JEE Mains · Maths · STD 12 - 1. relation and function
Let \(P\) be the relation defined on the set of all real numbers such that \(P = \left\{ {\left( {a,b} \right):{{\sec }^2}\,a - {{\tan }^2}\,b = 1\,} \right\}\). Then \(P\) is
- A reflexive and symmetric but not transitive
- B reflexive and transitive but not symmetric
- C symmetric and transitive but not reflexive
- D an equivalence relation
Answer & Solution
Correct Answer
(D) an equivalence relation
Step-by-step Solution
Detailed explanation
\(P = \left\{ {\left( {a,b} \right):{{\sec }^2}a - {{\tan }^2}b = 1} \right\}\) For reflexive: \({\sec ^2}a - {\tan ^2}b = 1\) \(\left( {true\,\,\forall \,\,a} \right)\) For symmetric: \({\sec ^2}b - {\tan ^2}a = 1\) \(L.H.S\)…
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 each \(t \in R\), let \([t]\) be the greatest integer less than or equal to \(t\). Then \(\mathop {\lim }\limits_{x \to 1 + } \,\frac{{\left( {1 - \left| x \right| + \sin \left| {1 + x} \right|} \right)\,\sin \,\left( {\frac{\pi }{2}\,\left[ {1 - x} \right]} \right)}}{{\left| {1 - x} \right|\left| {1 - x} \right|}}\)JEE Mains 2019 Hard
- Let \(\vec{a}=\vec{i}-\alpha \vec{j}+\beta \hat{k}, \vec{b}=3 \hat{i}+\beta \hat{j}-\alpha \hat{k}\) and \(\vec{c}=-\alpha \hat{i}-2 \hat{j}+\hat{k}\), where \(\alpha\) and \(\beta\) are integers. If \(\vec{a} \cdot \vec{b}=-1\) and \(\overrightarrow{\mathrm{b}} \cdot \overrightarrow{\mathrm{c}}=10\), then \((\overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{b}}) \cdot \overrightarrow{\mathrm{c}}\) is equal to \(.....\)JEE Mains 2021 Hard
- The greatest positive integer \(\mathrm{k},\) for which \(49^k+1\) is a factor of the sum \(49^{125}+49^{124}+\ldots .49^{2}+49+1,\) isJEE Mains 2020 Hard
- If the midpoint of a chord of the ellipse \(\frac{x^2}{9}+\frac{y^2}{4}=1\) is \((\sqrt{2}, 4 / 3)\), and the length of the chord is \(\frac{2 \sqrt{\alpha}}{3}\), then \(\alpha\) is :JEE Mains 2025 Medium
- Two parabolas with a common vertex and with axes along \(x-\) axis and \(y-\) axis, respectively, intersect each other in the first quadrant. if the length of the latus rectum of each parabola is \(3\) , then the equation of the common tangent to the two parabolas is?JEE Mains 2018 Hard
- If domain of the function \(\log _e\left(\frac{6 x^2+5 x+1}{2 x-1}\right)+\cos ^{-1}\left(\frac{2 x^2-3 x+4}{3 x-5}\right)\) is \((\alpha, \beta) \cup(\gamma, \delta]\), then \(18\left(\alpha^2+\beta^2+\gamma^2+\delta^2\right)\) is equal to \(....\).JEE Mains 2023 Hard
More PYQs from JEE Mains
- Let \(\lambda\) be an interger. If the shortest distance between the lines \(x -\lambda=2 y -1=-2 z\) and \(x = y +2 \lambda= z -\lambda\) is \(\frac{\sqrt{7}}{2 \sqrt{2}},\) then the value of
\(|\lambda|\) is ...... .JEE Mains 2021 Hard - Let \(N\) denote the set of all natural numbers. Define two binary relations on \(N\) as \(R_1 = \{(x,y) \in N \times N : 2x + y= 10\}\) and \(R_2 = \{(x,y) \in N\times N : x+ 2y= 10\} \). ThenJEE Mains 2018 Hard
- Let \(\vec{a}\) and \(\vec{b}\) be two vector such that \(|\vec{a}|=\sqrt{14}\), \(|\vec{b}|=\sqrt{6}\) and \(|\vec{a} \times \vec{b}|=\sqrt{48}\). Then \((\vec{a} \cdot \vec{b})^2\) is equal to \(...........\).JEE Mains 2023 Easy
- Let the line \(\ell: x =\frac{1- y }{-2}=\frac{ z -3}{\lambda}, \lambda \in R\) meet the plane \(P : x +2 y +3 z =4\) at the point \((\alpha, \beta, \gamma)\). If the angle between the line \(\ell\) and the plane \(P\) is \(\cos ^{-1}\left(\sqrt{\frac{5}{14}}\right)\), then \(\alpha+2 \beta+6 \gamma\) is equal toJEE Mains 2023 Hard
- Let \( \vec a ,\vec b\) and \(\vec c \) be three non-zero vectors such that no two of them are collinear and \(\left( {\vec a \times \vec b} \right) \times \vec c = \frac{1}{3}\left| \vec b \right|\left| \vec c \right|\vec a\). If \(\theta \) is the angle between vectors \(\vec b\) and \(\vec c\) , then a value of \(\sin \theta \) is :JEE Mains 2015 Hard
- If P is a point on the circle \( x^{2}+y^{2}=4 \), Q is a point on the straight line \( 5x+y+2=0 \) and \( x-y+1=0 \) is the perpendicular bisector of PQ, then 13 times the sum of abscissa of all such point P is ........... .JEE Mains 2026 Hard