JEE Mains · Maths · STD 12 - 1. relation and function
Let \(A=\{1,2,3,4\}\) and \(R\) be a relation on the set \(A \times A\) defined by \(R=\{((a, b),(c, d)): 2 a+3 b=4 c+5 d\}\). Then the number of elements in \(R\) is:
- A \(6\)
- B \(5\)
- C \(4\)
- D \(3\)
Answer & Solution
Correct Answer
(A) \(6\)
Step-by-step Solution
Detailed explanation
\(A =\{1,2,3,4\}\) \(R =\{( a , b ),( c , d )\}\) \(2 a +3 b =4 c +5 d =\alpha \text { let }\) \(2 a =\{2,4,6,8\} \quad 4 c =\{4,8,12,16\}\) \(3 b =\{3,6,9,12\} \quad 5 d =\{5,10,15,20\}\)…
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
- The number of solutions of the equation \(\cos 2 \theta \cos \frac{\theta}{2}+\cos \frac{5 \theta}{2}=2 \cos ^3 \frac{5 \theta}{2}\) in \(\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]\) is :JEE Mains 2025 Medium
- Let \(\mathrm{f}(\mathrm{x})\) be a quadratic polynomial such that \(\mathrm{f}(-1)+\mathrm{f}(2)=0 .\) If one of the roots of \(\mathrm{f}(\mathrm{x})=0\) is \(3,\) then its other root lies inJEE Mains 2020 Medium
- The shortest distance between the lines \(\vec{r}=\left(\dfrac{1}{3}\hat{i}+2\hat{j}+\dfrac{8}{3}\hat{k}\right)+\lambda(2\hat{i}-5\hat{j}+6\hat{k})\) and \(\vec{r}=\left(-\dfrac{2}{3}\hat{i}-\dfrac{1}{3}\hat{k}\right)+\mu(\hat{j}-\hat{k})\), \(\lambda,\mu \in \mathbb{R}\), is:JEE Mains 2026 Medium
- Let \(A\) and \(B\) be two invertible matrices of order \(3 \times 3\). If det \((ABA^T) = 8\) and \(det\,(AB^{-1}) = 8\), then \(det\, (BA^{-1} B^T)\) is equal toJEE Mains 2019 Hard
- Let \(R\) be the interior region between the lines \(3 x-y+1=0\) and \(x+2 y-5=0\) containing the origin. The set of all values of a, for which the points \(\left(a^2, a+1\right)\) lie in \(R\), is :JEE Mains 2024 Hard
- An arithmetic progression is written in the following way
The sum of all the terms of the \(10^{\text {th }}\) row is ..........JEE Mains 2024 Hard
More PYQs from JEE Mains
- The number of values of \(k\) for which the system of linear equations, \((k + 2) x + 10y = k,\,\,kx + (k + 3)y = k - 1\) has no solution, isJEE Mains 2018 Hard
- If \(\alpha=\lim _{x \rightarrow 0^{+}}\left(\frac{e^{\sqrt{\tan x}}-e^{\sqrt{x}}}{\sqrt{\tan x}-\sqrt{x}}\right)\) and \(\beta=\lim _{x \rightarrow 0}(1+\sin x)^{\frac{1}{2} \cot x}\) are the roots of the quadratic equation \(a x^2+b x-\sqrt{e}=0\), then 12 \(\log _e(a+b)\) is equal to .............JEE Mains 2024 Hard
- The integral \(\int_{1 / 4}^{3 / 4} \cos \left(2 \cot ^{-1} \sqrt{\frac{1-\mathrm{x}}{1+\mathrm{x}}}\right) \mathrm{dx}\) is equal to :JEE Mains 2024 Medium
- If the system of equations \(x + y+ z = 5\) ; \(x + 2y + 3z = 9\) ; \(x + 3y + \alpha z = \beta \) has infinitely many solutions, then \(\beta - \alpha \) equalsJEE Mains 2019 Hard
- A hyperbola passes through the foci of the ellipse \(\frac{ x ^{2}}{25}+\frac{ y ^{2}}{16}=1\) and its transverse and conjugate axes coincide with major and minor axes of the ellipse, respectively. If the product of their eccentricities in one, then the equation of the hyperbola is ...... .JEE Mains 2021 Medium
- If \(A\) is a \(3\times3\) matrix such that \(\left| {5.adjA} \right| = 5\), then \(\left| A \right|\) is equal toJEE Mains 2015 Hard