Let S1=∑j=110 j(j−1) 10CjS2=∑j=110 j 10Cj and  S3=∑j=110 j2 10CjStatement-1 S3=55×29Statement-2 S1=90×28 and S2=10×28

# Let  and Statement-1 ${S}_{3}=55×{2}^{9}$Statement-2 ${S}_{1}=90×{2}^{8}$ and ${S}_{2}=10×{2}^{8}$

1. A

STATEMENT-1 is True, STATEMENT-2 is True;
STATEMENT-2 is a correct explanation for STATEMENT-1

2. B

STATEMENT-1 is True, STATEMENT-2 is True;
STATEMENT-2 is NOT a correct explanation for STATEMENT-1

3. C

STATEMENT-1 is True, STATEMENT-2 is False

4. D

STATEMENT-1 is False, STATEMENT-2 is True

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### Solution:

We have

Differentiating both the sides with respect to x, we get

(1)

Again differentiating both the sides with respect to x, we get

(2)

Putting $x=1$ in (1) and (2), we get

and

Adding the above two equation, we get

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

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