JEE Mains · Maths · STD 11 - 1. set theory
Let \(A=\{n \in N: H . C . F .(n, 45)=1\}\) and Let \(B=\{2 k: k \in\{1,2, \ldots, 100\}\}\). Then the sum of all the elements of \(A \cap B\) is
- A \(5264\)
- B \(5265\)
- C \(5255\)
- D \(5235\)
Answer & Solution
Correct Answer
(A) \(5264\)
Step-by-step Solution
Detailed explanation
Sum of elements in \(A \cap B\) \(=\underbrace{(2+4+6+\ldots+200)}_{\text {Multiple of } 2}-\underbrace{(6+12+\ldots+198)}_{\text {Multiple of } 2 \; and\; 3 \text { i.e. } 6}\)…
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
- If \(y(x)=\left(x^{x^{x}}\right), x>0\) then \(\frac{d^{2} x}{d y^{2}}+20\) at \(x=1\) is equal toJEE Mains 2022 Hard
- If \(\lim _{x \rightarrow \infty}\left(\sqrt{x^{2}-x+1}-a x\right)=b\), then the ordered pair \((a, b)\) is:JEE Mains 2021 Hard
- \(\frac{2^{3}-1^{3}}{1 \times 7}+\frac{4^{3}-3^{3}+2^{3}-1^{3}}{2 \times 11}+\)\(\frac{6^{3}-5^{3}+4^{3}-3^{3}+2^{3}-1^{3}}{3 \times 15}+\ldots .+\) \(\frac{30^{3}-29^{3}+28^{3}-27^{3}+\ldots+2^{3}-1^{3}}{15 \times 63}\)is equal to.JEE Mains 2022 Hard
- The minimum value of \(2^{sin x}+2^{cos x}\) isJEE Mains 2020 Hard
- Let \(y=f(x)=\sin ^3\left(\frac{\pi}{3}\left(\cos \left(\frac{\pi}{3 \sqrt{2}}\left(-4 x^3+5 x^2+1\right)^{\frac{3}{2}}\right)\right)\right)\) .Then, at \(x =1\),JEE Mains 2023 Hard
- Let \(S_n\) be the sum to n-terms of an arithmetic progression \(3,7,11, \ldots\) If \(40<\left(\frac{6}{\mathrm{n}(\mathrm{n}+1)} \sum_{\mathrm{k}=1}^{\mathrm{n}} \mathrm{S}_{\mathrm{k}}\right)<42\), then \(\mathrm{n}\) equalsJEE Mains 2024 Hard
More PYQs from JEE Mains
- For, \(\alpha, \beta, \gamma, \delta \in N\), if \(\int\left(\left(\frac{x}{e}\right)^{2 x}+\left(\frac{e}{x}\right)^{2 x}\right) \log _{ e } x d x=\frac{1}{\alpha}\left(\frac{ x }{ e }\right)^{\beta x}-\frac{1}{\gamma}\left(\frac{ e }{ x }\right)^{\delta x }+ C ,\) Where \(e =\sum \limits_{ n =0}^{\infty} \frac{1}{ n !}\) and \(C\) is constant of integration, then \(\alpha+2 \beta+3 \gamma-4 \delta\) is equal to:JEE Mains 2023 Hard
- Consider a rectangle \(ABCD\) having \(5,7,6,9\) points in the interior of the line segments \(AB,CD , BC , DA\) respectively. Let \(\alpha\) be the number of triangles having these points from different sides as vertices and \(\beta\) be the number of quadrilaterals having these points from different sides as vertices. Then \((\beta-\alpha)\) is equal to :JEE Mains 2021 Medium
- Let \(g\left( x \right) = \cos {x^2},f\left( x \right) = \sqrt x \) and \(\alpha ,\beta (\alpha < \beta )\) be the roots of the quadratic equation \(18{x^2} - 9\pi x + {\pi ^2} = 0\). Then the area (in sq. units) bounded by the curve \(y = \left( {gof} \right)\left( x \right)\) and the lines \(x = \alpha ,x = \beta \) and \(y = 0\) is :JEE Mains 2018 Hard
- \(ABCD \) is a trapezium such that \(AB\) and \(CD \) are parallel and \(BC\; \bot CD\). If \(\angle ADB = \theta \),\(BC=p\) and \( CD=q\) , then \(AB\) is equal to:JEE Mains 2013 Hard
- The number of points of discontinuity of the function \(f(\mathrm{x})=\left[\frac{\mathrm{x}^2}{2}\right]-[\sqrt{\mathrm{x}}], \mathrm{x} \in[0,4]\), where \([\cdot]\) denotes the greatest integer function is ________JEE Mains 2025 Easy
- If \(a=\lim _{x \rightarrow 0} \frac{\sqrt{1+\sqrt{1+x^4}}-\sqrt{2}}{x^4}\) and \(b=\lim _{x \rightarrow 0} \) \(\frac{\sin ^2 x}{\sqrt{2}-\sqrt{1+\cos x}}\), then the value of \(a b^3\) isJEE Mains 2024 Hard