AIEEE 2005 | Binomial Theorem Question 199 | Mathematics

If the coefficients of r^th, (r+1)^th, and (r + 2)^th terms in the binomial expansion of $${{\rm{(1 + y )}}^m}$$ are in A.P., then m and r satisfy the equation

$${m^2} - m(4r - 1) + 4\,{r^2} - 2 = 0$$

$${m^2} - m(4r + 1) + 4\,{r^2} + 2 = 0$$

$${m^2} - m(4r + 1) + 4\,{r^2} - 2 = 0$$

$${m^2} - m(4r - 1) + 4\,{r^2} + 2 = 0$$

AIEEE 2004

MCQ (Single Correct Answer)

-1

The coefficient of the middle term in the binomial expansion in powers of $$x$$ of $${\left( {1 + \alpha x} \right)^4}$$ and $${\left( {1 - \alpha x} \right)^6}$$ is the same if $$\alpha $$ equals

$${3 \over 5}$$

$${10 \over 3}$$

$${{ - 3} \over {10}}$$

$${{ - 5} \over {3}}$$

AIEEE 2004

MCQ (Single Correct Answer)

-1

The coefficient of $${x^n}$$ in expansion of $$\left( {1 + x} \right){\left( {1 - x} \right)^n}$$ is

$${\left( { - 1} \right)^{n - 1}}n$$

$${\left( { - 1} \right)^n}\left( {1 - n} \right)$$

$${\left( { - 1} \right)^{n - 1}}{\left( {n - 1} \right)^2}$$

$$\left( {n - 1} \right)$$

AIEEE 2004

MCQ (Single Correct Answer)

-1

Out of Syllabus

If $${S_n} = \sum\limits_{r = 0}^n {{1 \over {{}^n{C_r}}}} \,\,and\,\,{t_n} = \sum\limits_{r = 0}^n {{r \over {{}^n{C_r}}},\,} $$then $${{{t_{ n}}} \over {{S_n}}}$$ is equal to

$${{2n - 1} \over 2}$$

$${1 \over 2}n - 1$$

n - 1

$${1 \over 2}n$$

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