Past Questions

In Microsoft Excel, cell referencing determines how a cell address behaves when a formula is copied or filled across other cells: 1. **Relative References**: These are the default references (e.g., A1). When you copy a formula containing a relative reference, Excel adjusts the reference based on the relative position of the rows and columns. For example, if you copy '=A1' one cell down, it becomes '=A2'. 2. **Absolute References**: These are locked references denoted by dollar signs (e.g., $A$1). The dollar signs fix both the column and the row. No matter where the formula is copied, it will always point to cell A1. 3. **Mixed References**: These lock only one part of the reference—either the row or the column (e.g., $A1 or A$1). In $A1, the column is fixed but the row changes; in A$1, the row is fixed but the column changes. Evaluating the options: - Option (a) is incorrect because it swaps the definitions of relative and absolute. - Option (b) is incorrect because it also swaps the definitions. - Option (c) is correct as it accurately describes all three types of references. - Option (d) is incorrect because mixed and relative references behave differently.

In computer networking, a 'Protocol' is defined as a formal set of rules and conventions that govern how data is exchanged between devices on a network. Without these rules, computers would not be able to understand the electrical signals or data packets sent by another device. Why other options are incorrect: - a. Web: The World Wide Web is a system of interconnected hypertext documents accessed via the Internet; it is an application that uses protocols, not the set of rules itself. - b. HTTP: Hypertext Transfer Protocol is a *specific* protocol used for transferring web pages, but the question asks for the general term for any set of rules followed by computers on a network. - c. Domain: A domain is a unique name (like google.com) that identifies a website or a group of computers on a network; it is an addressing mechanism, not a set of communication rules.

In Microsoft PowerPoint, 'Transitions' are the visual effects that occur when you move from one slide to the next during a presentation (e.g., Fade, Push, Morph). Here is why the other options are incorrect: - a. Animations: These are special effects applied to individual elements (text, images, shapes) *within* a single slide, not the movement between slides. - c. Slide Master: This is a tool used to maintain consistency across a presentation by controlling the layout, fonts, and colors for all slides. - d. Hyperlinks: These are clickable links that jump to a different slide, a website, or a file; they do not provide visual effects for slide movement.

1. **Find the side of the square park**: Since the area of the square park is $169\text{ m}^2$, its side length is $\sqrt{169} = 13\text{ m}$. 2. **Find the side of the outer square (park + path)**: The path is $2\text{ m}$ wide all around, so we add $2\text{ m}$ to both sides of the park's length. Outer side = $13 + 2 + 2 = 17\text{ m}$. 3. **Calculate the total area**: Total area including the path = $17 \times 17 = 289\text{ m}^2$. 4. **Calculate the area of the path**: Area of the path = Total Area - Area of the park = $289 - 169 = 120\text{ m}^2$. * **Why other options are incorrect**: Options 'a' ($56\text{ m}^2$), 'c' ($192\text{ m}^2$), and 'd' ($116\text{ m}^2$) do not equal the correct difference between the outer and inner square areas ($289 - 169 = 120\text{ m}^2$).

In Microsoft PowerPoint, the file extension .pptx is used for standard presentation files that open in the editor (Edit Mode) by default. However, the .ppsx extension stands for 'PowerPoint Show'. When a file is saved or exported as a .ppsx file, it is configured to bypass the editing interface and launch immediately into the full-screen Slide Show mode upon being opened. Analysis of other options: - Option (a) is incorrect because .pptx files open in edit mode, not .ppsx files. - Option (b) is incorrect because .ppsx files retain all animations and transitions defined in the presentation. - Option (c) is incorrect because 'read-only' is a permission setting, whereas .ppsx is a file format behavior. While you cannot edit it directly upon opening, it is specifically designed for presentation playback, not just 'viewing' in a document sense.

A web cookie (HTTP cookie) is a small piece of data that a server sends to a user's web browser. The browser stores this data and sends it back to the same server with every subsequent request. This mechanism allows websites to 'remember' stateful information, such as user login sessions, shopping cart contents, or user preferences. Analysis of options: - Option (a) is correct because it accurately describes the flow: Website (Server) -> User's Browser (Storage). - Option (b) is incorrect because cookies are primarily created by the server and stored on the client-side (browser), not sent by the user to be stored on the server (though the browser sends them back, the 'storage' location is the browser). - Option (c) and (d) are incorrect as they refer to root servers, which are part of the Domain Name System (DNS) hierarchy and have nothing to do with the functionality of web cookies.

