrt{2}=24 \sqrt{2} \ln 2 \ln 3 $

$ \therefore a=24 \sqrt{2}, a^2=576 \times 2=1152$

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 5. continuity and differentiation→5. continuity and differentiation — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

$\int_0^\pi {x\sin x\,dx = } $
→
Let $f(x)=x^3+a x^2+b x+c$ where $a, b, c$ are real numbers. If $f(x)$ has a local minimum at $x=1$ and a local maximum at $x=-\frac{1}{3}$ and $f(2)=0$, then $\int_{-1}^1 f(x) d x$ equals
→
If the projection of $\vec{\text{a}}=\hat{\text{i}}-2\hat{\text{j}}+3\hat{\text{k}}$ on $\vec{\text{b}}=2\hat{\text{i}}+\lambda\hat{\text{k}}$ is zero, then the value of $\lambda$ is:
  1. $0$
  2. $1$
  3. $\frac{-2}{3}$
  4. $\frac{-3}{2}$
→
If $P $ and  $ Q $ be the middle points of the sides $BC$  and $ CD$  of the parallelogram $ABCD$ , then $\overrightarrow {AP} + \overrightarrow {AQ} = $
→
Consider the set of eight vectors $V=\{a \hat{i}+b \hat{j}+c \hat{k}: a, b, c \in\{-1,1\}\}$. Three non-coplanar vectors can be chosen from $V$ in $2^p$ ways. Then $p$ is
→
If $y = {(\sin x)^{\tan x}}$, then ${{dy} \over {dx}}$ is equal to
→
If a particle moves such that the displacement is proportional to the square of the velocity acquired, then its acceleration is
→
The equation of the normal to the curve 3x2 - y2 = 8 which is parallel to x + 3y = 8 is:
  1. x + 3y = 8
  2. x + 3y + 8 = 0
  3. x + 3y ± 8 = 0
  4. x + 3y = 0
→
Mark the wrong statement:
→
The value of the integral $\int_0^{\log 5} {\frac{{{e^x}\sqrt {{e^x} - 1} }}{{{e^x} + 3}}} \,dx = $
→