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Past Questions — 2025
Find the side of the largest possible square slabs which can be paved on the floor of a room 2m50cm long and 1m50cm broad.
A)
25 cm
B)
30 cm
C)
50 cm
D)
72 cm
To find the side of the largest possible square slab that can pave a rectangular floor without leaving any gaps, we need to find the Highest Common Factor (HCF) of the length and the breadth of the room.
Step 1: Convert all measurements to a single unit (centimeters).
Length = 2m 50cm = (2 × 100) + 50 = 250 cm
Breadth = 1m 50cm = (1 × 100) + 50 = 150 cm
Step 2: Find the HCF of 250 and 150.
- Prime factorization of 250: 2 × 5 × 5 × 5 = 2^1 × 5^3
- Prime factorization of 150: 2 × 3 × 5 × 5 = 2^1 × 3^1 × 5^2
Step 3: The HCF is the product of the lowest powers of common prime factors:
- Common factors are 2 and 5.
- Lowest power of 2 is 2^1.
- Lowest power of 5 is 5^2.
- HCF = 2^1 × 5^2 = 2 × 25 = 50 cm.
Therefore, the side of the largest possible square slab is 50 cm.
Verification of options:
- a. 25 cm: This is a common factor, but not the highest.
- b. 30 cm: 250 is not divisible by 30.
- c. 50 cm: Correct (HCF).
- d. 72 cm: Neither 250 nor 150 is divisible by 72.
What option should fill the blank? SCD, TEF, UGH, ____, WKL
A)
CMN
B)
UJI
C)
VIJ
D)
IJT
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. These letters skip one letter in between (C, [d], E, [f], G, [h], I, [j], K). Following this pattern, the letter after G is I.
3. Third Letter: D → F → H → ? → L. These letters also skip one letter in between (D, [e], F, [g], H, [i], J, [k], L). Following this pattern, the letter after H is J.
Combining these results, the missing group is V + I + J = VIJ.
Comparing with the options:
- a. CMN: Incorrect (does not follow the sequence).
- b. UJI: Incorrect (first letter should be V).
- c. VIJ: Correct.
- d. IJT: Incorrect (first letter should be V).
If A is the brother of B; B is the sister of C; and C is the father of D, how is D related to A?
A)
Brother
B)
Sister
C)
Nephew
D)
Cannot be established
Let's break down the relationships step-by-step:
1. A is the brother of B: This means A is male and A and B are siblings.
2. B is the sister of C: This means B is female and B, A, and C are all siblings.
3. C is the father of D: This means C is male and D is the child of C.
Now, we determine the relationship between D and A:
- Since A is the brother of C, and C is the father of D, A is the paternal uncle of D.
- Conversely, D is the child of A's brother (C).
- In blood relation terminology, the child of one's sibling is either a 'Nephew' (if male) or a 'Niece' (if female).
Crucially, the problem does not specify the gender of D. Without knowing if D is male or female, we cannot determine if D is A's nephew or A's niece. Therefore, the exact relationship cannot be established from the given information.
If 243 * 27^(a+1) = 3^b, find b.
A)
3a+5
B)
a+5
C)
a+8
D)
3a+8
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 (a+1) term.
- Option b (a+5) is incorrect as it fails to account for the base 27 being 3^3.
- Option c (a+8) is incorrect as it fails to account for the base 27 being 3^3.
- Option d (3a+8) matches our derived result.
The average weight of 24 students in a class is 35 kg. If the weight of the teacher is included, the average weight becomes 36 kg. Find the weight of the teacher.
A)
60 kg
B)
57 kg
C)
55 kg
D)
50 kg
To find the weight of the teacher, we can use two methods: the Total Sum method or the Deviation method.
Method 1: Total Sum Method
1. Calculate the total weight of the 24 students:
Total weight = Number of students × Average weight = 24 × 35 = 840 kg.
2. Calculate the total weight after the teacher is included. The number of people becomes 25 (24 students + 1 teacher) and the new average is 36 kg:
New total weight = 25 × 36 = 900 kg.
3. The weight of the teacher is the difference between the new total weight and the previous total weight:
Teacher's weight = 900 kg - 840 kg = 60 kg.
Method 2: Deviation Method (Shortcut)
1. When the teacher joins, the average weight increases by 1 kg (from 35 to 36).
2. This 1 kg increase is distributed among all 25 people (24 students + 1 teacher).
3. Total increase = 25 people × 1 kg = 25 kg.
4. The teacher's weight = Old average + Total increase = 35 kg + 25 kg = 60 kg.
Comparing this result to the options:
- Option (a) 60 kg matches our calculation.
