ME GATE 2013 - Online Test
Q1. A tourist covers half of his journey by train at 60 km/h, half of the remainder by
bus at 30 km/h and the rest by cycle at 10 km/h. The average of the tourist in
km/h during his entire journey is
Answer : Option C
Explaination / Solution:
Let the total distance covered be ‘D’
Now, average speed = D/Total time taken
Q2. The current erection cost of a structure is Rs. 13,200. If the labour wages per
day increase by 1/5 of the current wages and the working hours decrease by
1/24 of the current period, then the new cost of erection in Rs. is
Answer : Option B
Explaination / Solution:
Let ‘W’ be the labour wages, and ‘T’ be the working hours.
Now, total cost is a function of W ×T
Increase in wages = 20%
∴ Revised wages = 1.2 W
Decrease in labour time = (100/24)%
Re vised time = (1- (1/24))T = 23/24 T
Re vised Total cost = 1.2 × (23/24)WT = 1.15 WT
= 1.15 × 13200 = 15180
Q3. The partial differential equation 
is a
is a
Answer : Option D
Explaination / Solution:
No Explaination.
Q4. The eigen values of symmetric matrix are all
Answer : Option C
Explaination / Solution:
No Explaination.
Q5. Match the CORRECT pairs:
Answer : Option D
Explaination / Solution:
No Explaination.
Q6. Let X be a nominal variable with mean 1 and variance 4. The probability P(X < 0) is
Answer : Option B
Explaination / Solution:
which is greater than zero and less than 0.5
Q7. Choose the CORRECT set of functions, which are linearly dependent.
Answer : Option C
Explaination / Solution:
No Explaination.
Q8. The following surface integral is to be evaluated over a sphere for the given
steady velocity vector field, F = xi + yj + zk defined with respect to a Cartesian
coordinate system having i, j, and k as unit base vectors.
Where S is the sphere, x2 + y2 + z2 = 1 and n is the outward unit normal vector to
the sphere. The value of the surface integral is
Answer : Option A
Explaination / Solution:
Q9. The function f(t) satisfies the differential equation 
and the auxiliary
conditions,
The Laplace transform of f(t) is given by
and the auxiliary
conditions, The Laplace transform of f(t) is given by
Answer : Option C
Explaination / Solution:
Q10. A linear programming problem is shown below:
Maximize 3x + 7y
3x + 7y ≤ 10
Subject to 4x + 6y ≤ 8
x, y ≥ 0
It has
Answer : Option B
Explaination / Solution:
