GATE-CS-2016 (Set 2)

Question 11

In a 2 × 4 rectangle grid shown below, each cell is a rectangle. How many rectangles can be observed in the grid?

• 21
• 27
• 30
• 36

Question 12

Choose the correct expression for f(x) given in the graph.

• A
• B
• C
• D

Question 13

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 ___________ . [This Question was originally a Fill-in-the-blanks Question]

• 8
• 7
• 9
• 10

Question 14

The minimum number of colours that is sufficient to vertex-colour any planar graph is _______________ [This Question was originally a Fill-in-the-blanks Question]

• 1
• 2
• 3
• 4

Question 15

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?

• I, II and III are true
• Only II and III are true
• Only III is true
• None of them is true

Question 16

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 :   Note : This question was asked as Numerical Answer Type.

• 0.55
• 0.7
• 0.4
• 0.35

Question 17

Suppose that the eigenvalues of matrix A are 1, 2, 4. The determinant of (A⁻¹)^T is _________ [This Question was originally a Fill-in-the-blanks Question]

• 1/8
• 1
• 1/4
• 2

Question 18

Consider an eight-bit ripple-carry adder for computing the sum of A and B, where A and B are integers represented in 2’s complement form. If the decimal value of A is one, the decimal value of B that leads to the longest latency for the sum to stabilize is _____________ [This Question was originally a Fill-in-the-blanks Question]

• -1
• 2
• 1
• -2

Question 19

Let, x1⊕x2⊕x3⊕x4 = 0 where x1, x2, x3, x4 are Boolean variables, and ⊕ is the XOR operator. Which one of the following must always be TRUE ?

• x1x2x3x4 = 0
• x1x3+x2 = 0
• x′1⊕x′3=x′2⊕x′4
• x1+x2+x3+x4 = 0

Question 20

Let X be the number of distinct 16-bit integers in 2’s complement representation. Let Y be the number of distinct 16-bit integers in sign magnitude representation. Then X −Y is _________ [This Question was originally a Fill-in-the-blanks Question]

• 1
• 2
• 3
• 0