JEE Main 2020 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 3 September 2020, Shift 1, Maths Q53

Question 53 of 75 in this shift, Maths question 3 of 25.

The value of

(2\cdot{}^1P_0-3\cdot{}^2P_1+4\cdot{}^3P_2-\ldots

up to

51^{th}

term

)+(1!-2!+3!-\ldots

up to

51^{th}

term

)

is equal to :

(1) $1+(52)!$ Official answer
(2) $1$
(3) $1+(51)!$
(4) $1-51(51)!$

Official answer

Option 1

NTA final key (Sep 2020).

Chapter: Permutations and Combinations
Topic: Permutations and Combinations
Idea tested: Permutations of Distinct Objects

Same idea in other shifts

Asked 10× in all

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15 Apr 2023, Shift 1 · Q22A person forgets his 4-digit ATM pin code. But he remembers that in the code all the digits are different, the greatest digit is 7 and the…HardNumerical value
25 Jun 2022, Shift 2 · Q27The total number of three-digit numbers, with one digit repeated exactly two times, is ____________.MediumNumerical value
29 Jun 2022, Shift 1 · Q30Let $b_1b_2b_3b_4$ be a 4-element permutation with $b_i \in \{1, 2, 3, \ldots\ldots, 100\}$ for $1 \le i \le 4$ and $b_i \ne b_j$ for…MediumNumerical value
30 Jun 2022, Shift 1 · Q21The number of 6-digit numbers made by using the digits 1, 2, 3, 4, 5, 6, 7, without repetition and which are multiple of 15 is __________.MediumNumerical value
26 Aug 2021, Shift 1 · Q81The number of three-digit even numbers, formed by the digits 0, 1, 3, 4, 6, 7 if the repetition of digits is not allowed, is __________.EasyNumerical value
25 Feb 2021, Shift 1 · Q84The total number of numbers, lying between 100 and 1000 that can be formed with the digits 1, 2, 3, 4, 5, if the repetition of digits is…MediumNumerical value
25 Jul 2021, Shift 2 · Q63If ${}^nP_r={}^nP_{r+1}$ and ${}^nC_r={}^nC_{r-1}$ , then the value of r is equal to :EasySingle 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.