JEE MATHEMATICS MCQ: BINOMIAL THEOREM

1 Hard

1 of 1

Application +4 | -1

If the ninth term in the expansion of

{\left\{ {{3^{{{\log }_3}\sqrt {{{25}^{x - 1}} + 7} }} + {3^{ - 1/8{{\log }_3}\left( {{5^{x - 1}} + 1} \right)}}} \right\}^{10}}

is equal to 180 and

x > 1,

then

x

equals

View answer and explanation

Correct option: B

{\log _5}15

Option B (

{\log _5}15

) is correct because it is the solution to the equation derived from the given binomial expansion and condition.

More Questions from BINOMIAL THEOREM

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\left({ }^{10} C_0\right)^2-\left({ }^{10} C_1\right)^2+\ldots-\left({ }^{10} C_9\right)^2+\left({ }^{10} C_{10}\right)^2

a

d

\left( {n + 1} \right)

a{C_0} - \left( {a + d} \right){C_1} + \left( {a + 2d} \right){C_2} - ... + ...

(1-x)^{201}\left(1+x+x^2\right)^{200}

\left(\frac{1}{x}+2 x\right)^n

{x^5}

\frac{{1 + {x^2}}}{{1 + x}},\left| x \right| < 1,

\left(\begin{array}{c}2 n+1 \\ 0\end{array}\right)+\left(\begin{array}{c}2 n+1 \\ 3\end{array}\right)+\left(\begin{array}{c}2 n+1 \\ 6\end{array}\right)+\ldots=170

n