enEnglishguગુજરાતી
JEE Mains · Maths · STD 12 - 6. Application of derivatives
The maximum value of the term independent of \('t'\) in the expansion of \(\left( tx ^{\frac{1}{5}}+\frac{(1- x )^{\frac{1}{10}}}{ t }\right)^{10}\) where \(x \in(0,1)\) is
- A \(\frac{10 !}{\sqrt{3}(5 !)^{2}}\)
- B \(\frac{2.10 !}{3 \sqrt{3}(5 !)^{2}}\)
- C \(\frac{2.10 !}{3(5 !)^{2}}\)
- D \(\frac{10 !}{3(5 !)^{2}}\)
Answer & Solution
Correct Answer
(B) \(\frac{2.10 !}{3 \sqrt{3}(5 !)^{2}}\)
Step-by-step Solution
Detailed explanation
Term independent of \(t\) will be the middle term due to exect same magnitude but opposite sign powers of t in the binomial expression given So \(T _{6}={ }^{10} C _{5}\left( tx ^{2} 5\right)^{5}\left(\frac{(1- x )^{\frac{1}{10}}}{ t }\right)^{5}\)…
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
- Bag \(A\) contains \(2\) white, \(1\) black and \(3\) red balls and bag \(B\) contains \(3\) black, \(2\) red and \(n\) white balls. One bag is chosen at random and \(2\) balls drawn from it at random, are found to be \(1\) red and \(1\) black. If the probability that both balls come from Bag \(A\) is \(\frac{6}{11}\), then \(n\) is equal toJEE Mains 2022 Hard
- The sum \(\sum\limits_{k=1}^{20}(1+2+3+\ldots+k)\) isJEE Mains 2020 Medium
- Let \(0 \leq \mathrm{r} \leq \mathrm{n}\). If \({ }^{\mathrm{n}+1} \mathrm{C}_{\mathrm{r}+1}:{ }^{\mathrm{n}} \mathrm{C}_{\mathrm{r}}:{ }^{\mathrm{n}-1} \mathrm{C}_{\mathrm{r}-1}=55: 35: 21\), then \(2 n+5 r\) is equal to :JEE Mains 2024 Hard
- \(f(x)=4 \log _{e}(x-1)-2 x^{2}+4 x+5, x>1\), which one of the following is NOT correct?JEE Mains 2022 Hard
- The area (in sq. units) of the region \(\left\{(\mathrm{x}, \mathrm{y}) \in \mathrm{R}^{2}: \mathrm{x}^{2} \leq \mathrm{y} \leq 3-2 \mathrm{x}\right\},\) isJEE Mains 2020 Hard
- If the term independent of \(x\) in the expansion of \(\left(\sqrt{\mathrm{ax}}{ }^2+\frac{1}{2 \mathrm{x}^3}\right)^{10}\) is 105 , then \(\mathrm{a}^2\) is equal to :JEE Mains 2024 Medium
More PYQs from JEE Mains
- If \(A\, = \,\left[ {\begin{array}{*{20}{c}}
1&2&x\\
3&{ - 1}&2
\end{array}} \right]\) and \(B\, = \,\left[ {\begin{array}{*{20}{c}}
y\\
x\\
1
\end{array}} \right]\) be such that \(AB\, = \,\left[ {\begin{array}{*{20}{c}}
6\\
8
\end{array}} \right],\) thenJEE Mains 2014 Hard - If \((20)^{19}+2(21)(20)^{18}+3(21)^2(20)^{17}+\ldots \ldots\). \(+20(21)^{19}= k (20)^{19}\), then \(k\) is equal toJEE Mains 2023 Hard
- The value of \(\int \limits_{-\pi / 2}^{\pi / 2} \frac{1}{1+ e ^{\sin x}} d x\)JEE Mains 2020 Medium
- Let \(P\) be the plane passing through the points \((5,3\), \(0),(13,3,-2)\) and \((1,6,2)\). For \(\alpha \in N\), if the distances of the points \(A (3,4, \alpha)\) and \(B (2, \alpha\), a) from the plane \(P\) are \(2\) and \(3\) respectively, then the positive value of a isJEE Mains 2023 Hard
- The mean and variance of \(7\) observations are \(8\) and \(16\) respectively. If one observation \(14\) is omitted a and \(b\) are respectively mean and variance of remaining \(6\) observation, then \(a+3 b-5\) is equal to \(..........\).JEE Mains 2023 Hard
- The integral \(\int\limits_0^{\frac{1}{2}} {\frac{{\ln \,\left( {1 + 2x} \right)}}{{1 + 4{x^2}}}} dx\) , equalsJEE Mains 2014 Hard