JEE MATHEMATICS MCQ: BINOMIAL THEOREM

1 Easy

1 of 1

Analyzing +4 | -1

\sum\limits_{r=0}^n(-1)^r{ }^n C_r\left[\frac{1}{2^r}+\frac{3^r}{2^{2 r}}+\frac{7^r}{2^{3 r}}+\ldots\right.

upto

m

terms

]

=f(n)\left(1-\frac{1}{2^{m n}}\right)

\int_{-3}^3 f\left(x^3 \ln x\right) d\left(x^3 \ln x\right)

is equal to

View answer and explanation

Correct option: D

Cannot be determined

Option D (Cannot be determined) is correct because the integral cannot be calculated due to the presence of

\ln x

with a lower limit of integration at -3, which is outside the domain of the natural logarithm.

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