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Sets & Relations: Let Relation Defined Following False

JEE Maths question with a full step-by-step solution.

Question
Let RR be a relation in NN defined by R={(1+x, 1+x2):x≤5, x∈N}R = \{(1 + x,\ 1 + x^2) : x \le 5,\ x \in N\}. Which of the following is false?
AR={(2,2),(3,5),(4,10),(5,17),(6,25)}R = \{(2, 2), (3, 5), (4, 10), (5, 17), (6, 25)\}correct
BDomain of R={2,3,4,5,6}R = \{2, 3, 4, 5, 6\}
CRange of R={2,5,10,17,26}R = \{2, 5, 10, 17, 26\}
DNone of these
Solution
Substitute x=1,2,3,4,5x = 1, 2, 3, 4, 5 into (1+x, 1+x2)(1 + x,\ 1 + x^2):
(2,2), (3,5), (4,10), (5,17), (6,26)(since 1+52=26).(2, 2),\ (3, 5),\ (4, 10),\ (5, 17),\ (6, 26) \qquad (\text{since } 1 + 5^2 = 26).
∴Domain={2,3,4,5,6},Range={2,5,10,17,26}.\therefore \text{Domain} = \{2, 3, 4, 5, 6\}, \quad \text{Range} = \{2, 5, 10, 17, 26\}.
 Option (1) writes the last pair as (6,25)(6, 25) instead of (6,26)(6, 26), so it is false. Correct answer: (1)
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