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JEE MATHEMATICS MCQ: SEQUENCE OF SERIES

1 Hard

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Application +4 | -1

If

x,y,z

are three consecutive positive integers, then

{\log _e}\sqrt x + {\log _e}\sqrt z + \left( {\frac{1}{{2xz + 1}}} \right) + \frac{1}{3}{\left( {\frac{1}{{2xz + 1}}} \right)^3} + \frac{1}{5}{\left( {\frac{1}{{2xz + 1}}} \right)^5} + \;...

is

View answer and explanation

Correct option: B

{\log _e}y

Option B (

{\log _e}y

) is correct because the expression simplifies to

{\log _e}\sqrt{xz} + \frac{1}{2}{\log _e}\left[ {\frac{{1 + \frac{1}{{2xz + 1}}}}{{1 - \frac{1}{{2xz + 1}}}}} \right]

which further simplifies to

{\log _e}y

when x, y, and z are consecutive integers.

More Questions from SEQUENCE OF SERIES

Practice All Chapter MCQs →

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

, then find the following
(i)

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

A-(B \cap C)

(B \cup C)-A

a,b,c

a,x,b

are in G.P. and

b,y,c

are in G.P., then

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

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

is expressed as a polynomial in

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

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