1st/2parts 3 ways: tn-1 + tn = n^2 where tn = nth triangular number

2nd/2ways: count perm Show P(n,2)+P(n,1)=n^2

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

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

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2nd way: integral ∫ log √x(x^n) dx

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logic: If p then q ...

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Evaluate the 2 integrals

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3 ways: trig Show sec(2x)=sec^2(x)/(2-sec^2(x))

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2 ways: integral ∫x/(x+a) dx

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2 ways: Σ 1? where k=m to n

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

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logic: tautology (¬p→q)∧(¬p→¬q) →p

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Always ZERO

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2 ways: sq root derivative 1/(√√(1/√x))

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2 ways: The following measurements were taken by an antique dealer as he weighted to the ...

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3 ways: trig integral 1/(1+cos(x)) dx

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alternate way: count sum 1+2+3+ ... +n

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2nd/2ways: count perm Show P(n,n)=P(n,n-1)

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2 ways: Find a formula for d/dx[f^m(x) g^n(x)], where f & g are differentiable functions ...

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3rd way: nCr = (n-1)Cr + (n-1)C(r-1)

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