Home
Class 12
MATHS
If ""^(n)C(4),""^(n)C(5) and ""^(n)C(6) ...

If `""^(n)C_(4)`,`""^(n)C_(5)` and `""^(n)C_(6)` are in A.P. then the value of n is

A

14

B

11

C

9

D

12

Text Solution

Verified by Experts

The correct Answer is:
A
as `.^(n)C_(4), .^(n)C_(5), .^(n)C_(6)` are in A.P.
`rArr 2. (n!)/((n-5)!5!) = (n!)/((n-4)!4!) + (n!)/((n-6)|6!) rArr (2)/((n-5)xx5) = (1)/((n-4)(n-5)) + (1)/(6.5)`
`rArr (2)/((n-5) xx5) - (1)/((n-4)(n-5)) = (1)/(65) rArr 6(2n-13) = n^(2) - 9n + 20`
`rArr n^(2) - 21n + 98 = 0 rArr (n - 14)(n - 7) = 0 rArr n = 7` or = 14
`rArr n = 14`
Promotional Banner

Topper's Solved these Questions

  • JEE MAIN REVISION TEST - 7|JEE - 2020

    VMC MODULES ENGLISH|Exercise Mathematics (Section - 2) Numercial type questions|5 Videos

  • JEE MAIN REVISION TEST - 4 JEE - 2020

    VMC MODULES ENGLISH|Exercise MATHEMATICS|25 Videos

  • JEE MAIN REVISION TEST -14

    VMC MODULES ENGLISH|Exercise MATHEMATICS (SECTION 2)|5 Videos

Similar Questions

Explore conceptually related problems

If .^(n)C_(4),.^(n)C_(5), .^(n)C_(6) are in A.P., then find the value of n.

If ^nC_4, ^nC_5, ^nC_6 are in A.P. then the value of n is

If ""^(n)C_4= ""^(n)C_6, find n.

If .^(n)C_(8)=.^(n)C_(6) , then find .^(n)C_(2) .

Find n if ""^(n)C_(4)=""^(n)C_(6)

If .^(n+2)C_(8) : ^(n-2)P_(4)=57:16 , then the value of (n)/(2) is

If .^(n)C_(12) = .^(n)C_(16) , find the value of n

If .^(n)C_(5) = .^(n)C_(7) , then find .^(n)P_(3)

If ""^(n)C_(x) = 56 and ""^(n)P_(x) = 336 , then n is equal to

If \ ^n C_(12)=\ \ ^n C_5,\ find the value of n