Sets, Relations & Functions · JEE Main previous year questions

2012 6 questions

1. Q122012 · 26 May 2012 · Shift 1

   Let $A$ and $B$ be non empty sets in $R$ and $f:A\to B$ is a bijective function. Statement 1: $f$ is an onto function. Statement 2: There exists a function $g:B\to A$ such that $fog=I_B$.

   1. A.Statement 1 is true, Statement 2 is false.
   2. B.Statement 1 is true, Statement 2 is true; Statement 2 is a correct explanation for Statement 1.
   3. C.Statement 1 is false, Statement 2 is true.
   4. D.Statement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation for Statement 1.
   Show answer

   Answer: D

2. Q92012 · 12 May 2012 · Shift 1

   If $A=\{x\in z^{+}:x<10\text{ and }x\text{ is a multiple of 3 or 4}\}$, where $z^{+}$ is the set of positive integers, then the total number of symmetric relations on $A$ is

   1. A.$2^5$
   2. B.$2^{15}$
   3. C.$2^{10}$
   4. D.$2^{20}$
   Show answer

   Answer: B

3. Q112012 · 12 May 2012 · Shift 1

   Statement 1: If $A$ and $B$ be two sets having $p$ and $q$ elements respectively, where $q>p$. Then the total number of functions from set $A$ to set $B$ is $q^p$. Statement 2: The total number of selections of $p$ different objects out of $q$ objects is ${}^q{C}_p$.

   1. A.Statement 1 is true, Statement 2 is false.
   2. B.Statement 1 is true, Statement 2 is true; Statement 2 is not a correct explanation of Statement 1.
   3. C.Statement 1 is false, Statement 2 is true.
   4. D.Statement 1 is true, Statement 2 is true; Statement 2 is a correct explanation of Statement 1.
   Show answer

   Answer: D

4. Q32012 · 7 May 2012 · Shift 1

   If the number of 5-element subsets of the set $A=\{a_1,a_2,\dots ,a_{20}\}$ of 20 distinct elements is $k$ times the number of 5-element subsets containing $a_4$, then $k$ is

   1. A.5
   2. B.$\frac{20}{7}$
   3. C.4
   4. D.$\frac{10}{3}$
   Show answer

   Answer: C

5. Q132012 · 7 May 2012 · Shift 1

   The range of the function $f(x)=\frac{x}{1+|x|},x\in R$, is

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

   Answer: B

6. Q152012 · 7 May 2012 · Shift 1

   If $x+|y|=2y$, then $y$ as a function of $x$, at $x=0$ is

   1. A.differentiable but not continuous
   2. B.continuous but not differentiable
   3. C.continuous as well as differentiable
   4. D.neither continuous nor differentiable
   Show answer

   Answer: B