JEE Mains · Maths · STD 11 - 7. binomial theoram
The number of integral terms in the expansion of \(\left(3^{\frac{1}{2}}+5^{\frac{1}{4}}\right)^{680}\) is equal to
- A \(170\)
- B \(171\)
- C \(172\)
- D \(173\)
Answer & Solution
Correct Answer
(B) \(171\)
Step-by-step Solution
Detailed explanation
The number of integral term in the expression of \(\left(3^{\frac{1}{2}}+5^{\frac{1}{4}}\right)^{680}\) is equal to General term \(={ }^{680} C _{ r }\left(3^{\frac{1}{2}}\right)^{680- r }\left(5^{\frac{1}{4}}\right)^{ r }\)…
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 length of the chord of the ellipse \(\frac{x^2}{25}+\frac{y^2}{16}=1\), whose mid point is \(\left(1, \frac{2}{5}\right)\), is equal to :JEE Mains 2024 Hard
- If the length of the perpendicular drawn from the point \(P ( a , 4,2), a >0\) on the line \(\frac{x+1}{2}=\frac{y-3}{3}=\frac{z-1}{-1}\) is \(2 \sqrt{6}\) units and \(Q \left(\alpha_{1}, \alpha_{2}, \alpha_{3}\right)\) is the image of the point \(P\) in this line, then \(a+\sum_{i=1}^{3} \alpha_{i}\) is equal to.JEE Mains 2022 Hard
- Out of \(11\) consecutive natural numbers if three numbers are selected at random (without repetition), then the probability that they are in \(A.P.\) with positive common difference, isJEE Mains 2020 Hard
- A man \(X\) has \(7\) friends, \(4\) of them are ladies and \(3\) are men. His wife \(Y\) also has \(7\) friends, \(3\) of them are ladies and \(4\) are men. Assume \(X\) and \(Y\) have no comman friends. Then the total number of ways in which \(X\) and \(Y\) together can throw a party inviting \(3\) ladies and \(3\) men, so that \(3\) friends of each of \(X\) and \(Y\) are in this party is :JEE Mains 2017 Hard
- Let \(y=y(x)\) be the solution of the differential equation \(d y=e^{a x+y} d x ; \alpha \in N\). If \(y\left(\log _{e} 2\right)=\log _{e} 2\) and \(y(0)=\log _{e}\left(\frac{1}{2}\right)\), then the value of \(\alpha\) is equal to \(.....\)JEE Mains 2021 Medium
- Let \(\vec{a}=6 \hat{i}+9 \hat{j}+12 \hat{k}, \vec{b}=\alpha \hat{i}+11 \hat{j}-2 \hat{k}\) and \(\vec{c}\) be vectors such that \(\vec{a} \times \vec{c}=\vec{a} \times \vec{b}\). If \(\vec{a} \cdot \vec{c}=-12\), \(\vec{c} .(\hat{i}-2 \hat{j}+\hat{k})=5\), then \(\vec{c} \cdot(\hat{i}+\hat{j}+\hat{k})\) is equal to \(.............\).JEE Mains 2023 Hard
More PYQs from JEE Mains
- The angle of elevation of the top of a hill from a point on the horizontal plane passing through the foot of the hill is found to be \(45^{\circ} .\) After walking a distance of \(80\) meters towards the top, up a slope inclined at an angle of \(30^{\circ}\) to the horizontal plane, the angle of elevation of the top of the hill becomes \(75^{\circ} .\) Then the height of the hill (in meters) isJEE Mains 2020 Hard
- If \(e ^{\left(\cos ^{2} x+\cos ^{4} x+\cos ^{6} x+\ldots \ldots \infty\right) \log _{e} 2}\) satisfies the equation \(t ^{2}-9 t +8=0,\) then the value of \(\frac{2 \sin x}{\sin x+\sqrt{3} \cos x}\left(0 < x < \frac{\pi}{2}\right)\) isJEE Mains 2021 Hard
- Let \([\cdot]\) denote the greatest integer function. Then the value of \(\displaystyle\int_0^3 \left(\dfrac{e^x + e^{-x}}{[x]!}\right) dx\) is :JEE Mains 2026 Medium
- The normal to the curve \(y\left( {x - 2} \right)\left( {x - 3} \right) = x + 6\) at the point where the curve intersects the \(y - \)axis passes through the point :JEE Mains 2017 Medium
- Let \(\vec{p}=2 \hat{i}+3 \hat{j}+k\) and \(\vec{q}=\hat{i}+2 \hat{j}+k\) be two vectors. If \(a\) vector \(\vec{r}=(a \hat{i}+\beta \hat{j}+\gamma k)\) is perpendicular to each of the vectors \((\vec{p}+\bar{q})\) and \((\vec{p}-\vec{q})\), and \(|\vec{r}|=\sqrt{3}\), then \(|\alpha|+|\beta|+|\gamma|\) is equal to \(.....\)JEE Mains 2021 Hard
- Coasider a cuboid of sides \(2 x , 4 x\) and \(5 x\) and a closed hemisphere of radius \(r\). If the sum of their surface areas is a constant \(k\), then the ratio \(x: r\), for which the sum of their volumes is maximum, isJEE Mains 2022 Hard