CE GATE 2016 PAPER 01 - Online Test

Q1. Archimedes s said, “Give me a lever long enough and a fulcrum on which to place it, and I will move the world” The sentence above is an example of a ___________statement.
Answer : Option A
Explaination / Solution:
No Explaination.


Q2. A cube is built using 64 cubic blocks of side one unit. After it is built, one cubic block is removed from every corner of the cube. The resulting surface area of the body (in square units) after the removal is ___________.
Answer : Option D
Explaination / Solution:

Four blocks are needed for each direction(totally 3 directions) to build a bigger cube containing 64 blocks. So area of one side of the bigger cube= 4 × 4 =16units There are 6 faces so total area= 6 × 16 = 96units When cubes at the corners are removed they introduce new surfaces equal to exposes surfaces so the area of the bigger cube does not change from 96

Q3. A shaving set company sells 4 different types of razors, Elegance, Smooth, Soft and Executive. Elegance sells at Rs. 48, Smooth at Rs. 63, Soft at Rs. 78 and Executive at Rs. 173 per piece. The table below shows the numbers of each razor sold in each quarter of a year.

Which product contributes the greatest fraction to the revenue of the company in that year?
Answer : Option B
Explaination / Solution:
No Explaination.


Q4. Consider the following statements relating to the level of poker play of four players P, Q, R and S. 
I. P always beats Q 
II. R always beats S 
III. S loses to P only sometimes 
IV. R always loses to Q 
Which of the following can be logically inferred from the above statements? 
(i) P is likely to beat all the three other players 
(ii) S is the absolute worst player in the set 
Answer : Option A
Explaination / Solution:
No Explaination.


Q5. In a process, the number of cycles to failure decreases exponentially with an increase in load. At a load of 80 units, it takes 100 cycles for failure. When the load is halved, it takes 10000 cycles for failure. The load for which the failure will happen in 5000 cycles is __________.
Answer : Option B
Explaination / Solution:

From the data given we assume 
load = exp onent/log(cycles)
80 = x/log(10000)
x = 160
40 = x/log(10000)
x = 160
load = 160/log 5000 = 43.25

Q6. If f(x7) = 2x7 + 3x - 5, which of the following is a factor of f(x)?
Answer : Option B
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)

Q7. The type of partial differential equation 
Answer : Option C
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. 

Q8. If the entries in each column of a square matrix M add up to 1, then an eigen value of M is
Answer : Option D
Explaination / Solution:

Consider the '2x2 ' square matrix  Characteristic equation of M is
λ- (a + d)λ + (ad - bc) = 0......................(1)
Put λ =1, weget 
1 - (a + d) + ad - bc = 0 
1 - a - d + ad - (1 - d)(1 - a) = 0 
1 - a - d + ad - 1 + a + d - ad = 0 
0 = 0,which is true
λ = 1 Satisfies the equation (1) but λ = 2,3,4 does not satisfy the equation (1). For all possible values of a,d 


Q9. Type II error in hypothesis testing is
Answer : Option A
Explaination / Solution:

Type II Errors means acceptance of the null hypothesis when it is false and should be rejected.

Q10. The solution of the partial differential equation  is of the form
Answer : Option B
Explaination / Solution: