Sets, Relations & Functions · JEE Main previous year questions

2021 30 questions

1. Q202021 · 26 Feb 2021 · Shift 1

   Let f be any function defined on R and let it satisfy the condition : $|f(x)-f(y)|\le |(x-y{)}^2|,\forall (x,y)\in R$ If $f(0)=1$, then :

   1. A.f(x) can take any value in R
   2. B.$f(x)<0,\forall x\in R$
   3. C.$f(x)>0,\forall x\in R$
   4. D.$f(x)=0,\forall x\in R$
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   Answer: C

2. Q82021 · 26 Feb 2021 · Shift 2

   Let $A=\{1,2,3,\dots \dots ,10\}$ and $f:A\to A$ be defined as $f(k)=\{\begin{array}{ll}k+1& \text{if }k\text{ is odd}\\ k& \text{if }k\text{ is even}\end{array}$ Then the number of possible functions $g:A\to A$ such that $g\circ f=f$ is :

   1. A.$5^5$
   2. B.$10^5$
   3. C.$5!$
   4. D.${}^{10}{\mathrm{C}}_5$
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   Answer: B

3. Q102021 · 26 Feb 2021 · Shift 2

   Let $f(x)={\sin }^{-1}x$ and $g(x)=\frac{x^2-x-2}{2x^2-x-6}$. If $g(2)={\lim }_{x\to 2}g(x)$, then the domain of the function fog is :

   1. A.$(-\infty ,-2]\cup \left[-\frac{4}{3},\infty \right)$
   2. B.$(-\infty ,-2]\cup [-1,\infty )$
   3. C.$(-\infty ,-2]\cup \left[-\frac{3}{2},\infty \right)$
   4. D.$(-\infty ,-1]\cup [2,\infty )$
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   Answer: A

4. Q32021 · 25 Feb 2021 · Shift 2

   Let x denote the total number of one-one functions from a set A with 3 elements to a set B with 5 elements and y denote the total number of one-one functions form the set A to the set $A\times B$. Then :

   1. A.$2y=273x$
   2. B.$y=91x$
   3. C.$2y=91x$
   4. D.$y=273x$
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   Answer: C

5. Q252021 · 25 Feb 2021 · Shift 2· Numerical answer

   A function f is defined on $[-3,3]$ as $$f(x)=\{\begin{array}{ll}\min \{|x|,2-x^2\},& -2\le x\le 2\\ [|x|],& 2<|x|\le 3\end{array}$$ where [x] denotes the greatest integer $\le$ x. The number of points, where f is not differentiable in $(-3,3)$ is ______ .

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   Answer: 5