Let s₁ = Σ j = 1 ¹⁰ j(j - 1)¹⁰ C j, s₂ = Σ j = 1 ¹⁰ j.¹⁰C j and s₃ = Σ j = 1 ¹⁰ j².¹⁰C j. Statement-1: S₃ = 55 × 2⁹. Statement-2: S₁ = 90 × 2⁸ and S₂ = 10 × 2⁸.

(B) Statement - 1 is true, Statement-2 is false.

(A) Statement - 1 is true, Statement- 2 is true; Statement - 2 is not a correct explanation for Statement - 1.

(C) Statement - 1 is false, Statement-2 is true.

(D) Statement - 1 is true, Statement-2 is true: -Statement - 2 is a correct explanation for Statement - 1.

Binomial Theorem and Its Simple Applications: JEE Main 2010 Mathematics question

JEE Main 2010 · Annual, Paper 1 · Q2971

JEE Main 2010Annual, Paper 1MathematicsMediumBinomial Theorem and Its Simple Applications131× since 2002

Let

{s_1} = \sum\limits_{j = 1}^{10} {j\left( {j - 1} \right){}^{10}} {C_j}

{{s_2} = \sum\limits_{j = 1}^{10} {} } j.{}^{10}{C_j}

and

{{s_3} = \sum\limits_{j = 1}^{10} {{j^2}.{}^{10}{C_j}.} }

Statement-1 :

{{S_3} = 55 \times {2^9}}

. Statement-2 :

{{S_1} = 90 \times {2^8}}

and

{{S_2} = 10 \times {2^8}}

JEE Main 2010 · Annual, Paper 1 · Q2971

JEE Main 2010Annual, Paper 1MathematicsMediumBinomial Theorem and Its Simple Applications131× since 2002

Let

{s_1} = \sum\limits_{j = 1}^{10} {j\left( {j - 1} \right){}^{10}} {C_j}

{{s_2} = \sum\limits_{j = 1}^{10} {} } j.{}^{10}{C_j}

and

{{s_3} = \sum\limits_{j = 1}^{10} {{j^2}.{}^{10}{C_j}.} }

Statement-1 :

{{S_3} = 55 \times {2^9}}

. Statement-2 :

{{S_1} = 90 \times {2^8}}

and

{{S_2} = 10 \times {2^8}}