JEE Mains · Maths · STD 11 - 6. permutation and combination
The number of three-digit even numbers, formed by the digits \(0,1,3,4,6,7\) if the repetition of digits is not allowed, is .... .
- A \(26\)
- B \(52\)
- C \(32\)
- D \(20\)
Answer & Solution
Correct Answer
(B) \(52\)
Step-by-step Solution
Detailed explanation
\((i)\) When \(' 0 '\) is at unit place \([image]\,(1)\) Number of numbers \(=20\) \((ii)\) When \(4\) or \(6\) are at unit place \([image]\,(2)\) Number of numbers \(=32\) So number of numbers \(=52\)
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
- For \(\alpha, \beta, z \in C\) and \(\lambda>1\), if \(\sqrt{\lambda-1}\) is the radius of the circle \(|z-\alpha|^2+|z-\beta|^2=2 \lambda\), then \(|\alpha-\beta|\) is equal to \(.............\).JEE Mains 2023 Hard
- If the tangent to the curve \(y=x+\sin y\) at a point \((a, b)\) is parallel to the line joining \(\left(0, \frac{3}{2}\right)\) and \(\left(\frac{1}{2}, 2\right),\) thenJEE Mains 2020 Medium
- Let \(Q(a,b,c)\) be the image of the point \(P(3,2,1)\) in the line \(\frac{x-1}{1}=\frac{y}{2}=\frac{z-1}{1}.\) Then the distance of Q from the line \(\frac{x-9}{3}=\frac{y-9}{2}=\frac{z-5}{-2}\) isJEE Mains 2026 Hard
- Let the line \(\mathrm{L}\) intersect the lines \(\mathrm{x}-2=-\mathrm{y}=\mathrm{z}-1,2(\mathrm{x}+1)=2(\mathrm{y}-1)=\mathrm{z}+1\) and be parallel to the line \(\frac{x-2}{3}=\frac{y-1}{1}=\frac{z-2}{2}\). Then which of the following points lies on \(\mathrm{L}\) ?JEE Mains 2024 Hard
- The integral \(16 \int \limits_1^2 \frac{d x}{x^3\left(x^2+2\right)^2}\) is equal toJEE Mains 2023 Hard
- If \(\frac{{dy}}{{dx}} + y\tan x = \sin 2x\) and \(y(0)\,=1\) , then \(y(\pi)\) is equal toJEE Mains 2014 Hard
More PYQs from JEE Mains
- If all the words (with or without meaning) having five letters, formed using the letters of the word \(SMALL\) and arranged as in a dictionary; then the position of the word \(SMALL\) is :JEE Mains 2016 Hard
- If \(\alpha \) and \(\beta \) are roots of the equation \(x^2 + px + \frac {3p}{4} = 0,\) such that \(\left| {\alpha - \beta } \right| = \sqrt {10} ,\) then \(p\) belongs to the setJEE Mains 2013 Hard
- Let \(\alpha = 3\sin^{-1}\left(\dfrac{6}{11}\right)\) and \(\beta = 3\cos^{-1}\left(\dfrac{4}{9}\right)\), where inverse trigonometric functions take only the principal values.
Given below are two statements:
Statement I: \(\cos(\alpha+\beta) > 0\).
Statement II: \(\cos(\alpha) < 0\).
In the light of the above statements, choose the correct answer from the options given below:JEE Mains 2026 Medium - Let \(\vec{a} = 4\hat{i} - \hat{j} + 3\hat{k}\), \(\vec{b} = 10\hat{i} + 2\hat{j} - \hat{k}\) and a vector \(\vec{c}\) be such that \(2(\vec{a}\times\vec{b}) + 3(\vec{b}\times\vec{c}) = \vec{0}\). If \(\vec{a}\cdot\vec{c} = 15\), then \(\vec{c}\cdot(\hat{i}+\hat{j}-3\hat{k})\) is equal to:JEE Mains 2026 Medium
- Line \(L_1\) passes through the point \((1,2,3)\) and is parallel to Z -axis. Line \(\mathrm{L}_2\) passes through the point \((\lambda, 5,6)\) and is parallel to \(y\)-axis. Let for \(\lambda=\lambda_1, \lambda_2, \lambda_2 \lt \lambda_1\), the shortest distance between the two lines be 3 . Then the square of the distance of the point \(\left(\lambda_1, \lambda_2, 7\right)\) from the line \(\mathrm{L}_1\) isJEE Mains 2025 Medium
- The sum of all rational terms in the expansion of \(\left(1+2^{1 / 3}+3^{1 / 2}\right)^6\) is equal toJEE Mains 2025 Easy