If a = displaystyle∑ r =033 33 C r , b = displaystyle∑ r =033 66 C 2 r , c = displaystyle∑ r =033 99 C 3 r , then

Question

If a = displaystyle∑ r =033 33 C r , b = displaystyle∑ r =033 66 C 2 r , c = displaystyle∑ r =033 99 C 3 r , then (A)  3 c =2( ab +1)  (B)  a 3=3 c +2  (C)  3 c =2( ab -1)  (D) a 2=2 b

Tardigrade Admin · Accepted Answer

n C 0+ n C 1+ n C 2 ldots . n C n =2 n ⇒ a =233 n C0+ n C2+ n C4+ ldots=2n-1 ⇒ b=265 (1+x)n= n C0+ n C1 x+ n C2 x2+ n C3 x3+ ldots . .+ n Cn xn Put x=1, ω and ω2 and add them, we get C =(299-2/3) Now check the answer

Q. If $a = r = 0 \sum 33^{33} C_{r}, b = r = 0 \sum 33^{66} C_{2 r}, c = r = 0 \sum 33^{99} C_{3 r}$ , then

$3 c = 2 (ab + 1)$

$a^{3} = 3 c + 2$

$3 c = 2 (ab - 1)$

$a^{2} = 2 b$

Q. If a=r=0∑33​33Cr​,b=r=0∑33​66C2r​,c=r=0∑33​99C3r​, then

3c=2(ab+1)

a3=3c+2

3c=2(ab−1)

a2=2b

nC0​+nC1​+nC2​….nCn​=2n⇒a=233 nC0​+nC2​+nC4​+…=2n−1⇒b=265 (1+x)n=nC0​+nC1​x+nC2​x2+nC3​x3+…..+nCn​xn Put x=1,ω and ω2 and add them, we get C=3299−2​ Now check the answer

Q. If $a = r = 0 \sum 33^{33} C_{r}, b = r = 0 \sum 33^{66} C_{2 r}, c = r = 0 \sum 33^{99} C_{3 r}$ , then

$3 c = 2 (ab + 1)$

$a^{3} = 3 c + 2$

$3 c = 2 (ab - 1)$

$a^{2} = 2 b$