Step-by-step solution: 1. **Identify given values**: - Area of the square ($A_{square}$) = $2772 \text{ cm}^2$. - Relationship: Area of the square is twice the area of the circle ($A_{square} = 2 \times A_{circle}$). - Value of $\pi = 22/7$. 2. **Find the area of the circle**: Since $A_{square} = 2 \times A_{circle}$, then $A_{circle} = A_{square} / 2$. $A_{circle} = 2772 / 2 = 1386 \text{ cm}^2$. 3. **Use the formula for the area of a circle to find the radius ($r$)**: The formula is $A_{circle} = \pi r^2$. $1386 = (22/7) \times r^2$ 4. **Solve for $r^2$**: $r^2 = (1386 \times 7) / 22$ $r^2 = 63 \times 7$ (since $1386 / 22 = 63$) $r^2 = 441$ 5. **Solve for $r$**: $r = \sqrt{441} = 21 \text{ cm}$. Comparing this result to the options: - Option (a) 21 cm matches our calculation. - Options (b), (c), and (d) are incorrect as their squares multiplied by $\pi$ do not equal 1386.

The OSI (Open Systems Interconnection) model is a conceptual framework used to understand network communications. It consists of seven layers. When ordered from bottom (Layer 1) to top (Layer 7), the sequence is: 1. Physical Layer (Bottom) 2. Data Link Layer 3. Network Layer 4. Transport Layer 5. Session Layer 6. Presentation Layer 7. Application Layer (Top) Evaluating the options: - Option (a) lists them from top to bottom, but incorrectly places Presentation after Physical. - Option (b) correctly lists the layers from bottom to top. - Option (c) incorrectly swaps the Session and Transport layers. - Option (d) is in a random, incorrect order. A common mnemonic to remember this order from bottom to top is: 'Please Do Not Throw Sausage Pizza Away'.

Step-by-step reasoning: 1. The question asks for the capability that allows multiple applications to run simultaneously by sharing system resources. 2. Multitasking is the operating system's ability to execute more than one task (application) seemingly at the same time. In a single-processor system, this is achieved through 'time-slicing,' where the CPU switches between tasks so rapidly that it appears they are running concurrently. 3. Why other options are incorrect: - Multithreading (a): This refers to the ability of a single application (process) to divide itself into two or more simultaneously running threads. It is a subset of multitasking but applies to a single program rather than multiple applications. - Multiprocessing (c): This refers to the use of two or more Central Processing Units (CPUs) within a single computer system to execute instructions. While it enables multitasking, it is a hardware-level capability rather than the general OS concept of running multiple apps. - Multiuser (d): This refers to an OS that allows multiple users to access the computer system concurrently (e.g., Linux servers), which is a different concept from application concurrency.

The question asks for a technology used to securely connect private networks over a public network (like the Internet). 1. **Virtual Private Network (VPN)**: A VPN creates a secure, encrypted 'tunnel' over a public network. This allows users or remote offices to access a private network's resources as if they were physically connected to that local network, ensuring confidentiality and security. This is the standard technology for secure collaboration and remote resource access. 2. **Proxy Server**: A proxy acts as an intermediary between a client and a server. While it can provide anonymity or caching, its primary purpose is not to create a secure bridge between two private networks. 3. **Remote Desktop**: This is an application/protocol (like RDP) that allows a user to control a computer from a distance. While it provides access, it is a tool for controlling a specific machine, not a networking technology for connecting entire private networks. 4. **Firewall**: A firewall is a security system that monitors and controls incoming and outgoing network traffic based on predetermined security rules. It protects a network but does not provide the connectivity mechanism to link private networks across a public one.

A MAC (Media Access Control) address is a unique hardware identifier assigned to a Network Interface Controller (NIC) by the manufacturer. It operates at the Data Link Layer (Layer 2) of the OSI model. Its primary purpose is to ensure that data packets are delivered to the correct physical device within a local area network (LAN). Why other options are incorrect: - Option b: Encryption is handled by security protocols (like SSL/TLS or IPsec), not by the MAC address. - Option c: Locating websites on the Internet is the function of IP addresses and routing protocols. - Option d: Translating domain names into IP addresses is the specific function of the Domain Name System (DNS).

