JEE Mains · Maths · STD 11 - 7. binomial theoram
The coefficient of \(x^5\) in the expansion of \(\left(2 x^3-\frac{1}{3 x^2}\right)^5\) is
- A \(8\)
- B \(9\)
- C \(\frac{80}{9}\)
- D \(\frac{26}{3}\)
Answer & Solution
Correct Answer
(C) \(\frac{80}{9}\)
Step-by-step Solution
Detailed explanation
\(\left(2 x^3-\frac{1}{3 x^2}\right)^5\) \(T_{r+1}={ }^5 C_r\left(2 x^3\right)^{5-r}\left(\frac{-1}{3 x^2}\right)^r={ }^5 C_r \frac{(2)^{5-r}}{(-3)^r}(x)^{15-5 r}\) \(\therefore 15-5 r =5\) \(\therefore r =2\) \(T_3=10\left(\frac{8}{9}\right) x^5\) So, coefficient is…
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
- Let \(k\) and \(m\) be positive real numbers such that the function \(\quad f ( x )=\left\{\begin{array}{cc}3 x ^2+ k \sqrt{ x +1}, & 0< x <1 \\ mx ^2+ k ^2, & x \geq 1\end{array}\right.\) is differentiable for all \(x > 0\). Then \(\frac{8 f^{\prime}(8)}{f^{\prime}\left(\frac{1}{8}\right)}\) is equal to \(.............\).JEE Mains 2023 Hard
- The value of the integral \(\int \limits_{-\pi / 2}^{\pi / 2} \frac{d x}{\left(1+e^{x}\right)\left(\sin ^{6} x+\cos ^{6} x\right)}\) is equal toJEE Mains 2022 Hard
- Let \(P\) be the point of intersection of the line \(\frac{x+3}{3}=\frac{y+2}{1}=\frac{1-z}{2}\) and the plane \(x + y + z =2\) If the distance of the point \(P\) from the plane \(3 x-4 y+12 z=32\) is \(q\), then \(q\) and \(2 q\) are the roots of the equationJEE Mains 2023 Hard
- The angle of elevation of the top of a vertical tower from a point \(P\) on the horizontal ground was observed to be \(\alpha \). After moving a distance \(2\, metres\) from \(P\) towards the foot of the tower, the angle of elevation changes to \(\beta \). Then the height (in metres) of the tower isJEE Mains 2014 Hard
- Given : \(f(x)=\left\{\begin{array}{ccc}{x} & {,} & {0 \leq x < \frac{1}{2}} \\ {\frac{1}{2}} & {,} & {x=\frac{1}{2}} \\ {1-x} & {,} & {\frac{1}{2} < x \leq 1}\end{array}\right.\) and \(g(x)=\left(x-\frac{1}{2}\right)^{2}, x \in R .\) Then the area (in sq. units) of the region bounded by the curves, \(y=f(x)\) and \(y=g(x)\) between the lines, \(2 \mathrm{x}=1\) and \(2 \mathrm{x}=\sqrt{3},\) isJEE Mains 2020 Hard
- The remainder, when \(7^{103}\) is divided by 23 , is equal to :JEE Mains 2025 Medium
More PYQs from JEE Mains
- The tangents at the point \(A (1,3)\) and \(B (1,-1)\) on the parabola \(y ^{2}-2 x -2 y =1\) meet at the point \(P\). Then the area (in unit \({ }^{2}\) ) of the triangle \(PAB\) is :-JEE Mains 2022 Hard
- The number of elements in the set \(S =\left\{\theta \in[0,2 \pi]: 3 \cos ^4 \theta-5 \cos ^2 \theta-2 \sin ^6 \theta+2=0\right\}\) is \(...........\).JEE Mains 2023 Hard
- If \(S = \left\{\theta \in [-\pi, \pi] : \cos\theta \cos\dfrac{5\theta}{2} = \cos 7\theta \cos\dfrac{7\theta}{2}\right\}\), then \(n(S)\) is equal to _______.JEE Mains 2026 Hard
- Let \(A=\{z \in C: 1 \leq 1 z-(1+i) \leq 2\}\) and \(B=\{z \in A:|z-(1-i)|=1\}\). Then, \(B\)JEE Mains 2022 Hard
- Let \(y=y(x)\) be the solution of the differential equation \(d y=e^{a x+y} d x ; \alpha \in N\). If \(y\left(\log _{e} 2\right)=\log _{e} 2\) and \(y(0)=\log _{e}\left(\frac{1}{2}\right)\), then the value of \(\alpha\) is equal to \(.....\)JEE Mains 2021 Medium
- If equation of the plane that contains the point \((-2,3,5)\) and is perpendicular to each of the planes \(2 x+4 y+5 z=8\) and \(3 x-2 y+3 z=5\) is \(\alpha x+\beta y+\gamma z+97=0\) then \(\alpha+\beta+\gamma=...........\).JEE Mains 2023 Hard