Q.Check whether the relation R defined on the set $A = \{1, 2, 3, 4, 5, 6\}$ as $R = \{(a, b) : b = a + 1\}$ is reflexive, symmetric or transitive.

Showing the 12 most recent of 62 on this concept.

1. CBSE 2026Set V11 markMCQ
   Q.If a relation $R$ in the set $\{1, 2, 3\}$ be defined by $R = \{(1, 1),(2, 2)\}$ then $R$ is

   (a) symmetric but not transitive

   (b) transitive but not symmetric

   (c) symmetric and transitive

   (d) neither symmetric nor transitive

   ›Reveal solutionSolution

   $R=\{(1,1),(2,2)\}$ is both symmetric and transitive, so the answer is (c).

   Symmetry: whenever $(a,b)\in R$ we need $(b,a)\in R$. Here the only pairs are $(1,1)$ and $(2,2)$, and each is its own reverse, so symmetry holds. …

   🔒 Start your 14-day free trial to see the full solution →
2. CBSE 2026Set A1 markMCQ
   Q.What type of a relation is "less than" in the set of real numbers?

   (a) Only symmetric

   (b) Only transitive

   (c) Only reflexive

   (d) Equivalence

   ›Reveal solutionSolution

   "$<$" on $\mathbb{R}$ is transitive only.

   Consider the relation "$a < b$" on $\mathbb{R}$:

   • Reflexive? $a < a$ is false for every $a$, so NOT reflexive.
   • Symmetric? $a < b$ does not imply $b < a$, so NOT symmetric. …

   🔒 Start your 14-day free trial to see the full solution →
3. CBSE 2026Set ANNUAL1 markMCQ
   Q.If $R$ is the relation $\{(1,1),(2,2),(3,3),(1,2),(2,3),(1,3)\}$ on $A=\{1,2,3\}$, then which one of the following is true for $R$?

   (a) Reflexive but not symmetric

   (b) Reflexive but not transitive

   (c) Symmetric and transitive

   (d) Neither symmetric nor transitive

   ›Reveal solutionSolution

   $R$ is reflexive (it contains every $(x,x)$) but not symmetric, since $(1,2)\in R$ while $(2,1)\notin R$.

   Given: $R=\{(1,1),(2,2),(3,3),(1,2),(2,3),(1,3)\}$ on $A=\{1,2,3\}$.

   Reflexivity: $R$ is reflexive if $(x,x)\in R$ for every $x\in A$. Here $(1,1),(2,2),(3,3)$ are all present, so $R$ is reflexive.

   Symmetry: $R$ is symmetric if $(x,y)\in R\Rightarrow(y,x)\in R$. Here $(1,2)\in R$ but $(2,1)\notin R$. So $R$ is not symmetric.

   …

   🔒 Start your 14-day free trial to see the full solution →
4. CBSE 2026Set ANNUAL1 markMCQ
   Q.Let $R$ be the relation in the set $N$ given by $R = \{(a, b) : a = b - 2, b > 6\}$, choose the correct answer:

   (a) $(2, 4) \in R$

   (b) $(3, 8) \in R$

   (c) $(6, 8) \in R$

   (d) $(8, 6) \in R$

   ›Reveal solutionSolution

   Check each pair against both conditions $a=b-2$ and $b>6$.

   $R=\{(a,b): a=b-2,\ b>6\}$

   1. $(2,4)$: $a=b-2 \Rightarrow 2=2$ ✓, but $b>6 \Rightarrow 4>6$ ✗. Not in $R$.
   2. $(3,8)$: $a=b-2 \Rightarrow 3=6$ ✗. Not in $R$. …

   🔒 Start your 14-day free trial to see the full solution →
5. CBSE 2026Set ANNUAL1 markMCQ
   Q.The value of \tan^{-1}\left(\frac{1}{x}\right) will be:

   (a) \tan x

   (b) \cot x

   (c) \cot^{-1}\frac{1}{x}

   (d) \cot^{-1} x

   ›Reveal solutionSolution

   $\tan^{-1}(1/x)$ and $\cot^{-1}x$ are the same angle for positive $x$, because tangent and cotangent are reciprocal functions.

   Concept: For $x>0$, the standard identity is

   $\tan^{-1}\left(\frac{1}{x}\right) = \cot^{-1} x$ …

   🔒 Start your 14-day free trial to see the full solution →
6. CBSE 2026Set ANNUAL1 markMCQ
   Q.Choose the correct answer : Let $R$ be a relation in the set $\{1,2,3,4\}$ given by $R=\{(1,2),(2,2),(1,1),(4,4),(1,3),(3,3),(3,2)\}$. Then

   (a) $R$ is reflexive and symmetric but not transitive

   (b) $R$ is reflexive and transitive but not symmetric

   (c) $R$ is symmetric and transitive but not reflexive

   (d) $R$ is an equivalence relation

   ›Reveal solutionSolution

   Test $R$ against the three defining properties (reflexive, symmetric, transitive) one at a time, directly from its listed ordered pairs.

   $R=\{(1,2),(2,2),(1,1),(4,4),(1,3),(3,3),(3,2)\}$ on $\{1,2,3,4\}$.

   Reflexive? Need $(a,a)\in R$ for every $a\in\{1,2,3,4\}$: $(1,1)$ ✓, $(2,2)$ ✓, $(3,3)$ ✓, $(4,4)$ ✓. All present — $R$ is reflexive.

