JEE Mains · Maths · STD 11 - 6. permutation and combination
If \(\left({ }^{30} C_1\right)^2+2\left({ }^{30} C_2\right)^2+3\left({ }^{30} C_3\right)^2 \ldots \ldots \ldots . .30\left({ }^{30} C_{30}\right)^2=\frac{\alpha 60!}{(30!)^2}\), then \(\alpha\) is equal to
- A 30
- B 60
- C 15
- D 10
Answer & Solution
Correct Answer
(C) 15
Step-by-step Solution
Detailed explanation
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 shortest distance between the lines \(\frac{x-\lambda}{3}=\frac{y-2}{-1}=\frac{z-1}{1}\) and \(\frac{x+2}{-3}=\frac{y+5}{2}=\frac{z-4}{4}\) is \(\frac{44}{\sqrt{30}}\), then the largest possible value of \(|\lambda|\) is equal to ..........JEE Mains 2024 Hard
- Let \(A\) be a matrix of order \(3 \times 3\) and \(|A|=5\). If \(|2 \operatorname{adj}(3 \mathrm{~A} \operatorname{adj}(2 \mathrm{~A}))|=2^\alpha \cdot 3^\beta \cdot 5^\gamma \alpha, \beta, \gamma \in \mathrm{N}\) then \(\alpha+\beta+\gamma\) is equal toJEE Mains 2025 Medium
- If \(z\) is a complex number such that \(\left| z \right| \ge 2\) , then the minimum value of \(\left| {z + \frac{1}{2}} \right|\):JEE Mains 2014 Medium
- If the system of equations \(x+2 y+3 z=3\) ; \(4 x+3 y-4 z=4\) ; \(8 x+4 y-\lambda z=9+\mu\) has infinitely many solutions, then the ordered pair \((\lambda, \mu)\) is equal toJEE Mains 2023 Hard
- Let a function \(f: R \rightarrow R\) be defined as \(f(x)=\sin x-e^{x} \,\,\,\, \text { if } x \leq 0\) \(\quad\quad\quad a+[-x] \,\,\,\, \text { if } 0\,<\,x\,<\,1\) \(\quad\quad\quad 2 x-b \,\,\,\,\,\,\,\, \text { if } \geq 1\) where \([\mathrm{x}]\) is the greatest integer less than or equal to \(\mathrm{x}\). If \(\mathrm{f}\) is continuous on \(\mathrm{R}\), then \((\mathrm{a}+\mathrm{b})\) is equal to:JEE Mains 2021 Hard
- Let \(\frac{\sin \mathrm{A}}{\sin \mathrm{B}}=\frac{\sin (\mathrm{A}-\mathrm{C})}{\sin (\mathrm{C}-\mathrm{B})}\), where \(\mathrm{A}, \mathrm{B}, \mathrm{C}\) are angles f a triangle \(\mathrm{ABC}\). If the lengths of the sides pposite these angles are \(\mathrm{a}, \mathrm{b}, \mathrm{c}\) respectively, then :JEE Mains 2021 Hard
More PYQs from JEE Mains
- The least positive integer \(n\) such that \(1 - \frac{2}{3} - \frac{2}{{{3^2}}} - .... - \frac{2}{{{3^{n - 1}}}} < \frac{1}{{100}},\) isJEE Mains 2014 Hard
- If \(\mathrm{A}(1,-1,2), \mathrm{B}(5,7,-6), \mathrm{C}(3,4,-10)\) and \(\mathrm{D}(-1,-4,-2)\) are the vertices of a quadrilateral \(\mathrm{ABCD}\), then its area is :JEE Mains 2024 Medium
- If \(\int\limits_0^x {f\left( t \right)} dt = {x^2} + \int\limits_x^1 {{t^2}f\left( t \right)dt} \), then \(f'(1/2)\) isJEE Mains 2019 Hard
- The value of \(\sum \limits_{ r =0}^{20}{ }^{50- r } C _{6}\) is equal toJEE Mains 2020 Hard
- If the function \(\mathrm{f}\) defined on \(\left(-\frac{1}{3}, \frac{1}{3}\right)\) by \(f(x)=\left\{\begin{array}{ll}{\frac{1}{x} \log _{e}\left(\frac{1+3 x}{1-2 x}\right)} & {, \text { when } x \neq 0} \\ {k} & {, \text { when } x=0}\end{array}\right.\) is continuous, then \(\mathrm{k}\) is equal toJEE Mains 2020 Hard
- If non-zero real numbers \(b\) and \(c\) are such that \(min \,f\left( x \right) > \max \,g\left( x \right)\), where \(f\left( x \right) = {x^2} + 2bx + 2{c^2}\) and \(g\left( x \right) = {-x^2} - 2cx + {b^2}\)\(\left( {x \in R} \right)\); then \(\left| {\frac{c}{b}} \right|\) lies in the intervalJEE Mains 2014 Hard