## GATE 2016 [Set-2]

 Question 1

The man who is now Municipal Commissioner worked as _______________.

 A the security guard at a university B a security guard at the university C a security guard at university D the security guard at the university
Aptitude       Verbal       Video-Explanation
Question 1 Explanation:
Security guard is a general post, so we use the artical 'a' before the security.
And coming to university it is an organization.
So we use are 'the' before university.
 Question 2

Nobody knows how the Indian cricket team is going to cope with the difficult and seamer-friendly wickets in Australia.

Choose the option which is closest in meaning to the underlined phrase in the above sentence.

 A put up with B put in with C put down to D put up against
Aptitude       Verbal       Video-Explanation
Question 2 Explanation:
"Put up with" is means that "tolerate" which is the closest meaning of "cope with".
→ Cope with is doesn't means that put someone into competition with some other.
 Question 3

Find the odd one in the following group of words.

mock,   deride,   praise,   jeer
 A mock B deride C praise D jeer
Aptitude       Verbal       Video-Explanation
Question 3 Explanation:
Mock = Tease or laugh
Deride = express contempts for; ridicule
Jeer = Make rude and mocking remarks
→ These three are negative things
Praise = express warm approval
 Question 4

Pick the odd one from the following options.

 A CADBE B JHKIL C XVYWZ D ONPMQ
Aptitude       Numerical       Video-Explanation
Question 4 Explanation:
In all the given options except D, the 1st, 3rd, 5th alphabets are consecutive (increasing order) and 2nd and 4th are consecutive (increasing order).
But in D, 2nd and 4th are in decreasing order.
 Question 5

In a quadratic function, the value of the product of the roots (α, β) is 4. Find the value of A n4 B 4n C 22n-1 D 4n-1
Aptitude       Numerical       Video-Explanation
Question 5 Explanation:
Given,
Product of roots (α, β) = 4
⇒ αβ = 4 (αβ)n = 4n
 Question 6

Among 150 faculty members in an institute, 55 are connected with each other through Facebook® and 85 are connected through WhatsApp®. 30 faculty members do not have Facebook® or WhatsApp® accounts. The number of faculty members connected only through Facebook® accounts is ______________.

 A 35 B 45 C 65 D 90
Aptitude       Numerical       Video-Explanation
Question 6 Explanation:
Total number of faculty = 150
Number of faculty members connected through Facebook = 55
Number of faculty members connected through Whatsapp = 85
Number of faculty members with Facebook (or) Whatsapp accounts = 30
Number of faculty members with either Facebook (or) Whatsapp accounts = 150 - 30 = 120
Number of faculty members with both Facebook and Whatsapp accounts = 85 + 55 - 120 = 20
Number of faculty members with only Facebook accounts = 55 - 20 = 35
 Question 7

Computers were invented for performing only high-end useful computations. However, it is no understatement that they have taken over our world today. The internet, for example, is ubiquitous. Many believe that the internet itself is an unintended consequence of the original invention. With the advent of mobile computing on our phones, a whole new dimension is now enabled. One is left wondering if all these developments are good or, more importantly, required.

Which of the statement(s) below is/are logically valid and can be inferred from the above paragraph?

(i) The author believes that computers are not good for us.
(ii) Mobile computers and the internet are both intended inventions.
 A (i) only B (ii) only C both (i) and (ii) D neither (i) nor (ii)
Aptitude       Verbal       Video-Explanation
Question 7 Explanation:
The author, has no where said that the computers are bad, authoring is talking about the way computers are being used today and the author questioned this way.
So, statement I does not follow.
→ "Many believes that the internet itself is unintended consequence of the original invention.
So, statement II does not follow, so Answer is Option D.
 Question 8

All hill-stations have a lake. Ooty has two lakes.

Which of the statement(s) below is/are logically valid and can be inferred from the above sentences?

(i) Ooty is not a hill-station.
(ii) No hill-station can have more than one lake.
 A (i) only B (ii) only C both (i) and (ii) D neither (i) nor (ii)
Aptitude       Verbal       Video-Explanation
Question 8 Explanation:
Given,
All hill-stations have a lake → (1)
Ooty has two lakes → (2)
From (1), it cannot be inferred that every place having a lake is a hill station.
⇒ (i) cannot be logically intended.
From (1), it cannot be inferred how many lakes will be there in a hill station.
⇒ (ii) cannot be logically inferred.
 Question 9

In a 2 × 4 rectangle grid shown below, each cell is a rectangle. How many rectangles can be observed in the grid? A 21 B 27 C 30 D 36
Aptitude       Numerical       Video-Explanation
Question 9 Explanation:
Number of rectangles in a grid with 'm' horizontal and 'n' vertical lines = 5C2 × 3C2 = 10 × 3 = 30
 Question 10 Choose the correct expression for f(x) given in the graph.

