enEnglishguગુજરાતી
JEE Mains · Maths · STD 11 - 6. permutation and combination
Two families with three members each and one family with four members are to be seated in a row. In how many ways can they be seated so that the same family members are not separated ?
- A \(2 ! 3 ! 4 !\)
- B \((3 !)^{3} \cdot(4 !)\)
- C \((3 !)^{2} \cdot(4 !)\)
- D \(3 !(4 !)^{3}\)
Answer & Solution
Correct Answer
(B) \((3 !)^{3} \cdot(4 !)\)
Step-by-step Solution
Detailed explanation
Total numbers in three familes \(=3+3+4=10\) so total arrangement \(=10 !\) \( \begin{array}{|c|c||c|}\hline \text { Family 1 } & \text { Family 2 } & \text { Family 3 } \\3 & 3 & 4 \\\hline\end{array}\) Favourable cases…
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 \(A=\{n \in N: H . C . F .(n, 45)=1\}\) and Let \(B=\{2 k: k \in\{1,2, \ldots, 100\}\}\). Then the sum of all the elements of \(A \cap B\) isJEE Mains 2022 Medium
- \(\int_0^{\pi / 4} \frac{\cos ^2 x \sin ^2 x}{\left(\cos ^3 x+\sin ^3 x\right)^2} d x\) is equal toJEE Mains 2024 Medium
- Let \(PQ\) be a double ordinate of the parabola, \(y^2\, = - 4x\), where \(P\) lies in the second quadrant. If \(R\) divides \(PQ\) in the ratio \(2 : 1\) then the locus of \(R\) isJEE Mains 2015 Hard
- The value of \(\cot \frac{\pi}{24}\) is :JEE Mains 2021 Hard
- Let \(\mathrm{f}: \mathrm{R} \rightarrow \mathrm{R}\) be a function defined \(f(x)=\frac{x}{\left(1+x^4\right)^{1 / 4}}\) and \(g(x)=f(f(f(f(x))))\) then \(18 \int_0^{\sqrt{2 \sqrt{5}}} x^2 g(x) d x\)JEE Mains 2024 Hard
- Let the tangents at two points \(A\) and \(B\) on the circle \(x ^{2}+ y ^{2}-4 x +3=0\) meet at origin \(O (0,0)\). Then the area of the triangle of \(OAB\) is.JEE Mains 2022 Hard
More PYQs from JEE Mains
- Let \(R =\{ a , b , c , d , e \}\) and \(S =\{1,2,3,4\}\). Total number of onto function \(f: R \rightarrow S\) such that \(f(a) \neq\) 1 , is equal to \(.............\).JEE Mains 2023 Hard
- The values of \(\lambda\) and \(\mu\) for which the system of linear equations \(x+y+z=2\) \(x+2 y+3 z=5\) \(x+3 y+\lambda z=\mu\) has infinitely many solutions are, respectivelyJEE Mains 2020 Medium
- Let \(A\) be a \(3 \times 3\) real matrix such that \(\mathrm{A}\left(\begin{array}{l}1 \\ 0 \\ 1\end{array}\right)=2\left(\begin{array}{l}1 \\ 0 \\ 1\end{array}\right), \mathrm{A}\left(\begin{array}{l}-1 \\ 0 \\ 1\end{array}\right)=4\left(\begin{array}{l}-1 \\ 0 \\ 1\end{array}\right), \mathrm{A}\left(\begin{array}{l}0 \\ 1 \\ 0\end{array}\right)=2\left(\begin{array}{l}0 \\ 1 \\ 0\end{array}\right)\). Then, the system \((A-3 I)\left(\begin{array}{l}x \\ y \\ z\end{array}\right)=\left(\begin{array}{l}1 \\ 2 \\ 3\end{array}\right)\) hasJEE Mains 2024 Hard
- Let \(f(x)\) be a function such that \(f(x+y)=f(x) \cdot f(y)\) for all \(x , y \in N\). If \(f (1)=3\) and \(\sum \limits_{ k =1}^{ n } f ( k )=3279\), then the value of \(n\) is \(.........\)JEE Mains 2023 Hard
- Let \(\alpha, \beta\) be the roots of the equation \(x^2-a x-b=0\) with \(\operatorname{Im}(\alpha) \lt \operatorname{Im}(\beta)\). Let \(P_n=\alpha^n-\beta^n\). If \(\mathrm{P}_3=-5 \sqrt{7} i, \mathrm{P}_4=-3 \sqrt{7} i, \mathrm{P}_5=11 \sqrt{7} i\) and \(\mathrm{P}_6=45 \sqrt{7} i\), then \(\left|\alpha^4+\beta^4\right|\) is equal to __________.JEE Mains 2025 Medium
- Let a curve \(y=f(x)\) pass through the points \((0,5)\) and \(\left(\log _e 2, k\right)\). If the curve satisfies the differential equation \(2(3+y) e^{2 x} d x-\left(7+e^{2 x}\right) d y=0\), then \(k\) is equal toJEE Mains 2025 Medium