JEE Mains · Maths · STD 11 - 7. binomial theoram
The number of rational terms in the binomial expansion of \(\left(4^{\frac{1}{4}}+5^{\frac{1}{6}}\right)^{120}\) is \(....\)
- A \(120\)
- B \(21\)
- C \(41\)
- D \(61\)
Answer & Solution
Correct Answer
(B) \(21\)
Step-by-step Solution
Detailed explanation
\(\left(4^{1 / 4}+5^{1 / 6}\right)^{120}\) \(T_{r+1}={ }^{120} C_{r}\left(2^{1 / 2}\right)^{120-r}(5)^{r / 6}\) for rational terms \(\mathrm{r}=6 \lambda\,\,\,\, 0 \leq \mathrm{r} \leq 120\) so total no of forms are \(21\)
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 \(g \) is the inverse of a function \(f \) and \(f'\left( x \right) = \frac{1}{{1 + {x^5}}}\) thne \(g'\left( x \right)\) is equal to :JEE Mains 2014 Medium
- The coefficient of \(x^5\) in the expansion of \(\left(2 x^3-\frac{1}{3 x^2}\right)^5\) isJEE Mains 2023 Medium
- Three persons enter in a lift at the ground floor. The lift will go up to \(10^{\text {th }}\) floor. The number of ways, in which the three persons can exit the lift at three different floors, if the lift does not stop at first, second and third floors, is equal to ___ .JEE Mains 2026 Hard
- If \(\int \operatorname{cosec}^5 x d x=\alpha \cot x \operatorname{cosec} x\left(\operatorname{cosec}^2 x+\frac{3}{2}\right)+\beta \log _e\left|\tan \frac{x}{2}\right|+C\) where \(\alpha, \beta \in \mathbb{R}\) and \(\mathrm{C}\) is constant of integration , then the value of \(8(\alpha+\beta)\) equals ...........JEE Mains 2024 Hard
- If in a parallelogram \(ABDC\), the coordinates of \(A, B\) and \(C\) are respectively \((1, 2), (3, 4)\) and \((2, 5)\), then the equation of the diagonal \(AD\) isJEE Mains 2019 Hard
- A box contains \(5\) blue, \(6\) yellow and \(4\) red balls. The number of ways, of drawing \(8\) balls containing at least two balls of each colour, is :JEE Mains 2026 Easy
More PYQs from JEE Mains
- If the system of equations \(\alpha x+y+z=5, x+2 y+\) \(3 z=4, x+3 y+5 z=\beta\) has infinitely many solutions, then the ordered pair \((\alpha, \beta)\) is equal to:JEE Mains 2022 Medium
- The maximum area (in sq. units) of a rectangle having its base on the \(x-\) axis and its other two vertices on the parabola, \(y = 12 -x^2\) such that the rectangle lies inside the parabola, isJEE Mains 2019 Hard
- The line \(l_1\) passes through the point \((2,6,2)\) and is perpendicular to the plane \(2 x+y-2 z=10\). Then the shortest distance between the line \(l_1\) and the line \(\frac{ x +1}{2}=\frac{ y +4}{-3}=\frac{ z }{2}\) is :JEE Mains 2023 Hard
- Let \(p , q \in R\) and \((1-\sqrt{3} i )^{200}=2^{199}( p + iq )\), \(i =\sqrt{-1}\) Then \(p + q + q ^2\) and \(p - q + q ^2\) are roots of the equation.JEE Mains 2023 Hard
- Let \(S_{ k }=\frac{1+2+\ldots .+ K }{ K }\) and \(\sum_{j=1}^n S_j^2=\frac{n}{A}\left( Bn ^2+ Cn + D \right)\), where \(A , B , C , D \in N\) and \(A\) has least value. ThenJEE Mains 2023 Hard
- The total number of \(3-digit\) numbers, whose sum of digits is \(10,\) isJEE Mains 2020 Hard