If `alpha=^m C_2,t h e n^(alpha)C_2` is equal to a. `^m+1C_4` b. `^m-1C_4` c. `3^(m+2)C_4` d. `3^(m+1)C_4`

If alpha= ""^m C_2 , then ""^(alpha)C_2 is equal to a. ""^(m+1)C_4 b. ""^(m-1)C_4 c. 3 ""^(m+2)C_4 d. 3 ""^(m+1)C_4

If alpha=mC_(2), then ^(alpha)C_(2) is equal to a.m+1C_(4) b.^(m-1)C_(4) c.3^(m+2)C_(4) d.3^(m+1)C_(4)

If m=""^(n)C_(2) , then ""^(m)C_(2) is equal to a) 3""^(n)C_(4) b) ""^(n+1)C_(4) c) 3""^(n+1)C_(4) d) 3""^(n+1)C_(3)

The value of .^(n)C_(1)+.^(n+1)C_(2)+.^(n+2)C_(3)+"….."+.^(n+m-1)C_(m) is equal to a. .^(m+n)C_(n) - 1 b. .^(m+n)C_(n-1) c. .^(m)C_(1) + ^(m+1)C_(2) + ^(m+2)C_(3) + "…." + ^(m+n-1)C_(n) d. .^(m+n)C_(m) - 1

The value of ^n C_1+^(n+1)C_2+^(n+2)C_3++^(n+m-1)C_m is equal to (a) ^m+n C_(n-1) (b) ^m+n C_(n-1) (c) ^mC_(1)+^(m+1)C_2+^(m+2)C_3++^(m+n-1) (d) ^m+1C_(m-1)

The value of ^n C_1+^(n+1)C_2+^(n+2)C_3++^(n+m-1)C_m is equal to (a)^m+n C_(n-1) (b)^m+n C_(n-1) (c)^mC_(1)+^(m+1)C_2+^(m+2)C_3++^(m+n-1) (d)^m+1C_(m-1)

If m= "^nC_2 , prove that "^m C_2 =3xx ^(n+1)C_4 .

Using binomial theorem (without using the formula for .^n C_r ) , prove that .^nC_4+^m C_2-^m C_1.^n C_2 = .^m C_4-^(m+n)C_1.^m C_3+^(m+n)C_2.^m C_2-^(m+n)C_3^m.C_1 +^(m+n)C_4dot

Using binomial theorem (without using the formula for .^n C_r ) , prove that .^nC_4+^m C_2-^m C_1.^n C_2 = .^m C_4-^(m+n)C_1.^m C_3+^(m+n)C_2.^m C_2-^(m+n)C_3^m.C_1 +^(m+n)C_4dot

If m=.^(n)C_(2) show that , .^(m)C_(2)=3.^(n+1)C_(4)