Find the Coefficient of t⁴ in the Expansion of [(1 − t⁶)/(1 − t)]³
JEE Main 2019 PYQ: find the coefficient of t^4 in [(1-t^6)/(1-t)]^3 by rewriting it as (1-t^6)^3 (1-t)^-3 and using the negative-binomial expansion.
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The Coefficient of x⁷ in the Expansion of (1 − x − x² + x³)⁶ Is
AIEEE PYQ: find the coefficient of x⁷ in (1-x-x²+x³)⁶ by first factoring the base as (1-x)²(1+x), then expanding it as a product of two simpler binomials.
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Find the Term Independent of x in the Expansion of [(x+1)/(x^(2/3) − x^(1/3) + 1) − (x−1)/(x − x^(1/2))]¹⁰
Find the term independent of x in the expansion of [(x+1)/(x^(2/3)−x^(1/3)+1) − (x−1)/(x−x^(1/2))]^10, by simplifying both fractions using sum/difference-of-cubes and -squares factoring first.
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If 1²·¹⁵C₁ + 2²·¹⁵C₂ + 3²·¹⁵C₃ + ⋯ + 15²·¹⁵C₁₅ Is Equal to 2ⁿ3ᵐ5ᵏ, Then m + n + k Is Equal To
Evaluate the sum 1²·15C1+2²·15C2+…+15²·15C15 using the standard identity for Σr²·nCr, then find m+n+k from its prime factorisation.
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Remainder When 19^200+23^200 Is Divided by 49
Find the remainder when 19^200+23^200 is divided by 49, by writing 19 and 23 as 21∓2 and applying the binomial theorem twice.
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Binomial (1+x)^(n+4): 5th, 6th, 7th Coefficients in AP, Find Largest Coefficient
For some n≠10, the 5th, 6th and 7th coefficients of (1+x)^(n+4) are in AP. Find n, then the largest coefficient of the expansion.
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The Remainder When (2021)^2023 Is Divided by 7 Is
Find the remainder when (2021)^2023 is divided by 7 — a modular arithmetic problem solved by reducing the base first, then finding a repeating power cycle.
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If the Sum From r = 1 to 30 of r²(³⁰Cᵣ)²/(³⁰Cᵣ₋₁) = α·2²⁹, Then the Value of α Is
A JEE Main 2025 binomial coefficient summation simplified by rewriting the ratio of consecutive coefficients, then splitting into two telescoping sums.