Sets, Relations & Functions: JEE Main Mathematics Previous Year Questions

734 previous year questions from Sets, Relations & Functions. Here are the 25 most important ones; open any question for the correct answer and a full step-by-step solution.

1. 1.Let $A=\text{1,2,3}$. The number of relations on $A$, containing $\text{(}1\text{,}2\text{)}$ and $\text{(}2\text{,}3\text{)}$, which are refle…
2. 2.Let $a\text{,}b\text{,}c$ be real numbers. A set formed with $a$. $b\text{,}c$ whose order of occurrence is pre-assigned is called .......
3. 3.$\text{lim}x\to 2\frac{x^3-x^2-x-2}{2x^3-3x^2-3x+2}=$
4. 4.$\text{lim}y\to 1(\frac{1}{y^2-1}-\frac{2}{y^4-1})=$
5. 5.The number of elements in the set {n $\in$ Z :|$n^2$ - 10n + 19|< 6} is_______.
6. 6.…
7. 7.For $x\text{∈}\left(0\text{,}\frac{3}{2}\right)$, let $f\left(x\right)=\sqrt{x}\text{,}g\left(x\right)=\text{tan}x$ and $h\left(x\right)=\frac{1-x^2}{1+x^2}$.…
8. 8.If $x^2+y^2=t-\frac{1}{t}\text{,}{x}^4+y^4=t^2+\frac{1}{t^2}$ then $\frac{\text{dy}}{\text{dx}}=$
9. 9.If the function $f\text{(}x\text{)}=\frac{\text{log}\text{⁡}\text{(}1+\text{ax}\text{)}-\text{log}\text{⁡}\text{(}1-\text{bx}\text{)}}{x}$, $x\ne 0$ is continuous at…
10. 10.If a function defined by $f\text{(}x\text{)}=\frac{{(3^x-1)}^2}{\text{sin}\text{⁡}\text{xlog}\text{⁡}\text{(}1+x\text{)}}\text{,}x\ne 0$, is continuous at $x=0$,…
11. 11.The range of the function $f\text{(}x\text{)}=\sqrt{9-x^2}$ is
12. 12.Let $R_1$={(a,b) $\text{∈}$ NxN:|a-b|$\le$13}and $R_2$ ={(a,b) $\text{∈}$ NxN: |a-b|$\ne$13}. Then on N:
13. 13.On the set of all non-zero reals, an operation $\ast$ is defined as $a\ast b=\frac{3\text{ab}}{2}$. In this group, a solution of $\text{(}2\ast x\text{)}\ast 3^{-1}=4^{-1}$ is
14. 14.${\text{lim}}_{x\to a}\frac{\sqrt{a+2x}-\sqrt{3x}}{\sqrt{3a+x}-2\sqrt{x}}=$
15. 15.The derivative of $y=\text{(}\text{sin}\text{⁡}x{\text{)}}^{x^2}$ with respect to $x$ is
16. 16.${\text{Lt}}_{x\to 0}\text{⁡}\frac{x{2}^x-x}{1-\text{cos}\text{⁡}x}=$
17. 17.Among the relations $S(\left(a\text{,}b\right)\text{:}a\text{,}bϵR-\left(0\right)\text{,}2+\frac{a}{b}>0)$ and…
18. 18.If ${\text{cos}}^{-1}\text{⁡}\left(\frac{y}{b}\right)=n\text{log}\text{⁡}\left(\frac{x}{n}\right)$, then
19. 19.The number of points on the parabola $y^2=x$ at which the slope of the normal drawn at the point is equal to the $x$-coordinate of that point is
20. 20.If $f\text{(}x\text{)}=\frac{1+\text{sec}\text{⁡}x}{2\text{(}\text{sec}\text{⁡}x-1\text{)}}$ for $0<x<\frac{\pi }{2}$ and…
21. 21.If $D$ is the domain and $G$ is the range of the real valued function $f\text{(}x\text{)}=\sqrt{\frac{1-x^2}{1+x^2}}$, then $D\text{∩}G=$
22. 22.In a certain town $65\text{\%}$ families own cell phones, 15000 families own scooter and $15\text{\%}$ families own both. Taking into consideration that the families ow…
23. 23.If the range of…
24. 24.If $A=(x\text{∈}R/\frac{\pi }{4}\le x\le \frac{\pi }{3})$ and $f\text{(}x\text{)}=\text{sin}\text{⁡}x-x$, then $f\text{(}A\text{)}$ is equal to
25. 25.If $f\text{(}x\text{)}={\text{cot}}^{-1}\text{⁡}\left(\frac{x^x-x^{-x}}{2}\right)$, then $f^{\text{’}}\text{(}1\text{)}=$