Top 50 Most Repeated RELATIONS AND FUNCTIONS PYQs | JEE MAINS
A curated collection of the most important questions from RELATIONS AND FUNCTIONS, fully solved with step-by-step concepts to prepare for JEE MAINS.
A curated collection of the most important questions from RELATIONS AND FUNCTIONS, fully solved with step-by-step concepts to prepare for JEE MAINS.
Reflexivity requires that each element of the set be related to itself. The second option defines symmetry, the third defines transitivity, and the fo...
Read Full Step-by-Step Solution →Set \(y=3x-5\). Solving for \(x\) gives \(x=(y+5)/3\). Since the original linear function is bijective on \(\mathbb{R}\), the inverse is defined for a...
Read Full Step-by-Step Solution →A linear function with non‑zero slope is one‑to‑one, hence invertible. Solving $y=3x-5$ for $x$ gives $x=(y+5)/3$, so $f^{-1}(x)=(x+5)/3$....
Read Full Step-by-Step Solution →Bijective functions from set to itself are permutations. For 3 elements, 3! = 6....
Read Full Step-by-Step Solution →For an odd function, f(−x) = −f(x). Substituting −x gives (−x)³ − 4(−x) = −x³ + 4x = −(x³ − 4x) = −f(x), confirming odd symmetry. Hence the graph is s...
Read Full Step-by-Step Solution →$g(x) > 1$ and $x \ne 2$ ⇒ $x < 1.5$ or $x > 3$; only $x>3$ valid....
Read Full Step-by-Step Solution →R is an equivalence relation: reflexive (a-a=0), symmetric (if 3|a-b then 3|b-a), transitive (if 3|a-b and 3|b-c then 3|a-c)....
Read Full Step-by-Step Solution →An equivalence relation must be reflexive, symmetric, and transitive. The relation defined by an even difference satisfies all three properties, where...
Read Full Step-by-Step Solution →Let $x=n+f$ with $n=\lfloor x\rfloor$ and $0\le f<1$. Then $\lfloor 2x\rfloor =2n+\lfloor 2f\rfloor$. Solving
A reflexive relation must contain (a,a) for every element a. Symmetry requires that if (a,b) is present, (b,a) must also be present. The given set inc...
Read Full Step-by-Step Solution →First compute \(g(2)=2^{2}-1=3\). Then evaluate \(f(3)=2\times3+3=9\). Hence \((f\circ g)(2)=9\)....
Read Full Step-by-Step Solution →$f$ is one-one if $D \le 0$.
Reflexivity requires that each element of the set be related to itself. The second option defines symmetry, the third defines transitivity, and the fo...
Read Full Step-by-Step Solution →Set \(y=3x-5\). Solving for \(x\) gives \(x=(y+5)/3\). Since the original linear function is bijective on \(\mathbb{R}\), the inverse is defined for a...
Read Full Step-by-Step Solution →A linear function with non‑zero slope is one‑to‑one, hence invertible. Solving $y=3x-5$ for $x$ gives $x=(y+5)/3$, so $f^{-1}(x)=(x+5)/3$....
Read Full Step-by-Step Solution →Bijective functions from set to itself are permutations. For 3 elements, 3! = 6....
Read Full Step-by-Step Solution →For an odd function, f(−x) = −f(x). Substituting −x gives (−x)³ − 4(−x) = −x³ + 4x = −(x³ − 4x) = −f(x), confirming odd symmetry. Hence the graph is s...
Read Full Step-by-Step Solution →$g(x) > 1$ and $x \ne 2$ ⇒ $x < 1.5$ or $x > 3$; only $x>3$ valid....
Read Full Step-by-Step Solution →R is an equivalence relation: reflexive (a-a=0), symmetric (if 3|a-b then 3|b-a), transitive (if 3|a-b and 3|b-c then 3|a-c)....
Read Full Step-by-Step Solution →An equivalence relation must be reflexive, symmetric, and transitive. The relation defined by an even difference satisfies all three properties, where...
