`[(^n C_0+^n C_3+)1//2(^n C_1+^n C_2+^n C_4+^n C_5]^2+3//4(^n C_1-^n C_2+^n C_4-^n C_5+)^2=` `3` b. `4` c. `2` d. `1`

[(^nC_0+^n C_3+)-1/2(^n C_1+^n C_2+^n C_4+^n C_5]^2 + 3/4(^n C_1-^n C_2+^n C_4 +)^2= a. 3 b. 4 c. 2 d. 1

[(. ^nC_0+^n C_3+)-1/2(.^n C_1+^n C_2+^n C_4+^n C_5]^2 + 3/4(.^n C_1-^n C_2+^n C_4 +)^2= equals to a. 3 b. 4 c. 2 d. 1

1. ^n C_0+4^1. ^n C_1+4^2. ^n C_2 + 4^3. ^n C_3+….+4^n. ^n C_n =

[(^(n)C_(0)+^(n)C_(3)+...)1/2(^(n)C_(1)+^(n)C_(2)+^(n)C_(4)+^(n)C_(5)...]^(2)+3/4(^(n)C_(1)-^(n)C_(2)+^(n)C_(4)-^(n)C_(5)+...)^(2)=3b.4c.2d.1

Prove that ^n C_0 ^(2n)C_n- ^n C_1 ^(2n-2)C_n+ ^n C_2^(2n-4)C_n-=2^ndot

Prove that .^n C_0 . ^(2n) C_n- ^n C_1 . ^(2n-2)C_n+^n C_2 . ^(2n-4)C_n-=2^ndot

The value of |1 1 1^n C_1^(n+2)C_1^(n+4)C_1^n C_2^(n+2)C_2^(n+4)C_2| is

Prove that C_0 + 2.C_1 + 4.C_2 + 8.C_3 + ……+2^n.C_n = 3^n

Prove that C_0 + 2.C_1 + 4.C_2 + 8.C_3 + ……+2^n.C_n = 3^n

C_0 + C_1 + 2.C_2(3) + 3.C_3(3^2)+ 4.C_4(3^3) + ……+n.C_n 3^(n-1) =