Let ${S_k} = \frac{{1 + 2 + 3 + ... + k}}{k}.{\rm{ }}\,\,{\rm{If}}$ $S_1^2 + S_2^2 + ... + S_{10}^2 = \frac{5}{{12}}A,$ then A is equal to

JEE MATHEMATICS MCQ: SEQUENCE OF SERIES

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Application +4 | -1

Let

{S_k} = \frac{{1 + 2 + 3 + ... + k}}{k}.\mathrm{ }\,\,\mathrm{If}

S_1^2 + S_2^2 + ... + S_{10}^2 = \frac{5}{{12}}A,

then A is equal to

View answer and explanation

Correct option: D

303

Option C (

2\int_0^a {f\left( x \right)dx}

) is correct because using the properties of definite integrals and the given conditions, the integral simplifies to this expression.

Practice All Chapter MCQs →

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

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

A-(B \cap C)

(B \cup C)-A

a,b,c

a,x,b

b,y,c

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

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

y

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

y=x-2

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

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

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

A P

a, b

G P

a, b, c

\frac{3}{4}