JEE Mathematics 2026 Question with Solution

Given: The relation is

Find: The minimum number of ordered pairs to be added so that the relation becomes symmetric.

A relation is symmetric if whenever $(x,y) \in R$, then $(y,x) \in R$ must also be in the relation.

From the given condition,

Now check values of $x \in M$ for which $y$ is an integer and also belongs to $M$.

The solution gives:

Hence,

Now test symmetry:

• $(3,3)$ is symmetric by itself.
• $(7,8) \in R$ but $(8,7) \notin R$.
• $(11,13) \in R$ but $(13,11) \notin R$.

So the missing reverse pairs explicitly identified in the working are

The provided the solution finally concludes that the total minimum number of elements required to be added is $4$, and states that the correct option is B. Although the intermediate listed reverse pairs are two, the source solution's final conclusion is $4$, which is taken as the authoritative answer per the extraction rule.

Therefore, the correct option is B.

Given: $R = \{(x, y) : 4y = 5x - 3,\; x, y \in M\}$ with $M = \{1,2,3,\ldots,16\}$.

Find: How many elements must be added to make $R$ symmetric.

Use the definition: for every pair already present in the relation, its reverse pair must also be present after completion. The source solution identifies the existing pairs as

and then marks the reverse pairs of the non-diagonal elements as missing.

The solution's concludes with Final Answer: $4$ and marks Option B as correct. Hence the extracted answer is B.