Limits and Derivatives · Question 11

JEE Main 2025 (Online) 8th April Evening ShiftMCQMedium📈 Topic in 32% papers+4−1

Given below are two statements: In the light of the above statements, choose the correct answer from the options given below:

Statement I is false but Statement II is true
Both Statement I and Statement II are false
Both Statement I and Statement II are true
Statement I is true but Statement II is false

Answer

(3) Both Statement I and Statement II are true

Solution

Statement I: Using series expansions near x = 0:

-1x = x - x33 + x55 -

e 1+x1-x = 12 [ e(1+x) - e(1-x) ] = x + x33 + x55 +

-1x + e 1+x1-x - 2x = 2x55 + (terms in x7, x9, )

x 0 -1x + e 1+x1-x - 2xx5 = 25 Statement I is true.

Statement II: 1 form, so

x 1x 21-x = e x 1(x - 1) 21-x = e-2 = 1e2 Statement II is true.

Answer: (3)

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