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CS and IT GATE 2022 Questions with Answer

Ques 40 Discrete Mathematics

Which of the following statements is/are TRUE for a group G ?

A

If for all x, y ∈ G, (xy)2 = x2 y2 then G is commutative.

B

If for all x ∈ G, x2= 1, then G is commutative. Here, 1 is the identity element of G.

C

If the order of G is 2, then G is commutative.

D

If G is commutative, then a subgroup of G need not be commutative.



Ques 41 Mathematics

A function y(x) is defined in the interval [0, 1] on the 𝑥-axis as

CS 2022 Mathematics
Which one of the following is the area under the curve for the interval [0, 1] on the 𝑥-axis?

A

5/6

B

6/5

C

13/6

D

6/13



Ques 42 Mathematics

The value of the following limit is ____________

CS 2022 Mathematics 2


-0.5 is the correct answer.


Ques 43 Mathematics

The number of arrangements of six identical balls in three identical bins is______.

A

36

B

21

C

12

D

7



Ques 44 Mathematics

Consider the following two statements with respect to the matrices Am×n , Bn×m , Cn×n and Dn×n

Statement 1: tr(AB) = tr(BA)
Statement 2: tr(CD) = tr(DC)
where tr() represents the trace of a matrix. Which one of the following holds?

A

Statement 1 is correct and Statement 2 is wrong.

B

Statement 1 is wrong and Statement 2 is correct.

C

Both Statement 1 and Statement 2 are correct.

D

Both Statement 1 and Statement 2 are wrong.



Ques 45 Operating System

Consider four processes P, Q, R, and S scheduled on a CPU as per round robin algorithm with a time quantum of 4 units. The processes arrive in the order P, Q, R, S, all at time t = 0. There is exactly one context switch from S to Q, exactly one context switch from R to Q, and exactly two context switches from Q to R. There is no context switch from S to P. Switching to a ready process after the termination of another process is also considered a context switch. Which one of the following is NOT possible as CPU burst time (in time units) of these processes?

A

P=4, Q=10, R=6, S=2

B

P=2, Q=9, R=5, S=1

C

P=4, Q=12, R=5, S=4

D

P=3, Q=7, R=7, S=3



Ques 46 Operating System

Which of the following statements is/are TRUE with respect to deadlocks?

A

Circular wait is a necessary condition for the formation of deadlock.

B

In a system where each resource has more than one instance, a cycle in its wait-for graph indicates the presence of a deadlock.

C

If the current allocation of resources to processes leads the system to unsafe state, then deadlock will necessarily occur.

D

In the resource-allocation graph of a system, if every edge is an assignment edge, then the system is not in deadlock state.



Ques 47 Operating System

Consider a demand paging system with four-page frames (initially empty) and an LRU page replacement policy. For the following page reference string 7, 2,7,3, 2,5,3, 4,6,7,7,1,5,6,1 the page fault rate, defined as the ratio of number of page faults to the number of memory accesses (rounded off to one decimal place) is_________.


0.6 is the correct answer.


Ques 48 Operating System

A cache memory that has a hit rate of 0.8 has an access latency 10 ns and miss penalty 100 ns. Optimization is done on the cache to reduce the miss rate. However, the optimization results in an increase of cache access latency to 15 ns, whereas the miss penalty is not affected. The minimum hit rate (rounded off to two decimal places) needed after the optimization such that it should not increase the average memory access time is _____.


0.85 is the correct answer.


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