- Options (b), (c), and (d) are incorrect as they do not satisfy the mathematical requirement of increasing the average of 25 people to 36 kg.
When inserting a chart linked to Excel, which paste option allows future updates?
A)
Paste as Picture
B)
Embed Object
C)
Paste Link
D)
Paste Values
When integrating data between Microsoft Excel and other MS Office applications (like Word or PowerPoint), the 'Paste Link' option creates a dynamic connection between the source file (Excel) and the destination document. If the data in the original Excel spreadsheet is changed, the linked chart in the destination document will automatically update to reflect those changes.
Here is why the other options are incorrect:
- a. Paste as Picture: This converts the chart into a static image. It cannot be edited or updated if the source data changes.
- b. Embed Object: Embedding places a copy of the data into the destination file. While you can edit the embedded data using Excel tools within the document, it is no longer connected to the original source file; changes to the original file will not update the embedded object.
- d. Paste Values: This option pastes only the raw data (numbers/text) without any formatting or chart structure, and it is a static paste that does not update.
In MS Word, the difference between “Section Break (Next Page)” and “Page Break” is:
A)
Both are identical in function
B)
Page Break creates a new page; Section Break creates a new section with different formatting options
C)
Section Break deletes existing content, Page Break doesn’t
D)
Page Break is only for headers, Section Break is only for footnotes
In MS Word, it is crucial to distinguish between a Page Break and a Section Break:
1. **Page Break**: This simply tells Word to end the current page and start a new one. The formatting (margins, orientation, headers/footers, and page numbering) remains consistent across the break. It is used when you have reached the end of a chapter or a specific topic and want to start fresh on a new page.
2. **Section Break (Next Page)**: This not only starts a new page but also creates a 'Section'. Sections allow you to apply different page setups to different parts of the document. For example, you can have Page 1 in Portrait orientation and Page 2 in Landscape orientation, or have different headers and footers for different chapters.
Analysis of other options:
- **Option a** is incorrect because they serve fundamentally different purposes (content flow vs. structural formatting).
- **Option c** is incorrect because neither a Page Break nor a Section Break deletes content; they only manage the positioning of content.
- **Option d** is incorrect because Page Breaks have nothing to do with headers specifically, and Section Breaks are used for much more than just footnotes (e.g., columns, margins, orientation).
Which of the following is the fastest memory unit in a computer system?
A)
Registers
B)
SSD
C)
Cache
D)
RAM
In a computer system, memory is organized in a hierarchy based on speed, cost, and capacity.
1. **Registers (Option a):** These are small storage locations located directly inside the CPU (Central Processing Unit). Because they are integrated into the processor core and operate at the same clock speed as the CPU, they provide the fastest possible access time.
2. **Cache (Option c):** Cache memory (L1, L2, L3) is also very fast and located on or near the CPU chip, but it is slower than registers because it is larger and requires more complex addressing logic.
3. **RAM (Option d):** Random Access Memory is the main system memory. It is significantly slower than cache and registers because it is located further from the CPU and communicates via the system bus.
4. **SSD (Option b):** Solid State Drives are secondary storage. While much faster than traditional Hard Disk Drives (HDDs), they are orders of magnitude slower than RAM, cache, and registers because they store data non-volatily on flash memory chips.
Therefore, the hierarchy of speed from fastest to slowest is: Registers > Cache > RAM > SSD.
In Excel, which feature lets you restrict editing in specific cells while allowing changes in others?
A)
Freeze Sheet
B)
Protect Sheet
C)
Data Validation
D)
Lock Panes
In Microsoft Excel, the 'Protect Sheet' feature is used to prevent unauthorized changes to the contents of a worksheet. By default, all cells in an Excel sheet are marked as 'Locked'. However, this locking mechanism only takes effect once the 'Protect Sheet' command is activated. To allow changes in specific cells while restricting others, a user must first select the cells they want to remain editable, go to Format Cells > Protection, and uncheck the 'Locked' box. After this, applying 'Protect Sheet' (found under the Review tab) will lock all cells except those that were explicitly unlocked.
Why other options are incorrect:
- a. Freeze Sheet: This is not a standard Excel term. 'Freeze Panes' exists, but it is for visibility, not editing restrictions.
- c. Data Validation: This feature restricts the *type* of data or values that can be entered into a cell (e.g., only numbers between 1 and 10), but it does not prevent a user from editing or deleting the cell content entirely.
