Engineering BE Information Technology Sem 3 May 2019 2019 Applied Mathematics III Question Paper - Mumbai University | munotes
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Questions asked in this paper
Total Marks: 80 Hours: 3 hrs
Note : 1) Question no. | is compulsory
2) Attempt any three questions out of five questions
a) If any 11 numbers between 1| and 20 are chosen show that at least two of them will be
multiplies of each other. (05)
b) A function f : R- is defined by f (x) = , Prove that f is bijective
and find the rule for . (05)
c) Find (05)
d) Prove that there does not exist an analytic function whose imaginary part is
b) What is the chance of throwing ten with four dice? (06)
c) In a certain examination there are multiple choice questions. There are four possible
answers to each questions and one of them is correct. An intelligent student can solve 90%
questions correctly by reasoning and for the remaining 10% questions he gives answer by
guessing. A week student can solve 20% question correctly by reasoning and for the
remaining 80% questions he gives answer by guessing. An intelligent student gets the correct
answer. What is the probability that he was guessing. (08)
a) A can hit a target 2 times in 5 shots, B 3 times in 4 shots, C 2 times in 3 shots. They fire a
volley. What is the probability that at least 2 shots hit the target? (06)
b) Find (06)
c) If R is the relation on the set of integers such that aRb if and only if 2a+3b is divisible by 5
Find the equivalence classes. (08)
a) Evaluate (06)
b) Find (06)
c) Find the bilinear Transformation which maps the points on to the
Also find image of |z|=1of z-plane to w-plane. (08)
a) A family consisting of an old man, 6 adults and 4 children is to be seated row for
dinner. The children wish to occupy two seats at each end and the old man refuse to
child on either side of him. In how many ways can the seating arrangement be made for the
b) Find the analytic function f (z)=u+iv in terms of z if u-v=(x- +4xy+
c) Solve with =0, y =0, y” (0) = I. 08
a) Prove that (06)
b) Draw the Hasse diagram of D,,; . (06)
c) Find Laplace Transformation of the following
Note : 1) Question no. | is compulsory
2) Attempt any three questions out of five questions
a) If any 11 numbers between 1| and 20 are chosen show that at least two of them will be
multiplies of each other. (05)
b) A function f : R- is defined by f (x) = , Prove that f is bijective
and find the rule for . (05)
c) Find (05)
d) Prove that there does not exist an analytic function whose imaginary part is
b) What is the chance of throwing ten with four dice? (06)
c) In a certain examination there are multiple choice questions. There are four possible
answers to each questions and one of them is correct. An intelligent student can solve 90%
questions correctly by reasoning and for the remaining 10% questions he gives answer by
guessing. A week student can solve 20% question correctly by reasoning and for the
remaining 80% questions he gives answer by guessing. An intelligent student gets the correct
answer. What is the probability that he was guessing. (08)
a) A can hit a target 2 times in 5 shots, B 3 times in 4 shots, C 2 times in 3 shots. They fire a
volley. What is the probability that at least 2 shots hit the target? (06)
b) Find (06)
c) If R is the relation on the set of integers such that aRb if and only if 2a+3b is divisible by 5
Find the equivalence classes. (08)
a) Evaluate (06)
b) Find (06)
c) Find the bilinear Transformation which maps the points on to the
Also find image of |z|=1of z-plane to w-plane. (08)
a) A family consisting of an old man, 6 adults and 4 children is to be seated row for
dinner. The children wish to occupy two seats at each end and the old man refuse to
child on either side of him. In how many ways can the seating arrangement be made for the
b) Find the analytic function f (z)=u+iv in terms of z if u-v=(x- +4xy+
c) Solve with =0, y =0, y” (0) = I. 08
a) Prove that (06)
b) Draw the Hasse diagram of D,,; . (06)
c) Find Laplace Transformation of the following
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