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Hard General term and middle term and simple applications MCQs for JEE

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Hard General term and middle term and simple applications MCQs train multi-concept problem solving — attempt after mastering easy and medium sets (7+ on Goodmarks).

Push your limits with hard General term and middle term and simple applications MCQs designed for JEE Advanced-level thinking. 7+ questions with detailed solutions.

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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 x9x^{9} in the expansion of (x3+12t)11,\left(x^{3}+\frac{1}{2^{t}}\right)^{11}, where t=log⁡2(x32)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 (x+xlog⁡10x)3\left(x+x^{\log _{10} x}\right)^{3} is 10610^{6} then xx is equal to
Q3MathsUnit 5: Binomial Theorem and Its Simple Applications
If the middle term in the expansion of (x2+1x)n\left(x^{2}+\frac{1}{x}\right)^{n} is 924x6,924 x^{6}, then n=n=
Q4MathsUnit 5: Binomial Theorem and Its Simple Applications
Coefficient of x50\boldsymbol{x}^{\mathbf{5 0}} (x>0),(x>0), in (1+x)1000+2x(1+(1+x)^{1000}+2 x(1+ x)999+3x2(1+x)998+…\boldsymbol{x})^{999}+\mathbf{3} \boldsymbol{x}^{2}(\mathbf{1}+\boldsymbol{x})^{998}+\ldots is
Q5MathsUnit 5: Binomial Theorem and Its Simple Applications
The total number of terms in the expansion of (x+y)50+(x−y)50(x+y)^{50}+(x-y)^{50} is
Q6MathsUnit 5: Binomial Theorem and Its Simple Applications
Evaluate (3−2)6+(3+2)6(\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 (31/5+71/3)100\left(3^{1 / 5}+7^{1 / 3}\right)^{100} is

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