   Symmetric? Need: whenever $(a,b)\in R$, also $(b,a)\in R$. Take $(1,2)\in R$: is $(2,1)\in R$? It is not in the list. So $R$ is not symmetric.

   Transitive? Need: whenever $(a,b)\in R$ and $(b,c)\in R$, also $(a,c)\in R$. Checking every chain:

   • $(1,1),(1,2)\Rightarrow(1,2)$ ✓
   • $(1,1),(1,3)\Rightarrow(1,3)$ ✓
   • $(1,2),(2,2)\Rightarrow(1,2)$ ✓
   • $(1,3),(3,3)\Rightarrow(1,3)$ ✓
   • $(1,3),(3,2)\Rightarrow(1,2)$ ✓ …

   🔒 Start your 14-day free trial to see the full solution →
7. CBSE 2026Set ANNUAL1 markMCQ
   Q.If $R$ be the relation in the set $N$ given by $R = \{(a,b): a = b - 2, b > 6\}$, then

   (a) $(2, 4) \in R$

   (b) $(3, 8) \in R$

   (c) $(6, 8) \in R$

   (d) $(8, 7) \in R$

   ›Reveal solutionSolution

   Only $(6,8)$ satisfies $a=b-2$ with $b>6$.

   …

   🔒 Start your 14-day free trial to see the full solution →
8. CBSE 2025Set X11 markMCQ
   Q.A relation $R$ in a set $A$ is called Reflexive relation if

   (a) $(a, a) \in R$ for all $a \in A$

   (b) $(a, a) \in R$ for atleast one $a \in A$

   (c) $(a, b) \in R$ implies $(b, a) \in R$

   (d) $(a, b) \in R$ and $(b, c) \in R$ implies $(a, c) \in R$

   ›Reveal solutionSolution

   Tests the definition of a reflexive relation — correct option is (a).

   A relation $R$ on a set $A$ is reflexive when every element is related to itself. Formally, $(a,a)\in R$ must hold for all $a\in A$ — not just for at least one element. Option (c) states symmetry ($(a,b)\in R\Rightarrow(b,a)\in R$) and option (d) states transitivit …

   🔒 Start your 14-day free trial to see the full solution →
9. CBSE 2025Set ANNUAL1 markMCQ
   Q.Value of $\tan^{-1}\left(\tan \dfrac{7\pi}{6}\right)$ is:

   (a) $\dfrac{\pi}{6}$

   (b) $\dfrac{7\pi}{6}$

   (c) $\dfrac{1}{\sqrt{3}}$

   (d) $\dfrac{5\pi}{6}$

   ›Reveal solutionSolution

   Use periodicity of $\tan$ to bring the angle into the principal range $\left(-\tfrac{\pi}{2},\tfrac{\pi}{2}\right)$ of $\tan^{-1}$.

   Since $\tan$ has period $\pi$: $\tan\dfrac{7\pi}{6} = \tan\left(\dfrac{7\pi}{6}-\pi\right) = \tan\dfrac{\pi}{6}$.

   …

   🔒 Start your 14-day free trial to see the full solution →
10. CBSE 2025Set IX1 markMCQ
    Q.A relation $R = \{(a, b) : a = b - 1,\ b \geq 3\}$ is defined on set $N$, then

    (a) $(2, 4) \in R$

    (b) $(4, 5) \in R$

    (c) $(4, 6) \in R$

    (d) $(1, 3) \in R$

    ›Reveal solutionSolution

    Only $(4,5)$ satisfies $a=b-1$ with $b\ge 3$; option (b).

    Concept. A pair $(a,b)$ belongs to $R$ only if it satisfies both conditions: $a=b-1$ and $b\ge 3$.

    • $(2,4)$: $b-1=3\ne 2$. ✗ …

    🔒 Start your 14-day free trial to see the full solution →
11. CBSE 2025Set A1 mark
    Q.If $-1 \le x \le 1$, then $\sin(\sin^{-1}x) =$ ______.

    ›Reveal solutionSolution

    $\sin$ and $\sin^{-1}$ are inverse functions of each other on $[-1,1]$, so applying one after the other returns the original input.

    For $-1 \le x \le 1$, $\sin^{-1}x$ is defined and gives an angle $\theta \in \left[-\dfrac{\pi}{2},\dfrac{\pi}{2}\right]$ such that $\sin\theta = x$. Applying $\sin$ to this angle simply recovers $x$: …

    🔒 Start your 14-day free trial to see the full solution →
12. CBSE 2025Set ANNUAL1 markMCQ
    Q.If $A=\{1,2,3,4\}$ and $R=\{(a,b)\mid a+b\ \text{is an odd number},\ a,b\in A\}$ is a relation from $A$ to $A$, then which of the following is true for the relation $R$?

    (i) Reflexive

    (ii) Symmetric

    (iii) Transitive

    (iv) Equivalent

    ›Reveal solutionSolution

    Check each property directly: $R$ turns out to be symmetric only.

    $A=\{1,2,3,4\}$, $R=\{(a,b): a+b \text{ is odd}\}$.

    Reflexive? $(a,a)$ needs $a+a=2a$ to be odd — but $2a$ is always even. So $R$ is not reflexive.

    Symmetric? If $a+b$ is odd, then $b+a=a+b$ is the same sum, also odd. So $(a,b)\in R \Rightarrow (b,a)\in R$. $R$ is symmetric.

    …

    🔒 Start your 14-day free trial to see the full solution →