JEE Mains · Maths · STD 11 - 7. binomial theoram
If \( (\frac{1}{^{15}C_{0}}+\frac{1}{^{15}C_{1}})(\frac{1}{^{15}C_{1}}+\frac{1}{^{15}C_{2}})...(\frac{1}{^{15}C_{12}}+\frac{1}{^{15}C_{13}}) = \frac{a^{13}}{^{14}C_{0}^{14}C_{1}...^{14}C_{12}} \) then 30a is equal to :
- A 30
- B 32
- C 60
- D 15
Answer & Solution
Correct Answer
(B) 32
Step-by-step Solution
Detailed explanation
\( \prod_{r=0}^{12}(\frac{1}{^{15}C_{r}}+\frac{1}{^{15}C_{r+1}})=\prod_{r=0}^{12}\frac{\frac{16}{r+1}^{15}C_{r}}{^{15}C_{r}^{15}C_{r+1}} \) \( =\prod_{r=0}^{12}\frac{16}{(r+1)\cdot\frac{15}{r+1}^{14}C_{r}}=\prod_{r=0}^{12}\frac{(\frac{16}{15})}{^{14}C_{r}} \)…
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
- Two adjacent sides of a parallelogram PQRS are given by \(\vec{PQ} = \hat{j} + \hat{k}\) and \(\vec{PS} = \hat{i} - \hat{j}\). If the side PS is rotated about the point P by an acute angle \(\alpha\) in the plane of the parallelogram so that it becomes perpendicular to the side PQ, then \(\sin^2\left(\dfrac{5\alpha}{2}\right) - \sin^2\left(\dfrac{\alpha}{2}\right)\) is equal to:JEE Mains 2026 Hard
- Let \(a, b \in R\). If the mirror image of the point \(P( a ,6,9)\) with respect to the line \(\frac{x-3}{7}=\frac{y-2}{5}=\frac{z-1}{-9}\) is \((20, b,-a-9),\) then \(|a+b|\) is equal to :JEE Mains 2021 Hard
- The area bounded by the curves \(y=\left|x^{2}-1\right|\) and \(y=1\) is.JEE Mains 2022 Medium
- For \(x \in R\) , \(f\left( x \right) = \left| {\log 2 - \sin x} \right|\) and \(g\left( x \right) = f\left( {f\left( x \right)} \right)\) then .. .JEE Mains 2016 Hard
- Let \(\omega=z \bar{z}+k_1 z+k_2 i z+\lambda(1+i), k_1, k_2 \in R\). Let \(\operatorname{Re}(\omega)=0\) be the circle \(C\) of radius 1 in the first quadrant touching the line \(y=1\) and the \(y\)-axis. If the curve \(\operatorname{Im}(\omega)=0\) intersects \(C\) at \(A\) and \(B\), then \(30(A B)^2\) is equal to \(.......\).JEE Mains 2023 Hard
- 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
More PYQs from JEE Mains
- Let \(A=\{(a,b,c): a,b,c \text{ are non-negative integers and } a+b+2c=22\}\). Then \(n(A)\) is equal to:JEE Mains 2026 Medium
- Let a function \(g:[0,4] \rightarrow R\) be defined as \(g ( x )=\left\{\begin{array}{ll}\max _{0 \leq t \leq x }\left\{ t ^{3}-6 t ^{2}+9 t -3\right\} & , 0 \leq x \leq 3 \\ 4- x & , 3 < x \leq 4\end{array}\right.\) then the number of points in the interval \((0,4)\) where \(g(x)\) is NOT differentiable, is \(.....\)JEE Mains 2021 Hard
- Let \(f : R \rightarrow R\) be a function defined by \(f ( x )=\) \(\log _{\sqrt{m}}\{\sqrt{2}(\sin x-\cos x)+m-2\}\), for some \(m\), such that the range of \(f\) is \([0,2]\). Then the value of \(m\) is \(............\)JEE Mains 2023 Hard
- The number of one-one function \(f :\{ a , b , c , d \} \rightarrow\) \(\{0,1,2, \ldots ., 10\}\) such that \(2 f(a)-f(b)+3 f(c)+\) \(f ( d )=0\) isJEE Mains 2022 Hard
- The number of real solutions of the equation, \(x^{2}-|x|-12=0\) is:JEE Mains 2021 Easy
- If the integral \(\int {\frac{{\cos \,8x + 1}}{{\cot \,2x - \tan \,2x}}} dx = A\,\cos \,8x + k,\) where \(k\) is an arbitrary constant, then \(A\) is equal toJEE Mains 2013 Hard