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Yukti Vault

Algebra

Sets, Relations and Function: JEE Main & Advanced PYQs

214 previous year questions on Sets, Relations and Function from JEE Main and JEE Advanced papers, each with its exam and year, an answer and a solution.

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Questions 201-214 of 214

  1. Solve the following equation for $x$: $2\log_{x}a+\log_{ax}a+3\log_{a^{2}x}a=0$, $a>0$.
  2. The number $\log_{2}7$ is
  3. The maximum value of $z$ in the following equation $z=6xy+y^{2}$, where $3x+4y\le100$ and $4x+3y\le75$ for $x\ge0$ and $y\ge0$ is $\_\_\_\_\_\_$ .
  4. In a survey of $220$ students of a higher secondary school, it was found that at least $125$ and at most $130$ students studied Mathematics; at least $85$ and at most …
  5. Let a relation $R$ on $\mathbb{N}\times\mathbb{N}$ be defined as: $(x_1,y_1)\,R\,(x_2,y_2)$ if and only if $x_1\le x_2$ or $y_1\le y_2$. Consider the two statements: (I) …
  6. If $S=\{a\in\mathbf{R}:|2a-1|=3[a]+2\{a\}\}$, where $[t]$ denotes the greatest integer less than or equal to $t$ and $\{t\}$ represents the fractional part of $t$, then …
  7. Let $A=\{a,b,c\}$ and $B=\{1,2,3,4\}$. Then the number of elements in the set $C=\{f:A\to B\mid2\in f(A)\text{ and }f\text{ is not one-one}\}$ is $\_\_\_\_\_\_\_\_$ .
  8. Set $A$ has $m$ elements and Set $B$ has $n$ elements. If the total number of subsets of $A$ is $112$ more than the total number of subsets of $B$, then the value of …
  9. Let $A=\{1,2,3,\ldots,10\}$ and $B=\left\{\dfrac{m}{n}:m,n\in A,\ m<n\text{ and }\gcd(m,n)=1\right\}$. Then $n(B)$ is equal to :
  10. The number of non-empty equivalence relations on the set $\{1,2,3\}$ is :
  11. Let $A=\{1,2,3,4\}$ and $B=\{1,4,9,16\}$. Then the number of many-one functions $f:A\to B$ such that $1\in f(A)$ is equal to :
  12. Let $A=\{1,2,3\}$. The number of relations on $A$, containing $(1,2)$ and $(2,3)$, which are reflexive and transitive but not symmetric, is $\_\_\_\_\_\_\_\_$ .
  13. Let $R=\{(1,2),(2,3),(3,3)\}$ be a relation defined on the set $\{1,2,3,4\}$. Then the minimum number of elements, needed to be added in $R$ so that $R$ becomes an …
  14. Let $R=\{(x,y):x,y\in N$ and $x^{2}-4xy+3y^{2}=0\}$, where $N$ is the set of all natural numbers. Then the relation $R$ is :

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