Mathematics · JEE

General term and middle term and simple applications Concepts for JEE

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Quick answer

Master General term and middle term and simple applications by understanding definitions, standard results, and typical JEE question patterns — then practise with syllabus-aligned MCQs on Goodmarks.

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Concept explainer

General term and middle term and simple applications is a core JEE Main Mathematics subtopic under Binomial Theorem and Its Simple Applications. Master the definitions, standard results, and typical MCQ patterns tested in JEE Main and Advanced.

Key points

Understand the definition and scope of General term and middle term and simple applications in the JEE syllabus
Memorise key formulas and standard results linked to General term and middle term and simple applications
Practise 20–40 syllabus-aligned MCQs with step-by-step solutions

JEE tips

Revise General term and middle term and simple applications with a one-page formula sheet before attempting mixed tests
After each practice set, log mistakes specific to General term and middle term and simple applications and reattempt after 48 hours

Common trap

Students often rush General term and middle term and simple applications questions without checking units, sign conventions, or boundary conditions — always verify assumptions before calculating.

Syllabus context

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

Free sample questions

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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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Frequently asked questions

What concepts in General term and middle term and simple applications are essential for JEE?

Focus on core ideas across General term and middle term and simple applications. JEE tests application, not just memorisation.