JEE Mains · Maths · STD 11 - 6. permutation and combination
\(8-\) digit numbers are formed using the digits \(1, 1, 2, 2, 2, 3, 4, 4.\) The number of such numbers in which the odd digits do no occupy odd places, is
- A \(160\)
- B \(120\)
- C \(60\)
- D \(48\)
Answer & Solution
Correct Answer
(B) \(120\)
Step-by-step Solution
Detailed explanation
In \(8\) digits numbers, \(4\) places are odd places. Also, in the given \(8\) digits,there are three odd digits \(1,1\) and \(3\). No. of ways three odd digits arranged at four even places \( = \frac{{4{P_3}}}{{2!}} = \frac{{4!}}{{2!}}\) No. of ways the remaining five digits…
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 tangent be drawn to the ellipse \(\frac{x^{2}}{27}+y^{2}=1\) at \((3 \sqrt{3} \cos \theta, \sin \theta)\) where \(\theta \in\left(0, \frac{\pi}{2}\right)\). Then the value of \(\theta\) such that the sum of intercepts on axes made by this tangent is minimum is equal to ..... .JEE Mains 2021 Hard
- From a group of \(10\) men and \(5\) women, four member committees are to be formed each of which must contain at least one woman. Then the probability for these committees to have more women than men, isJEE Mains 2017 Hard
- Let \(Z\) be the set of integers. If \(A\, = \,\{ x\, \in \,Z\,:\,{2^{(x + 2)({x^2} - 5x + 6)}} = 1\} \) and \(B\, = \,\{ x\, \in \,Z\,:\, - 3\, < \,2x\, - 1\, < \,9\} ,\) then the number of subsets of the set \(A \times B\) isJEE Mains 2019 Hard
- If a curve passes through the point \(\left( {2\,,\,\frac{7}{2}} \right)\) and has slope \(\left( {1 - \frac{1}{{{x^2}}}} \right)\) at anypoint \((x, y)\) on it, then the ordinate of the point on the curve whose abscissa is \(- 2\) isJEE Mains 2013 Hard
- Let \(A=\left[\begin{array}{ll}x & 1 \\ 1 & 0\end{array}\right], x \in R\) and \(A^{4}=\left[a_{i j}\right] .\) If \(a_{11}=109,\) then \(a_{22}\) is equal toJEE Mains 2020 Hard
- The foot of the perpendicular drawn from the origin, on the line, \(3x + y = \lambda \,\left( {\lambda \ne 0} \right)\) is \(P\). If the line meets \(x-\) axis at \(A\) and \(y-\) axis at \(B\), then the ratio \(BP : PA\) isJEE Mains 2018 Hard
More PYQs from JEE Mains
- Let \(z_1=2+3 i\) and \(z_2=3+4 i\). The set \(S =\left\{ z \in C :\left| z - z _1\right|^2-\left|z-z_2\right|^2=\left|z_1-z_2\right|^2\right\}\) represents aJEE Mains 2023 Hard
- Let slope of the tangent line to a curve at any point \(P ( x , y )\) be given by \(\frac{ xy ^{2}+ y }{ x } .\) If the curve intersects the line \(x+2 y=4\) at \(x=-2,\) then the value of \(y ,\) for which the point \((3, y )\) lies on the curve, is ..... .JEE Mains 2021 Hard
- Let \(x\) and \(y\) be distinct integers where \(1 \leq x \leq 25\) and \(1 \leq y \leq 25\). Then, the number of ways of choosing \(x\) and \(y\), such that \(x + y\) is divisible by \(5\) , is \(.........\).JEE Mains 2023 Hard
- Given below are two statements:
Statement I: The function \(f:R\rightarrow R\) defined by \(f(x)=\frac{x}{1+|x|}\) is one-one.
Statement II: The function \(f:R\rightarrow R\) defined by \(f(x)=\frac{x^{2}+4x-30}{x^{2}-8x+18}\) is many-one.
In the light of the above statements, choose the correct answer from the options given below :JEE Mains 2026 Easy - Let \(N\) be the foot of perpendicular from the point \(P\) \((1,-2,3)\) on the line passing through the points \((4,5,8)\) and \((1,-7,5)\). Then the distance of \(N\) from the plane \(2 x-2 y+z+5=0\) is \(.......\).JEE Mains 2023 Hard
- Let the foci of a hyperbola \(\mathrm{H}\) coincide with the foci of the ellipse \(E: \frac{(x-1)^2}{100}+\frac{(y-1)^2}{75}=1\) and the eccentricity of the hyperbola \(\mathrm{H}\) be the reciprocal of the eccentricity of the ellipse \(E\). If the length of the transverse axis of \(\mathrm{H}\) is \(\alpha\) and the length of its conjugate axis is \(\beta\), then \(3 \alpha^2+2 \beta^2\) is equal to :JEE Mains 2024 Hard