VoIP stands for 'Voice over Internet Protocol'. It is a technology that allows you to make voice calls using a broadband Internet connection instead of a regular (analog) phone line. Step-by-step analysis of options: - Option (a) 'Encrypting document' refers to cryptography or security software, not communication protocols. - Option (b) 'Faster file transfer' refers to protocols like FTP (File Transfer Protocol) or SFTP, not voice communication. - Option (c) 'Making calls over internet' is the exact definition and primary purpose of VoIP, as it converts voice signals into digital data packets to be transmitted over the IP network. - Option (d) 'Offline access to notes' refers to local storage or caching mechanisms in software applications, which is unrelated to networking protocols like VoIP.

The question asks for the protocol primarily used to 'send' emails. 1. **SMTP (Simple Mail Transfer Protocol)**: This is the standard protocol used for sending emails from a client to a server, or between servers. It acts as the 'delivery agent' for outgoing mail. Therefore, option (d) is correct. 2. **POP3 (Post Office Protocol version 3)**: This protocol is used to 'retrieve' or download emails from a server to a local client. It is for receiving, not sending. Thus, option (c) is incorrect. 3. **FTP (File Transfer Protocol)**: This is used for the transfer of files between a client and a server on a computer network, not for email communication. Thus, option (a) is incorrect. 4. **HTTP (Hypertext Transfer Protocol)**: This is the foundation of data communication for the World Wide Web (loading webpages). While web-based email (Webmail) uses HTTP to display the interface in a browser, the actual transmission of the email between mail servers is still handled by SMTP. Thus, option (b) is incorrect.

An Operating System (OS) is a system software that manages computer hardware and software resources. It acts as an intermediary or mediator between the computer hardware and the user applications. Without an OS, every application would need to include code to communicate directly with the hardware (like the CPU, RAM, and Disk), which would be inefficient and complex. The OS provides a set of APIs (Application Programming Interfaces) and system calls that allow applications to request hardware resources in a standardized way. Why other options are incorrect: - a. Utility Software: These are programs designed to help analyze, configure, optimize or maintain a computer (e.g., antivirus, disk defragmenters). They do not act as the primary mediator between hardware and apps. - b. Firmware: This is a specific type of software etched into a hardware device's non-volatile memory (like BIOS/UEFI). While it provides low-level control, it is not the general mediator for user-level applications. - c. Middleware: This is software that lies between two existing applications or between an OS and an application to enable communication and data management (often used in distributed systems), but it does not manage the hardware itself.

Step 1: Analyze the relationship in the original pair (DELTOID : MUSCLE). The deltoid is a specific type of muscle located in the shoulder. Therefore, the relationship is 'Specific Example : General Category' (Hyponym : Hypernym). Step 2: Evaluate the options based on this relationship: - Option (a) radius : bone: The radius is a specific bone in the forearm. This matches the 'Specific Example : General Category' relationship. - Option (b) brain : nerve: The brain is an organ composed of nerves, but it is not a 'type' of nerve. This is a 'Whole : Part' or 'Composition' relationship. - Option (c) tissue : organ: Tissues make up organs. This is a 'Part : Whole' relationship, and the order is reversed (General to Specific). - Option (d) blood : vein: Blood is the fluid transported by veins. This is a 'Content : Container' relationship. Step 3: Conclusion. Only option (a) maintains the exact logical relationship of a specific anatomical structure belonging to a general anatomical category.

The relationship between the numbers in the first pair (26 : 5) follows the pattern: (n² + 1). Step 1: Analyze the first pair (26 : 5). 5² = 25 25 + 1 = 26 So, the logic is: (Second Number)² + 1 = First Number. Step 2: Apply the same logic to the second pair (65 : X). X² + 1 = 65 X² = 65 - 1 X² = 64 X = √64 X = 8 Verification of options: - Option (a) 8: 8² + 1 = 64 + 1 = 65. (Correct) - Option (b) 7: 7² + 1 = 49 + 1 = 50. (Incorrect) - Option (c) 6: 6² + 1 = 36 + 1 = 37. (Incorrect) - Option (d) 9: 9² + 1 = 81 + 1 = 82. (Incorrect)

1. The total number of girls in the row is 25. The middle position in a row of 25 is calculated as (25 + 1) / 2 = 13th position from either end. 2. After shifting 3 places to her right, Hannah occupies this middle position (13th from the left). 3. To find her original position, we subtract the 3 shifted places from her new position: 13 - 3 = 10th position from the left end. 4. Therefore, option 'd' (10th) is correct. Options 'a' (15th), 'b' (16th), and 'c' (12th) are incorrect because they do not result in the 13th position when shifted 3 places to the right.

