Mathematics · JEE

Important Questions: General term and middle term and simple applications for JEE

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Syllabus context

Part of Binomial Theorem and Its Simple Applications in JEE Main Mathematics.

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Q1MathsUnit 5: Binomial Theorem and Its Simple Applications

The coefficient of

x^{9}

in the expansion of

\left(x^{3}+\frac{1}{2^{t}}\right)^{11},

where

t=\log _{\sqrt{2}}\left(x^{\frac{3}{2}}\right)

Q2MathsUnit 5: Binomial Theorem and Its Simple Applications

If it is known that the third term of the binomial expansion

\left(x+x^{\log _{10} x}\right)^{3}

10^{6}

then

x

is equal to

Q3MathsUnit 5: Binomial Theorem and Its Simple Applications

If the middle term in the expansion of

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

924 x^{6},

then

n=

Q4MathsUnit 5: Binomial Theorem and Its Simple Applications

Coefficient of

\boldsymbol{x}^{\mathbf{5 0}}

(x>0),

(1+x)^{1000}+2 x(1+

\boldsymbol{x})^{999}+\mathbf{3} \boldsymbol{x}^{2}(\mathbf{1}+\boldsymbol{x})^{998}+\ldots

Q5MathsUnit 5: Binomial Theorem and Its Simple Applications

The total number of terms in the expansion of

(x+y)^{50}+(x-y)^{50}

Q6MathsUnit 5: Binomial Theorem and Its Simple Applications

Evaluate

(\sqrt{\mathbf{3}}-\sqrt{\mathbf{2}})^{\mathbf{6}}+(\sqrt{\mathbf{3}}+\sqrt{\mathbf{2}})^{\mathbf{6}}

Q7MathsUnit 5: Binomial Theorem and Its Simple Applications

Number of irrational terms in the binomial expansion of

\left(3^{1 / 5}+7^{1 / 3}\right)^{100}

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Important questions test core concepts that appear frequently across JEE Main and Advanced papers — definitions, standard formulas, and classic problem types.

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Key areas include General term and middle term and simple applications. Prioritise these before moving to edge cases.

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Revise 30–50 important MCQs per unit in the last month before JEE. Focus on questions you got wrong at least once.

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