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1. a) Solve the following ordinary differential equations:
i) dy/dx + 4xy = x
ii) d²y/dx² + 4dy/dx - 12y = cos2x .
i) dy/dx + 4xy = x
ii) d²y/dx² + 4dy/dx - 12y = cos2x .
The set of discontinuous functions from [1,0] to R form a ring with respect to pointwise addition and multiplication. Is this statement true or false, justify your answer.
The characteristic of a finite field is zero. Is this statement true or false, justify your answer.
If a ring has a unit, then it has only one unit. Is this statement true or false ,justify your answer.
If σ ∈ Sn (n ≥ 3 ) is a product of an even number of disjoint cycles, then sign (σ) = 1. Is this statement true or false, justify your answer.
If R is a ring and I is an ideal of R , then xr = rx ∀ x ∈ I and r ∈ R . Is this statement true or false, justify your answer .
Every element of Sn has order at most n . Is this statement true or false, justify your answer.
If G is a group and H∆G , then | G : H |= 2 . Is this statement true or false, justify your answer.
In a circle the centre point is 'O' and OABC is a parallelogram then find angle OAC and angle OAB.
top is 12 meters across: straight line down is 7.81 meters, slope is 2:1. what is the base
