Computer Science (Theory) Official 2023-2024 ISC (Commerce) Class 12 Question Paper Solution

According to the Principle of duality, the Boolean equation

(A+ B') • (A+ 1) =A+ B' will be equivalent to ______.

(A' + B) • (A'+ 1) = A' + B

(A • B') +(A • 0) = A • B'

(A' • B) +(A' • 1) =A' • B

(A' • B) +(A' • 0) =A' • B

When a sequence of OR, NOT, NOR are connected in series, the logic gate obtained is ______.

AND

NOT

OR

XOR

Idempotence Law states that ______.

X + X = X

X + X' = 0

X + X = 1

X + X' = X

Assertion: For proposition ∼A=> B, its contrapositive is B =>∼A

Reason: Contrapositive is the converse of inverse for any proposition.

Both Assertion and Reason are true, and Reason is the correct explanation for the Assertion.

Both Assertion and Reason are true, but Reason is not the correct explanation for the Assertion.

Assertion is true but Reason is false.

Assertion is false but Reason is true.

The complement of the Boolean expression (P' • Q) (R • S') is ______.

(P' + Q) • (R' + S)

(P + Q') • (R' + S)

(P' + Q) • (R + S')

(P + Q') • (R + S')

Assertion: Recursive data structure follows the LIFO principle.

Reason: Execution of recursive code follows the concepts of data structure Queue.

Both Assertion and Reason are true, and Reason is the correct explanation for the Assertion.

Both Assertion and Reason are true, but Reason is not the correct explanation for the Assertion.

Assertion is true but Reason is false.

Assertion is false but Reason is true.

State any one use of interfaces in Java.

Write the cardinal form of the maxterm X + Y' + Z.

Write the canonical SOP expression for F (A, B) = A <=> B.

State any one difference between instance variable and class variable.

Convert the following infix notation to postfix form.

(P + Q * R - S)/T * U

An array ARR [ -5 .....15, 10.....20] stores elements in Row Major Wise with each element requiring 2 bytes of storage. Find the address of ARR [10] [15] when the base address is 2500.

The following function is a part of some class:

int jolly(int[] x, int n, int m)
  {
if (n<0)
  return m;
else if(n<x.length)
  m=(x[n]>m)?x[n]:m;
return jolly(x, --n, m);
  }

1. What will be the output of jolly() when the value of x[ ]={6,3,4,7,1}, n=4 and m=0?
2. What function does jolly() perform, apart from recursion?

The following function is a part of some class which is used to find the smallest digit present in a number. There are some places in the code marked by ?1?, ?2?, ?3? which must be replaced by an expression/a statement so that the function works correctly.

int small_dig(int n)
{   int min=?1?;
    while(n!=0)
    {
    int q=n/10;
    int r=?2?*10;
    min=r>min ? ?3? : r;
    n=q;
    }
    return min;
} 
    

1. What is the expression or statement at ?1?
2. What is the expression or statement at ?2?
3. What is the expression or statement at ?3?

To be recruited as the Principal in a renowned College, a candidate must satisfy any one of the following criteria:

• The candidate must be a Postgraduate and should either possess a B.Ed. degree or a teaching experience of more than 15 years?
                                 OR
• The candidate must be an employee of the same college with a teaching experience of more than 15 years.
                                 OR
• The candidate must be a Postgraduate but not an employee of the same college and should have a teaching experience of more than 15 years.

The inputs are:

(In all the above cases, 1 indicates yes and 0 indicates no)

Output: X - Denotes eligibility of a candidate [1 indicates eligibility and 0 indicates ineligibility in all cases]

Draw the truth table for the inputs and outputs given above and write the SOP expression for X (P, S, E, B).

Reduce the above expression X (P, S, E, B) by tiifig 4-variable Karnaugh map, showing the various groups (i.e., octal, quads and pairs).

Draw the logic gate diagram for the reduced expression. Assume that the variables and their complements are available as inputs.

Reduce the Boolean function F (A,B,C,D) = π (0, 2, 4, 6, 8, 9, 10, 11, 14) by using 4-variable Karnaugh map, showing the various groups (i.e., octal, quads and pairs).

Draw the logic gate diagram for the reduced expression. Assume that the variables and their complements are available as inputs.

Verify if the following proposition is a Tautology, Contradiction or Contingency using a truth table.

((A=>B)^∧(B=>C))=>(A=>C)

Find the complement of the following expression and reduce it by using Boolean laws.

P•( 13 ± Q)•Q•(Q+R')

How is a decoder different from a multiplexer?

Draw the logic circuit for 3:8 decoder (Octal decoder). Which multiplexer can be derived from the Octal decoder?

Draw the logic gate diagram for 2-input OR gate using NAND gates only. Show the expression at each Step.

Write the canonical form of the cardinal terms, m₃ and M₅ for F (A, B, C, D).

Design a class DeciHex to accept a positive integer in decimal number system from the user and display its hexadecimal equivalent.

Example 1:

Decimal number= 25

Hexadecimal equivalent= 19

Example 2:

Decimal number =28

Hexadecimal equivalent = 1C

Some of the members of the class are given below.

Specify the class DeciHex giving details of the constructor( ), void getNum( ), void convert(int) and void display(). Define a main() function to create an object and call all the functions accordingly to enable the task.

A class Ins Sort contains an array of integers which sorts the elements in a particular order.

Some of the members of the class are given below.

Specify the class InsSort giving details of the constructor(), void getArray( ), void insertionSort( ), double find() and void display(). Define a main( ) function to create an object and call all the functions accordingly to enable the task.

Design a class Coding to perform some string related operations on a word containing alphabets only.

Example: Input: "Java"

Output: Original word: Java

J=74

a=97

v= 118

a=97

Lowest ASCII code: 74

Highest ASCII code: 118

Some of the members of the class are given below:

Specify the class Coding giving details of the constructor( ), void accept( ), void find( ) and void show(). Define a main() function to create an object and call all the functions accordingly to enable the task.

CardGame is a game of mental skill, built on the simple premise of adding and removing the cards from the top of the card pile.

The details of the class CardGame are given below.

1. Specify the class CardGame giving details of the functions void addCard(int) and int drawCard( ). Assume that the other functions have been defined.
   The main() function and algorithm need NOT be written.
2. Name the entity described above and state its principle.

A super class EmpSal has been defined to store the details of an employee. Defie a subclass (overtime to compute the total salary of the employee, after adding the overtime amount based on the following criteria.

• If hours are more than 40, then 5000 are added to salary as an overtime amount
• If hours are between 30 and 40 (both inclusive), then 3000 are added to salary as an overtime amount
• If hours are less than 30, then the salary remains unchanged The details of the members of both the classes are given below:

Assume that the super class EmpSal has been defined. Using the concept of inheritance, specify the class Overtime giving the details of the constructer (...), void calSal() and void show().

The super class, main function and algorithm need NOT be written.

With the help of an example, briefly explain the dominant term in complexity.

Answer the following questions based on the diagram of a Binary Tree given below:

1. Name the external nodes of the tree.
2. State the degree of node M and node L.
3. Write the post-order traversal of the above tree structure.