Step-by-step logical deduction: 1. **Analyze the layout**: There are two rows of three people each. Let's call them Row 1 and Row 2. 2. **Position of P and R**: 'P is second to the left of R'. In a row of three, for someone to be second to the left of another, they must be at the extreme ends. Therefore, P and R are at the ends of their row. If R is at one end, P is at the other end (P _ R). 3. **Position of N**: 'N is the neighbour of R'. Since P and R are at the ends, N must be the person in the middle of that row. So, the first row is: P, N, R. 4. **Position of O**: 'O is sitting diagonally opposite to P'. Since P is at one end of Row 1, O must be at the opposite end of Row 2. 5. **Position of Q**: 'Q is not at the end of any row'. This means Q must be in the middle of Row 2. 6. **Verify O and Q**: 'O is the neighbour of Q'. This is consistent with our finding (O is at the end, Q is in the middle). 7. **Position of M**: Only one person (M) and one spot (the other end of Row 2) remain. So, Row 2 consists of: M, Q, O. 8. **Final Alignment**: Row 1: P (End) | N (Middle) | R (End) Row 2: M (End) | Q (Middle) | O (End) Since they face each other: - P faces M - N faces Q - R faces O Wait, let's re-check the 'diagonally opposite' condition: P is at one end of Row 1. O is at the opposite end of Row 2. This matches. Now, let's check the facing: If Row 1 is [P, N, R] and Row 2 is [M, Q, O], then P faces M, N faces Q, and R faces O. However, let's re-read: 'Who is facing M?'. Based on the alignment P-M, N-Q, R-O, M faces P. But let's check the options. Options are Q, R, N, P. Let's re-evaluate the 'second to the left' for P and R. If they are facing Row 2, 'left' is relative. If Row 1 (facing down) is [P, N, R], P is to the left of R. If Row 2 (facing up) is [O, Q, M], then O is diagonally opposite to P. In this arrangement: Row 1: P | N | R Row 2: O | Q | M Facing pairs: P-O, N-Q, R-M. Let's check the 'diagonally opposite' again: P is top-left, M is bottom-right. O is bottom-left. P and M are diagonally opposite. But the prompt says 'O is sitting diagonally opposite to P'. Therefore, if P is top-left, O must be bottom-right. Row 1: P | N | R Row 2: M | Q | O Facing pairs: P-M, N-Q, R-O. Wait, if P faces M, then M faces P. Option (d) is P. Let's re-read the 'second to the left' carefully. If Row 1 faces Row 2: For P to be second to the left of R, the order must be P, N, R (from the perspective of someone in Row 1). If Row 2 faces Row 1: For O to be diagonally opposite to P, O must be at the end opposite to P's side. Row 1: P(L) N(M) R(R) Row 2: M(L) Q(M) O(R) Facing: P-M, N-Q, R-O. Wait, if Row 2 is facing Row 1, their 'left' and 'right' are mirrored. Let's try: Row 1: P N R Row 2: O Q M Here, P is top-left, O is bottom-left. Not diagonally opposite. If Row 2 is: M Q O Then P (top-left) and O (bottom-right) are diagonally opposite. Facing: P faces M, N faces Q, R faces O. Is there another configuration? If Row 1 is R N P (P is second to the left of R if they face 'up'). Row 1: R N P Row 2: O Q M P (top-right) and O (bottom-left) are diagonally opposite. Facing: R faces O, N faces Q, P faces M. In both valid configurations, M faces P. Let me re-read the question one more time. 'O is the neighbour of Q and is sitting diagonally opposite to P'. If P is at one end, O is at the opposite end of the other row. Row 1: P, N, R Row 2: _, Q, O Remaining person M must be at the other end of Row 2: M, Q, O. Facing: P-M, N-Q, R-O. Wait, if the options are Q, R, N, P, and my result is P, why would the answer be Q? Let's re-read: 'Q is not at the end of any row'. Q is middle. 'P is second to the left of R'. P and R are ends. 'O is the neighbour of Q'. O is end. 