- d. Lock Panes: This is a misnomer for 'Freeze Panes', which keeps specific rows or columns visible while scrolling through the rest of the sheet; it has no impact on editing permissions.
Which feature in a word processor prevents words from being cut off at the edge of the page by moving them to the next line?
A)
AutoFit
B)
Word Wrap
C)
Page Break
D)
Alignment
Step-by-step reasoning:
1. **Understanding the Requirement**: The question asks for the feature that automatically moves a word to the next line when it reaches the right margin of the page, preventing it from being cut off or extending beyond the printable area.
2. **Analyzing 'Word Wrap'**: Word Wrap is a standard feature in all modern word processors (like MS Word). It automatically detects the end of a line based on the page margins and shifts the cursor and the subsequent text to the beginning of the next line. This ensures that text remains visible and formatted within the page boundaries.
3. **Evaluating Other Options**:
- **AutoFit**: This is primarily a feature used in Tables to adjust the width of columns to fit the content or the window size; it does not handle general text line breaks.
- **Page Break**: This is a manual or automatic command that forces the text following it to start on a completely new page, regardless of how much space is left on the current page.
- **Alignment**: This refers to the positioning of text relative to the margins (Left, Right, Center, or Justified), but it does not control the mechanism of moving text to a new line.
Therefore, Word Wrap is the correct feature.
Which spreadsheet feature is MOST useful in analyzing large data sets with summarized views, filtering, and grouping?
A)
PivotTable
B)
VLOOKUP
C)
Data Validation
D)
Goal Seek
Step-by-step reasoning:
1. Analyze the requirements: The question asks for a feature that handles 'large data sets', provides 'summarized views', allows 'filtering', and enables 'grouping'.
2. Evaluate Option (a) PivotTable: A PivotTable is specifically designed to aggregate large amounts of data. It allows users to summarize data (sum, count, average), filter specific criteria, and group data (e.g., grouping dates by month or year) without changing the original dataset. This matches all criteria.
3. Evaluate Option (b) VLOOKUP: This is a lookup function used to find a specific value in a table based on a unique identifier. It does not summarize, group, or provide a high-level view of large datasets.
4. Evaluate Option (c) Data Validation: This is a tool used to control what a user can enter into a cell (e.g., creating a dropdown list). It is a data entry control tool, not an analysis tool.
5. Evaluate Option (d) Goal Seek: This is a 'What-If Analysis' tool used to find the input value needed to achieve a specific result. It is used for single-variable forecasting, not for summarizing large datasets.
Conclusion: PivotTable is the only feature among the options that provides comprehensive summarization, filtering, and grouping capabilities for large data sets.
In Windows OS, the Recycle Bin does not store files deleted from:
A)
Desktop
B)
Internal hard disk
C)
Documents folder
D)
Removable drives (USB)
In the Windows Operating System, the Recycle Bin acts as a temporary storage area for files deleted from the local system to allow for easy recovery.
1. Files deleted from the Desktop (Option a), Internal hard disk (Option b), and Documents folder (Option c) are moved to the Recycle Bin because these are part of the local file system managed by the OS.
2. However, files deleted from removable storage devices, such as USB flash drives, SD cards, or external drives formatted as removable, are permanently deleted immediately. They bypass the Recycle Bin because the OS does not allocate a hidden 'recycle' folder on these external devices to avoid consuming space or causing file system inconsistencies across different computers.
Note: If a user holds the 'Shift' key while deleting a file from a local drive, it will also bypass the Recycle Bin, but among the provided location-based options, the removable drive is the correct answer.
In MS Excel, the function =IF(AND(A1>50,B1<100), “Pass”,”Fail”) will return “Pass” only if:
A)
A1 is less than 50 and B1 is greater than 100
B)
A1 is greater than 50 and B1 is less than 100
C)
A1 and B1 are both equal to 100
D)
None of the above
The given formula is =IF(AND(A1>50, B1<100), "Pass", "Fail").
1. The AND function is a logical operator that returns TRUE only if all its arguments are true. In this case, it checks two conditions: (A1 > 50) AND (B1 < 100).
2. The IF function follows the syntax: =IF(logical_test, value_if_true, value_if_false).
3. Here, the 'logical_test' is the AND function. If both A1 is greater than 50 AND B1 is less than 100, the result is TRUE, and the function returns the 'value_if_true', which is "Pass".
