lease explain in simple steps how you calculate the last two digits of 21000 in modular arithmetic in group theory.

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A: According to Q&A guidelines, I can answer only one question. So I answered Q.8

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Q: Taking inverse Laplace on both sides, we get 6s+16 . (s+2)(s-2) 7 1 s-2 s+2 L-1{Y(s)} = L { =…

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A: The equation of the plane :Point : "As per the policy guidelines, only the first question will be…

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Q: (a) r(t) = ln ti + (t² + 3t)j + 4√tk; (0,4,4) 1 1 b) r(t) = (727); (1,1,1) t' t2,

A: (a)

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Q: 3) Find the solution of initial and boundary value problem Ut - 2Uxx = 0, 0 0 u (0. t) u (π, t) = 0,…

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Q: In the solution of the differential equation. d²x dt² obtained with the +2 +5x3 = 0 condition x=1…

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A: We have

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Q: (a) Gauss quadrature on [-1, 1] with three node points is given by 5 +31 (-15). f (VTS) G3(f) 5 +af…

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Q: Solve it using Gaussian Elimination 1 2 136-6 Р 0

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Q: Compute the exact value of the sum from n=1 to infinity of (n^2)/(2^n)

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Q: Let a₁ = 1 5 -1 a₂ -6 - 25 3 and b = 3 -5 . For what value(s) of h is b in the plane spanned by a,…

A: “Since you have posted multiple questions, we will provide the solution only to the first question…

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Q: [y(4)]² + 4 y™ + 3 y² + 2y² = cos3x 2y¹ + (y)¹/3 + 3y = √5 O y + 4y" + 5y = lny"

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A: Given that, varies inversely with , when .To find the equation of the variation.

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Q: Ex. 2 By use of the augmented matrix, solve (3x+Sy=9 2x+3y=5

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Q: 13 15. 6 10 14 Draw the circuit produced using the nearest neighbor algorithm starting at the vertex…

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