JEE MATHEMATICS MCQ: BINOMIAL THEOREM

1 Medium

1 of 1

Application +4 | -1

If sum of coefficients in expansion of

(1+2 \mathrm{x})^{\mathrm{m}} \&(2+\mathrm{x})^{\mathrm{n}}

are respectively

6561 \& 243

, then position of point

(\mathrm{m}, \mathrm{n})

w.r.t. circle

\mathrm{x}^2+\mathrm{y}^2-4 \mathrm{x}-6 \mathrm{y}-32=0

View answer and explanation

Correct option: B

inside the circle

Option B (inside the circle) is correct because substituting m=8 and n=5 into the circle's equation results in a negative value, indicating the point lies inside the circle.

More Questions from BINOMIAL THEOREM

Practice All Chapter MCQs →

\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

equals If

a

and

d

are two complex numbers, then the sum to

\left( {n + 1} \right)

terms of the following series

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

is The number of different terms in the expansion of

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

is The sum of the coefficient of the binomial expansion of

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

is equal to 6561 . The constant term in the expansion is The coefficient of

{x^5}

in the expansion of

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

is If

\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

, then

n

equals