JEE Mains · Maths · STD 11 - 6. permutation and combination
The number of \(9\) digit numbers, that can be formed using all the digits of the number \(123412341\) so that the even digits occupy only even places, is \(..........\)
- A \(58\)
- B \(59\)
- C \(60\)
- D \(61\)
Answer & Solution
Correct Answer
(C) \(60\)
Step-by-step Solution
Detailed explanation
Even digits occupy at even places \(\frac{4 !}{2 ! 2 !} \times \frac{5 !}{2 ! 3 !}=\frac{24 \times 120}{4 \times 12}=60\)
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
- Let a random variable \(X\) have a binomial distribution with mean \(8\) and variance \(4\). If \(P\left( {X \le 2} \right) = \frac{k}{{{2^{16}}}}\), then \(k\) is equal toJEE Mains 2019 Hard
- If \([\mathrm{x}]\) be the greatest integer less than or equal to \(\mathrm{x}\), then \(\sum_{\mathrm{n}=8}^{100}\left[\frac{(-1)^{n} \mathrm{n}}{2}\right]\) is equal to:JEE Mains 2021 Easy
- Let \(g\) be a differentiable function such that \(\int_0^x g(t) d t=x-\int_0^x \operatorname{tg}(t) d t, x \geq 0\) and let \(y=y(x)\) satisfy the differential equation \(\frac{d y}{d x}-y \tan x=\) \(2(x+1) \sec x g(x), x \in\left[0, \frac{\pi}{2}\right)\). If \(y(0)=0\), then \(y\left(\frac{\pi}{3}\right)\) is equal toJEE Mains 2025 Medium
- Let the plane \(P\) contain the line \(2 x+y-z-3=0=5 x-3 y+4 z+9\) and be parallel to the line \(\frac{x+2}{2}=\frac{3-y}{-4}=\frac{z-7}{5}\). Then the distance of the point \(A (8,-1,-19)\) from the plane P measured parallel to the line \(\frac{x}{-3}=\frac{y-5}{4}=\frac{2-z}{-12}\) is equal to \(............\).JEE Mains 2023 Hard
- If \(A=\begin{bmatrix}2&3\\ 3&5\end{bmatrix}\), then the determinant of the matrix \((A^{2025}-3A^{2024}+A^{2023})\) isJEE Mains 2026 Medium
- If the constant term in the binomial expansion of \(\left(\frac{x^{\frac{5}{2}}}{2}-\frac{4}{x^{\ell}}\right)^9\) is \(-84\) and the Coefficient of \(x^{-3 \ell}\) is \(2^\alpha \beta\), where \(\beta < 0\) is an odd number, Then \(|\alpha \ell-\beta|\) is equal toJEE Mains 2023 Hard
More PYQs from JEE Mains
- Let \(f\) be a real valued continuous function on \([0,1]\) and \(f(x)=x+\int\limits_{0}^{1}(x-t) f(t) d t\). Then which of the following points \(( x , y )\) lies on the curve \(y =f( x )\) ?JEE Mains 2022 Hard
- The remainder on dividing \(5^{99}\) by \(11\) isJEE Mains 2023 Hard
- Let \(f ( x )=2 x ^{ n }+\lambda, \lambda \in R , n \in N\), and \(f (4)=133\), \(f(5)=255\). Then the sum of all the positive integer divisors of \(( f (3)- f (2))\) isJEE Mains 2023 Hard
- The number of natural numbers less than \(7,000\) which can be formed by using the digits \(0, 1, 3, 7, 9\) (repetition of digits allowed) is equal toJEE Mains 2019 Hard
- If \(\sum_{ k =1}^{10} K ^{2}\left(10_{ C _{ K }}\right)^{2}=22000 L\), then \(L\) is equal to \(.....\)JEE Mains 2022 Hard
- Let a curve \(y=y(x)\) be given by the solution of the differential equation \(\cos \left(\frac{1}{2} \cos ^{-1}\left(e^{-x}\right)\right) d x=\sqrt{e^{2 x}-1} \,d y\) If it intersects \(y\)-axis at \(y=-1\), and the intersection point of the curve with \(x\)-axis is \((\alpha, 0)\) the \(\mathrm{e}^{\alpha}\) is equal to \(.....\)JEE Mains 2021 Hard