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Solve ∂^2U/∂x^2=9(∂^2U/∂x^2)

1. Cos(3x - y)
2. x^2 + y^2
3. Sin (3x - y)
4. e^-3/pix Sin(piy)
Find x and y , given that
(5x+y, 3x-y) = (2, 2x) ∈Q×Q
Draw a Venn diagram of sets A, B and C where A ⊆ B, A ∩ C ≠ φ, B∩ C = φ
What is the universal set you have chosen? Justify your choice of sets in the
diagram.
For any two sets A and B , in a universal set U , prove that
A ⊆ B ⇔ A ∪ B = B.
A sol was obtained by mixing of equal volumes of 0.4 M Copper Sulfate and 0.07 M Sodium Carbonate solutions. Write the reaction equation and micelle structure. What is the charge sign of the micelle?
Estimate pH in a 0.1 M solution of L-3-hydroxybutanoic acid (pKa=4.7).
Solve
x^4-8x^3+21x^2-20x+5=0
given that the sum of two of its roots is 4 .
Find the roots of the equation
2x^3-x^2-22x-24=0
if two of them are in the
ratio 4:3 .
Obtain the discriminant of the equation 2x^3-23x^2+82x-78=0
Hence provide the nature of its roots.
Find the polynomial over R of least degree which has i−3 and √7+5i as its
roots.
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