Read Full Step-by-Step Solution →Let $x=n+f$ with $n=\lfloor x\rfloor$ and $0\le f<1$. Then $\lfloor 2x\rfloor =2n+\lfloor 2f\rfloor$. Solving
A reflexive relation must contain (a,a) for every element a. Symmetry requires that if (a,b) is present, (b,a) must also be present. The given set inc...
Read Full Step-by-Step Solution →First compute \(g(2)=2^{2}-1=3\). Then evaluate \(f(3)=2\times3+3=9\). Hence \((f\circ g)(2)=9\)....
Read Full Step-by-Step Solution →$f$ is one-one if $D \le 0$.
Reflexivity requires that each element of the set be related to itself. The second option defines symmetry, the third defines transitivity, and the fo...
Read Full Step-by-Step Solution →Set \(y=3x-5\). Solving for \(x\) gives \(x=(y+5)/3\). Since the original linear function is bijective on \(\mathbb{R}\), the inverse is defined for a...
Read Full Step-by-Step Solution →A linear function with non‑zero slope is one‑to‑one, hence invertible. Solving $y=3x-5$ for $x$ gives $x=(y+5)/3$, so $f^{-1}(x)=(x+5)/3$....
Read Full Step-by-Step Solution →Bijective functions from set to itself are permutations. For 3 elements, 3! = 6....
Read Full Step-by-Step Solution →For an odd function, f(−x) = −f(x). Substituting −x gives (−x)³ − 4(−x) = −x³ + 4x = −(x³ − 4x) = −f(x), confirming odd symmetry. Hence the graph is s...
Read Full Step-by-Step Solution →$g(x) > 1$ and $x \ne 2$ ⇒ $x < 1.5$ or $x > 3$; only $x>3$ valid....
Read Full Step-by-Step Solution →R is an equivalence relation: reflexive (a-a=0), symmetric (if 3|a-b then 3|b-a), transitive (if 3|a-b and 3|b-c then 3|a-c)....
Read Full Step-by-Step Solution →An equivalence relation must be reflexive, symmetric, and transitive. The relation defined by an even difference satisfies all three properties, where...
Read Full Step-by-Step Solution →Let $x=n+f$ with $n=\lfloor x\rfloor$ and $0\le f<1$. Then $\lfloor 2x\rfloor =2n+\lfloor 2f\rfloor$. Solving
A reflexive relation must contain (a,a) for every element a. Symmetry requires that if (a,b) is present, (b,a) must also be present. The given set inc...
Read Full Step-by-Step Solution →First compute \(g(2)=2^{2}-1=3\). Then evaluate \(f(3)=2\times3+3=9\). Hence \((f\circ g)(2)=9\)....
Read Full Step-by-Step Solution →$f$ is one-one if $D \le 0$.
Reflexivity requires that each element of the set be related to itself. The second option defines symmetry, the third defines transitivity, and the fo...
Read Full Step-by-Step Solution →Set \(y=3x-5\). Solving for \(x\) gives \(x=(y+5)/3\). Since the original linear function is bijective on \(\mathbb{R}\), the inverse is defined for a...
Read Full Step-by-Step Solution →A linear function with non‑zero slope is one‑to‑one, hence invertible. Solving $y=3x-5$ for $x$ gives $x=(y+5)/3$, so $f^{-1}(x)=(x+5)/3$....
Read Full Step-by-Step Solution →Bijective functions from set to itself are permutations. For 3 elements, 3! = 6....
Read Full Step-by-Step Solution →For an odd function, f(−x) = −f(x). Substituting −x gives (−x)³ − 4(−x) = −x³ + 4x = −(x³ − 4x) = −f(x), confirming odd symmetry. Hence the graph is s...
Read Full Step-by-Step Solution →$g(x) > 1$ and $x \ne 2$ ⇒ $x < 1.5$ or $x > 3$; only $x>3$ valid....
Read Full Step-by-Step Solution →R is an equivalence relation: reflexive (a-a=0), symmetric (if 3|a-b then 3|b-a), transitive (if 3|a-b and 3|b-c then 3|a-c)....
Read Full Step-by-Step Solution →