JEE Mains · Maths · STD 11 - 6. permutation and combination
The number of numbers greater than 5000, less than 9000 and divisible by 3, that can be formed using the digits 0, 1, 2, 5, 9, if the repetition of the digits is allowed, is ___ .
- A 40
- B 42
- C 44
- D 46
Answer & Solution
Correct Answer
(B) 42
Step-by-step Solution
Detailed explanation
(1) all different 5, 0, 1, 9 \(\Rightarrow\lfloor 3=6\) ways (2) 2 alike, 2 different \(5,0,0,1 \Rightarrow 3\) ways \(5,1,1,2 \Rightarrow 3\) ways \(5,2,2,0 \Rightarrow 3\) ways \(5,2,2,9 \Rightarrow 3\) ways \(5,5,0,2 \Rightarrow 6\) ways \(5,5,2,9 \Rightarrow 6\) ways…
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 triangle \(PQR\) be such that \(P\) and \(Q\) lie on the line \(\dfrac{x+3}{8} = \dfrac{y-4}{2} = \dfrac{z+1}{2}\) and are at a distance of \(6\) units from \(R(1, 2, 3)\). If \((\alpha, \beta, \gamma)\) is the centroid of \(\triangle PQR\), then \(\alpha + \beta + \gamma\) is equal to :JEE Mains 2026 Medium
- If \(P = \left[ {\begin{array}{*{20}{c}}1&\alpha &3\\1&3&3\\2&4&4\end{array}} \right]\) is the adjoint of \(3×3 \) matrix \(A\) and \( |A|=4\) then \(\alpha \) is equal toJEE Mains 2013 Medium
- Let \([ x ]\) denote greatest integer less than or equal to \(x .\) If for \(n \in N ,\left(1-x+x^{3}\right)^{n}=\sum_{j=0}^{3 n} a_{j} x^{j}\), then \(\sum_{j=0}^{\left[\frac{3 n}{2}\right]} a_{2 j}+4 \sum_{j=0}^{\left[\frac{3 n-1}{2}\right]} a_{2 j+1}\) is equal toJEE Mains 2021 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
- If Rolle's theorem holds for the function \(f(x)=x^{3}-a x^{2}+b x-4, x \in[1,2]\) with \(f ^{\prime}\left(\frac{4}{3}\right)=0,\) then ordered pair \(( a , b )\) is equal toJEE Mains 2021 Medium
- Let \(X\) be a binomially distributed random variable with mean \(4\) and variance \(\frac{4}{3}\). Then \(54 P ( X \leq 2)\) is equal to.JEE Mains 2022 Medium
More PYQs from JEE Mains
- If the function \(f\) defined as \(f(x)\, = \frac{1}{x} - \frac{{k - 1}}{{{e^{2x}} - 1}}\) ,\(x\, \ne \,0,\) is continuous at \(x = 0.\) then the ordered pair \((k,f(0))\) is equal to?JEE Mains 2018 Hard
- If \(n \geq 2\) is a positive integer, then the sum of the series \({ }^{ n +1} C _{2}+2\left({ }^{2} C _{2}+{ }^{3} C _{2}+{ }^{4} C _{2}+\ldots+{ }^{ n } C _{2}\right)\) is ...... .JEE Mains 2021 Hard
- The value of \(\int\limits_{0}^{2 \pi} \frac{x \sin ^{8} x}{\sin ^{8} x+\cos ^{8} x} d x\) is equal toJEE Mains 2020 Hard
- If the mean and variance of six observations \(7,10,11,15, a, b\) are \(10\) and \(\frac{20}{3}\), respectively, then the value of \(|a-b|\) is equal to:JEE Mains 2021 Medium
- Let \(f(x)\) and \(g(x)\) be twice differentiable functions satisfying \(f''(x) = g''(x)\) for all \(x \in \mathbf{R}\), \(f'(1) = 2g'(1) = 4\) and \(g(2) = 3f(2) = 9\). Then \(f(25) - g(25)\) is equal to :JEE Mains 2026 Medium
- The area of the region \(\left\{(x, y): y^2 \leq 4 x, x<4, \frac{x y(x-1)(x-2)}{(x-3)(x-4)}>0, x \neq 3\right\}\) isJEE Mains 2024 Hard