JT(IT) 2018 PARTB Computer Science
Question 1 
Which of the following numerical values is NOT a valid constant in C language?
12345L  
018CDF
 
9.3e12  
0XBCF

→ 018CDF starts with 0 means octal number but actually we are given decimal and hexa numbers. So it is not a valid constant.
→ 9.3e12 float number
→ 0XBCF is hexa number. Valid constant.
Question 2 
Let P, Q and R be three atomic prepositional assertions, and
 X : (P ∨ Q) → R
Y : (P → R) ∨ (Q → R)
Which one of the following is a tautology?
X → Y
 
Y → X  
X ≣ Y  
~Y → X

Question 3 
Which of the following is NOT a symmetric key algorithm?
Ellipse Curve Cryptography
 
Advanced Encryption standard
 
Data Encryption Standard
 
Blowfish 
Question 4 
Which of the following statements is FALSE?
The long term scheduler controls the degree of multiprogramming
 
Multiple process of a single program cannot exist  
Ready queue of the processes resides in main memory
 
A process can have multiple sub processes

→ Ready queue of the processes resides in main memory.
→ A process can have multiple sub processes.
→ Multiple process of a single program cannot exist because each program can have only one process.
Question 5 
Which of the following Boolean equations is/are correct?
X(X'+ Y) = XY' X + XY = X X + X'Y = X + Y
only (iii)  
only (ii)
 
only (i)  
Both (ii) and (iii)

Question 6 
With respect to compiler design, "recursive descent" is a ____ parsing technique that reads the inputs from ____.
topdown, right to left
 
topdown, left to right
 
bottom up, right to left  
bottom up, left to right

→ Top down parsers reads the input from left to right and bottom up parsers are reads the input from left to right and reverse.
Question 7 
Which of the following statements is/are FALSE?
 (i) XML element names are case sensitive
(ii) In XML, empty element can be represented as
(iii) XML element names can contain spaces
only (iii)  
only (ii) and (iii)
 
only (i) and (iii)
 
only (ii)

1. text
2. attributes
3. other elements or a mix of the above
Note: XML element names cannot contain spaces.
Question 8 
For what values of k, the points(k+1, 2k),(k, 22K) and (4k, 62k) are collinear?
0, 1
 
1, 1  
1, 1/2
 
1/2, 1/2

1/2[X1(Y2  Y3) + X2(Y3  Y1) + X3(Y1  Y2)] = 0
Here, X1 = k + 1, Y1 = 2k, X2 = k, Y2 = 2 – 2k, X3 = 4  k, Y3 = 6 – 2k
1/2[k + 1(2 – 2k  6 + 2k) + k(6 – 2k  2k)  4 k(2k  2 + 2k)] = 0
1/2[k + 1(4) + k(6  4k) 4  k(4k  2)] = 0
1/2[4k  4 + 6k  4k^{2}  16k + 8  4k^{2} + 2k)] = 0
1/2(8k^{2}  4k + 4) = 0
8k^{2}  4k + 4 = 0
8k^{2}  8k + 4k + 4 = 0
8K(k + 1) + 4(k + 1) = 0
(k + 1) (4  8k) = 0
k + 1 = 0
k = 1
4  8k = 0
k = 4/8
k = 1/2
So, the value of k is 1 and 1/2 .
Question 9 
If a connected graph G has planar embedding with 4 faces and 4 vertices, then what will be the number of edges in G?
7  
6  
4  
3 
For any(connected) planar graph with v vertices, e edges and faces, we have
V  E + F = 2
= 4  E + 4 =2
E = 4  2 + 4
E = 6
Question 10 
What is the area bounded by the parabola 2y = x^{2} and the line x = y  4?
18  
36  
72  
6 
and the line x = y – 4  (2)
Then y = x+4
Now, Substitute Y value in Equation(1)
x^{2} = 2 ( x + 4 )  (3)
Solving equation3 we get x = 4,  2.
Place Values of x in equation (1) and (2) we will get y = 8, 2.
Then the points of intersection are (8, 4), (2, –2).
After solving the integration, we will get 18.
Question 11 
The following circuit represents the function of a 2–input __________ logic gate.
ExclusiveOR
 
ExclusiveNOR
 
NAND
 
NOR

Step2:
Step3: We have to apply not operation then we are getting ExNOR.
Question 12 
What is the possible number of reflexive relations on a set of 5 elements?
2^{25}
 
2^{15}  
2^{10}
 
2^{20}

Step2: The possible number of reflexive relations on a set of 5 elements 2^{(n2n)} which is 2^{20} for n=5.
Question 13 
XML documents form a ___ structure.
Binary tree
 
