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• Digital Signature → Confirms authenticity and integrity 
• Hash Function → Produces a fixed-size digest 
• AES → Symmetric encryption algorithm 
• RSA → Asymmetric encryption algorithm

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• LL(0) is the weakest (no lookahead, top-down).
• LR(0) is stronger than LL(0) (bottom-up, no lookahead).
• SLR(1) adds 1-symbol lookahead using FOLLOW sets → accepts more grammars than LR(0).
• LALR(1) merges LR(1) states; more powerful than SLR(1) but below LR(1).
• LR(1) is the most powerful among these deterministic bottom-up parsers.

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• An adjacency matrix represents a graph using a 2D array (matrix).
• This type of storage uses sequential memory allocation — rows and columns are stored in contiguous memory.
• Hence, this method is called a Sequential Representation of a graph.

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• User-Mode Programs have the lowest priority and are preemptible.
• Kernel System Service Routines run in kernel mode and can be preempted by higher priority tasks like interrupts.
• Bottom Half Interrupt Handlers execute after the top half and have higher priority than kernel threads.
• Top Half Interrupt Handlers handle immediate hardware responses and have the highest priority.

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Goal: Find a set of attributes whose closure covers all attributes of R = {A, B, C, D, E}.

Check (1) CD⁺:
From C → F we get F. D gives nothing further. So CD⁺ = {C, D, F}.
Missing A, B, E ⇒ not a key.

Check (2) EC⁺:
Start {E, C}. Using E → A ⇒ add A. Using A → B ⇒ add B. Using EC → D ⇒ add D.
Therefore EC⁺ = {E, C, A, B, D} = {A, B, C, D, E}. Covers all attributes of R ⇒ key.

Check (3) AE⁺:
A → B gives B; E → A adds nothing new. No way to reach C or D ⇒ not a key.

Check (4) AC⁺:
A → B gives B; C → F gives F. No E or D ⇒ not a key.

Answer: (2) EC

Note: F is outside R, so while C → F is valid, a key must cover only attributes of R. EC⁺ covers {A, B, C, D, E}.

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Answer: 4) B and C only

• Binary Search Tree (BST): Not necessarily balanced; height can degrade to O(n).
• AVL Tree: Height-balanced by definition (balance factor −1, 0, +1); height is O(log n).
• Red-Black Tree: Enforces black-height properties that keep height O(log n); treated as a height-balanced binary tree.
• B-Tree: Balanced (all leaves at the same level) but not a binary tree; the term “height-balanced tree” typically refers to binary trees. Hence excluded here.

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Translate each statement:
(a) “If intelligent then unhappy” ⇒ P → ¬Q.
(b) “Neither intelligent nor happy” ⇒ ¬P ∧ ¬Q.
(c) “Being not intelligent is necessary for being happy” ⇒ Q → ¬P.
(d) “Not intelligent implies unhappy” ⇒ ¬P → ¬Q.

Only Option 3 matches all four translations.

Answer: 3

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Answer: (4) C, B, D, A

Explanation:
The standard steps for designing a dynamic programming algorithm are:

1. (C) Characterize the structure of an optimal solution.
2. (B) Recursively define the value of an optimal solution.
3. (D) Compute the value of an optimal solution (usually bottom-up).
4. (A) Construct the optimal solution from the computed information.

Hence, the correct order is C → B → D → A.

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Since the cards are drawn “one after the other” and order matters, we use permutations:
Number of ways = \( ^{42}P_3 = 42 \times 41 \times 40 \).

Compute: \( 42 \times 41 = 1722 \), and \( 1722 \times 40 = 68880 \).

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• A. Address Space → Virtual Address (IV)
  Address space refers to the range of virtual addresses a process can use in memory.
• B. Memory Space → Physical Address (III)
  Memory space corresponds to the actual physical memory locations in RAM.
• C. Cache Memory → Associative Mapping (I)
  Cache memory uses mapping techniques such as associative mapping to store data efficiently.
• D. Segmented Program → Logical Address (II)
  In segmentation, programs are divided into segments, each referenced by logical addresses.

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Using perceptron learning rule: Δw = η (t − y) x, where y = 1 if y_in > 0 else 0.

