JEE Mains · Maths · STD 12 - 1. relation and function
If \(\mathrm{R}=\left\{(\mathrm{x}, \mathrm{y}): \mathrm{x}, \mathrm{y} \in \mathrm{Z}, \mathrm{x}^{2}+3 \mathrm{y}^{2} \leq 8\right\}\) is a relation on the set of integers \(\mathrm{Z},\) then the domain of \(\mathrm{R}^{-1}\) is
- A \(\{-2,-1,1,2\}\)
- B \(\{-1,0,1\}\)
- C \(\{-2,-1,0,1,2\}\)
- D \(\{0,1\}\)
Answer & Solution
Correct Answer
(B) \(\{-1,0,1\}\)
Step-by-step Solution
Detailed explanation
\(R=\left\{(x, y): x, y \in z, x^{2}+3 y^{2} \leq 8\right\}\) For domain of \(\mathrm{R}^{-1}\) Collection of all integral of y's For \(x=0, \quad 3 y^{2} \leq 8\) \(\Rightarrow \mathrm{y} \in\{-1,0,1\}\)
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 \(f(x)=x^3-x^2 f^{\prime}(1)+x f^{\prime \prime}(2)-f^{\prime \prime \prime}(3), x \in R\), thenJEE Mains 2023 Hard
- Let \(B\) and \(C\) be the two points on the line \(y+x=0\) such that \(B\) and \(C\) are symmetric with respect to the origin. Suppose \(A\) is a point on \(y -2 x =2\) such that \(\triangle ABC\) is an equilateral triangle. Then, the area of the \(\triangle ABC\) isJEE Mains 2023 Hard
- If for some \(x \in R\), the frequency distribution of the marks obtained by \(20\) students in a test is
Marks \(2\) \(3\) \(5\) \(7\)
Frequency \((x+1)^2\) \(2x -5\) \(x^2 -3x\) \(x\)
Then the mean of the marks isJEE Mains 2019 Medium - Let \(ABC\) be a triangle whose circumcentre is at \(P\).If the position vectors \(A, B, C\) and \(P\) are \(\vec a,\vec b,\vec c\) and \(\frac{{\vec a + \vec b + \vec c}}{4}\) respectivey, then the position vector of the orthocentre of this triangle, isJEE Mains 2016 Hard
- Two sides of a parallelogram are along the lines \(4 x+5 y=0\) and \(7 x+2 y=0\). If the equation of one of the diagonals of the parallelogram is \(11 \mathrm{x}+7 \mathrm{y}=9\), then other diagonal passes through the point:JEE Mains 2021 Hard
- There are \(m\) men and two women participating in a chess tournament. Each participant plays two games with every other participant. If the number of games played by the men between themselves exceeds the number of games played between the men and the women by \(84,\) then the value of \(m\) isJEE Mains 2019 Hard
More PYQs from JEE Mains
- Slope of a line passing through \(P(2, 3)\) and intersecting the line, \(x + y = 7\) at a distance of \(4\) units from \(P,\) isJEE Mains 2019 Hard
- If the point \(\left( {2,\alpha ,\beta } \right)\) lies on the plane which passes through the points \((3, 4, 2)\) and \((7, 0, 6)\) and is perpendicular to the plane \(2x - 5y = 15\) , then is equal to \({2\alpha - 3\beta }\) is equal toJEE Mains 2019 Hard
- For \(\mathrm{x} \geq 0\), the least value of \(\mathrm{K}\), for which \(4^{1+\mathrm{x}}+4^{1-\mathrm{x}}\), \(\frac{\mathrm{K}}{2}, 16^{\mathrm{x}}+16^{-\mathrm{x}}\) are three consecutive terms of an \(A.P.\) is equal to :JEE Mains 2024 Hard
- Let the functions \(f: R \rightarrow R\) and \(g: R \rightarrow R\) be defined as \(f(x)=\left\{\begin{array}{ll}x+2, & x<0 \\ x^{2}, & x \geq 0\end{array}\right.\) and \(g(x)=\left\{\begin{array}{lr}x^{3}, & x<1 \\ 3 x-2, & x \geq 1\end{array}\right.\) Then, the number of points in \(R\) where \((fog)( x )\) is \(NOT\) differentiable is equal toJEE Mains 2021 Hard
- The number of real roots of the equation \(\sqrt{x^2-4 x+3}+\sqrt{x^2-9}=\sqrt{4 x^2-14 x+6}\), is:JEE Mains 2023 Hard
- The circle passing through the intersection of the circles, \(x^{2}+y^{2}-6 x=0\) and \(x^{2}+y^{2}-4 y=0\) having its centre on the line, \(2 x-3 y+12=0\), also passes through the pointJEE Mains 2020 Hard