Q21: The Laplacian of the function f(x, y, z) = A sin(ax) sin(by) sin(cz) (A)-(a² + b²+c²)ƒ(x,y,z) (C)-(a+b+c)f(x,y,z) Q22: The solution of y"+y=0 is- (A) ₁ + ₂* (B)(a² + b² + c²)f(x,y,z) (D) (a+b+c)f(x, y, z) (B) ce"* + Czxe (D) C₁+C₂e* (C) Ge*+c₂e-* Q23: The integrating factor for the differential equation 2xydx-x²dy = Ois: (A) +/ (D) y² (0) Q24: The value of the line integral [(2x+3y)dx + (3x + 4y)dy] where cis the straight-line segment (C) 4 (D) 116 y = 2x + 3 from the point (0,3) to the point (2,7) is: (A) 126 (B) 63 Q25: The solution of y"+y = 0 is- (A) Ge*+c₂e-* (C) c cosx + c sinx (B) ce+c₂xe-x (D) cicosx + C2xsinx

Q: 2. Evaluate, using the laws of logarithms. 2 log, 64 x v64* |+log, 46 43 256

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

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A:

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A: Solve  5x =-5 3

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A: We can solve the quinary number system problem as below.

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A:

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A: Solution:

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A: Given that  8-2y=4               ⇒2y=8-4               ⇒2y=4                ⇒y=2…

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A: Note- Since you have posted multiple questions, as per our guidelines we are supposed to answer only…

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A: Given query is to find the value of x.

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A: Answer

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A: Please see the below pictures for detailed solution.

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A: Given query is to find the value of x.