Paragraph Let (1+x+x^2 )²⁰=a₀+a₁ x+a₂ x^2+ +a₄₀ x⁴⁰ . Further S= _ r=0 ⁴⁰ a_r . Two coefficients are chosen from the coefficients a ₀, a ₁, , a ₄₀ and the probability that they are equal is p (considering no three coefficients are equal). U

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Paragraph Let (1+x+x^2 )²⁰=a₀+a₁ x+a₂ x^2+ +a₄₀ x⁴⁰ . Further S= _ r=0 ⁴⁰ a_r . Two coefficients are chosen from the coefficients a ₀, a ₁, , a ₄₀ and the probability that they are equal is p (considering no three coefficients are equal). Units digit of S is equal to b and a= 1-p 10 p . On the basis of above information, answer the following : Question If ( a-b +b)^6=I+F , where 0 F 1 and I N , then the value of I is

Quantrex Academy · Accepted Answer

Correct answer: C. 415

S=3²⁰ unit's digit of S is b=1 aligned & Also p = ²⁰ C ₁ ⁴¹ C ₂ = 1 41 & a =4 aligned ( 3 +1)^6= I + F where 0 F 1 Let ( 3 -1)^6= G where 0 G 1 I + F + G =( 3 +1)^6+( 3 -1)^6=2 ^6 C ₀( 3 )^6+ ^6 C ₂( 3 )^4+ ^6 C ₄( 3 )^2+ ^6 C ₆ =2 1.27+15.9+15.3+1 =416 But 0 F + G 2 and F + G has to be an integer I=416-1=415

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