4. If either condition (or both) is false, the function returns the 'value_if_false', which is "Fail".
Evaluating the options:
- Option (a) is the opposite of the required conditions.
- Option (b) matches the logical requirements of the AND function exactly.
- Option (c) would result in 'Fail' because A1=100 (True) but B1=100 (False, since 100 is not less than 100).
In Windows OS, which shortcut is used to switch between open applications?
A)
Ctrl + S
B)
Alt + F4
C)
Ctrl + C
D)
Alt + Tab
In the Windows Operating System, the 'Alt + Tab' shortcut is the standard keyboard command used to switch between open applications. When you hold the Alt key and press Tab, a switcher window appears showing all active programs, allowing the user to cycle through them quickly.
Analysis of other options:
- a. Ctrl + S: This is the universal shortcut used to 'Save' the current document or file.
- b. Alt + F4: This shortcut is used to 'Close' the currently active window or application.
- c. Ctrl + C: This is the standard shortcut used to 'Copy' selected text or an object to the clipboard.
Which among the following is true about Primary vs Secondary memory?
A)
Primary memory is non-volatile, Secondary memory is volatile
B)
Primary memory is faster but temporary, Secondary memory is slower but permanent
C)
Both are volatile in nature
D)
Secondary memory directly communicates with CPU
To determine the correct statement, we must analyze the characteristics of Primary and Secondary memory:
1. **Primary Memory (e.g., RAM):** It is the main memory of the computer. It is directly accessible by the CPU, making it extremely fast. However, it is 'volatile,' meaning it loses its data when the power is turned off (temporary).
2. **Secondary Memory (e.g., HDD, SSD):** It is used for long-term storage. It is 'non-volatile,' meaning it retains data even without power (permanent). Because it is not directly connected to the CPU via the memory bus in the same way RAM is, it is significantly slower.
Evaluating the options:
- **Option a:** Incorrect. It swaps the definitions; Primary is volatile and Secondary is non-volatile.
- **Option b:** Correct. Primary memory is faster (due to proximity to CPU) but temporary (volatile), while Secondary memory is slower but permanent (non-volatile).
- **Option c:** Incorrect. Only Primary memory (specifically RAM) is volatile; Secondary memory is non-volatile.
- **Option d:** Incorrect. The CPU communicates directly with Primary memory (RAM) and Cache. To access data in Secondary memory, it must first be loaded into Primary memory.
Which of the following Excel features allows you to restrict the type of data that can be entered into a cell?
A)
Data Validation
B)
Conditional Formatting
C)
Cell Protection
D)
Solver
Step-by-step reasoning:
1. Analysis of the requirement: The question asks for a feature that 'restricts the type of data' entered into a cell. This is a control mechanism to ensure data integrity.
2. Evaluating Option (a) Data Validation: This feature is specifically designed to control what a user can enter into a cell. It allows the administrator to set rules, such as allowing only whole numbers, dates, a specific length of text, or providing a drop-down list of predefined options. If a user enters data that violates these rules, Excel displays an error message and prevents the entry.
3. Evaluating Option (b) Conditional Formatting: This feature changes the appearance (color, font, border) of a cell based on its value. It does not restrict what can be typed into the cell; it only reacts to what is already there.
4. Evaluating Option (c) Cell Protection: This feature (often used with 'Protect Sheet') prevents users from editing or deleting the contents of a cell entirely. While it restricts 'editing', it does not restrict the 'type' of data being entered during the input phase.
5. Evaluating Option (d) Solver: This is an add-in used for 'what-if' analysis to find an optimal value for a formula in one cell subject to constraints on other cells. It is a mathematical optimization tool, not an input restriction tool.
Conclusion: Data Validation is the only feature that restricts the specific type of data input.
What does the “https://” part of a URL indicate?
A)
The protocol used to transfer data
B)
The server address
C)
The file location
D)
The search engine
A URL (Uniform Resource Locator) consists of several parts. The 'https://' part is known as the 'scheme' or 'protocol'.
1. **HTTPS** stands for Hypertext Transfer Protocol Secure. It is the standard protocol used to communicate between a web browser and a web server, ensuring that data is encrypted and secure during transfer.
2. **Option b (The server address)** refers to the domain name (e.g., 'www.google.com'), which follows the protocol.
3. **Option c (The file location)** refers to the path (e.g., '/images/logo.png'), which comes after the domain name.
4. **Option d (The search engine)** refers to a software system (like Google or Bing) used to search for information, not a part of the URL syntax itself.
