Home
Class 12
MATHS
If ""^nCr-84,""^nC(r-1)=36 and ""^nC(r+1...

If `""^nC_r-84,""^nC_(r-1)=36 and ""^nC_(r+1)=126` , then n equals :

Text Solution

Verified by Experts

Here, `(.^(n)C_(r))/(.^(n)C_(r-1))=(84)/(36)`
`implies(n-r+1)/(r)=(7)/(3)" "[because(.^(n)C_(r))/(.^(n)C_(r-1))=(n-r+1)/(r)]`
`implies3n-3r+3=7r` ltrgt `implies10r-3n=3` . . (i)
and `(.^(n)C_(r+1))/(.^(n)C_(r))=(n-(r+1)+1)/((r+1))=(126)/(84)" "because(.^(n)C_(r))/(.^(n)C_(r-1))=(n-r+1)/(r)]`
`implies(n-r)/(r+1)=(3)/(2)`
`implies2n-2r=3r+3`
`implies5r-2n=-3`
or `10r-4n=-6` . . . (ii)
On subtracting Eq. (ii) from Eq. (i) we get
`n=9`
From Eq. (i) we get
`10r-27=3 implies10r=30`
`thereforer=3`
Promotional Banner

Similar Questions

Explore conceptually related problems

If ""^nC_(12)=""^nC_8 , then n is equal to :

If ""^(n-1)C_r=(k^2-3)""^nC_(r+1) , then kin :

If C_(r) stands for ""^(n)C_(r) and sum_(r=1)^(n)(r*C_(r))/(C_(r-1))=210 , then n equals:

If .^nP_r=840, .^nC_r=35, then find n=

Prove that ""^(n)C_(r)+""^(n)C_(r-1)=""^(n+1)C_(r) .

If s_n=sum_(r=0)^n1/(""^nC_r)and t_n=sum_(r=0)^nr/(""^nC_r), then t_n/s_n is equal to :

If .^(n+1)C_(r+1):^(n)C_(r):^(n-1)C_(r-1)=11:6:3 , find the values of n and r.

If ,^(n) P_r=^n P_(r+1) and ^n C_r=^n C_(r-1,) then the value of n+r is.

If a_n=sum_(r=0)^n1/(""^nC_r) , then sum_(r=0)^nr/(""^nC_r) equals :

If ""^nC_r denotes the number of combinations of n things , taken r at a time , then the expression : ""^nC_(r+1)+""^nC_(r-1)+2""^nC_r equals :