JEE MATHEMATICS MCQ: SEQUENCE OF SERIES

1 Easy

1 of 1

Analyzing +4 | -1

Let

\left[ x \right]

denote greatest integer less than or equal to

x

. If for

n \in N,\,{\left( {1 - x + {x^3}} \right)^n} = \sum\limits_{j = 0}^{3n} {{a_j}{x^j}}

, then

\sum\limits_{j = 0}^{\left[ {\frac{{3n}}{2}} \right]} {{a_{2j}} + 4} \sum\limits_{j = 0}^{\left[ {\frac{{3n - 1}}{2}} \right]} {{a_{2j + 1}}}

is equal to:

View answer and explanation

Correct option: A

Option A (1) is correct because by substituting x=1 and x=-1 into the given equation and adding/subtracting, we can isolate the required summation and find its value.

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