JEE Mains · Maths · STD 11 - 6. permutation and combination
Numbers are to be formed between \(1000\) and \(3000\), which are divisible by \(4\), using the digits \(1,2,3,4,5\) and \(6\) without repetition of digits. Then the total number of such numbers is.
- A \(3\)
- B \(30\)
- C \(60\)
- D \(15\)
Answer & Solution
Correct Answer
(B) \(30\)
Step-by-step Solution
Detailed explanation
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
- The value of \(\left(\frac{1+\sin \frac{2 \pi}{9}+i \cos \frac{2 \pi}{9}}{1+\sin \frac{2 \pi}{9}-i \cos \frac{2 \pi}{9}}\right)^3\) isJEE Mains 2023 Medium
- The positive integer n, for which the solutions of the equation \( x(x+2)+(x+2)(x+4)+....+(x+2n-2)(x+2n) = \frac{8n}{3} \) are two consecutive even integers, is :-JEE Mains 2026 Hard
- Let \(\alpha, \beta \in \mathbb{R}\) be such that the system of linear equations
\(x + 2y + z = 5\)
\(2x + y + \alpha z = 5\)
\(8x + 4y + \beta z = 18\)
has no solution. Then \(\dfrac{\beta}{\alpha}\) is equal to :JEE Mains 2026 Medium - The value of \(\int_{-1}^1 \frac{(1+\sqrt{|x|-x}) e^x+(\sqrt{|x|-x}) e^{-x}}{e^x+e^{-x}} d x\) is equal toJEE Mains 2025 Medium
- Let \(\mathrm{A}=\{-3,-2,-1,0,1,2,3\}\) and R be a relation on \(A\) defined by \(x R y\) if and only if \(2 x-y \in\{0,1\}\). Let \(l\) be the number of elements in R. Let \(m\) and \(n\) be the minimum number of elements required to be added in R to make it reflexive and symmetric relations, respectively. Then \(l+\mathrm{m} \mathrm{n}\) is equal to :-JEE Mains 2025 Easy
- If a function \(f(x)\) defined by \(f(x)=\left\{\begin{array}{ll}a e^{x}+b e^{-x}, & -1 \leq x<1 \\ c x^{2}, & 1 \leq x \leq 3 \\ a x^{2}+2 c x, & 3 < x \leq 4\end{array}\right.\) be continuous for some \(a, b, c \in R\) and \(f ^{\prime}(0)+ f ^{\prime}(2)= e ,\) then the value of of \(a\) isJEE Mains 2020 Hard
More PYQs from JEE Mains
- A tangent to the curve, \(y\, = f(x)\) at \(P(x,y)\) meets \(x-\) axis at \(A\) and \(y-\) axis at \(B\). If \(AP : BP\,= 1: 3\) and \(f(a)\, = 1\) , then the curve also passes through the pointJEE Mains 2017 Hard
- If the equation \(\cos ^{4} \theta+\sin ^{4} \theta+\lambda=0\) has real solutions for \(\theta,\) then \(\lambda\) lies in the intervalJEE Mains 2020 Hard
- If \(m\) and \(n\) respectively are the numbers of positive and negative value of \(\theta\) in the interval \([-\pi, \pi]\) that satisfy the equation \(\cos 2 \theta \cos \frac{\theta}{2}=\cos 3 \theta \cos \frac{9 \theta}{2}\), then \(mn\) is equal to \(.............\).JEE Mains 2023 Hard
- Let \(\vec{a}=\hat{i}+2 \hat{j}+\hat{k}\) and \(\vec{b}=2 \hat{i}+\hat{j}-\hat{k}\). Let \(\hat{c}\) be a unit vector in the plane of the vectors \(\vec{a}\) and \(\vec{b}\) and be perpendicular to \(\vec{a}\). Then such a vector \(\hat{c}\) is :JEE Mains 2025 Medium
- If \(y(\theta)=\frac{2 \cos \theta+\cos 2 \theta}{\cos 3 \theta+4 \cos 2 \theta+5 \cos \theta+2}\) then at \(\theta=\frac{\pi}{2}, y^{\prime \prime}+y^{\prime}+y\) is equal to :JEE Mains 2024 Hard
- If each term of a geometric progression \(a_1, a_2, a_3, \ldots\) with \(a_1=\frac{1}{8}\) and \(a_2 \neq a_1\), is the arithmetic mean of the next two terms and \(S_n=a_1+a_2+\ldots+a_n\), then \(\mathrm{S}_{20}-\mathrm{S}_{18}\) is equal toJEE Mains 2024 Hard