JEE Mains · Maths · STD 11 - 7. binomial theoram
The coefficient of \(x^{18}\) in the expansion of \(\left(x^4-\frac{1}{x^3}\right)^{15}\) is \(...........\).
- A \(5004\)
- B \(5003\)
- C \(5002\)
- D \(5005\)
Answer & Solution
Correct Answer
(D) \(5005\)
Step-by-step Solution
Detailed explanation
\(\left(x^4-\frac{1}{x^3}\right)^{15}\) \(T_{r+1}={ }^{15} C_r\left(x^4\right)^{15-r}\left(\frac{-1}{x^3}\right)^r\) \(60-7 r=18\) \(r=6\) Hence coeff. of \(x^{18}={ }^{15} C _6=5005\)
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 minimum number of elements that must be added to the relation \(R =\{( a , b ),( b , c )\}\) on the set \(\{a, b, c\}\) so that it becomes symmetric and transitive is:JEE Mains 2023 Hard
- Let \(R =\{( P , Q ) \mid P\) and \(Q\) are at the same distance from the origin \(\}\) be a relation, then the equivalence class of \((1,-1)\) is the setJEE Mains 2021 Medium
- The equation of a tangent to the parabola, \(x^2 = 8y,\) which makes an angle \(\theta \) with the positive direction of \(x-\) axis, isJEE Mains 2019 Hard
- Let the observations \(\mathrm{x}_{\mathrm{i}}(1 \leq \mathrm{i} \leq 10)\) satisfy the equations, \(\sum\limits_{i=1}^{10}\left(x_{i}-5\right)=10\) and \(\sum\limits_{i=1}^{10}\left(x_{i}-5\right)^{2}=40\) If \(\mu\) and \(\lambda\) are the mean and the variance of the observations, \(\mathrm{x}_{1}-3, \mathrm{x}_{2}-3, \ldots ., \mathrm{x}_{10}-3,\) then the ordered pair \((\mu, \lambda)\) is equal to :JEE Mains 2020 Hard
- Let \(f:(0, \infty) \rightarrow \mathbf{R}\) be a function which is differentiable at all points of its domain and satisfies the condition \(x^2 f^{\prime}(x)=2 x f(x)+3\), with \(f(1)=4\). Then \(2 f(2)\) is equal to :JEE Mains 2025 Medium
- Let a variable line passing through the centre of the circle \(x^2+y^2-16 x-4 y=0\), meet the positive co-ordinate axes at the point \(\mathrm{A}\) and \(\mathrm{B}\). Then the minimum value of \(\mathrm{OA}+\mathrm{OB}\), where \(\mathrm{O}\) is the origin, is equal toJEE Mains 2024 Hard
More PYQs from JEE Mains
- If the angle of intersection at a point where the two circles with radii \(5\, cm\) and \(12\, cm\) intersect is \(90^o\), then the length (in \(cm\)) of their common chord isJEE Mains 2019 Hard
- The mean and standard deviation of \(15\) observations are found to be \(8\) and \(3\) respectively. On rechecking it was found that, in the observations, \(20\) was misread as \(5\) . Then, the correct variance is equal to......JEE Mains 2022 Medium
- The term independent of \(x\) in the binomial expansion of \(\left( {1 - \frac{1}{x} + 3{x^5}} \right){\left( {2{x^2} - \frac{1}{x}} \right)^8}\) isJEE Mains 2015 Hard
- Let the lines \(l_1: \frac{ x +5}{3}=\frac{ y +4}{1}=\frac{ z -\alpha}{-2}\) and \(l_2: 3 x +\) \(2 y+z-2=0=x-3 y+2 z-13\) be coplanar. If the point \(P ( a , b , c )\) on \(l_1\) is nearest to the point \(Q (-\) \(4,-3,2)\), then \(|a|+|b|+|c|\) is equal toJEE Mains 2023 Hard
- Sum of squares of modulus of all the complex numbers \(z\) satisfying \(\bar{z}=i z^{2}+z^{2}-z\) is equal toJEE Mains 2022 Hard
- If \(f(t)=\int_0^\pi \frac{2 x d x}{1-\cos ^2 \sin ^2 x}, 0 < t < \pi\), then the value of \(\int_0^{\frac{\pi}{2}} \frac{\pi^2 d t}{f(t)}\) equals ..........JEE Mains 2024 Hard