CS and IT GATE 2021 SET-2 Questions with Answer

Ques 27 Mathematics

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If θ is the angle, in degrees, between the longest diagonal of the cube and any one of the edges of the cube, then, cos θ =

A

1/2

B

1/√3

C

1/√2

D

√3/2

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Ques 28 Mathematics

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If (x-1/2)² - (x-3/2)² = x + 2, then the value of x is:

A

2

B

4

C

6

D

8

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Ques 29 Mathematics

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The number of students in three classes is in the ratio 3:13:6. If 18 students are added to each class, the ratio changes to 15:35:21. The total number of students in all the three classes in the beginning was:

A

22

B

66

C

88

D

110

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Ques 30 Mathematics

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The number of units of a product sold in three different years and the respective net profits are presented in the figure above. The cost/unit in Year 3 was ₹1, which was half the cost/unit in Year 2. The cost/unit in Year 3 was one-third of the cost/unit in Year 1. Taxes were paid on the selling price at 10%, 13% and 15% respectively for the three years. Net profit is calculated as the difference between the selling price and the sum of cost and taxes paid in that year. The ratio of the selling price in Year 2 to the selling price in Year 3 is

A

4:3

B

1:1

C

3:4

D

1:2

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Ques 31 Mathematics

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Consider the following sets, where n ≥ 2:
S₁: Set of all n x n matrices with entries from the set {a,b,c}
S₂: Set of all functions from the set {0,1,2,...,n²-1} to the set {0,1,2}
Which of the following choice(s) is/are correct?

A

There does not exist a bijection from S₁ to S₂.

B

There exists a surjection from S₁ to S₂.

C

There exists a bijection from S₁ to S₂.

D

There does not exist an injection from S₁ to S₂.

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Ques 32 Mathematics

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For a given biased coin, the probability that the outcome of a toss is a head is 0.4. This coin is tossed 1,000 times. Let X denote the random variable whose value is the number of times that head appeared in these 1,000 tosses. The standard deviation of X (rounded to 2 decimal places) is _______.

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Ques 33 Mathematics

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Suppose that P is a 4 x 5 matrix such that every solution of the equation Px = 0 is a scalar multiple of [2 5 4 3 1]^T. The rank of P is _______.

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Ques 34 Mathematics

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Suppose that f: R → R is a continuous function on the interval [-3,3] and a differentiable function in the interval (-3,3) such that for every x in the interval, f'(x) ≤ 2. If f(-3) = 7 then f(3) is at most _______.

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Ques 35 Mathematics

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In an examination, a student can choose the order in which two questions (QuesA and QuesB) must be attempted.
If the first question is answered wrong, the student gets zero marks. If the first question is answered correctly and the second question is not answered correctly, the student gets the marks only for the first question. If both the questions are answered correctly, the student gets the sum of the marks of the two questions. The following table shows the probability of correctly answering a question and the marks of the question respectively.

Assuming that the student always wants to maximize her expected marks in the examination, in which order should she attempt the questions and what is the expected marks for that order (assume that the questions are independent)?

A

First QuesA and then QuesB. Expected marks 14.

B

First QuesB and then QuesA. Expected marks 14.

C

First QuesB and then QuesA. Expected marks 22.

D

First QuesA and then QuesB. Expected marks 16.

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Ques 36 Mathematics

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Let S be a set consisting of 10 elements. The number of tuples of the form (A, B) such that A and B are subsets of S, and A ⊆ B is _______.

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Ques 37 Operating Systems

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Which of the following statement(s) is/are correct in the context of CPU scheduling?

A

Turnaround time includes waiting time.

B

The goal is to only maximize CPU utilization and minimize throughput.

C

Round-robin policy can be used even when the CPU time required by each of the processes is not known apriori.

D

Implementing preemptive scheduling needs hardware support.

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Ques 38 Operating Systems

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Consider the following multi-threaded code segment (in a mix of C and pseudo-code), invoked by two processes P1 and P2, and each of the processes spawns two threads T1 and T2:
int x = 0; // global
Lock L1; // global
main() {
create a thread to execute foo(); // Thread T1
create a thread to execute foo(); // Thread T2
wait for the two threads to finish execution;
print (x); }
foo() {
int y = 0;
Acquire L1;
x = x + 1;
y = y + 1;
Release L1;
print (y); }
Which of the following statement(s) is/are correct?

A

Both P1 and P2 will print the value of x as 2.

B

At least one of P1 and P2 will print the value of x as 4.

C

At least one of the threads will print the value of y as 2.

D

Both T1 and T2, in both the processes, will print the value of y as 1.

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Ques 39 Operating Systems

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Consider a computer system with multiple shared resource types, with one instance per resource type. Each instance can be owned by only one process at a time. Owning and freeing of resources are done by holding a global lock (L). The following scheme is used to own a resource instance:

Which of the following choice(s) about the above scheme is/are correct?

A

The scheme ensures that deadlocks will not occur.

B

The scheme may lead to live-lock.

C

The scheme may lead to starvation.

D

The scheme violates the mutual exclusion property.

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