Let s_1=\sum_{j=1}^{10} j(j-1)^{10} C_j, s_2=\sum_{j=1}^{10} j \cdot{ }^{10} C_j and s_3=\sum_{j=1}^{10} j^2 \cdot{ }^{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. [AIEEE 2010]

Correct Answer is : Statement −1 is true, Statement- 2 is false.

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

Statement -1 is true, Statement- 2 is false.

Statement -1 is false, Statement- 2 is true.

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

Binomial Theorem Part 1

Section: Mathematics

Question : 80 of 100

Marks: +1, -0

Let s1=

∑

j=1

j(j−1)10Cj,
s2=

∑

j=1

j⋅‌10Cj and
s3=

∑

j=1

j2⋅‌10Cj
Statement-1 : S3=55×29.
Statement-2: S1=90×28 and S2=10×28.

[AIEEE 2010]

Statement −1 is true, Statement- 2 is true; Statement −2 is not a correct explanation for Statement - 1.
Statement −1 is true, Statement- 2 is false.
Statement −1 is false, Statement- 2 is true.
Statement - 1 is true, Statement- 2 is true: -Statement - 2 is a correct explanation for Statement - 1.

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