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Hard Binomial Theorem and Its Simple Applications MCQs for JEE

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Hard Binomial Theorem and Its Simple Applications MCQs train multi-concept problem solving — attempt after mastering easy and medium sets (21+ on Goodmarks).

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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
Sum of coefficients in the expeansion of (a+b+c)8(a+b+c)^{8} is
Q3MathsUnit 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
Q4MathsUnit 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=
Q5MathsUnit 5: Binomial Theorem and Its Simple Applications
Evaluate the following (0.98)2(0.98)^{2}
Q6MathsUnit 5: Binomial Theorem and Its Simple Applications
The coeffcient of x10x^{10} in the expansion of (1+x)2(1+x2)3(1+x3)4(1+x)^{2}\left(1+x^{2}\right)^{3}\left(1+x^{3}\right)^{4} is equal to
Q7MathsUnit 5: Binomial Theorem and Its Simple Applications
The number of terms with integral coefficients in the expansion of (71/3+51/2⋅x)600\left(7^{1 / 3}+5^{1 / 2} \cdot x\right)^{600} is
Q8MathsUnit 5: Binomial Theorem and Its Simple Applications
∀n∈N,33n−26n\forall n \in N, 3^{3 n}-26^{n} is divisible by

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