Binomial theorem for a positive integral index; general term and middle term; properties of binomial coefficients and simple applications.
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Q1 · Binomial Theorem and its Simple Applications · EASY
Find the coefficient of x^5 in the expansion of (2x + 3)^7.
Q2 · Binomial Theorem and its Simple Applications · MEDIUM
In the expansion of (1 + x)^n, if the coefficients of the 5th, 6th and 7th terms are in arithmetic progression, then the value of n is:
Q3 · Binomial Theorem and its Simple Applications · MEDIUM
The term independent of x in the expansion of (x^2 - 1/x)^9 is:
Q4 · Binomial Theorem and its Simple Applications · HARD
If the middle term in the expansion of (1 + x)^(2n) is the greatest term, then the range of x is:
Q5 · Binomial Theorem and its Simple Applications · EASY
The sum of the coefficients in the expansion of (1 + 2x + x^2)^10 is: