JEE Main 2017 (Online) 9th April Morning Slot | Binomial Theorem Question 181 | Mathematics

The coefficient of x⁻⁵ in the binomial expansion of

$${\left( {{{x + 1} \over {{x^{{2 \over 3}}} - {x^{{1 \over 3}}} + 1}} - {{x - 1} \over {x - {x^{{1 \over 2}}}}}} \right)^{10}},$$ where x $$ \ne $$ 0, 1, is :

$$-$$ 4

$$-$$ 1

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MCQ (Single Correct Answer)

-1

If (27)⁹⁹⁹ is divided by 7, then the remainder is :

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MCQ (Single Correct Answer)

-1

Out of Syllabus

The value of $$\left( {{}^{21}{C_1} - {}^{10}{C_1}} \right) + \left( {{}^{21}{C_2} - {}^{10}{C_2}} \right) + \left( {{}^{21}{C_3} - {}^{10}{C_3}} \right)$$
$$\left( {{}^{21}{C_4} - {}^{10}{C_4}} \right)$$$$ + .... + \left( {{}^{21}{C_{10}} - {}^{10}{C_{10}}} \right)$$ is

$${2^{21}} - {2^{10}}$$

$${2^{20}} - {2^{9}}$$

$${2^{20}} - {2^{10}}$$

$${2^{21}} - {2^{11}}$$

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MCQ (Single Correct Answer)

-1

If the coefficients of x⁻² and x⁻⁴ in the expansion of $${\left( {{x^{{1 \over 3}}} + {1 \over {2{x^{{1 \over 3}}}}}} \right)^{18}},\left( {x > 0} \right),$$ are m and n respectively, then $${m \over n}$$ is equal to :

182

$${4 \over 5}$$

$${5 \over 4}$$

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