1st/2ways: permutation Show P(n,2)+P(n,1)=n^2

Solve the following differential equation cos^2(x)dy/dx +y = tan(x)

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Find the expected value & the variance of a geometric r.v. X

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AI 2008 Hindustan: Evaluate integral ∫ 2/3 cos(x)/sin^2(x) dx

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MP 8,93,96,97,99 Hindustan: Evaluate ∫ sec(x)/(sec(x)-tan(x)) dx

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CBSE 2000 Hindustan: integral (1+tan(x))/(x+log(sec(x)) dx

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MP 98 Hindustan: Evaluate (i) ∫e^loge(x) dx (ii) ∫e^(-loge(x)) dx

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MP 2000 Hindustan: Evaluate ∫(tan(x)+cot(x))^2 dx

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A box contains 8 blue & 6 red socks. What is the number of ways that 2 socks can be drawn ...

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2nd way: derivative (x^x)^x

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MPPET 1996 Hindustan: trig integral ∫ sin^2(x) -cos^2(x)/(sin^2(x) cos^2(x)) dx

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RPET 2003 Hindustan: integral ∫sin^4(x)-cos^4(x) dx

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Review: Multiplying each obs. by a CONSTANT results in new variance =

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Doraemon in Hindi Season 01 Episode 46

Pixel PlayHouse

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derivative x^n vs n^x vs x^x

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Alternate way: ∫1/(x^2+a^2) dx

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#10 2023 MIT Integration Bee Qualifying Exam

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#17 2022 MIT Integration Bee Qualifying Exam

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#9 2023 MIT Integration Bee Qualifying Exam

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Find f'(x) in terms of g'(x)

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derivative a^(f(x)g(x))^h(x)

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