Home
Class 12
MATHS
The value of underset(r=0)overset(3)sum....

The value of `underset(r=0)overset(3)sum.^(8)C_(r)(.^(5)C_(r+1)-.^(4)C_(r))` is `"_____"`.

Text Solution

Verified by Experts

The correct Answer is:
220
`""^(4)C_(r )+""^(4)C_(r +1)=""^(5)C_(r+1)`
`""^(4)C_(r+1)=""^(5)C_(r+1)-""^(4)C_(r )`
`sum_(r =0)^(3) ""^(8)C_(r )*""^(4)C_(r+1)=""^(8)C_(0)*""^(4)C_(1)+""^(8)C_(1)*""^(4)C_(2)+""^(8)C_(2)*""^(4)C_(3)+""^(8)C_(3)*""^(4)C_(4)`
`=""^(8)C_(8)*""^(4)C_(1)+""^(8)C_(7)*""^(4)C_(2)+""^(8)C_(6)*""^(4)C_(3)+""^(8)C_(5)*""^(4)C_(4)`
`""^(12)C_(9)=(12xx11xx10)/(6)=220`
Promotional Banner

Topper's Solved these Questions

  • MOCK TEST 1

    VMC MODULES ENGLISH|Exercise PART III : MATHEMATICS (SECTION-2)|10 Videos

  • MATRICES AND DETERMINANTS

    VMC MODULES ENGLISH|Exercise JEE ADVANCED ARCHIVE|78 Videos

  • MOCK TEST 10

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

Similar Questions

Explore conceptually related problems

The value of underset(r=0)overset(40)sumr.^(40)C_(r).^(30)C_(r) is

underset(r=1)overset(n)(sum)r(.^(n)C_(r)-.^(n)C_(r-1)) is equal to

The value of sum_(r=0)^(3) ""^(8)C_(r)(""^(5)C_(r+1)-""^(4)C_(r)) is "_____" .

Find underset(r=0) overset(10)sumr^ (10)C_(r).3^(r).(-2)^(10-r)

Find the value of underset(r = 0) overset(oo)sum tan^(-1) ((1)/(1 + r + r^(2)))

The value of ""^(50)C_4 + underset(r=1) overset(6)sum ""^(56-r)C_3 is

Let n be a positive integer and (1+x)^(n)+C_(0)+C_(1)x+C_(2)x^(2)+C_(3)x^(3)+ . . .+C_(r)x^(r)+ . . .+C_(n-1)x^(n-1)+C_(n)x^(n) Where C_(r) stands for .^(n)C_(r) , then Q. The values of underset(r=0)overset(n)(sum)underset(s=0)overset(n)(sum)(C_(r)+C_(S)) is

Let n be a positive integer and (1+x)^(n)+C_(0)+C_(1)x+C_(2)x^(2)+C_(3)x^(3)+ . . .+C_(r)x^(r)+ . . .+C_(n-1)x^(n-1)+C_(n)x^(n) Where C_(r) stands for .^(n)C_(r) , then Q. The value of underset(r=0)overset(n)(sum)underset(s=0)overset(n)(sum),C_(r),C_(S) is

Statement-1: If underset(r=1)overset(n)(sum)r^(3)((.^(n)C_(r))/(.^(n)C_(r-1)))^(2)=196 , then the sum of the coeficients of powerr of xin the expansion of the polynomial (x-3x^(2)+x^(3))^(n) is -1. Statement-2: (.^(n)C_(r))/(.^(n)C_(r-1))=(n-r+1)/(r) AA n in N and r in W .

The value of sum_(r=0)^(n) sum_(p=0)^(r) ""^(n)C_(r) . ""^(r)C_(p) is equal to