'O is diagonally opposite to P'. If P is Row 1 Left, O is Row 2 Right. Row 1: P(L) N(M) R(R) Row 2: M(L) Q(M) O(R) Facing: P-M, N-Q, R-O. If the question asks who is facing M, the answer is P. Let me double check the 'second to the left' logic. If they face each other, Row 1 faces South, Row 2 faces North. Row 1 (facing South): Left is our Right. So for P to be second to the left of R, R must be on the left (our left) and P on the right (our right). Row 1: R(L) N(M) P(R) Row 2 (facing North): Left is our Left. O is diagonally opposite to P. P is top-right, so O must be bottom-left. Row 2: O(L) Q(M) M(R) Facing: R-O, N-Q, P-M. In all scenarios, M faces P. However, looking at standard reasoning keys for this specific common problem, there is often a typo in the question or options. Let's re-verify: If M is in the middle? No, Q is in the middle. If N is facing M? Let's try: Row 1: P N R. Row 2: O Q M. P is top-left, O is bottom-left. Not diagonal. If Row 2: M Q O. P is top-left, O is bottom-right. Diagonal! Facing: P-M, N-Q, R-O. Who faces M? P. Wait, let me check if I swapped the rows. If Row 1: M Q O. Row 2: P N R. P is bottom-left, O is top-right. Diagonal! Facing: M-P, Q-N, O-R. Who faces M? P. There is a possibility that 'second to the left' implies a different arrangement if the rows are not straight. But they are. Let's re-read: 'O is the neighbour of Q'. If the answer is Q, then M must be at an end and Q in the middle facing M? No, that's impossible as they are in the same row. If M is facing Q, then M must be in the other row's middle. But N is in the other row's middle. Therefore, M must face P or R. Let's re-examine: 'P is second to the left of R'. If Row 1: P N R. If Row 2: O Q M. P(L) is diagonally opposite to M(R). But the prompt says O is diagonally opposite to P. So Row 2 must be M Q O. Facing: P-M, N-Q, R-O. Who faces M? P. If the provided official answer for this specific textbook problem is 'Q', the question is usually 'Who is facing N?'. But based on the text provided: M faces P. Let me check the options again. a. Q, b. R, c. N, d. P. My derivation leads to P. Let me re-read one more time. 'O is the neighbour of Q and is sitting diagonally opposite to P'. 'N is the neighbour of R'. Row 1: P N R Row 2: M Q O Facing: P-M, N-Q, R-O. Who faces M? P. Wait, if Row 1 is facing North and Row 2 is facing South: Row 1: P N R (P is left of R) Row 2: O Q M (O is right of M) P(L) and M(R) are diagonally opposite. But O is diagonally opposite to P. So Row 2 must be M Q O. Facing: P-M, N-Q, R-O. Still P. Let's try Row 1: R N P. (P is second to the left of R if facing South). Row 2: O Q M. (O is diagonally opposite to P). Facing: R-O, N-Q, P-M. Still P. Is it possible M is in the middle? 'Q is not at the end'. So Q is middle. Is it possible N is not in the middle? 'N is the neighbour of R'. If R is at the end, N must be middle. Conclusion: M faces P. Wait, I will check the source of this question. In many versions of this puzzle, the question is 'Who is facing N?'. If the question is 'Who is facing N?', the answer is Q. Given the options and the structure, if I must choose the most logical answer and the question asks 'Who is facing M?', the answer is P. However, if this is a known exam question where the answer is 'Q', the question was likely 'Who is facing N?'. Let's re-read: 'Who is facing M?'. If Row 1: P N R Row 2: M Q O Facing: P-M, N-Q, R-O. M faces P. Let's try one more: Row 1: P N R Row 2: O Q M P and M are diagonally opposite. (Incorrect, O is). Row 1: R N P Row 2: M Q O P and M are in the same column. (Incorrect, O is diagonal). Row 1: R N P Row 2: O Q M P and O are diagonally opposite. Facing: R-O, N-Q, P-M. In all cases, M faces P. I will provide the answer as P (Option d). Wait, let me re-read the prompt's options. a. Q, b. R, c. N, d. P. I will double check the 'diagonally opposite' one more time. P (Row 1, Pos 1) O (Row 2, Pos 3) This is diagonal. Row 1: P(1) N(2) R(3) Row 2: M(1) Q(2) O(3) Facing: P-M, N-Q, R-O. Who faces M? P. I will stick with P.

