JEE Mains · Maths · STD 11 - 7. binomial theoram
The sum of all rational terms in the expansion of \(\left(1+2^{1 / 3}+3^{1 / 2}\right)^6\) is equal to
- A 600
- B 612
- C 622
- D 644
Answer & Solution
Correct Answer
(B) 612
Step-by-step Solution
Detailed explanation
The general term of multinomial expansion is \(\frac{6!}{\alpha!\beta!\gamma!}(1)^\alpha\left(2^{\frac{1}{3}}\right)^\beta\left(3^{\frac{1}{2}}\right)^\gamma\) For terms to be rational \(3 \mid \beta\) and \(2 \mid \gamma\)…
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 the differential equation representing the family of all circles touching \(x-\) axis at the origin is \(\left( {{x^2} - {y^2}} \right)\frac{{dy}}{{dx}} = g\left( x \right)y\) , then \(g(x)\) equalsJEE Mains 2014 Hard
- If the tangent of the curve, \(y=e^{x}\) at a point \(\left( c , e ^{ c }\right)\) and the normal to the parabola, \(y ^{2}=4 x\) at the point \((1,2)\) intersect at the same point on the \(x\)-axis, then the value of \(c\) isJEE Mains 2020 Hard
- The curve satisfying the differential equation, \(ydx-(x + 3y^2 )\, dy = 0\) and passing through the point \((1, 1)\) , also passes through the pointJEE Mains 2017 Hard
- Let \(z_1, z_2\) and \(z_3\) be three complex numbers on the circle \(|z|=1\) with \(\arg \left(z_1\right)=\frac{-\pi}{4}, \arg \left(z_2\right)=0\) and \(\arg \left(z_3\right)=\frac{\pi}{4}\). If \(\left|z_1 \bar{z}_2+z_2 \bar{z}_3+z_3 \bar{z}_1\right|^2=\alpha+\beta \sqrt{2}, \alpha, \beta \in \mathbf{Z}\), then the value of \(\alpha^2+\beta^2\) is :JEE Mains 2025 Medium
- If \(\int_0^{\frac{\pi }{2}} {\frac{{\cot \,x}}{{\cot \,x + \cos ec\,x}}} dx = m\left( {\pi + n} \right)\), then \(m.n\) is equal toJEE Mains 2019 Hard
- Let \(\mathrm{n}\) be a non-negative integer. Then the number of divisors of the form " \(4 \mathrm{n}+1\) " of the number \((10)^{10} \cdot(11)^{11} \cdot(13)^{13}\) is equal to \(....\)JEE Mains 2021 Hard
More PYQs from JEE Mains
- Let \(A =\left\{ z \in C :\left|\frac{ z +1}{ z -1}<1\right|\right\}\) and \(B =\left\{ z \in C : \arg \left(\frac{ z -1}{ z +1}\right)=\frac{2 \pi}{3}\right\}\) Then \(A \cap B\) isJEE Mains 2022 Hard
- The straight lines \(l_1\) and \(l_2\) pass through the origin and trisect the line segment of the line \(L: 9 x+5 y=\) 45 between the axes. If \(m_1\) and \(m_2\) are the slopes of the lines \(l_1\) and \(1_2\),then the point of intersection of the line \(y =\left( m _1+ m _2\right) x\) with \(L\) lies onJEE Mains 2023 Hard
- Let \(y=y(x)\) be the solution of the differential equation \(\left(1+x^2\right) \frac{d y}{d x}+y=e^{\tan ^{-1} x}, y(1)=0\). Then \(\mathrm{y}(0)\) isJEE Mains 2024 Hard
- Let \(A B C\) be an isosceles triangle in which \(A\) is at \((-1,0), \angle A=\frac{2 \pi}{3}, A B=A C\) and \(B\) is on the positive \(\mathrm{x}\)-axis. If \(\mathrm{BC}=4 \sqrt{3}\) and the line \(\mathrm{BC}\) intersects the line \(y=x+3\) at \((\alpha, \beta)\), then \(\frac{\beta^4}{\alpha^2}\) is :JEE Mains 2024 Hard
- \(\left|\frac{120}{\pi^3} \int_0^\pi \frac{x^2 \sin x \cos x}{\sin ^4 x+\cos ^4 x} d x\right|\) is equal to ...........JEE Mains 2024 Hard
- Total numbers of \(3-\)digit numbers that are divisible by 6 and can be formed by using the digits \(1, 2, 3, 4,5\) with repetition, is \(.......\).JEE Mains 2023 Hard