logic Show by truth table x∧(x→y)→y is Tautology

1st/2ways: 1+2+3+...+(n-1)+n+(n-1)+...+3+2+1 = n^2

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

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

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

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RPET 2003 Hindustan: integral ∫sin^4(x)-cos^4(x) 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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logic Idempotent law show x=xVx

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

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Screen Recording 2024-05-19 at 11.13.23 PM

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Screen Recording 2024-05-19 at 9.45.17 PM

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prob stat: A fair 6-sided dice, with sides numbered 1,1,2,2,3,55 is thrown.

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UC Davis #3 2nd way: ∫(2-x)/(x^2+5x)dx [integration by partial fraction]

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Sum/Difference of 2 EVEN function is EVEN

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sq root 𝖎𝖓𝖙𝖊𝖌𝖗𝖆𝖑 ∫1/(√x (1+√x))dx

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logic: Simplify the Boolean function F=XYZ+XY'Z+XYZ'

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A bag contains 5 red balls & 3 green balls. A ball is selected at random &

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Screen Recording 2024-05-06 at 11.53.23 PM

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example: Mean, Median & Mode

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2nd way: trig integral ∫sec^(3/2)(x) tan^3(x) dx

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