Home
Class 12
MATHS
The value of (.^(21)C(1) - .^(10)C(1)) +...

The value of `(.^(21)C_(1) - .^(10)C_(1)) + (.^(21)C_(2) - .^(10)C_(2)) + (.^(21)C_(3) - .^(10)C_(3)) + (.^(21)C_(4) - .^(10)C_(4)) + … + (.^(21)C_(10) - .^(10)C_(10))` is

A

`2^(20) - 2^(10)`

B

`2^(21) - 2^(11)`

C

`2^(21) - 2^(10)`

D

`2^(20) - 2^(9)`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Similar Questions

Explore conceptually related problems

The value of |(.^(10)C_(4) ^(10)C_(5) ^(11)C_(m)), ( .^(11)C_(6) ^(11)C_(7) ^(12)C_(m+2)), (. ^(12)C_(8) ^(12)C_(9) ^(13)C_(m+4))| is equal to zero when m is

Prove that .^(n-1)C_(3)+.^(n-1)C_(4) gt .^(n)C_(3) if n gt 7 .

Evaluate |{:(.^(x)C_(1),,.^(x)C_(2),,.^(x)C_(3)),(.^(y)C_(1),,.^(y)C_(2),,.^(y)C_(3)),(.^(x)C_(1),,.^(z)C_(2),,.^(z)C_(3)):}|

The sum of the series sum_(r=0)^(10) .^(20)C_(r) , is 2^(19)+{(.^(20)C_(10))/2} .

10 C_(1)+10 C_(3) +10 C_(5) +10 C_(7) +10 C_(9) = …….

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

Solve the inequality .^(x-1)C_(4)-.^(x-1)C_(3)-(5)/(2).^(x-2)C_(2)lt0,x inN .

The solution set "^10C_(x-1)>2 . "^10C_x is

If Delta=|{:(a_(11),a_(12),a_(13)),(a_(21),a_(22),a_(23)),(a_(31),a_(32),a_(33)):}| and C_(ij)=(-1)^(i+j) M_(ij), "where " M_(ij) is a determinant obtained by deleting ith row and jth column then then |{:(C_(11),C_(12),C_(13)),(C_(21),C_(22),C_(23)),(C_(31),C_(32),C_(33)):}|=Delta^(2). If |{:(1,x,x^(2)),(x,x^(2),1),(x^(2),1,x):}| =5 and Delta =|{:(x^(3)-1,0,x-x^(4)),(0,x-x^(4),x^(3)-1),(x-x^(4),x^(3)-1,0):}| then sum of digits of Delta^(2) is

((log)_(10)(x-3))/((log)_(10)(x^2-21))=1/2