→ In mathematics, particularly in linear algebra, a skew-symmetric (or antisymmetric or antimetric) matrix is a square matrix whose transpose equals its negative, that is, it satisfies the condition.
→ If A is skew symmetric matrix then A^T = -A
→ In terms of the entries of the matrix, if a_ij denotes the entry in the i^th row and j^th column, then the skew-symmetric condition is equivalent to
→ If A is skew symmetric matrix then a_ji=-a_ij

(A) Happens when A and B are independent.
(B) Happens when A and B are mutually exclusive.
(C) Not happens.
(D) P(A∪B) ≤ P(A) + P(B) is true because P(A∪B) = P(A) + P(B) - P(A∩B).

Here f(x)= x³-3x-5 and f¹(x) = 3x²-3
The Newton-Raphson iterative formula is

Since x₃ and x₄ are identical upto 3 places of decima,we take x₄=2.279 as the required root, correct to three places of the decimal.

→ A data dictionary(or) metadata repository, as defined in the IBM Dictionary of Computing, is a "centralized repository of information about data such as meaning, relationships to other data, origin, usage, and format".
→ Oracle defines it as a collection of tables with metadata. The term can have one of several closely related meanings pertaining to databases and database management systems (DBMS)
1. A document describing a database or collection of databases
2. An integral component of a DBMS that is required to determine its structure
3. A piece of middleware that extends or supplants the native data dictionary of a DBMS

→ Two-phase locking protocol (2PL) ensures the conflict serializable schedule but it may not free from deadlock.
→ Timestamp ordering protocol ensures conflict serializability and free from deadlock.

Atomicity: Execute the all the operations or none of them
→ Responsible for Transaction Manager
Consistency: Database should be consistent before and after the execution of the transaction
→ Responsible for user/application manager
Isolation: Each transaction Tie must be executed without knowing what is happening with other transactions. Responsible for Concurrency control manager
Durability: All updates done by a transaction must become permanent.
→ Responsible for recovery manager

Common attributes in both the table column are the department. So, we apply natural join, it will give the output as common tuples in both the table S and R.

Derived attributes are depicted by dashed ellipse.
Example:

Symmetrical Difference of A and B=(A–B)∪(B–A)

→ 2-SAT is the first non polynomial problem is solved in polynomial time.
→ 3-SAT problem is NP- complete problem

According to the Chomsky hierarchy, both the statements are correct.

→ NPDA is more powerful than DPDA because
1. DPDA accept only a proper subset of CFL's ie. LL grammars.
2. NPDA can accept any CFL, which makes them more powerful over DPDA
3. Every NPDA can not be converted to an equivalent DPDA

Option C is correct because it indicates L followed by (L + D)* where * means 0 or more occurences of L or D.

Binary search in a sorted array
The time to search in an array of ‘n’ elements is equal to the time to search in an array of n/2 elements plus k comparison.
T(n)=T(n/2)+k // k is constant

Selection sort requires minimum number of swaps i.e O(n)

There are three situation for inserting element and deleting an element in Circular linked list.
1.Insertion at the front of Circular linked list.
2.Insertion in the middle of the Circular linked list.
3.Insertion at the end of the Circular linked list.

Step-1: RAM size required is 32Kx32 bits
= 32x1024x32 bits. [Note: 1k=1024 bytes]

Step-2: Given RAM chip capacity is 128x8 bits
Step-3: Required size/Given size
=(32*1024*32) / (128*8)
=1024

Indirect addressing:
Indirect addressing means that the address of the data is held in an intermediate location so that the address is first 'looked up' and then used to locate the data itself.
Immediate addressing:
Immediate Addressing. An immediate operand has a constant value or an expression. When an instruction with two operands uses immediate addressing, the first operand may be a register or memory location, and the second operand is an immediate constant. Auto increment or decrements: can be one by using loops.

Interrupts are the signals generated by the external devices to request the microprocessor to perform a ask. There are 5 interrupt signals. Given low priority to high is
1. INTR
2. RST 5.5
3. RST 6.5
4. RST 7.5
5. TRAP
Maskable Interrupts: They can be enabled or disabled by software INTR,RST 5.5,RST 6.5 and RST 7.5
Un maskable Interrupts: TRAP