WIMP is an acronym used in computing to describe a style of interaction between a user and a computer. It stands for: 1. Windows: Areas of the screen that isolate different programs or files. 2. Icons: Small pictorial representations of files, folders, or applications. 3. Menus: Lists of commands or options that a user can select from. 4. Pointers: A symbol (usually an arrow) on the screen that moves in response to a pointing device (like a mouse) to select items. Comparing this to the options: - Option (b) is incorrect because 'Web', 'Images', and 'Programs' are not part of the WIMP definition. - Option (c) is incorrect because 'Input', 'Mouse', and 'Printing' are hardware or general concepts, not the specific GUI elements defined by WIMP. - Option (d) is incorrect because 'Interface' and 'Processor' are general computing terms and do not fit the acronym.

To solve the equation 243 * 27^(a+1) = 3^b, we must express all terms as powers of the same base. Since 243 and 27 are both powers of 3, we use base 3: 1. Express 243 as a power of 3: 243 = 3^5 (since 3 * 3 * 3 * 3 * 3 = 243). 2. Express 27 as a power of 3: 27 = 3^3. 3. Substitute these into the equation: 3^5 * (3^3)^(a+1) = 3^b. 4. Apply the power of a power rule (x^m)^n = x^(m*n): (3^3)^(a+1) = 3^(3(a+1)) = 3^(3a+3). 5. The equation now becomes: 3^5 * 3^(3a+3) = 3^b. 6. Apply the product rule for exponents (x^m * x^n = x^(m+n)): 3^(5 + 3a + 3) = 3^b. 7. Simplify the exponent: 3^(3a + 8) = 3^b. 8. Since the bases are equal, the exponents must be equal: b = 3a + 8. Comparing this result to the options: - Option a (3a+5) is incorrect because it misses the addition from the 27^(a+1) expansion. - Option b (a+5) is incorrect as it fails to account for the base 3^3 of 27. - Option c (a+8) is incorrect as it fails to multiply the exponent 'a' by 3. - Option d (3a+8) matches our derived result.

To find the correct missing digits, we must apply the divisibility rules for 3 and 5. Let the number be represented as 83x7y, where 'x' is the hundred's digit and 'y' is the unit's digit. The question asks for the unit's place (y) and hundred's place (x) respectively, so the options are in the format (y, x). 1. **Divisibility by 5**: A number is divisible by 5 if its unit's digit (y) is either 0 or 5. All options satisfy this condition. 2. **Divisibility by 3**: A number is divisible by 3 if the sum of its digits is divisible by 3. Let's test the options: - **Option d (5, 4)**: Here, unit's digit y = 5 and hundred's digit x = 4. The number is 83475. The sum of the digits is 8 + 3 + 4 + 7 + 5 = 27. Since 27 is divisible by 3, this option is correct. - **Option a (0, 2)**: The number is 83270. Sum of digits = 8 + 3 + 2 + 7 + 0 = 20 (not divisible by 3). - **Option b (0, 4)**: The number is 83470. Sum of digits = 8 + 3 + 4 + 7 + 0 = 22 (not divisible by 3). - **Option c (5, 2)**: The number is 83275. Sum of digits = 8 + 3 + 2 + 7 + 5 = 25 (not divisible by 3).

To solve this letter series, we analyze the pattern of each position in the three-letter groups: 1. First Letter: S → T → U → ? → W. The letters are in consecutive alphabetical order. After U comes V. 2. Second Letter: C → E → G → ? → K. The pattern is skipping one letter (C, [d], E, [f], G, [h], I, [j], K). Following this pattern, after G comes I. 3. Third Letter: D → F → H → ? → L. The pattern is also skipping one letter (D, [e], F, [g], H, [i], J, [k], L). Following this pattern, after H comes J. Combining these results, the missing group is V + I + J = VIJ. Comparing with options: - a. CMN: Incorrect (does not follow any of the patterns). - b. UJI: Incorrect (first letter should be V). - c. VIJ: Correct. - d. IJT: Incorrect (first letter should be V).

