enEnglishguગુજરાતી
JEE Mains · Maths · STD 11 - 7. binomial theoram
If for positive integers \(r> 1, n > 2\), the coefficients of the \((3r)^{th}\) and \((r + 2)^{th}\) powers of \(x\) in the expansion of \(( 1 + x)^{2n}\) are equal, then \(n\) is equal to
- A \(2r+ 1\)
- B \(2r- 1\)
- C \(3r\)
- D \(r+1\)
Answer & Solution
Correct Answer
(A) \(2r+ 1\)
Step-by-step Solution
Detailed explanation
Expansion of \((1+x)^{2 n}\) is \(1+^{2 n} C_{1} x+^{2 n} C_{2} x^{2}\) \(+\ldots \ldots+^{2 n} C_{r} x^{r}+^{2 n} C_{r+1} x^{r+1}+\ldots \ldots+^{2 n} C_{2 n} x^{2 n}\) As given \(^{2n}{{\text{C}}_{r + 2}}{ = ^{2n}}{{\text{C}}_{3r}}\)…
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 the tangent to the circle \(x^{2}+y^{2}=25\) at the point \(R (3,4)\) meet \(x\) -axis and \(y\) -axis at point \(P\) and \(Q\), respectively. If \(r\) is the radius of the circle passing through the origin \(O\) and having centre at the incentre of the triangle \(OPQ ,\) then \(r ^{2}\) is equal toJEE Mains 2021 Hard
- If the ratio of the fifth term from the begining to the fifth term from the end in the expansion of \(\left(\sqrt[4]{2}+\frac{1}{\sqrt[4]{3}}\right)^n\) is \(\sqrt{6}: 1\), then the third term from the beginning is:JEE Mains 2023 Hard
- Let \(y=y(x)\) be the solution of the differential equation \(\frac{d y}{d x}=(y+1)\left((y+1) e^{x^{2} / 2}-x\right), y(2)=0\) then \(y'(1)\) equal to . . . .JEE Mains 2021 Hard
- Let \(\mathrm{A}\) be a fixed point \((0,6)\) and \(\mathrm{B}\) be a moving point \((2 \mathrm{t}, 0)\). Let \(\mathrm{M}\) be the mid-point of \(\mathrm{AB}\) and the perpendicular bisector of \(\mathrm{AB}\) meets the \(\mathrm{y}\)-axis at \(\mathrm{C}\). The locus of the mid-point \(\mathrm{P}\) of \(\mathrm{MC}\) is :JEE Mains 2021 Hard
- The value of \( \text{cosec}10^{\circ}-\sqrt{3}\ \text{sec}10^{\circ} \) is equal to:JEE Mains 2026 Hard
- Let the vectors \(\overrightarrow{ u }_1=\hat{ i }+\hat{ j }+ a \hat{ k }, \overrightarrow{ u }_2=\hat{ i }+ b \hat{ j }+\hat{ k }\) and \(\overrightarrow{ u }_3=c \hat{ i }+\hat{ j }+\hat{ k }\) be coplanar. If the vectors \(\overrightarrow{ v }_1=(a+b) \hat{i}+c \hat{j}+c \hat{k}, \quad \overrightarrow{ v }_2=a \hat{i}+(b+c) \hat{j}+a \hat{k} \quad\) and \(\overrightarrow{ v }_3=b \hat{ i }+ b \hat{ j }+( c + a ) \hat{ k }\) are also coplanar, then \(6( a +\) \(b + c )\) is equal to \(..............\).JEE Mains 2023 Hard
More PYQs from JEE Mains
- A variable line \(\mathrm{L}\) passes through the point \((3,5)\) and intersects the positive coordinate axes at the points \(\mathrm{A}\) and \(\mathrm{B}\). The minimum area of the triangle \(\mathrm{OAB}\), where \(\mathrm{O}\) is the origin, is :JEE Mains 2024 Medium
- Let \(S=\{1,2,3,4,5,6\} .\) Then the probability that a randomly chosen onto function \(\mathrm{g}\) from \(\mathrm{S}\) to \(\mathrm{S}\) satisfies \(g(3)=2 g(1)\) is :JEE Mains 2021 Medium
- If \(S\) is the set of distinct values of \('b'\) for which the following system of linear equations \(x + y + z = 1;x + ay + z = 1;ax + by + z = 0\) has no solution , then \(S\) is :JEE Mains 2017 Hard
- If \(\int \sin ^{-1}\left(\sqrt{\frac{x}{1+x}}\right) d x=A(x) \tan ^{-1}(\sqrt{x})+B(x)+C\) where \(C\) is a constant of integration, then the ordered pair \(( A ( x ), B ( x ))\) can beJEE Mains 2020 Hard
- Let \(\mathrm{A}=\left[\begin{array}{ll}1 & 2 \\ 0 & 1\end{array}\right]\) and \(\mathrm{B}=\mathrm{I}+\operatorname{adj}(\mathrm{A})+(\operatorname{adj} \mathrm{A})^2+\ldots+\) \((\operatorname{adj} \mathrm{A})^{10}\). Then, the sum of all the elements of the matrix \(B\) is :JEE Mains 2024 Medium
- The value of \(\int\limits_{ - \pi /2}^{\pi /2} {\frac{{dx}}{{\left[ x \right] + \left[ {\sin \,x} \right] + 4}}} \) where \([t]\) denotes the greatest integer less than or equal to \(t\), isJEE Mains 2019 Hard