jee_main_2025_24_jan_morning - Definite Integrals Topics

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QUESTION #52 Properties of Definite Integrals
If I(m,n) = ∫₀¹ xm-1 (1-x)ⁿ⁻¹ dx where m, n > 0, then I(9,14) + I(10,13) is :
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QUESTION #71 Differentiating Under the Integral Sign
Let f be a differentiable function such that 2(x+2)²f(x) - 3(x+2)² = 10∫₀x(t+2)f(t)dt for x ≥ 0. Then f(2) is equal to ________.
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JEE Physics: Waves (+15.5%) | Electrostatics: Concentric Shells (-29.7%) | Modern Physics: Photoelectric Clones (+34.2%) | Mathematics: Definite Integrals (+18.1%) | Chemistry: Coordination Splitting (-11.4%) | JEE Physics: Waves (+15.5%) | Electrostatics: Concentric Shells (-29.7%) | Modern Physics: Photoelectric Clones (+34.2%) | Mathematics: Definite Integrals (+18.1%) | Chemistry: Coordination Splitting (-11.4%)

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