 A f(x) = 1 - |x - 1| B f(x) = 1 + |x - 1| C f(x) = 2 - |x - 1| D f(x) = 2 + |x - 1|
Aptitude       Numerical       Video-Explanation
Question 10 Explanation:
From the graph,
x = -1 ⇒ f(x) = 0
x = 0 ⇒ f(x) = 1
We have check, which option satisfies both the conditions.
Only option (C) satisfies both of them.
 Question 11
Consider the following expressions:
(i) false
(ii) Q
(iii) true
(iv) P ∨ Q
(v) ¬Q ∨ P
The number of expressions given above that are logically implied by P ∧ (P ⇒ Q) is _________.
 A 4 B 5 C 6 D 7
Engineering-Mathematics       Propositional-Logic       Video-Explanation
Question 11 Explanation:
The expression is logically implied by P ∧ (P → Q) means
(P ∧ (P → Q))→ expression is a tautology. So we have to find
How many tautological formulas are there for the given inputs.
(P ∧ (P → Q)) → True is always tautology
(P ∧ (P → Q)) → False is not a tautology
(P ∧ (P → Q)) → Q is a tautology
(P ∧ (P → Q)) → ¬Q ∨ P is a tautology
(P ∧ (P → Q)) → P ∨ Q is a tautology
So there are 4 expressions logically implied by (P ∧ (P → Q))
 Question 12

Let f(x) be a polynomial and g(x) = f'(x) be its derivative. If the degree of (f(x) + f(-x)) is 10, then the degree of (g(x) - g(-x)) is __________.

 A 9 B 10 C 11 D 12
Engineering-Mathematics       Calculus       Video-Explanation
Question 12 Explanation:
If the degree of a polynomial is ‘n’ then the derivative of that function have (n – 1) degree.
It is given that f(x) + f(-x) degree is 10.
It means f(x) is a polynomial of degree 10.
Then obviously the degree of g(x) which is f’(x) will be 9.
 Question 13

The minimum number of colours that is sufﬁcient to vertex-colour any planar graph is ________.

 A 4 B 5 C 6 D 7
Engineering-Mathematics       Graph-Theory       Video-Explanation
Question 13 Explanation:
The 4-colour theorem of the planar graph describes that any planar can atmost be colored with 4 colors.
Here it is asked about the sufficient number of colors, so with the worst case of 4 colors we can color any planar graph.
 Question 14
Consider the systems, each consisting of m linear equations in n variables.
I. If m < n, then all such systems have a solution
II. If m > n, then none of these systems has a solution
III. If m = n, then there exists a system which has a solution
Which one of the following is CORRECT?
 A I, II and III are true B Only II and III are true C Only III is true D None of them is true
Engineering-Mathematics       Linear-Algebra       Video-Explanation
Question 14 Explanation:
i) If m In AX = B,
If R(A) ≠ R(A|B)
then there will be no solution.
ii) False, because if R(A) = R(A|B),
then there will be solution possible.
iii) True, if R(A) = R(A|B),
then there exists a solution.
 Question 15

Suppose that a shop has an equal number of LED bulbs of two different types. The probability of an LED bulb lasting more than 100 hours given that it is of Type 1 is 0.7, and given that it is of Type 2 is 0.4. The probability that an LED bulb chosen uniformly at random lasts more than 100 hours is _________.

 A 0.55 B 0.56 C 0.57 D 0.58
Engineering-Mathematics       Probability       Video-Explanation
Question 15 Explanation: The bulbs of Type 1, Type 2 are same in number.
So, the probability to choose a type is 1/2.
The probability to choose quadrant ‘A’ in diagram is
P(last more than 100 hours/ type1) = 1/2 × 0.7
P(last more than 100 hours/ type2) = 1/2 × 0.4
Total probability = 1/2 × 0.7 + 1/2 × 0.4 = 0.55
 Question 16

Suppose that the eigenvalues of matrix A are 1, 2, 4. The determinant of (A-1)T is _________.

 A 0.125 B 0.126 C 0.127 D 0.128
Engineering-Mathematics       Linear-Algebra       Video-Explanation
Question 16 Explanation:
Determinant of a matrix is product of the eigen values.
Given that eigen values are 1, 2, 4.
So, its determinant is 1*2*4 = 8
The determinant of (A-1)T = 1/ AT = 1/|A| = 1/8 = 0.125
There are 16 questions to complete.

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