GATE-CS-2015 (Set 2)

Question 1

We __________ our friend’s birthday and we ________ how to make it up to him.

• A. Completely forgot --- don’t just know
• B. Forgot completely --- don’t just know
• C. Completely forgot --- just don’t know
• D. Forgot completely --- just don’t know

Answer: (C)

GATE-CS-2015 (Set 2) English
Discuss it

We Completely forgot our friend’s birthday and we just don’t know how to make it up to him.

Question 2

Choose the statement where underlined word is used correctly.

• A. The industrialist had a personnel jet
• B. I write my experience in my personnel diary
• C. All personnel are being given the day off
• D. Being religious is a personnel aspect

Answer: (C)

GATE-CS-2015 (Set 2) English
Discuss it

personnel mean a body of persons employed in an organization or place of work.

Question 3

Based on the given statements, select the most appropriate option to solve the given question. What will be the total weight of 10 poles each of same weight?

Statements: 
  (I) One fourth of the weight of a pole is 5 kg
  (II) The total weight of these poles is 160 kg more
       than the total weight of two poles.

• A. Statement II alone is not sufficient
• B. Statement II alone is not sufficient
• C. Either I or II alone is sufficient
• D. Both statements I and II together are not sufficient.

Answer: (C)

GATE-CS-2015 (Set 2) General Aptitude
Discuss it

(I) is sufficient. We can determine total weight of 10
   poles as 10 * 4 * 5 = 200 Kg

(II) is also sufficient, we can determine the weight.
  Let x be the weight of 1 pole.
  10*x - 2*x = 160 Kg
  x = 20 Kg
  10x = 200 Kg 

Question 4

Consider a function f(x) = 1 – |x| on –1 ≤ x ≤ 1. The value of x at which the function attains a maximum and the maximum value of the function are:

• A. 0, –1
• B. –1, 0
• C. 0, 1
• D. –1, 2

Answer: (C)

GATE-CS-2015 (Set 2) Numerical Methods and Calculus
Discuss it

f(x) = 1 – |x|
f(0) = 1
f(1) = f(-1) = 0
f(0.5) = f(-0.5) = 0.5

The maximum is attained at x = 0, and the maximum value is 1.

Question 5

A generic term that includes various items of clothing such as a skirt, a pair of trousers and a shirt is

• A. fabric
• B. textile
• C. fibre
• D. apparel

Answer: (D)

GATE-CS-2015 (Set 2) English
Discuss it

apparel means clothing.

Question 6

If the list of letters, P, R, S, T, U is an arithmetic sequence, which of the following are also in arithmetic sequence? 1. 2P, 2R, 2S, 2T, 2U 2. P–3, R–3, S–3, T–3, U–3 3. P², R², S², T², U²

• A. 1 only
• B. 1 and 2
• C. 2 and 3
• D. 1 and 3

Answer: (B)

GATE-CS-2015 (Set 2) General Aptitude
Discuss it

1 is AP with common difference as double of that of original series. 2 is AP with common difference as same as original series.

Question 7

Four branches of a company are located at M, N, O and P. M is north of N at a distance of 4 km; P is south of O at a distance of 2 km; N is southeast of O by 1 km. What is the distance between M and P in km?

• A. 5.34
• B. 6.74
• C. 28.5
• D. 45.49

Answer: (A)

GATE-CS-2015 (Set 2) General Aptitude
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Question 8

In a triangle PQR, PS is the angle bisector of ∠ QPR and ∠ QPS = 60°. What is the length of PS?

• A. a
• B. b
• C. c
• D. d

Answer: (B)

GATE-CS-2015 (Set 2) General Aptitude
Discuss it

Area of a Δ = 1/2 * ac sinB 
            = 1/2 * bc sinA 
            = 1/2 ab sinC

Here area (ΔPQR) = area (ΔPQS) + area (ΔPRS)

1/2 rq sin120 = 1/2 PS * r sin60 + 1/2 PS * q sin60

=> PS = rq/(r+q)

There seems to be something wrong with question as it says ∠ QPS = 60°. The question is same on GATE official site paper.

Question 9

If p, q, r, s are distinct integers such that:
f(p, q, r, s) = max (p, q, r, s)
g(p, q, r, s) = min (p, q, r, s)
h(p, q, r, s) = remainder of (p × q) / (r × s)  if (p × q) > (r × s) OR 
                remainder of (r × s) / (p × q) if (r × s) > (p × q)
Also a function fgh (p, q, r, s) =
                f(p, q, r, s) × g(p, q, r, s) × h(p, q, r, s).
Also the same operation are valid with two variable functions 
of the form f(p, q).

What is the value of fg(h(2, 5, 7, 3), 4, 6, 8)? 

• A. 6
• B. 7
• C. 8
• D. 9

Answer: (C)

GATE-CS-2015 (Set 2) General Aptitude
Discuss it

The question asks value of fg (h(2, 5, 7, 3), 4, 6, 8)

We need to first find value of h(2, 5, 7, 3) 

h is defined as 
h(p, q, r, s) = remainder of (p × q) / (r × s)  if (p × q) > (r × s)
                remainder of (r × s) / (r × q)  if (r × s) > (p × q)

h(2, 5, 7, 3) = remainder of (7 * 3) / (2 * 5)  since 7*3 > 2*5
              = 1

fg(1, 4, 6, 8) = f(1, 4, 6, 8) * g(1, 4, 6, 8)
               = max(1, 4, 6, 8) * min(1, 4, 6, 8)
               = 8 * 1
               = 8

Question 10

Out of the following four sentences, select the most suitable sentence with respect to grammar and usage:

• A. Since the report lacked needed information, it was of no use to them
• B. The report was useless to them because there were no needed information in it
• C. Since the report did not contain the needed information, it was not real useful to them
• D. Since the report lacked needed information, it would not had been useful to them

Answer: (A)

GATE-CS-2015 (Set 2) English
Discuss it

Only option (A) seems correct. In option (B) - were is wrong used here. In option (C) - real is wrong, should be really In option (D) - had is wrong. would not have been is correct.