JEE Main 2026 · 6 Apr · Shift 2 · Mathematics Q21

← JEE Main 2026 · 6 Apr · Shift 2

MathematicsInteger+4 / -1Question 21 of 75

Let $R=\left\{(x,y)\in\mathbf N\times\mathbf N:\log_e(x+y)\le2\right\}$ . Then the minimum number of elements, required to be added in R to make it a transitive relation, is ________.

Your answer

Answer and worked solution

Official answer: 15

R. $\log_e(x+y)\le2$ means $x+y\le e^2\approx7.39$ , so $x+y\le7$ . That is $\sum_{x=1}^6(7-x)=21$ pairs.

Transitive closure. For $a,c\le6$ , $(a,1)$ and $(1,c)$ are in R, so $(a,c)$ must be added. The set $\{1,\dots,6\}^2$ (36 pairs) is transitive and contains R.

Added: $36-21=15$ .

Answer: 15

Topics:Relations

← Previous question Next question →

JEE Main 2026 · 6 Apr · Shift 2, Mathematics question 21