S1 (0,0,t=0): y_in=0 ⇒ y=0 ⇒ no change ⇒ (w1,w2)=(0,0)

S2 (0,1,t=1): y_in=0 ⇒ y=0 ⇒ Δw=0.1(1−0)(0,1) ⇒ (w1,w2)=(0,0.1)

S3 (1,0,t=1): y_in=0 ⇒ y=0 ⇒ Δw=0.1(1−0)(1,0) ⇒ (w1,w2)=(0.1,0.1)

S4 (1,1,t=1): y_in=0.1+0.1=0.2>0 ⇒ y=1 ⇒ no change

Final Weights: w1=0.1, w2=0.1

Answer: (1)

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Increasing coupling (lower → higher):

• Stamp coupling (B): modules share a composite data structure but use only parts of it.

• Control coupling (C): one module controls another via flags/controls.

• External coupling (D): modules depend on externally imposed formats/protocols/devices.

• Common coupling (A): modules share global data.

• Content coupling (E): one module relies on or modifies another’s internal logic (worst).

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Explanation:

• $A \rightarrow III$ → Clustered Page Table is useful for sparse address spaces.
• $B \rightarrow I$ → Hierarchical Page Table is inappropriate for 64-bit architectures.
• $C \rightarrow IV$ → Segmentation supports user’s logical view.
• $D \rightarrow II$ → Inverted Page Table has only one entry per real page frame.

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Why: The LCS length for the two sequences is $4$. $2,3,2,1$ is a subsequence of both: $\{1,\underline{2},3,\underline{2},4,1,\underline{2}\}$ and $\{\underline{2},4,\underline{3},1,\underline{2},\underline{1}\}$. Option (4) has length $5$ (too long), and (1), (2) are not subsequences of both.

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Explanation:

• A → IV → Intersection → $\min(\mu_A(x), \mu_B(x))$
• B → III → Bounded Sum → $\min(1, \mu_A(x) + \mu_B(x))$
• C → II → Bounded Difference → $\max(0, \mu_A(x) - \mu_B(x))$
• D → I → Algebraic Sum → $\mu_A(x) + \mu_B(x) - \mu_A(x)\mu_B(x)$

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Why: Type-3 (regular) → right-linear (IV); Type-2 (context-free) → $V \to (V\cup\Sigma)^*$ (I); Type-1 (context-sensitive) → context-preserving form (II); Type-0 (unrestricted) → any string to any string (III).

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• Overloading → Compile-time polymorphism (III)
• Early Binding → Done at compile time (II)
• Overriding → Run-time binding; slower (I)
• Late Binding → Supports run-time polymorphism (IV)

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Consider ar as a 3-dimensional array declared as:

data_type ar[a][b][c];

Here, the array element ar[m][n][o] can be represented in pointer form as:

*(*(*(ar + m) + n) + o)

Step-by-step understanding:

• ar is a pointer to the first 2D array ar[0].
• ar + m moves the pointer to the m^th 2D array → ar[m].
• *(ar + m) gives the address of the first 1D array inside ar[m].
• *(ar + m) + n moves to the n^th 1D array → ar[m][n].
• *(*(ar + m) + n) gives the address of the first element of that 1D array.
• *(*(*(ar + m) + n) + o) finally gives the element ar[m][n][o].

✅ Final Answer: *(*(*(ar + m) + n) + o)

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For a fuzzy set $A$, the $\lambda$-cut is defined as: $$A_\lambda = \{x \mid \mu_A(x) \ge \lambda\}$$

• Union Property: $(A \cup B)_\lambda = A_\lambda \cup B_\lambda$ ✅
• Intersection Property: $(A \cap B)_\lambda = A_\lambda \cap B_\lambda$ ✅
• Monotonicity: If $\lambda \le \beta$, then $A_\beta \subseteq A_\lambda$ ✅
• Complement: $\mu_{\overline{A}}(x) = 1 - \mu_A(x)$ ⇒ $(\overline{A})_\lambda = \{x \mid 1 - \mu_A(x) \ge \lambda\} = \{x \mid \mu_A(x) \le 1 - \lambda\}$ ❌

Hence, $(\overline{A})_\lambda$ is not equal to $A_\lambda$, even when $\lambda = 1$. Therefore, the statement “except when $\lambda = 1$” is incorrect.

✅ Final Answer: Option 3 is not valid.

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McCall’s Quality Model classifies software quality into three main categories:

• Product Operation factors: Correctness, Reliability, Efficiency, Integrity, Usability
• Product Revision factors: Maintainability, Flexibility, Testability
• Product Transition factors: Portability, Reusability, Interoperability

- Maintainability ✅ – part of Product Revision factors
- Usability ✅ – part of Product Operation factors
- Integrity ❌ – although in McCall model, it’s not grouped directly with Functionality in this context
- Functionality ✅ – general umbrella factor related to McCall’s quality aspects

✅ Final Answer: A, B and D Only

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