Sets, Relations & Functions · JEE Main previous year questions

2018 7 questions

1. Q12018 · 16 Apr 2018 · Shift 1

   Let $\mathbf{N}$ denote the set of all natural numbers. Define two binary relations on $\mathbf{N}$ as $R_1=\{(x,y)\in \mathbf{N}\times \mathbf{N}:2x+y=10\}$ and $R_2=\{(x,y)\in \mathbf{N}\times \mathbf{N}:x+2y=10\}$. Then :

   1. A.Range of $R_1$ is $\{2,4,8\}$.
   2. B.Range of $R_2$ is $\{1,2,3,4\}$.
   3. C.Both $R_1$ and $R_2$ are symmetric relations.
   4. D.Both $R_1$ and $R_2$ are transitive relations.
   Show answer

   Answer: B

2. Q112018 · 16 Apr 2018 · Shift 1

   Let M and m be respectively the absolute maximum and the absolute minimum values of the function, $f(x)=2x^3-9x^2+12x+5$ in the interval [0, 3]. Then M $-$ m is equal to :

   1. A.5
   2. B.9
   3. C.4
   4. D.1
   Show answer

   Answer: B

3. Q12018 · 15 Apr 2018 · Shift 1

   Consider the following two binary relations on the set $A=\{a,b,c\}$ : $R_1=\{(c,a),(b,b),(a,c),(c,c),(b,c),(a,a)\}$ and $R_2=\{(a,b),(b,a),(c,c),(c,a),(a,a),(b,b),(a,c)\}$. Then :

   1. A.both $R_1$ and $R_2$ are not symmetric.
   2. B.$R_1$ is not symmetric but it is transitive.
   3. C.$R_2$ is symmetric but it is not transitive.
   4. D.both $R_1$ and $R_2$ are transitive.
   Show answer

   Answer: C

4. Q32018 · 15 Apr 2018 · Shift 1

   The set of all $\alpha \in \mathbf{R}$, for which $w=\frac{1+(1-8\alpha )z}{1-z}$ is purely imaginary number, for all $z\in \mathbf{C}$ satisfying $|z|=1$ and $\text{Re }z\ne 1$, is :

   1. A.an empty set
   2. B.$\{0\}$
   3. C.$\left\{0,\frac{1}{4},-\frac{1}{4}\right\}$
   4. D.equal to $\mathbf{R}$
   Show answer

   Answer: B

5. Q52018 · 15 Apr 2018 · Shift 1

   Let S be the set of all real values of k for which the system of linear equations $x+y+z=2$ $2x+y-z=3$ $3x+2y+kz=4$ has a unique solution. Then S is :

   1. A.an empty set
   2. B.equal to $\{0\}$
   3. C.equal to $\mathbf{R}$
   4. D.equal to $\mathbf{R}-\{0\}$
   Show answer

   Answer: D

6. Q112018 · 15 Apr 2018 · Shift 1

   Let $S=\{(\lambda ,\mu )\in \mathbf{R}\times \mathbf{R}:f(t)=(|\lambda |e^{|t|}-\mu ).\sin (2|t|),t\in \mathbf{R}\text{, is a differentiable function}\}$. Then S is a subset of :

   1. A.$\mathbf{R}\times [0,\infty )$
   2. B.$[0,\infty )\times \mathbf{R}$
   3. C.$\mathbf{R}\times (-\infty ,0)$
   4. D.$(-\infty ,0)\times \mathbf{R}$
   Show answer

   Answer: A

7. Q12018 · 8 Apr 2018 · Shift 1

   Two sets A and B are as under : $\mathrm{A}=\{(a,b)\in \mathrm{R}\times \mathrm{R}:|a-5|<1\text{ and }|b-5|<1\}$; $\mathrm{B}=\{(a,b)\in \mathrm{R}\times \mathrm{R}:4(a-6{)}^2+9(b-5{)}^2\le 36\}$; Then

   1. A.neither $\mathrm{A}\subset \mathrm{B}$ nor $\mathrm{B}\subset \mathrm{A}$
   2. B.$\mathrm{B}\subset \mathrm{A}$
   3. C.$\mathrm{A}\subset \mathrm{B}$
   4. D.$\mathrm{A}\cap \mathrm{B}=\varphi$ ( an empty set )
   Show answer

   Answer: C