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Solve an equation in nCr or factorials for n

This type of question, asked 3 times: 21 Apr 2025 S2, 19 Apr 2026 S2, 12 May 2026 S1. All 3 questions below, oldest first.

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  1. Question 1

    21 Apr 2025 S2

    133
    If  n+4Cn+1− n+3Cn=15(n+2)\ ^{n+ 4}C_{n+ 1}-\ ^{n+ 3}C_{n}= 15(n+ 2), then n=n=

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  2. Question 2

    19 Apr 2026 S2

    53
    If nC4,nC5^nC_4, {}^nC_5 and nC6^nC_6 are in arithmetic progression (A.P.), then the value of n is...

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  3. Question 3

    12 May 2026 S1

    57
    If (n+3)!(n2−4)(n+1)!=116\dfrac{(n + 3)!}{(n^2 - 4)(n + 1)!} = \dfrac{11}{6}, for n∈N,n≠2n \in N, n \neq 2, then the value of 3n−203n - 20 is equal to ...

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