JEE Mains · Maths · STD 11 - 7. binomial theoram
The term independent of \(x\) in the expansion of \(\left(\frac{(x+1)}{\left(x^{2 / 3}+1-x^{1 / 3}\right)}-\frac{(x+1)}{\left(x-x^{1 / 2}\right)}\right)^{10}, x\gt1\) is:
- A \(210\)
- B \(150\)
- C \(240\)
- D \(120\)
Answer & Solution
Correct Answer
(A) \(210\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \left(\frac{(x+1)}{\left(x^{\frac{2}{3}}+1-x^{\frac{1}{3}}\right)}-\frac{(x-1)}{\left(x-x^{\frac{1}{2}}\right)}\right)^{10} \\ & =\left(\left(x^{\frac{1}{3}}+1\right)-\left(\frac{\sqrt{x}+1}{\sqrt{x}}\right)\right)^{10} \\ &…
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
- If \(n\) be odd or even, then the sum of \(n\) terms of the series \(1 - 2 + \) \(3 - \)\(4 + 5 - 6 + ......\) will beJEE Mains 2022 Easy
- For \(a>0,\) let the curves \(C_{1}: y^{2}=a x\) and \(\mathrm{C}_{2}: \mathrm{x}^{2}=\) ay intersect at origin \(\mathrm{O}\) and a point \(\mathrm{P}\) Let the line \(\mathrm{x}=\mathrm{b}(0<\mathrm{b}<\mathrm{a})\) intersect the chord \(OP\) and the \(\mathrm{x}\) -axis at points \(\mathrm{Q}\) and \(\mathrm{R}\), respectively. If the line \(x=b\) bisects the area bounded by the curves, \(\mathrm{C}_{1}\) and \(\mathrm{C}_{2},\) and the area of \(\Delta \mathrm{OQR}=\frac{1}{2},\) then '\(a\)' satisfies the equationJEE Mains 2020 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 sum \(\sum\limits_{r = 1}^{10} {\left( {{r^2} + 1} \right)} \times \left( {r!} \right)\) is equal toJEE Mains 2016 Hard
- The integral \(\int {{{\sec }^{2/3}}\,x\,\cos e{c^{4/3}}} x\,dx\) is equal to : (Here \(C\) is a constant of integration)JEE Mains 2019 Hard
- Let \(f ( x )=\min \{1,1+ x \sin x \}, 0 \leq x \leq 2 \pi\). If \(m\) is the number of points, where \(f\) is not differentiable and \(n\) is the number of points, where \(f\) is not continuous, then the ordered pair \(( m , n )\) is equal toJEE Mains 2022 Medium
More PYQs from JEE Mains
- The mean and the standard deviation \((s.d.)\) of five observations are \(9\) and \(0,\) respectively. If one of the observations is changed such that the mean of the new set of five observations becomes \(10,\) then their \(s.d.\) is?JEE Mains 2018 Hard
- If \(A\) and \(B\) are two events such that \(P(A \cap B)=0.1\), and \(P(A \mid B)\) and \(P(B \mid A)\) are the roots of the equation \(12 x^2-7 x+1=0\), then the value of \(\frac{\mathrm{P}(\overline{\mathrm{A}} \cup \overline{\mathrm{B}})}{\mathrm{P}(\overline{\mathrm{A}} \cap \overline{\mathrm{B}})}\) is :JEE Mains 2025 Hard
- Let \(y(x)\) be the solution of the differential equation \(\left( {xlogx} \right)\frac{{dy}}{{dx}} + y = 2xlogx,\left( {x \ge 1} \right)\) . Then \(y(e) \) is equal to : \([y(1)=0]\)JEE Mains 2015 Hard
- In a box, there are \(20\) cards, out of which \(10\) are lebelled as \(\mathrm{A}\) and the remaining \(10\) are labelled as \(B\). Cards are drawn at random, one after the other and with replacement, till a second \(A-\)card is obtained. The probability that the second \(A-\)card appears before the third \(B-\)card isJEE Mains 2020 Hard
- \(\smallint \frac{{dx}}{{{x^2}{{\left( {{x^4} + 1} \right)}^{\frac{3}{4}}}}} = \)JEE Mains 2015 Hard
- Let \(r\) be the radius of the circle, which touches x -axis at point \((\mathrm{a}, 0), \mathrm{a} \lt 0\) and the parabola \(\mathrm{y}^2=9 \mathrm{x}\) at the point \((4,6)\). Then \(r\) is equal to ________JEE Mains 2025 Medium