Home
Class 12
MATHS
In the expansion of (1+x)^n , 7th and 8t...

In the expansion of `(1+x)^n ,` 7th and 8th terms are equal. Find the value of `(7//x+6)^2` .

Text Solution

Verified by Experts

The correct Answer is:
`n^(2)`
Since the `7^(th)` and `8^(th)` terms are equal , we have
`.^(n)C_(6)x^(6) =.^(n)C_(7)x^(7)`
or `x=(.^(n)C_(6))/(.^(n)C_(7))=(7)/(n-6)`
or `(7/x+6)=n^(2)`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE|Exercise Exercise 8.6|10 Videos

  • BINOMIAL THEOREM

    CENGAGE|Exercise Exercise 8.7|9 Videos

  • BINOMIAL THEOREM

    CENGAGE|Exercise Exercise 8.4|13 Videos

  • AREA UNDER CURVES

    CENGAGE|Exercise Question Bank|10 Videos

  • CIRCLE

    CENGAGE|Exercise MATRIX MATCH TYPE|6 Videos

Similar Questions

Explore conceptually related problems

If in the expansion of (a-2b)^(n) , the sum of 5^(th) and 6^(th) terms is 0, then th e values of a//b =

In the expansion of (1+ x + 7/x)^11 find the term not containing x.

In the binomial coefficients of (1 + x)^(n) , the coefficients of the 5th, 6th and 7th terms are in AP Find all values of n.

In the binomial coefficients of (1+x)^(n) , the coefficients of the 5^(th), 6^(th) and 7^(th) terms are in A.P. Find all values of n.

Statement 1: Greatest term in the expansion of (1+x)^(12),w h e nx=11//10 is 7th Statement 2: 7th term in the expansion of (1+x)^(12) has the factor ^12 C_6 which is greatest value of ^12 C_rdot

If the 2nd, 3rd and 4th terms in the binomial expansion of (x+a)^(n) are 240, 720 and 1080 for a suitable values of x, find x, a and n.

The 2^(Nd),3^(rd)and4^(th) terms in the binomial expansion of (x + a)^(n) are 240, 720 and 1080 for a suitable value of x. Find x, a and n.

In the binomial coefficients of (1+x)^(n) ,the coefficients of the 5^(th),6^(th)and7^(th) terms are in AP. Find all values of n.

The 2^(nd), 3^(rd) and 4^(th) terms in the binomial expansion of (x+a)^(n) are 240, 720 and 1080 for a suitable value of x. Find x, a and n.

If the middle term in the expansion of (x^2+1//x)^n is 924 x^6, then find the value of ndot

Home
Profile