If ¹P₁ + 2.²P₂ + 3.³P₃ +.... + 15.¹⁵P₁₅ = ^(q) P r - s,0 ≤ s ≤ 1, then ^(q + s)C r - s is equal to _ _ _ _ _ _ _.

Permutations and Combinations: JEE Main 2021 Mathematics question

JEE Main 2021 · 26 Aug, Morning shift · Q41

JEE Main 202126 Aug, Morning shiftMathematicsMediumPermutations and Combinations98× since 2002

{}^1{P_1} + 2.{}^2{P_2} + 3.{}^3{P_3} + .... + 15.{}^{15}{P_{15}} = {}^q{P_r} - s,0 \le s \le 1

, then

{}^{q + s}{C_{r - s}}

is equal to ______________.

Your answerType your answer. Integers and decimals are accepted.

JEE Main 2021 · 26 Aug, Morning shift · Q41

JEE Main 202126 Aug, Morning shiftMathematicsMediumPermutations and Combinations98× since 2002

{}^1{P_1} + 2.{}^2{P_2} + 3.{}^3{P_3} + .... + 15.{}^{15}{P_{15}} = {}^q{P_r} - s,0 \le s \le 1

, then

{}^{q + s}{C_{r - s}}

is equal to ______________.

Your answerType your answer. Integers and decimals are accepted.