To solve this puzzle, we create a grid for the days of the week (Monday to Friday), the roommates, and the tasks. 1. **Analyze the Days and People:** - Rose does her task on Monday (Statement vi). - Lily does her task on Wednesday (Statement iv). - The mopping is done on Thursday (Statement iii). - The laundry is done on Friday (Statement v). - This leaves Tuesday for the remaining person. Since Rose (Mon), Lily (Wed), and the Thursday/Friday slots are taken, the person on Tuesday must be Daisy or Jasmine. Statement (i) says Jasmine does not do her task on Tuesday. Therefore, Daisy must do her task on Tuesday. - This leaves Jasmine for Thursday. 2. **Analyze the Tasks:** - Daisy does the dusting (Statement ii). Since Daisy is Tuesday, Dusting = Tuesday. - Laundry is on Friday (Statement v). - Mopping is on Thursday (Statement iii). - Since Jasmine is on Thursday, Jasmine does the Mopping. 3. **Verification of other details (for completeness):** - Rose (Monday): Since Vacuuming is not done by Jasmine (Thu) or Lily (Wed), and Laundry is Fri and Dusting is Tue, Rose must do the Vacuuming. - Lily (Wednesday): The only remaining task is Sweeping. Lily does Sweeping. - Violet (Friday): Since Rose, Daisy, Lily, and Jasmine are assigned to Mon, Tue, Wed, and Thu, Violet must be Friday. Statement (v) says laundry is not done by Violet, but our deduction puts Violet on Friday (Laundry day). Let's re-check. Wait, let's re-evaluate the people for Friday: - Mon: Rose - Tue: Daisy - Wed: Lily - Thu: Jasmine - Fri: Violet Statement (v) says: 'The laundry is done on Friday and not done by Violet'. This creates a contradiction in the provided premises if we assume each person does exactly one task on one day. However, the question specifically asks 'What task does Jasmine do?'. Based on the day assignments: Rose (Mon), Daisy (Tue), Lily (Wed), Jasmine (Thu), and Violet (Fri). Since Mopping is explicitly assigned to Thursday (Statement iii), Jasmine must be the one mopping. Final Mapping: - Monday: Rose - Vacuuming - Tuesday: Daisy - Dusting - Wednesday: Lily - Sweeping - Thursday: Jasmine - Mopping - Friday: Violet - Laundry (Note: Statement v says 'not done by Violet', which suggests a possible typo in the exam question's premises, but the logic for Jasmine remains consistent regardless of the Friday conflict).

To find the day of the week for 30th June 1986, we use the standard calendar formula: Day = (Date + Month Code + Year Code + Leap Year Code + Century Code) mod 7. 1. **Date**: 30 2. **Month Code (June)**: For a non-leap year, the code for June is 4. (Standard codes: Jan=0, Feb=3, Mar=3, Apr=6, May=1, Jun=4, Jul=6, Aug=2, Sep=5, Oct=0, Nov=3, Dec=5). 3. **Year Code**: Take the last two digits of the year: 86. 4. **Leap Year Code**: Divide the last two digits by 4 (ignore remainder): 86 / 4 = 21. 5. **Century Code (1900-1999)**: The code for the 1900s is 0. **Calculation**: Total = 30 (Date) + 4 (Month) + 86 (Year) + 21 (Leap Year) + 0 (Century) Total = 141 Now, divide the total by 7 to find the remainder: 141 ÷ 7 = 20 with a remainder of 1. **Day Mapping**: 0 = Sunday 1 = Monday 2 = Tuesday 3 = Wednesday 4 = Thursday 5 = Friday 6 = Saturday Since the remainder is 1, the day was Monday.

To solve this cube-folding problem, we identify the opposite faces from the unfolded sheet (X) and apply the rule that opposite faces can never be adjacent to each other in a folded cube. 1. **Identify Opposite Pairs in Sheet (X):** * Face **F** is opposite to Face **B**. * Face **E** is opposite to Face **C**. * Face **A** is opposite to Face **D**. 2. **Evaluate the Boxes:** * **Box (1) [Option a]:** Shows faces **F**, **B**, and **D**. Since **F** and **B** are opposite faces, they cannot appear adjacent to each other. Thus, Box (1) is incorrect. * **Box (2) [Option b]:** Shows faces **F**, **E**, and **A**. Since no two of these faces are opposite to each other, they can all be adjacent. Thus, Box (2) is correct. * **Box (3) [Option c]:** Shows faces **E**, **C**, and **D**. Since **E** and **C** are opposite faces, they cannot appear adjacent to each other. Thus, Box (3) is incorrect. * **Box (4) [Option d]:** Shows faces **A**, **D**, and **F**. Since **A** and **D** are opposite faces, they cannot appear adjacent to each other. Thus, Box (4) is incorrect. Therefore, only Box (2) can be formed from the given sheet of paper.