Tree
 
Linear list  
Graph 
→ This specification does not specify how the document entity is to be located by an XML processor; unlike other entities, the document entity has no name and might well appear on a processor input stream without any identification at all.
Question 14 
Banker’s algorithm is used for:
Deadlock avoidance  
Deadlock recovery
 
Deadlock resolution
 
Deadlock prevention

Question 15 
Which one of the following is most affected by the presence of outliers in sample data?
Variance
 
Mean
 
Median
 
Mode

For the sample data set:
1, 1, 2, 2, 2, 2, 3, 3, 3, 4, 4
We find the following mean, median, mode, and standard deviation:
Mean = 2.58
Median = 2.5
Mode = 2
Standard Deviation = 1.08
If we add an outlier to the data set:
1, 1, 2, 2, 2, 2, 3, 3, 3, 4, 4, 400
The new values of our statistics are:
Mean = 35.38
Median = 2.5
Mode = 2
Standard Deviation = 114.74
Note: Outliers often has a significant effect on your mean and standard deviation.
Question 16 
Consider the matrix A defined as follows:
What is the eigenvalue of 3A^{3 }+ 5A^{2 } 6A + 21, where I is an identity matrix?
4, 110, 10
 
1, 27, 8
 
1, 9, 4
 
4, 27, 9

Eigenvalues of A^{3} are 1, 27 and –8.
Eigenvalues of A^{2} are 1, 9 and 4.
Eigenvalues of A are 1, 3 and –2.
Eigenvalues of I are 1, 1 and 1.
∴ The eigenvalues of 3A^{3} + 5A^{2} – 6A + 2I.
First eigenvalue = 3(1) + 5(1) – 6(1) + 2(1) = 4
Second eigenvalue = 3(27) + 5(9) – 6(3) + 2(1) = 110
Third eigenvalue = 3(–8) + 5(4) – 6(–2) + 2(1) = 10
∴ The required eigenvalues are 4, 110, and 10.
Question 17 
If A and B are sets and AUB = A∩B, then which of the following is correct?
A=B  
A=∅
 
B=∅  
A⊂B

= x belongs to A intersection B
= x belongs to A and x Belongs to B
= x belongs to B
so A subset of B  (2)
Now we will let y belong to B which implies y belongs to A U B
= y belongs to A intersection B
= y belongs to A and y belongs to B
= y belongs to A
Therefore, B subset of A  (3) from (2) and (3) we get A=B.
Question 18 
What is the total number of spanning trees of a complete graph of 4 vertices (K_{4})?
16  
8  
4  
15 
n^{n2} = 4^{2} = 16
Question 19 
Considering 0address instructions machine, what will be the top of the stack after executing the following sequence of instructions?
PUSH 15, PUSH 4, PUSH 6, MULT, PUSH 30, ADD, ADD
30  
69  
54  
10 
Step1: PUSH 15,PUSH 4 and PUSH 6 from bottom to top. Now top of the stack value is 6.
Step2: Perform MULT operation. 6*4=24. Now present stack values are from bottom is 15 and 24.
Step3: Next again PUSH 30. Now top of the stack is 30.
Step4: Perform ADD operation. 30+24=54
Step5: Now present stack values are from bottom is 15 and 54. Perform ADD operation.
Step6: 15+54=69
Question 20 
The maximum number of boolean functions that can be formed using 3 boolean variable is ____.
512  
256  
128  
1024 
→ For three Boolean variables (n = 3), there are 2^{3} = 8 different cases, giving us a total of 2^{8}
= 256 Boolean functions of 3 variables.
Question 21 
Which of the following statements is/are correct?

(i) If the rank of the matrix of given vectors is equal to the number of vectors, then the vectors are linearly independent.
(ii) If the rank of the matrix of given vectors is less than the number of vectors, then the vectors are linearly dependent.
Both (i) and (ii)
 
Only (ii)
 
Only (i)  
Neither (i) nor (ii) 
→ You can think of an r x c matrix as a set of r row vectors, each having c elements; or you can think of it as a set of c column vectors, each having r elements.
→ The rank of a matrix is defined as (a) the maximum number of linearly independent column vectors in the matrix or (b) the maximum number of linearly independent row vectors in the matrix. Both definitions are equivalent.
For an r x c matrix,
1. If r is less than c, then the maximum rank of the matrix is r.
2. If r is greater than c, then the maximum rank of the matrix is c.
→ The rank of a matrix would be zero only if the matrix had no elements. If a matrix had even one element, its minimum rank would be one.