JEE Mains · Maths · STD 11 - 1. set theory
Let \(A=\{1,2,3, \ldots, 10\}\) and \(B=\left\{\frac{m}{n}: m, n \in A, m \lt n\right.\) and \(\left.\operatorname{gcd}(m, n)=1\right\}\). Then \(n(B)\) is equal to :
- A \(36\)
- B \(31\)
- C \(37\)
- D \(29\)
Answer & Solution
Correct Answer
(B) \(31\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \mathrm{A}=\{1,2, \ldots, 10\} \\ & \mathrm{B}\left\{\frac{\mathrm{m}}{\mathrm{n}}=\mathrm{m}, \mathrm{n} \in \mathrm{A}, \mathrm{m} < \mathrm{n}, \operatorname{gcd}(\mathrm{m}, \mathrm{n})=1\right\} \\ & \mathrm{n}(\mathrm{B}) \end{aligned}\)…
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 \(\left(5, \frac{a}{4}\right)\), 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 \(A=\left[\begin{array}{ll}2 & 3 \\ a & 0\end{array}\right], a \in R\) be written as \(P+Q\) where \(P\) is a symmetric matrix and \(Q\) is skew symmetric matrix. If \(\operatorname{det}(Q)=9\), then the modulus of the sum of all possible values of determinant of \(P\) is equal to:JEE Mains 2021 Medium
- Let \([t]\) denote the greatest integer less than or equal to \(t\). Then the value of the integral \(\int_{-3}^{101}\left([\sin (\pi x)]+e^{[\cos (2 \pi x)]}\right) d x\) is equal toJEE Mains 2022 Hard
- If the locus of the point, whose distances from the point \((2,1)\) and \((1,3)\) are in the ratio \(5: 4\), is \(a x^2+b y^2+c x y+d x+e y+170=0\), then the value of \(\mathrm{a}^2+2 \mathrm{~b}+3 \mathrm{c}+4 \mathrm{~d}+\mathrm{e}\) is equal to :JEE Mains 2024 Hard
- Let \(\mathrm{x}_1, \mathrm{x}_2, \mathrm{x}_3, \mathrm{x}_4\) be in a geometric progression. \(2,7,9,5\) are subtracted respectively from \(x_1, x_2, x_3\) \(x_4\) then the resulting numbers are in an arithmetic progression. Then the value of \(\frac{1}{24}\left(x_1 x_2 x_3 x_4\right)\) is :JEE Mains 2025 Easy
- If \(y =\sum \limits_{ k =1}^{6} k \cos ^{-1}\left\{\frac{3}{5} \cos k x -\frac{4}{5} \sin k x \right\}\) then \(\frac{ dy }{ dx }\) at \(x =0\) isJEE Mains 2020 Medium
More PYQs from JEE Mains
- A coin is based so that a head is twice as likely to occur as a tail. If the coin is tossed \(3\) times, then the probability of getting two tails and one head is -JEE Mains 2024 Medium
- Two parabolas have the same focus \((4,3)\) and their directrices are the \(x\)-axis and the \(y\)-axis, respectively. If these parabolas intersects at the points \(A\) and \(B\), then \((A B)^2\) is equal to :JEE Mains 2025 Medium
- If the domain of the function \(f(x) = \sqrt{\log_{(0.6)}\left(\left|\dfrac{2x-5}{x^2-4}\right|\right)}\) is \((-\infty, a] \cup \{b\} \cup [c, d) \cup (e, \infty)\), then the value of \(a + b + c + d + e\) is _______.JEE Mains 2026 Hard
- If a variable line, \(3x + 4y -\lambda = 0\) is such that the two circles \(x^2 + y^2 -2x -2y + 1 = 0\) and \(x^2 + y^2 -18x -2y + 78 = 0\) are on its opposite sides, then the set of all values of \(\lambda \) is the intervalJEE Mains 2019 Hard
- If the parabolas \(y^2 = 4b\,(x -c)\) and \(y^2 = 8ax\) have a common normal, then which one of the following is a valid choice for the ordered triad \((a, b, c)\) ?JEE Mains 2019 Hard
- If \(\vec a \,\) and \(\vec b \,\) are non-collinear vectors, then the value of \(\alpha \) for which the vectors \(\vec u = \left( {\alpha - 2} \right)\vec a \, + \vec b \) and \(\,\vec v = \left( {2 + 3\alpha } \right)\vec a \, - 3\vec b \) are collinear is :JEE Mains 2013 Hard