# Engineering Mathematics (Test 2)

## Gate Exam : Ee Electrical Engineering

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Engineering Mathematics
| Engineering Mathematics |
Q.1
Find the sum of the expression

A. 7
B. 8
C. 9
D. 10
Explaination / Solution:

The expression can be written as

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Q.2
Which one of the following is NOT necessarily a property of a Group?
A. Commutativity
B. Associativity
C. Existence of inverse for every element
D. Existence of identity
Explaination / Solution:
No Explaination.

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Q.3
In a quadratic function, the value of the product of the roots (α, β) is 4. Find the value of
A. n4
B. 4n
C. 22n-1
D. 4n-1
Explaination / Solution:

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Q.4
If f(x7) = 2x7 + 3x - 5, which of the following is a factor of f(x)?
A. (x+ 8)
B. (x-1)
C. (2x-5)
D. (x+1)
Explaination / Solution:

from the option (b0 substitute x=1 in
2x7 + 3x - 5 = 0
2(1)7 + 3(1) - 5 = 0
5 - 5 = 0
So (x - 1) is a factor of f (x)

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Q.5
Consider the following system of equations
2x1 + x2 + x3 = 0,
x2 - x3 = 0,
x1 + x2 = 0.
This system has
A. A unique solution
B. No solution
C. Infinite number of solutions
D. Five solutions
Explaination / Solution:
No Explaination.

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Q.6
The inverse Laplace transform of 1/(s2 + s) is
A. 1 + et
B. 1 - et
C. 1 - e-t
D. 1 + e-t
Explaination / Solution:
No Explaination.

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Q.7
Let the eigenvalues of a 2 x 2 matrix A be 1, -2 with eigenvectors x1 and x2 respectively. Then the eigenvalues and eigenvectors of the matrix A− 3A + 4I would, respectively, be
A.
B.
C.
D.
Explaination / Solution:

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Q.8
Consider the set of all functions f : {0,1,...,2014} → {0,1...,2014} such that f (f (i)) = i for 0 ≤ i ≤ 2014. Consider the following statements.
P. For each such function it must be the case that for every i, f(i) = i,
Q. For each such function it must be the case that for some i,f(i) = i,
R. Each such function must be onto.
Which one of the following is CORRECT?
A. P, Q and R are true
B. Only Q and R are true
C. Only P and Q are true
D. Only R is true
Explaination / Solution:
No Explaination.

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Q.9
A hard disk has 63 sectors per track, 10 platters each with 2 recording surfaces and 1000 cylinders. The address of a sector is given as a triple〈c, h, s〉, where c is the cylinder number, h is the surface number and s is the sector number. Thus, the 0th sector is addressed as 〈 0, 0, 0〉 , the 1st sector as 〈 0, 0, 1〉 and so on.
The address of 1039th sector is

A. (0, 15, 31)
B. (0, 16, 30)
C. (0, 16, 31)
D. (0, 17, 31)
Explaination / Solution:
No Explaination.

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Q.10
You are given three coins: one has heads on both faces, the second has tails on both faces, and the third has a head on one face and a tail on the other. You choose a coin at random and toss it, and it comes up heads. The probability that the other face is tails is
A. 1/4
B. 1/3
C. 1/2
D. 2/3