CE GATE 2015 - Online Test
Q1. Mr. Vivek walks 6 meters North-East, then turns and walks 6 meters South- East, both at 60
degrees to East. He further moves 2 meters South and 4 meters West. What is the straight
distance in meters between the point he started from and the point he finally reached?
Answer : Option A
Explaination / Solution:
No Explaination.
Q2. There are 16 teachers who can teach Thermodynamics (TD), 11 who can teach Electrical
Sciences (ES), and 5 who can teach both TD and Engineering Mechanics (EM). There are a total
of 40 teachers, 6 cannot teach any of the three subjects, i.e. EM, ES or TD. 6 can teach only ES. 4
can teach all three subjects, i.e. EM, ES and TD. 4 can teach ES and TD. How many can teach
both ES and EM but not TD?
Answer : Option A
Explaination / Solution:
Q3. Read the following table giving sales data of five types of batteries for years 2006 to 2012
Out of the following, which type of battery achieved highest growth between the years 2006 and
2012?
Answer : Option D
Explaination / Solution:
Type-I achieved a growth of 53% in the period which is higher than any other type of battery
Q4. The given question is followed by two statements: select the most appropriate option that solves
the question
Capacity of a solution tank A is 70% of the capacity of tank B. How many gallons of solution are
in tank A and tank B?
Statements:
I. Tank A is 80% full and tank B is 40% full
II. Tank A if full contains 14,000 gallons of solution
Answer : Option D
Explaination / Solution:
Statement I can be used to solve the question if capacity of both tanks is already known
Statement-II can be used if it is known what quantity of each tank is full/empty.
Therefore, by using both statements
Let capacity of tank B is x
(70/100)x = 14000
x = 20000 gallons
Solution in tank A = (80/100)×14000 = 11200 gallons
Solution in tank B = (40/100) × 20000 = 8000 gallons
Total solution = 11200 + 8000 = 19200 gallons
Q5. A superspeedway in New Delhi has among the highest super-elevation rates of any track on the
Indian Grand Prix circuit. The track requires drivers to negotiate turns with a radius of 335 m and
33° banking. Given this information, the coefficient of side friction required in order to allow a
vehicle to travel at 320 km/h along the curve is
Answer : Option C
Explaination / Solution:
Q6. Four cards are randomly selected from a pack of 52 cards. If the first two cards are kings, what is
the probability that the third card is a king?
Answer : Option B
Explaination / Solution:
There are 4 kings in a pack of 52 cards.
If 2 cards are selected and both are kings, remaining cards will be 50 out of which 2 will be kings.
Q7. Given i = √-1 the value of the definite integral 
Answer : Option B
Explaination / Solution:
Q8. Let A = [ αij ], 1≤ i, j ≤ n with n ≥ 3 and aij = i.j . The rank of A is
Answer : Option B
Explaination / Solution:
Q9. 
is equal to
is equal to
Answer : Option D
Explaination / Solution:
Q10. The two Eigen values of the matrix 
have a ratio of 3 : 1 for p = 2. What is another value
of p for which the Eigen values have the same ratio of 3 : 1?
have a ratio of 3 : 1 for p = 2. What is another value
of p for which the Eigen values have the same ratio of 3 : 1?
Answer : Option D
Explaination / Solution:
Let A = 
Given that two eigen values of A are in 3:1
Ratio for p = 2
⇒ Characteristic equation λ2 -4λ+3 = 0 (by substituting p=2)
⇒ λ=1,3
Eigen values 5, 5/3 are in ratio 3:1
P = 14/3
