jee_main_2024_31_jan_morning - Integrals Topics

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QUESTION #21 Definite Integration by Substitution
If the integral 525 ∫₀(π)/(2) 2x (11)/(2)x (1 + (5)/(2)x)(1)/(2) dx is equal to (n√(2) - 64), then n is equal to
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QUESTION #30 Properties of Definite Integrals
Let f : R → R be a function defined by f(x) = (4^x)/(4^x + 2) and M = ∫f(a)f(1 - a) x ⁴(x(1 - x)) dx, N = ∫f(a)f(1 - a) ⁴(x(1 - x)) dx; a ≠ (1)/(2). If α M = β N, α, β in N, then the least value of α² + β² 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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