2 ways: trig Show tan(2x)=2/(cot(x)-tan(x))

prob stat: Compute Var(X) when X represents the outcome when we roll a fair die.

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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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2nd way: integral ∫ log √x(x^n) dx

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2nd/3ways: trig integral ∫sec(x) dx

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

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2nd/3 ways: How many chords can be drawn through 21 points on a circle?

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Growing patterns #3

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

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1st/2ways: exp e^g(x) (g'(x)f(x) + f'(x)) dx

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Screen Recording 2024-02-22 at 10.30.06 PM

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matrix product: AB=0 where A≠0 & B≠0

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derivative log f(g(x)) (a)

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2 ways: 𝖎𝖓𝖙𝖊𝖌𝖗𝖆𝖑 ∫3x/((x-2)(x+1)) dx

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Lamar U: Use log. differentiation to find the 1st derivative of the given function

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Screen Recording 2024-05-05 at 11.28.23 PM

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prob stat The events A & B are s.t P(A)=5/12, P(B)=2/3 & P(A' n B')=1/12.

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1st/2ways: logic Import-Export

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5 ways: trig Derivative of sin^2(x)

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

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