# Engineering Mathematics (Test 1)

## Gate Exam : Ee Electrical Engineering

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Q.1
Two coins R and S are tossed. The 4 joint events HRHS, TTS,HTS,THS have probabilities 0.28, 0.18, 0.30, 0.24, respectively, where H represents head and T represents tail. Which one of the following is TRUE?
A. The coin tosses are independent
B. R is fair, R it not.
C. S is fair, R is not
D. The coin tosses are dependent
Answer : Option D
Explaination / Solution: Workspace
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Q.2
Roots of the algebraic equation x3 + x2 + x + 1 = 0 are
A. (+1, +j, −j)
B. (+1, −1, +1)
C. (0,0,0)
D. (−1, +j, −j)
Answer : Option D
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Q.3
Let X and Y be finite sets and f : X → Y be a function. Which one of the following statements is TRUE?
A. For any subsets A and B of X, |f (A ∪ B)| = |f(A)| + |f(B)|
B. For any subsets A and B of X, f (A ∩ B) = f(A) ∩ f(B)
C. For any subsets A and B of X,|f (A ∩ B)| = min {|f(A)|,|f(B)|}
D. For any subsets S and T of Y, f-1(S ∩ T) = f-1(S) ∩ f-1(T)
Answer : Option D
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Q.4 Choose the correct expression for f(x) given in the graph.
A. f(x) = 1 - |x - 1|
B. f(x) = 1 + |x - 1|
C. f(x) = 2 - |x - 1|
D. f(x) = 2 + |x - 1|
Answer : Option C
Explaination / Solution:
No Explaination.

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Q.5
In the solution of the following set of linear equations by Gauss elimination using partial pivoting 5x + y + 2z = 34; ay - 3z = 12; and 10 - 2y + z = -4; the pivots for elimination of x and y are
A. 10 and 4
B. 10 and 2
C. 5 and 4
D. 5 and -4
Answer : Option A
Explaination / Solution:
No Explaination.

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Q.6
In shear design of an RC beam, other than the allowable shear strength of concrete (τc), there is also an additional check suggested in IS 456-2000 with respect to the maximum permissible shear stress (τc max). The check for τc max max is required to take care of
A. additional shear resistance from reinforcing steel
B. additional shear stress that comes from accidental loading
C. possibility of failure of concrete by diagonal tension
D. possibility of crushing of concrete by diagonal compression
Answer : Option D
Explaination / Solution:
No Explaination.

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Q.7
The two vectors [1,1,1] and [1, a, a2], where a = , are
A. Orthonormal
B. Orthogonal
C. Parallel
D. Collinear
Answer : Option B
Explaination / Solution:

Dot product of two vectors = 1 + a + a= 0
So orthogonal

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Q.8
The value of the integral given below is A. − 2π
B. π
C. −π
D.
Answer : Option A
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Q.9
A path AB in the form of one quarter of a circle of unit radius is shown in the figure. Integration of (x + y)2 on path AB traversed in a counter-clockwise sense is A. (π/2) - 1
B. (π/2) + 1
C. π/2
D. 1
Answer : Option B
Explaination / Solution:
No Explaination.

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Q.10
Which of the following is a solution to the differential equation A. X(t) = 3e-t
B. X(t) = 2e-3t
C. X(t) = -3/2 t2
D. X(t) = 3t2
Answer : Option B
Explaination / Solution: Workspace
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