JEE Main 2021 · MathsMultiple choiceSingle correctHardApplication

JEE Main 25 July 2021, Shift 2, Maths Q62

Question 62 of 90 in this shift, Maths question 2 of 30, Section A.

The lowest integer which is greater than

\left(1+\frac{1}{10^{100}}\right)^{10^{100}}

is __________.

(1) $1$
(2) $2$
(3) $3$ Official answer
(4) $4$

Official answer

Option 3

NTA final key.

Chapter: Binomial Theorem
Topic: Binomial Coefficients
Idea tested: Bounding Binomial Coefficients

Same topic in other shifts

All Binomial Coefficients questions

2 Apr 2026, Shift 1 · Q7The number of elements in the set…MediumSingle correct
2 Apr 2026, Shift 2 · Q6If for $3 \le r \le 30$ , $\binom{30}{C_{30-r}} + 3\binom{30}{C_{31-r}} + 3\binom{30}{C_{32-r}} + \binom{30}{C_{33-r}} = ^m C_r$ , then $m$ …MediumSingle correct
4 Apr 2026, Shift 1 · Q9Let the smallest value of $k\in\mathbb{N}$ , for which the coefficient of $x^3$ in…MediumSingle correct
5 Apr 2026, Shift 1 · Q23If the sum of the coefficients of $x^7$ and $x^{14}$ in the expansion of $\left(\frac{1}{x^3} - x^4\right)^n$ , $x \neq 0$ , is zero, then…MediumNumerical value
6 Apr 2026, Shift 1 · Q8If the coefficients of the middle terms in the binomial expansions of $(1+\alpha x)^{26}$ and $(1-\alpha x)^{28}$ , $\alpha\neq 0$ , are…EasySingle correct
8 Apr 2026, Shift 2 · Q8If…HardSingle correct

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.