EC GATE 2011 - Online Test
Q1. The system of equations
x + Y + z = 6
x + 4y + 6y = 20
x + 4y + λz = μ
has NO solution for values of λ and μ given by
Answer : Option B
Explaination / Solution:
Writing A:B we have
Apply R3⟶R3 – R2
For equation to have solution, rank of A and A:B must be same. Thus for no
solution; λ = 6, μ ≠ 20
Q2. A fair dice is tossed two times. The probability that the second toss results in a value that is higher than the first toss is
Answer : Option C
Explaination / Solution:
Total outcome are 36 out of which favorable outcomes are :
(1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 3), (2, 4), (2, 5), (2, 6);
(3, 4), (3, 5), (3, 6), (4, 5), (4, 6), (5, 6) which are 15.
P(E) = (No of favourable outcomes/No of total outcomes) = 15/36
= 5/12
Q3. Three friends, R, S and T shared toffee from a bowl. R took 1/3rd of the toffees, but returned four to the bowl. S took 1/4th of what was left but returned three toffees to the bowl. T took half of the remainder but returned two back into the bowl. If the bowl had 17 toffees left, how many toffees-were originally there in the bowl?
Answer : Option C
Explaination / Solution:
Let total no of toffees be x . The following table shows the all calculations.
Q4. Given that 
and q is any non-zero real number, the value
of |f(q) - f(-q)| is
and q is any non-zero real number, the value
of |f(q) - f(-q)| is
Answer : Option D
Explaination / Solution:
Q5. The sum of n terms of the series 4 + 44 + 444 + .... is
Answer : Option C
Explaination / Solution:
