JEE Mains · Maths · STD 11 - 12. limits
\(\lim\limits_{x \rightarrow 2} \frac{3^{x}+3^{3-x}-12}{3^{-x / 2}-3^{1-x}}\) is equal to
- A \(25\)
- B \(36\)
- C \(49\)
- D \(42\)
Answer & Solution
Correct Answer
(B) \(36\)
Step-by-step Solution
Detailed explanation
\(\lim _{x \rightarrow 2} \frac{3^{x}+3^{3-x}-12}{3^{-x / 2}-3^{1-x}} \Rightarrow \lim _{x \rightarrow 2} \frac{3^{2 x}-12.3^{x}+27}{3^{x / 2}-3}\) \(=\lim _{x \rightarrow 2} \frac{\left(3^{x}-9\right)\left(3^{x}-3\right)}{\left(3^{x / 2}-3\right)}\)…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- The largest value of \(r\) for which the region represented by the set \(\{ \omega \, \in \,C|\,\omega \, - \,4\, - \,i|\, \le \,r\} \) is contained in the region represented by the set \((z\, \in \,c/|\,z\, - \,1\,\,\left| \le \right|\,z\, + \,i|),\) is equal toJEE Mains 2015 Hard
- Let \(A=\left[\begin{array}{cc}\frac{1}{\sqrt{10}} & \frac{3}{\sqrt{10}} \\ \frac{-3}{\sqrt{10}} & \frac{1}{\sqrt{10}}\end{array}\right]\) and \(B =\left[\begin{array}{rr}1 & - i \\ 0 & 1\end{array}\right]\), where \(i =\sqrt{-1}\). If \(M = A ^{ T } BA\), then the inverse of the matrix \(AM ^{2023} A ^{ T }\) is \(.........\)JEE Mains 2023 Hard
- Out of \(60 \%\) female and \(40 \%\) male candidates appearing in an exam, \(60\%\) candidates qualify it. The number of females qualifying the exam is twice the number of males qualifying it. A candidate is randomly chosen from the qualified candidates. The probability, that the chosen candidate is a female, is.JEE Mains 2022 Medium
- Let \(p\) and \(q\) be two real numbers such that \(p+q=\) 3 and \(p^{4}+q^{4}=369\). Then \(\left(\frac{1}{p}+\frac{1}{q}\right)^{-2}\) is equal toJEE Mains 2022 Hard
- The sum of absolute maximum and absolute minimum values of the function \(f(x)=\left|2 x^{2}+3 x-2\right|+\sin x \cos x\) in the interval \([0,1]\) isJEE Mains 2022 Hard
- \(\lim _{n \rightarrow \infty} \frac{\left(1^2-1\right)(n-1)+\left(2^2-2\right)(n-2)+\ldots .+\left((n-1)^2-(n-1)\right) \cdot 1}{\left(1^3+2^3+\ldots .+n^3\right)-\left(1^2+2^2+\ldots . .+n^2\right)}\) is equal to:JEE Mains 2024 Hard
More PYQs from JEE Mains
- If an unbiased dice is rolled thrice, then the probability of getting a greater number in the \(i^{\text {th }}\) roll than the number obtained in the \((i-1)^{\text {th }}\) roll, \(i=2,3\), is equal to :JEE Mains 2024 Medium
- The integral \(\int{ \cfrac{d x}{(x+4)^{\frac{8}{7}}(x-3)^{\frac{6}{7}}}}\) is equal to (where \(\mathrm{C}\) is a constant of integration)JEE Mains 2020 Hard
- The minimum area of a triangle formed by any tangent to the ellipse \(\frac{{{x^2}}}{{16}} + \frac{{{y^2}}}{{81}} = 1\) and the co-ordinate axes isJEE Mains 2014 Hard
- Let a line \(L\) pass through the point \(P (2,3,1)\) and be parallel to the line \(x+3 y-2 z-2=0=x-y+2 z\). If the distance of \(L\) from the point \((5,3,8)\) is \(\alpha\), then \(3 \alpha^2\) is equal to \(......\).JEE Mains 2023 Hard
- For the system of linear equations \(a x+y+z=1\), \(x+a y+z=1, x+y+a z=\beta\), which one of the following statements is NOT correct ?JEE Mains 2023 Hard
- Let \(\vec{a}=4 \hat{i}+3 \hat{j}\) and \(\vec{b}=3 \hat{i}-4 \hat{j}+5 \hat{k}\) and \(\vec{c}\) is a vector such that \(\overrightarrow{ c } \cdot(\overrightarrow{ a } \times \overrightarrow{ b })+25=0, \overrightarrow{ c } \cdot(\hat{ i }+\hat{ j }+\hat{ k })=4\) and projection of \(\overrightarrow{ c }\) on \(\overrightarrow{ a }\) is \(1,\) then the projection of \(\overrightarrow{ c }\) on \(\overrightarrow{ b }\) equals:JEE Mains 2023 Hard