The solution to the differential equation where k is a constant,
subjected to the boundary conditions u(0)=0 and u(L)=U, is

**A. ** u = U(x/L)

**B. **

**C. **

**D. **

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

**Explaination / Solution: **

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Consider the differential equation . The general solution with
constant c is

**A. ** y = tan x^{2}/2 + tanc
**B. ** y = tan2((x/2) + c)
**C. ** y = tan2(x/2) + c
**D. ** y = tan((x2/2) + c)

**Answer : ****Option D**

**Explaination / Solution: **

No Explaination.

No Explaination.

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The analytic function has singularity at

**A. ** 1 and -1

**B. ** 1 and i

**C. ** 1 and -i

**D. ** i and -i

**Answer : ****Option D**

**Explaination / Solution: **

No Explaination.

No Explaination.

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If the entries in each column of a square matrix M add up to 1, then an eigen value of M
is

**A. ** 4

**B. ** 3

**C. ** 2

**D. ** 1

**Answer : ****Option D**

**Explaination / Solution: **

Consider the '2x^{2} ' square matrix Characteristic equation of M is

Consider the '2x

λ^{2 }- (a + d)λ + (ad - bc) = 0......................(1)

Put λ =1, weget

1 - (a + d) + ad - bc = 0

1 - a - d + ad - (1 - d)(1 - a) = 0

1 - a - d + ad - 1 + a + d - ad = 0

0 = 0,which is true

λ = 1
Satisfies the equation (1) but λ = 2,3,4
does not satisfy the equation (1). For all
possible values of a,d

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The divergence of the vector field at a point (1,1,1) is equal to

**A. ** 7

**B. ** 4

**C. ** 3

**D. ** 0

**Answer : ****Option C**

**Explaination / Solution: **

No Explaination.

No Explaination.

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A source emits bit 0 with probability 1/3 and bit 1 with probability 2/3. The emitted bits are communicated to the receiver. The receiver decides for either 0 or 1 based on the received value R. It is given that the conditional density functions of R are as

The minimum decision error probability is

Given the conditional density function of R as

Decision error probability that receiver decides 0 for a transmitted bit 1 is

f_{R/1} (r =
0) = 1/6

Again, the decision error probability that receiver decides 1 for a transmitted bit 0 is

fR/0 (r = 1) = 1/4

Hence, the minimum decision error probability is

fR/1 (r = 0) = 1/6

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With respect to the numerical evaluation of the definite integral, where a and b
are given, which of the following statements is/are TRUE?

**A. ** I only

**B. ** II only

**C. ** Both I and II

**D. ** Neither I nor II

**Answer : ****Option C**

**Explaination / Solution: **

(I) The value of K obtained using the trapezoidal rule is always greater than or equal to the
exact value of the definite integral.

(II) The value of K obtained using the Simpson’s rule is always equal to the exact value of
the definite integral.

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The solution of x(dy/dx) + y = x^{4} with the condition y(1) = 6/5 is

**A. ** y = (x^{4}/5) + (1/x)
**B. ** y = (4x4/5) + (4/5x)

**C. ** y = (x4/5) + 1

**D. ** y = (x5/5) + 1

**Answer : ****Option A**

**Explaination / Solution: **

No Explaination.

No Explaination.

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Consider a function f(x) = 1-|x| on -1≤ x ≤ 1. The value of x at which the function attains a
maximum, and the maximum value of the function are.

**A. ** 0,-1

**B. ** -1,0

**C. ** 0,1

**D. ** -1,2

**Answer : ****Option C**

**Explaination / Solution: **

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The Laplace transform of te^{t} is

**A. ** s/(s+1)2
**B. ** 1/(s-1)2

**C. ** 1/(s+1)2

**D. ** s/(s-1)

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

**Explaination / Solution: **

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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)