JEE MATHEMATICS MCQ: SEQUENCE OF SERIES

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Analyzing +4 | -1

Let

{S}_1=\sum\limits_{{j}=1}^{10} {j}({j}-1)^{10} \mathrm{C}_{{j}}, {S}_2=\sum\limits_{{j}=1}^{10} {j}^{10} \mathrm{C}_{{j}}

and

{S}_3=\sum\limits_{{j}=1}^{10} {j}^{2} \, {}^{10}\mathrm{C}_{{j}}

. Consider

Statement -1:

S_3=55 \times 2^9

Statement - 2:

S_1=90 \times 2^8

and

S_2=10 \times 2^8

, then

View answer and explanation

Correct option: B

Statement -1 is true, Statement - 2 is false

Statement -1 is true and Statement -2 is false. The values of S1, S2, and S3 are calculated using binomial theorem properties, revealing the discrepancy in Statement-2.

More Questions from SEQUENCE OF SERIES

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Given the sets

A=\{1,2,3\}, B=\{3,4\}, C=\{4,5,6\}

, then find the following
(i)

{A} \cup({B} \cap {C})

(ii)

A-(B \cap C)

(iii)

(B \cup C)-A

a,b,c

are in A.P.;

a,x,b

are in G.P. and

b,y,c

are in G.P., then

{x^2},{b^2},{y^2}

are in Suppose

P(x)=1-x+x^2-x^3+\ldots+x^{2012}

is expressed as a polynomial in

y

, as

Q(y)=a_0+a_1 y+\ldots+a_{2012} y^{2012}

where

y=x-2

, then

\sum\limits_{{i=0}}^{2012} a_i

equals If

\log \left(\frac{5 c}{a}\right), \log \left(\frac{3 b}{5 c}\right)

and

\log \left(\frac{a}{3 b}\right)

are in

A P

, where

a, b

and c are in

G P

, then

a, b, c

are the lengths of sides of If the sum of three numbers in G.P. is 63 and the product of the first and the second term is

\frac{3}{4}

of the third term, then the numbers are If the lengths of sides of a right angled triangle are in A.P., then their ratio is