# Engineering Mathematics (Test 6)

## Gate Exam : Ce Civil Engineering

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Engineering Mathematics
| Engineering Mathematics |
Q.1
The following sequence of numbers is arranged in increasing order: 1, x, x, x, y, y,9,16,18. Given that the mean and median are equal, and are also equal to twice the mode, the value of y is
A. 5
B. 6
C. 7
D. 8
Explaination / Solution:

Given, Mean = Median = 2Mode
Mean = Median = 2x [Mode = x].............. (1)
Mean of the data = (3x + 2y + 44)/9
2x = (3x + 2y + 44)/9
15x - 2y = 44.............(2)
Median of the data = y.........(3)
y = 2x ..........(4)
From (2); 11x = 44
x = 4
y = 8

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Q.2
(1217)8 is equivalent to
A. (1217)16
B. (028F)16
C. (2297)10
D. (0B17)16
Explaination / Solution:
No Explaination.

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Q.3
For a scalar function f(x,y,z) = x2 + 3y2 + 2z2,  the gradient at the point P(1,2, -1) is
A.
B.
C.
D. √56
Explaination / Solution:
No Explaination.

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Q.4
The type of partial differential equation
A. elliptic
B. parabolic
C. hyperbolic
D. none of these
Explaination / Solution:

Comparing the given equation with the general form of second order partial differential equation, we have A=1, B=3, C=1
B2- 4AC = 5 > 0
P.D.E is Hyperbola.

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Q.5
For a matrix  the transpose of the matrix is equal to the inverse of the matrix [M]T = [M]-1. The value of x is given by
A. -(4/5)
B. -(3/5)
C. 3/5
D. 4/5
Explaination / Solution:
No Explaination.

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Q.6
evaluates to
A. 0
B. 1
C. In 2
D. 1/2 In 2
Explaination / Solution:
No Explaination.

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Q.7
The value of

A. π/2
B. π
C. 3π/2
D. 1
Explaination / Solution:

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Q.8
Which one of the following graphs describes the function
A.
B.
C.
D.
Explaination / Solution:

This condition is satisfied by the graph shown in option (B).

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Q.9
The system of linear equations 4x + 2y = 7 2x + y = 6 has
A. a unique solution
B. no solution
C. an infinite number of solutions
D. exactly two distinct solutions
Explaination / Solution:

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Q.10
C is a closed path in the z -plane by |z| = 3 The value of the integral  is
A. -4π(1 + j2)
B. 4π(3 - j2)
C. -4π(3 + j2)
D. 4π(1 - j2)
Explaination / Solution:

Integral,
So, we have the singularity
z j + 2 = 0
z =- 2j
Since, z = -2j lies inside |z| = 3. Therefore, using cauchy’s integral, we get

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