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

A = The student answer the question correctly

E_{1} = Student knows the correct answer

E_{2} = Student guesses the correct answer

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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

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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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.

No Explaination.

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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.

No Explaination.

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.For the composition table of a cyclic group shown below

**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.

Which one of the following choices is correct?

No Explaination.

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Consider the following well-formed formulae:

**A. ** i and iii

**B. ** i and iv

**C. ** ii and iii

**D. ** ii and iv

**Answer : ****Option B**

**Explaination / Solution: **

No Explaination.

Which of the above are equivalent?

No Explaination.

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

**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

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

then the relationship between the sequences [p, q , r ] and [a, b, c] is

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]^{T }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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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)

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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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.

No Explaination.

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Consider the set S = {1, ω, ω^{2}}, where ω and ω^{2} 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.

No Explaination.

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**Preparation Study Material**- Engineering Mechanics (Study/Preparation)
- Structural Analysis I (Study/Preparation)
- Structural Analysis II (Study/Preparation)
- Engineering Geology (Study/Preparation)
- Mechanics of Solids (Study/Preparation)
- Mechanics of Fluids (Study/Preparation)
- Surveying I (Study/Preparation)
- Surveying II (Study/Preparation)
- Construction Materials (Study/Preparation)
- Strength of Materials (Study/Preparation)
- Applied Hydraulic Engineering (Study/Preparation)
- Soil Mechanics (Study/Preparation)
- Foundation Engineering (Study/Preparation)
- Environmental Science and Engineering (Study/Preparation)
- Environmental Engineering I (Study/Preparation)
- Environmental Engineering II (Study/Preparation)
- Highway Engineering (Study/Preparation)
- Railways and Airports and Harbour Engineering (Study/Preparation)
- Water Resources and Irrigation Engineering (Study/Preparation)