AIEEE 2007 | Binomial Theorem Question 192 | Mathematics

In the binomial expansion of $${\left( {a - b} \right)^n},\,\,\,n \ge 5,$$ the sum of $${5^{th}}$$ and $${6^{th}}$$ terms is zero, then $$a/b$$ equals

$${{n - 5} \over 6}$$

$${{n - 4} \over 5}$$

$${5 \over {n - 4}}$$

$${6 \over {n - 5}}$$

AIEEE 2007

MCQ (Single Correct Answer)

-1

Out of Syllabus

The sum of the series $${}^{20}{C_0} - {}^{20}{C_1} + {}^{20}{C_2} - {}^{20}{C_3} + .....\, - \,.....\, + {}^{20}{C_{10}}$$ is

$$0$$

$${}^{20}{C_{10}}$$

$$ - {}^{20}{C_{10}}$$

$${1 \over 2}{}^{20}{C_{10}}$$

AIEEE 2006

MCQ (Single Correct Answer)

-1

If the expansion in powers of $$x$$ of the function $${1 \over {\left( {1 - ax} \right)\left( {1 - bx} \right)}}$$ is $${a_0} + {a_1}x + {a_2}{x^2} + {a_3}{x^3}.....$$ then $${a_n}$$ is

$${{{b^n} - {a^n}} \over {b - a}}$$

$${{{a^n} - {b^n}} \over {b - a}}$$

$${{{a^{n + 1}} - {b^{n + 1}}} \over {b - a}}$$

$${{{b^{n + 1}} - {a^{n + 1}}} \over {b - a}}$$

AIEEE 2006

MCQ (Single Correct Answer)

-1

Out of Syllabus

For natural numbers $$m$$ , $$n$$, if $${\left( {1 - y} \right)^m}{\left( {1 + y} \right)^n}\,\, = 1 + {a_1}y + {a_2}{y^2} + ..........$$ and $${a_1} = {a_2} = 10,$$ then $$\left( {m,\,n} \right)$$ is

$$\left( {20,\,45} \right)$$

$$\left( {35,\,20} \right)$$

$$\left( {45,\,35} \right)$$

$$\left( {35,\,45} \right)$$

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