CE GATE 2017 PAPER 01 - Online Test

Q1. Two machines M1 and M2 are able to execute any of four jobs P, Q, R and S. The machines can perform one job on one object at a time. Jobs P, Q, R and S take 30 minutes, 20 minutes, 60 minutes and 15 minutes each respectively. There are 10 objects each requiring exactly 1 job. Job P is to be performed on 2 objects. Job Q on 3 objects. Job R on 1 object and Job S on 4 objects. What is the minimum time needed to complete all the jobs?
Answer : Option A
Explaination / Solution:



Q2. The number of parameters in the univariate exponential and Gaussian distributions, respectively, are
Answer : Option B
Explaination / Solution:

Probability density functions of univariable exponential distributes 

where µ and σ are parameters 

Q3. The reaction rate involving reactants A and B is given by  Which one of the following statements is valid for the reaction to be first –order reaction?
Answer : Option B
Explaination / Solution:

In chemical kinetics, the order of reaction with respect to given substance is defined as the index or exponent to which its concentration term in the rate equation is raised.

Order of reaction = α + β 
For first order reaction, α + β = 1

Q4. The matrix P is the inverse of a matrix Q. If I denotes the identity matrix, which one of the following options is correct?
Answer : Option C
Explaination / Solution:

Given P is inverse of Q ⇒ PQ = QP = I

Q5.  Let x be a continuous variable defined over the  interval (−∞, ∞), and 
Answer : Option B
Explaination / Solution:



Q6. For the function f(x) = a + bx, 0 ≤ x ≤ 1, to be a valid probability density function, which one of the following statements is correct?
Answer : Option B
Explaination / Solution:

f(x) =  a + bx 0 ≤ x ≤1 iis a valid probability density function

a=0.5, b=1 satisfies the above relation

Q7. Consider the matrix  Which one of the following statements is TRUE for the eigenvalues and eigenvectors of this matrix?
Answer : Option A
Explaination / Solution:


e(A) = 1
Number of linearly independent eigen vectors corresponding to eigen value λ = 3 is
n-r=2-1=1 where n= no. of unknowns, r= rank of( A − λI)
One linearly independent eigen vector exists corresponding to λ = 3

Q8. The solution of the equation (dQ/dt) + Q = 1 with Q = 0 at t = 0 is
Answer : Option D
Explaination / Solution:

(dQ/dt) + Q = 1 and  Q = 0 at t = 0
Comparing with first order linear differential equations


Q9. 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
Answer : Option D
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

Q10. If the radius of a right circular cone is increased by 50%, its volume increases by
Answer : Option C
Explaination / Solution:

Given, radius of a right circular cone is increased by 50%. 
Let, height of the circular cone=(h)