Question and Answers Forum
OthersQuestion and Answers: Page 10
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Question and Answers Forum |
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OthersQuestion and Answers: Page 10 |
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| find domine and range of function f(x,y) = (√((x+y^2 )/(x^2 +y^2 −4))) |
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| Calculer la valeur de la serie suivante: S=(3/2)+(5/8)+(7/(32))+(9/(128))+..... |
| What is the Inverse laplace transform of ((S + 2)/(S^2 +4S + 7)) Urgent! |
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| When a kichen is removed from an oven, its temperature is measured at 300^0 F. Three minutes later, its temperature is 200^0 F. How longwill it take the kitchen to cool of to a room temperature of 70^0 F? |
| A mass of 12kg rests on a smooth inclined plane which is 6m long and 1m high. The mass is connected by a light inextensible string which passes over a smooth pulley fixed at the top of the plane to a mass of 4kg which is hanging freely. With the string taut, the system is released from rest. Using Polya problem solving approach find the following: a. acceleration of the system b i. velocity with which the 4kg mass hits the ground. b ii. time the 4kg mass takes to hit the ground |
| 3^x + 4^x = 5^x find x ? |
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| Ques. 1 Let G = C_5 × C_(25) × C_(625) . Determine the number of elements of each order in G Ques. 2 List the abelian groups of order 16 and of order 27 up to Isomorphism. Ques. 3 Describe a Sylow 2−subgroup in S_5 , and how many Sylow 2−subgroups are in S_5 ? |
| question about tinkutara how can an answer be placed in a box. |
| Show that the kernel of a group homomorhism θ : G → H is a normal subgroup. Hint: Check the existence of the combination g^(−1) kg in the kernel. |
| Ques. 12 If Y = {0, 1, 2, 3, 4} is transversal for 5Z in (Z, +). Show whether or not Y is a subgroup of 5Z subgroup under addition of integers modulo of 5 |
| Ques. 11 Let {H_α } ∈ Ω be a family of subgroup of a group G then prove that ∩_(α=Ω) H_α is also a subgroup Ques. 12 Using GAP, find the elements A, B and C in D_5 such that AB = BC but A ≠ C. |
| Ques. Find the number of integers in the set S={1,2,3,...,60} which are not divisible by 2 nor by 3 nor by 5. Hello |
| Ques. 8 Find the signum (sign or sgn) of the permutation θ=(12345678). Hint : for any permutation β, take sgn β = {_(−1 if β is odd) ^(1 if β is even) Ques. 9 Prove that ∣S_n ∣ = n!. Ques. 10 Provd that for b∈S_n , sgn b = sgn b^(−1) . |
| Ques. 6 Let (G, ∗) be a group. and let C={c∈G : c∗a = a∗c ∀a∈G}. Prove that C is subgroup of G. hence or otherwise show that C is Abelian. [Note C is called the center of group G] Ques. 7 If (G, ∗) is a group such that (a∗b)^2 = a^2 ∗b^2 (multiplicatively) for all a,b∈G. Show that G must be Abelian |
| Ques. 5 Prove that if a,b are any elements of a group (G, ∗), then the equation y∗a=b has a unique solution in (G, ∗). Ques. 6 a) Show that the set G of all non-zero complex numbers, is a group under multiplication of complex numbers. b) Show that H={a∈G : a_1 ^2 + a_2 ^2 = 1}, where a_1 = Re a and a_2 = Im a is a subgroup of G. |