Home
Class 12
MATHS
If .^(n+1)C(r+1):^(n)C(r):^(n-1)C(r-1)=1...

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

Text Solution

Verified by Experts

Here, `(.^(n+1)C_(r+1))/(.^(n)C_(r))=(11)/(6)`
`implies(n+1)/(r+1)*(.^(n)C_(r))/(.^(n)C_(r))=(11)/(6)" "[because.^(n)C_(r)=(n)/(r)*^(n-1)C_(r-1)]`
`implies(n+1)/(r+1)=(11)/(6)`
`implies6n+6=11r+11`
`implies6n-11r=5` . . . (i)
and `(.^(n)C_(r))/(.^(n-1)C_(r-1))=(6)/(3)`
`implies(n)/(r)*(.^(n-1)C_(r-1))/(.^(n-1)C_(r-1))=(6)/(3)" "[because.^(n)C_(r)=(n)/(r)*^(n-1)C_(r-1)]`
`implies(n)/(r)=2`
`impliesn=2r` . . (ii)
On solving Eqs. (i) and (ii), we get n=10 and r=5.
Promotional Banner

Similar Questions

Explore conceptually related problems

If .^(2n)C_(3):^(n)C_(3)=11:1 , find the value of n.

If .^(20)C_(n+1) = ^ (n) C_(16) , then the value of n is

if .^(2n)C_(2):^(n)C_(2)=9:2 and .^(n)C_(r)=10 , then r is equal to

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

If \ ^(43)C_(r-6)=\ ^(43)C_(3r+1)\ then the value of r is

Determine n if ""^(2n)C_(3):""^(n)C_(3)=11:1

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

If 2n _(c_3) : n _(c_3) =11:1 find n Also find the value of n

If (1+x)^(n)=C_(0)+C_(1)x+C_(2)x^(2)+ . . .+C_(n)x^(n) , then the value of : C_(1)+2C_(2)+3C_(3)+ . . .+nC_(n) is:

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