JEE Mains · Maths · STD 11 - 6. permutation and combination
The total number of six digit numbers, formed using the digits \(4,5,9\) only and divisible by \(6\) , is \(.........\).
- A \(80\)
- B \(81\)
- C \(82\)
- D \(83\)
Answer & Solution
Correct Answer
(B) \(81\)
Step-by-step Solution
Detailed explanation
Taking single digit \(\rightarrow 444444 \quad \frac{6 !}{6 !}=1\) Taking two digit \(\rightarrow\) \((4,5) \quad 444555 \quad(4,9) \quad 444999\) \(\frac{5 !}{3 ! 2 !}=10 \quad \frac{5 !}{3 ! 2 !}=10\) Taking three digit \(4,5,9,4,4,4 \Rightarrow \frac{5 !}{3 !}=20\)…
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 the line of the shortest distance between the lines \(L_1: \vec{r}=(\hat{i}+2 \hat{j}+3 \hat{k})+\lambda(\hat{i}-\hat{j}+\hat{k})\) and \(L_2: \vec{r}=(4 \hat{i}+5 \hat{j}+6 \hat{k})+\mu(\hat{i}+\hat{j}-\hat{k})\) intersect \(\mathrm{L}_1\) and \(\mathrm{L}_2\) at \(\mathrm{P}\) and \(\mathrm{Q}\) respectively. If \((\alpha, \beta, \gamma)\) is the midpoint of the line segment \(PQ\), then \(2(\alpha+\beta+\gamma)\) is equal to ...........JEE Mains 2024 Hard
- If \(\int\limits_0^x {f\left( t \right)} dt = {x^2} + \int\limits_x^1 {{t^2}f\left( t \right)dt} \), then \(f'(1/2)\) isJEE Mains 2019 Hard
- For the curve \(y\, = 3\, sin\,\theta\, cos\,\theta\), \(x\, = e^{\theta}\, sin\,\theta\), \(0 \leq \theta \leq \pi \) , the tangent is parallel to \(x-\) axis when \(\theta \) isJEE Mains 2014 Hard
- Let \(a, b, c\) and \(d\) be non-zero numbers. If the point of intersection of the lines \(4ax + 2ay + c = 0\) and \(5bx + 2by + d =0\) lies in the fourth quadrant and is equidistant from the two axes thenJEE Mains 2014 Hard
- Let \(\left(5, \frac{a}{4}\right)\), be the circumcenter of a triangle with vertices \(A(a,-2), B(a, 6)\) and \(C\left(\frac{a}{4},-2\right)\). Let \(\alpha\) denote the circumradius, \(\beta\) denote the area and \(\gamma\) denote the perimeter of the triangle. Then \(\alpha+\beta+\gamma\) is ...........JEE Mains 2024 Medium
- Let the distance between two parallel lines be 5 units and a point \(P\) lie between the lines at a unit distance from one of them. An equilateral triangle \(P Q R\) is formed such that \(Q\) lies on one of the parallel lines, while \(R\) lies on the other. Then \((Q R)^2\) is equal to _______ -.JEE Mains 2025 Medium
More PYQs from JEE Mains
- The set of all values of \(\lambda \) for which the system of linear equations \(x - 2y - 2z = \lambda x\) ; \(x + 2y + z = \lambda y\) ; \(-x - y = \lambda z\) has non zero solutions.JEE Mains 2019 Hard
- If \( x^{2}+x+1=0 \) then the value of \( (x+\frac{1}{x})^{4}+(x^{2}+\frac{1}{x^{2}})^{4}+(x^{3}+\frac{1}{x^{3}})^{4}+...+(x^{25}+\frac{1}{x^{25}})^{4} \) is:JEE Mains 2026 Medium
- A pack of cards has one card missing. Two cards are drawn randomly and are found to be spades. The probability that the missing card is not a spade, isJEE Mains 2021 Medium
- The locus of the mid-points of the perpendiculars drawn from points on the line, \(\mathrm{x}=2 \mathrm{y}\) to the line \(\mathrm{x}=\mathrm{y}\) isJEE Mains 2020 Hard
- A square \(ABCD\) has all its vertices on the curve \(x ^{2} y ^{2}=1\). The midpoints of its sides also lie on the same curve. Then, the square of area of \(ABCD\) isJEE Mains 2021 Hard
- \(A\) and \(B\) alternately throw a pair of dice. \(A\) wins if he throws a sum of 5 before \(B\) throws a sum of 8 , and \(B\) wins if he throws a sum of 8 before \(A\) throws a sum of 5 . The probability, that \(A\) wins if A makes the first throw, isJEE Mains 2025 Medium