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Infinity Roy made an stadium with infinite number of seats. Where all the seats
are numbered as 1,2,3……… For a special guest stadium committee take the
decision to transfer the spectators from nth numbered seat to n+1th numbered seat
For this they refund him{(1÷n)-(1÷(n+1)) } tk . How many taka stadium committee needs
to transfer seat by this process.
are numbered as 1,2,3……… For a special guest stadium committee take the
decision to transfer the spectators from nth numbered seat to n+1th numbered seat
For this they refund him{(1÷n)-(1÷(n+1)) } tk . How many taka stadium committee needs
to transfer seat by this process.
Compute the torsion of the circular helix γ(t)=(acos t, asin t, bt)
If a list of 20 individuals who volunteered to supply blood, when it is needed for transfusion, has 15 individuals of type B blood and 3 individuals are selected random from the list, what is the probability that:
a) All 3 will be type B, b) 2 will be of type B and 1 will not, c) at least 1 will be of type B
a) All 3 will be type B, b) 2 will be of type B and 1 will not, c) at least 1 will be of type B
obtain the fourier series for the following periodic function which has period of 2π:
f(x) = x^2 for -π≤x≤π
f(x) = x^2 for -π≤x≤π
verify Cauchy Goursat formula where f(z) = z+1 and D is the region bounded by the triangle with vertices at 0,3 and 3+2i.
The perimeter of a regular hexagon is 3.04cm less than the perimeter of a regular pentagon. The perimeter of the regular hexagon is 21.06cm. What is the side length of the regular pentagon?
Prove the following statement by contradiction.
“There is no integer solution to the equation
(x^2)-6=0 ."
Prove and disprove the following statements.
(a) For all the odd integers n, n^4 mod 8 = 1
(b) There exist positive integers a, b and ab, which all the three belong to perfect
squares.”
State the contrapositive for the statement given below and hence, provide a proof for the
statement.
“For all integers a and b, if ab is even, then at least one of a or b is even.”
Prove or disprove the following statement.
“Let p and q be positive integers, if p mod 4 = 1 and q mod 4 = 2, then pq mod 4 = 2.”
“There is no integer solution to the equation
(x^2)-6=0 ."
Prove and disprove the following statements.
(a) For all the odd integers n, n^4 mod 8 = 1
(b) There exist positive integers a, b and ab, which all the three belong to perfect
squares.”
State the contrapositive for the statement given below and hence, provide a proof for the
statement.
“For all integers a and b, if ab is even, then at least one of a or b is even.”
Prove or disprove the following statement.
“Let p and q be positive integers, if p mod 4 = 1 and q mod 4 = 2, then pq mod 4 = 2.”
Prove or disprove the following statement.
“Let p and q be positive integers, if p mod 4 = 1 and q mod 4 = 2, then pq mod 4 = 2.”
“Let p and q be positive integers, if p mod 4 = 1 and q mod 4 = 2, then pq mod 4 = 2.”
If the probability is 0.60 that a divorce will remarry within 3 years, find the probability that of 5 divorces :
a) 3 out of 5 divorces will remarry within 3 years
b) At least 3 will remarry within 3 years
c) At most 3 will remarry within 3 years
a) 3 out of 5 divorces will remarry within 3 years
b) At least 3 will remarry within 3 years
c) At most 3 will remarry within 3 years
in a hospital 60% of the patients are married. What's the probability that a sample of one word with 8 patient, had 3 married
