1. In the expansion of (x³ - 2)² one of the terms is of the form ax¹1. Algebraically determine the value of a.

Q: Find the remainder when x51 is divided by x + 4 in Z7[x].

A: We have to find the remainder when x51 is divided by x+4 in Z7x. Let t be the remainder when x51 is…

Q: True or false: The coefficient of x4y7 in (3x – 4y)11 is (2)347. True False

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Q: Find the coefficient of x3y10 in the expansion of (−4x−4y)13

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Q: 12 Find the term of (a – 3b)" that has b in it.

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Q: Find the smallest integer x for which (x4 + 4x)/(x + 2) is O(xx). 01 02

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Q: Find AB if A = [4 -3 3 -1 0 -2] and B = 4 Use the tools in the

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Q: the expansion of omial theorem to determine the value of the consta 3 < (22²7³. 23 2 (2-3r³y) x…

A: Given expansion is 2-3x8y×2x2y3+3x3-2y219…

Q: What is the coefficient of xy- (the third term) in the expansion of (2x + 3y)'? 6. O -18 O 18 O 54

A: We have to find the coefficient of xy2 in the expansion of 2x+3y3.

Q: . Factor x12 -1 as a product of irreducible polynomials over Z.

A: Given: x12-1. We have to factor x12-1 as a product of irreducible polynomials over Z.

Q: Find the coefficient of x3y2z3w in the expansion of(2x + 3y − 4z + w)9.

A: The given expansion is 2x+3y-4z+w9. We have to find the coefficient of x3y2z3w.

Q: In real analysis,Prove that if A is countable, then m(A) =0.

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Q: Find the term indicated in the expansion (x + 2y)6; third term.

A: Find the term indicated in the expansion (x + 2y)6; third term.

Q: 22. Evaluate |(x – a) (x – b) (x – c) . . . (x – y) (x – z) where the second term of each factor…

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Q: i. Find the coefficient of x in the expansion of ( 2x –÷) . ii. Hence find the coefficient of x in…

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Q: ) Write the expansion of (3 + 2x) and use the first three terms of the expansion to approximate3.26.

A: Concept is binomial theoram  3.2 = (3+0.2) 0.2 = 2x0.1

Q: 1. 1+ x +x? + x' + x* Find the coefficient of x25 in the expansion of

A: We have to find the coefficient of x25 in the expansion of 11+x+x2+x3+x4.

Q: In the expansion of (4x + y) ^ 9, the coefficient of x3y4 is

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Q: Find the coefficient of a?bi in the expansion of (2a - bj)^5

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Q: y2, the y axis and y 1, rotated about the line y = 2. The rectangular elements are parallel The…

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Q: Find the term of (a – 2b)3 that has b in it. |

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Q: 1. The coefficient of x³y³ in the expansion of (2x + 2y)¹⁰ is 10 2. The constant term in the…

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Q: Find the coefficient of x8 y18  in the expansion of (1x2  -4y6)7

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Q: find the coefficient of t8 in expansion of 2t(3+t)20

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