JEE Mains · Maths · STD 11 - 6. permutation and combination
The number of \(3\) digit numbers, that are divisible by either \(3\) or \(4\) but not divisible by \(48\),is
- A \(472\)
- B \(432\)
- C \(507\)
- D \(400\)
Answer & Solution
Correct Answer
(B) \(432\)
Step-by-step Solution
Detailed explanation
Total \(3\) digit number \(=900\) Divisible by \(3=300\) (Using \(\frac{900}{3}=300\) ) Divisible by \(4=225\) (Using \(\frac{900}{4}=225\) ) Divisible by \(3 \& 4=108, \ldots\). (Using \(\frac{900}{12}=75\) ) Number divisible by either \(3\) or \(4\) \(=300+2250-75=450\) We…
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 \(x \in \left( {0,\frac{3}{2}} \right)\), let \(f\left( x \right) = \sqrt x \), \(g\left( x \right) = \tan \,x\) and \(h\left( x \right) = \frac{{1 - {x^2}}}{{1 + {x^2}}}\). If \(\phi \left( x \right) = \left( {\left( {hof} \right)og} \right)\left( x \right)\), then \(\phi \left( {\frac{\pi }{3}} \right)\) is equal toJEE Mains 2019 Hard
- If \(\int \limits_0^1\left(x^{21}+x^{14}+x^7\right)\left(2 x^{14}+3 x^7+6\right)^{1 / 7} d x=\frac{1}{l}(11)^{m / n}\) where \(l, m , n \in N , m\) and \(n\) are coprime then \(l+m+n\) is equal to \(...........\).JEE Mains 2023 Hard
- Let \(z \in C\) be such that \(\frac{z^2+3 i}{z-2+i}=2+3 i\). Then the sum of all possible values of \(z^2\) isJEE Mains 2025 Easy
- If the sum and product of the first three term in an \(A.P\). are \(33\) and \(1155\), respectively, then a value of its \(11^{th}\) tern isJEE Mains 2019 Hard
- Let \([ t ]\) denotes the greatest integer \(\leq t\). Then \(\frac{2}{\pi} \int \limits_{\pi / 6}^{5 \pi / 6}(8[\operatorname{cosec} x]-5[\cot x]) d x\) is equal toJEE Mains 2023 Hard
- \(\lim _{x \rightarrow 0^{+}} \frac{\tan \left(5(x)^{\frac{1}{3}}\right) \log _e\left(1+3 x^2\right)}{\left(\tan ^{-1} 3 \sqrt{x}\right)^2\left(e^{5(x)^{\frac{4}{3}}}-1\right)}\) is equal toJEE Mains 2025 Medium
More PYQs from JEE Mains
- Let \( \lim _{n \rightarrow \infty}\left(\frac{n}{\sqrt{n^4+1}}-\frac{2 n}{\left(n^2+1\right) \sqrt{n^4+1}}+\frac{n}{\sqrt{n^4+16}}-\frac{8 n}{\left(n^2+4\right) \sqrt{n^4+16}}\right. \) \( \left.+\ldots \ldots+\frac{n}{\sqrt{n^4+n^4}}-\frac{2 n \cdot n^2}{\left(n^2+n^2\right) \sqrt{n^4+n^4}}\right) \text { be } \frac{\pi}{k},\) using only the principal values of the inverse trigonometric functions. Then \(\mathrm{k}^2\) is equal to ..............JEE Mains 2024 Hard
- Let \(A=\left\{(x, y) \in R \times R \mid 2 x^{2}+2 y^{2}-2 x-2 y=1\right\}\) \(B=\left\{(x, y) \in R \times R \mid 4 x^{2}+4 y^{2}-16 y+7=0\right\} \text { and }\) \(C=\left\{(x, y) \in R \times R \mid x^{2}+y^{2}-4 x-2 y+5 \leq r^{2}\right\}\) Then the minimum value of \(|r|\) such that \(A \cup B \subseteq C\) is equal to:JEE Mains 2021 Hard
- A line, with the slope greater than one, passes through the point \(A (4,3)\) and intersects the line \(x -\) \(y-2=0\) at the point \(B\). If the length of the line segment \(AB\) is \(\frac{\sqrt{29}}{3}\), then \(B\) also lies on the line..JEE Mains 2022 Medium
- Let \(f(x) = \begin{cases} \dfrac{1}{3}, & x \leq \pi/2 \\ \dfrac{b(1-\sin x)}{(\pi-2x)^2}, & x > \pi/2 \end{cases}\). If \(f\) is continuous at \(x=\pi/2\), then the value of \(\displaystyle\int_{0}^{3b-6} |x^2+2x-3|\,dx\) is:JEE Mains 2026 Hard
- Let \( S=\{z\in\mathbb{C}:4z^{2}+\overline{z}=0\} \) Then \( \sum_{z\in S}|z|^{2} \) is equal to:JEE Mains 2026 Medium
- \(\lim _{x \rightarrow 0} \frac{\sin ^{2}\left(\pi \cos ^{4} x\right)}{x^{4}}\) is equal to :JEE Mains 2021 Hard