"The value of (2.1P0 – 3.2P1 + 4.3P2 .... up to 51th term) + (1! – 2! + 3! – ..... up to 51th term) is equal to :"

"(2. 1 P 0 \n – 3. 2 P 1 + 4. 3 P 2 .... up to\n51 th term) + (1! – 2! + 3! – ..... up to 51 th term)\n = ( 2.1! - 3.2! + 4.3! - ....+ 52.51!)\n + ( 1! – 2! + 3! – ..... + (51)! )\n = (2! - 3! + 4! .....+ 52! )\n + ( 1! - 2! + 3! - 4! + .....+ 51! )\n = 1 + (52)!"

Medium MCQ +4 / -1 PYQ · JEE Mains 2020

The value of (2.¹P₀ – 3.²P₁ + 4.³P₂ .... up to 51^th term)
+ (1! – 2! + 3! – ..... up to 51^th term) is equal to :

A 1
B 1 + (51)!
C 1 – 51(51)!
D 1 + (52)! Correct answer

Solution

(2.1P0 – 3.2P1 + 4.3P2 .... up to 51th term) + (1! – 2! + 3! – ..... up to 51th term) = ( 2.1! - 3.2! + 4.3! - ....+ 52.51!) + ( 1! – 2! + 3! – ..... + (51)! ) = (2! - 3! + 4! .....+ 52! ) + ( 1! - 2! + 3! - 4! + .....+ 51! ) = 1 + (52)!

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Subject: Mathematics · Chapter: Permutations and Combinations · Topic: Fundamental Counting Principle

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The value of (2.1P0 – 3.2P1 + 4.3P2 .... up to 51th term) + (1! – 2! + 3! – ..... up to 51th term) is equal to :

Solution

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The value of (2.¹P₀ – 3.²P₁ + 4.³P₂ .... up to 51^th term)
+ (1! – 2! + 3! – ..... up to 51^th term) is equal to :