# Engineering Mathematics (Test 7)

## Gate Exam : Ce Civil Engineering

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Engineering Mathematics
| Engineering Mathematics |
Q.1
The probability that a student knows the correct answer to a multiple choice question is 2/3. If the student does not know the answer, then the student guesses the answer. The probability of the guessed answer being correct is 1/4. Given that the student has answered the question correctly, the conditional probability that the student known the correct answer is
A. 2/3
B. 3/4
C. 5/6
D. 8/9
Answer : Option D
Explaination / Solution:

A = The student answer the question correctly
E1 = Student knows the correct answer
E2 = Student guesses the correct answer

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Q.2
he ratio of male to female students in a college for five years is plotted in the following line graph. If the number of female students in 2011 and 2012 is equal, what is the ratio of male students in 2012 to male students in 2011?

A. 1:1
B. 2:1
C. 1.5:1
D. 2.5:1
Answer : Option C
Explaination / Solution:

Take number of female students in 2011=100 ∴ Number of male in 2011=100 No. of female in 2012=100 No. of male in 2012=150 Ratio = 150/100 = 1.5:1

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Q.3
Let z = x + iy be a complex variable. Consider that contour integration is performed along the unit circle in anticlockwise direction. Which one of the following statements is NOT TRUE?
A. The residue of
B.
C.
D.  (complex conjugate of z ) is an analytical function
Answer : Option D
Explaination / Solution:
No Explaination.

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Q.4
Solution of the differential equation 3y(dy/dx) + 2x = 0 represents a family of
A. ellipses
B. circles
C. parabolas
D. hyperbolas
Answer : Option A
Explaination / Solution:
No Explaination.

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Q.5
.For the composition table of a cyclic group shown below

Which one of the following choices is correct?
A. a, b are generators
B. b, c are generators
C. c, d are generators
D. d, a are generators
Answer : Option C
Explaination / Solution:
No Explaination.

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Q.6
Consider the following well-formed formulae:

Which of the above are equivalent?
A. i and iii
B. i and iv
C. ii and iii
D. ii and iv
Answer : Option B
Explaination / Solution:
No Explaination.

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Q.7
Two sequences [a, b, c] and [A, B, C ] are related as.

If another sequence [p, q , r ] is derived as,

then the relationship between the sequences [p, q , r ] and [a, b, c] is
A. [p, q , r ] = [b, a, c]
B. [p, q , r ] = [b, c, a]
C. [p, q , r ] = [c, a, b]
D. [p, q , r ] = [c, b, a]
Answer : Option C
Explaination / Solution:

Given relation is

Comparing it with the DFT concept of taking fourier transform by matrix form. We may calculate that here we are taking the 3 order DFT of [a b c]whose
transformed output is [A B C]T . So,

Again, we consider the equation (1),

Since, the relation between cube roots of unity is given as

So, we solve the matrix equation as

Again, we consider the equation (2),

In above equation, we apply elementary row operation as

Hence, we can conclude that
[p q r] =[c a b]

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Q.8
Let δ denote the minimum degree of a vertex in a graph. For all planar graphs on n vertices with δ ≥3, which one of the following is TRUE?
A. In any planar embedding, the number of faces is at least (n/2) + 2
B. In any planar embedding, the number of faces is less than (n/2) + 2
C. There is a planar embedding in which the number of faces is less than (n/2) + 2
D. There is a planar embedding in which the number of faces is at most n/(δ+1)
Answer : Option A
Explaination / Solution:

We know that v + r = e+2 ⇒ e=n+r-2......(1)
Where V=  n (number of vertices); r = number of faces and
e = number of edges
Given, δ ≥ 3 then 3n ≤ 2e

Number of faces is atleast (n/2) + 2

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Q.9
The equation sin(z) = 10 has
A. no real or complex solution
B. exactly two distinct complex solutions
C. a unique solution
D. an infinite number of complex solutions
Answer : Option A
Explaination / Solution:
No Explaination.

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Q.10
Consider the set S = {1, ω, ω2}, where ω and ω2 are cube roots of unity. If * denotes the multiplication operation, the structure (S, *) forms
A. A group
B. A ring
C. An integral domain
D. A field
Answer : Option C
Explaination / Solution:
No Explaination.

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