If 1+(2+ 49 C 1+ 49 C 2+ ldots ldots+ 49 C 49) ( 50 C 2+ 50 C 4+ ldots . .+ 50 C 50) is equal to 2 n . m, where m is odd, then n + m is equal to

Question

If 1+(2+ 49 C 1+ 49 C 2+ ldots ldots+ 49 C 49) ( 50 C 2+ 50 C 4+ ldots . .+ 50 C 50) is equal to 2 n . m, where m is odd, then n + m is equal to (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

1+(1+249)(249-1)=298 m =1, n =98 m + n =99

Q. If $1 + (2 +^{49} C_{1} +^{49} C_{2} + \dots\dots +^{49} C_{49})$ $(^{50} C_{2} +^{50} C_{4} + \dots .. +^{50} C_{50})$ is equal to $2^{n} . m$ , where $m$ is odd, then $n + m$ is equal to

$1 + (1 + 2^{49}) (2^{49} - 1) = 2^{98}$
$m = 1, n = 98$
$m + n = 99$

Q. If 1+(2+49C1​+49C2​+……+49C49​) (50C2​+50C4​+…..+50C50​) is equal to 2n.m, where m is odd, then n+m is equal to

1+(1+249)(249−1)=298 m=1,n=98 m+n=99

Q. If $1 + (2 +^{49} C_{1} +^{49} C_{2} + \dots\dots +^{49} C_{49})$ $(^{50} C_{2} +^{50} C_{4} + \dots .. +^{50} C_{50})$ is equal to $2^{n} . m$ , where $m$ is odd, then $n + m$ is equal to

$1 + (1 + 2^{49}) (2^{49} - 1) = 2^{98}$
$m = 1, n = 98$
$m + n = 99$