JEE Mains · Maths · STD 11 - 7. binomial theoram
If \(n\) is the number of irrational terms in the expansion of \(\left(3^{1 / 4}+5^{1 / 8}\right)^{60},\) then \(( n -1)\) is divisible by
- A \(26\)
- B \(30\)
- C \(8\)
- D \(7\)
Answer & Solution
Correct Answer
(A) \(26\)
Step-by-step Solution
Detailed explanation
\(\left(3^{1 / 4}+5^{1 / 8}\right)^{60}\) \({ }^{60} C _{ r }\left(3^{1 / 4}\right)^{60- r } \cdot\left(5^{1 / 8}\right)^{ r }\) \({ }^{60} C _{ r }(3)^{\frac{60- r }{4}} .5^{\frac{ r }{8}}\) For rational terms. \(\frac{r}{8}=k ; \quad 0 \leq r \leq 60\) \(0 \leq 8 k \leq 60\)…
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 product of all possible values of \(\alpha\), for which \(\displaystyle\lim_{x \to 0}\left(\dfrac{1 - \cos(\alpha x)\cos((\alpha+1)x)\cos((\alpha+2)x)}{\sin^2((\alpha+1)x)}\right) = 2\), is:JEE Mains 2026 Hard
- Let the abscissae of the two points \(P\) and \(Q\) on a circle be the roots of \(x^{2}-4 x-6=0\) and the ordinates of \(P\) and \(Q\) be the roots of \(y ^{2}+2 y -7=\) 0.If \(PQ\) is a diameter of the circle \(x ^{2}+ y ^{2}+2 ax +\) \(2 by + c =0\), then the value of \((a+b-c)\) is.JEE Mains 2022 Hard
- An ellipse has its center at (1,-2), one focus at (3,-2) and one vertex at \((5,-2)\). Then the length of its latus rectum is :JEE Mains 2026 Medium
- The locus of the mid points of the chords of the hyperbola \(\mathrm{x}^{2}-\mathrm{y}^{2}=4\), which touch the parabola \(\mathrm{y}^{2}=8 \mathrm{x}\), is :JEE Mains 2021 Hard
- Define a relation \(R\) over a class of \(n \times n\) real matrices \(A\) and \(B\) as \("ARB\) iff there exists a non-singular matrix \(P\) such that \(PAP ^{-1}= B "\) Then which of the following is true?JEE Mains 2021 Hard
- Suppose that \(20\) pillars of the same height have been crected along the boundary of a circular stadium. If the top of each pillar has been connected by beams with the top of all its non-adjacent pillars, then the total number of beams isJEE Mains 2019 Hard
More PYQs from JEE Mains
- Let \(C\) be the circle in the complex plane with centre \(z_0=\frac{1}{2}(1+3 i)\) and radius \(r=1\). Let \(z_1=1+\) \(i\) and the complex number \(z_2\) be outside the circle \(C\) such that \(\left|z_1-z_0\right|\left|z_2-z_0\right|=1\). If \(z_0, z_1\) and \(z_2\) are collinear, then the smaller value of \(\left|z_2\right|^2\) is equal to \(.............\).JEE Mains 2023 Hard
- Let \(\mathrm{y}=\mathrm{y}(\mathrm{x})\) be a solution of the differential equation, \(\sqrt{1-\mathrm{x}^{2}} \frac{\mathrm{dy}}{\mathrm{dx}}+\sqrt{1-\mathrm{y}^{2}}=0,|\mathrm{x}|<1\) If \(\mathrm{y}\left(\frac{1}{2}\right)=\frac{\sqrt{3}}{2},\) then \(\mathrm{y}\left(\frac{-1}{\sqrt{2}}\right)\) is equal toJEE Mains 2020 Hard
- A random variable \(X\) has the following probability distribution
Then \(\mathrm{P}(\mathrm{X}> 2)\) is equal to\(X\) \(1\) \(2\) \(3\) \(4\) \(5\) \(P(X)\) \(K^2\) \(2K\) \(K\) \(2K\) \(5K^2\) JEE Mains 2020 Hard - The largest value of \(a,\) for which the perpendicular distance of the plane containing the lines \(\vec{r}=(\hat{i}+\hat{j})+\lambda(\hat{i}+a \hat{j}-\hat{k})\) and \(\vec{r}=(\hat{i}+\hat{j})+\mu(-\hat{i}+\hat{j}-a \hat{k})\) from the point \((2,1,4)\) is \(\sqrt{3}\), is\(...\)JEE Mains 2022 Hard
- If the system of equations \(2 x+y-z=5\) \(2 x-5 y+\lambda z=\mu\) \(x+2 y-5 z=7\) has infinitely many solutions, then \((\lambda+\mu)^2+(\lambda-\mu)^2\) is equal toJEE Mains 2023 Hard
- If \(2x = {y^{\frac{1}{5}}} + {y^{ - \frac{1}{5}}}\) and \((x^2 -1) \frac{{{d^2}y}}{{d{x^2}}} + \lambda x\frac{{dy}}{{dx}} + ky = 0\) , then \( \lambda + k\) is equal toJEE Mains 2017 Hard