Therefore, 'https://' specifically indicates the protocol being used for the data transfer.
Which protocol is primarily used to send emails?
A)
FTP
B)
HTTP
C)
POP3
D)
SMTP
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 'push' mechanism to move the mail from the sender to the recipient's mail server.
2. **POP3 (Post Office Protocol version 3)**: This is used for 'retrieving' or downloading emails from a server to a local client. It is a 'pull' mechanism, not a sending mechanism.
3. **HTTP (Hypertext Transfer Protocol)**: This is the foundation of data communication for the World Wide Web (loading webpages). While web-based email (like Gmail) uses HTTP to display the interface, the underlying transfer of mail between servers still relies on SMTP.
4. **FTP (File Transfer Protocol)**: This is used specifically for the transfer of files between a client and a server on a computer network, not for electronic mail.
Therefore, SMTP is the correct protocol for sending emails.
What does the term ‘WIMP’ stand for in GUI terminology?
A)
Windows, Icons, Menus, Pointers
B)
Web, Images, Menus, Programs
C)
Windows, Input, Mouse, Printing
D)
Windows, Interface, Menu, Processor
In the context of Graphical User Interfaces (GUI), 'WIMP' is a classic acronym used to describe the style of interaction that became standard with the rise of personal computing.
1. **Windows**: These are rectangular areas on the screen that isolate different programs or documents, allowing the user to multitask.
2. **Icons**: Small pictorial representations of files, folders, or applications that users can interact with.
3. **Menus**: Lists of commands or options presented to the user, reducing the need to memorize complex text-based commands.
4. **Pointers**: A symbol (usually an arrow) on the screen that moves in response to a pointing device (like a mouse), allowing the user to select and manipulate the other three elements.
Options b, c, and d are incorrect because they include terms like 'Web', 'Input', 'Printing', or 'Processor', which are general computing terms but are not part of the specific WIMP architectural definition of a GUI.
In a school, 60% students play cricket. A student who does not play cricket, plays football. Every football player has got a two- wheeler. Which of the following conclusions cannot be drawn from the above data? i. 60% of the students do not have two- wheelers. ii. No cricketer has a two-wheeler. iii. Cricket players do not play football.
A)
i and ii only
B)
ii and iii only
C)
i and iii only
D)
i, ii and iii
Let's analyze the given premises step-by-step:
1. **Premise 1:** 60% of students play cricket. This implies 40% of students do not play cricket.
2. **Premise 2:** A student who does not play cricket, plays football. This means all non-cricketers (40%) are football players.
3. **Premise 3:** Every football player has a two-wheeler. This means all 40% who play football definitely have two-wheelers.
Now let's evaluate the conclusions to see if they can be logically drawn (deduced) from the data:
- **Conclusion i: '60% of the students do not have two-wheelers.'**
We know 40% (football players) definitely have two-wheelers. However, the data tells us nothing about the 60% who play cricket. They might have two-wheelers, or they might not. We cannot conclude that they definitely do not have them. Thus, this cannot be drawn.
- **Conclusion ii: 'No cricketer has a two-wheeler.'**
The data states that football players have two-wheelers. It does not state that *only* football players have them. Cricketers could also own two-wheelers. There is no information to support the claim that no cricketer has one. Thus, this cannot be drawn.
- **Conclusion iii: 'Cricket players do not play football.'**
The data says 'A student who does not play cricket, plays football.' This establishes that non-cricketers are football players. It does NOT state that cricketers cannot also play football (they could be dual-sport athletes). Since there is no 'only' or 'exclusive' condition mentioned for football, we cannot conclude that cricketers do not play football. Thus, this cannot be drawn.
Since none of the three conclusions can be logically drawn from the provided data, the correct option is 'i, ii and iii'.
Window is to pane as book is to:
A)
Novel
B)
Page
C)
Cover
D)
Shelf
This is a 'Whole-to-Part' analogy. To solve it, we must identify the relationship between the first pair of words and apply that same logic to the second pair.
1. Analyze the first pair: 'Window' is the whole object, and a 'pane' is a single, constituent part (a sheet of glass) that makes up the window.
2. Apply the logic to the second pair: We are looking for the constituent part that makes up a 'book'.
Evaluating the options:
- a. Novel: This is a type of book (Category), not a part of a book.
- b. Page: A page is a single, constituent part that makes up a book. This matches the 'Whole-to-Part' relationship (Window : Pane :: Book : Page).
- c. Cover: While a cover is part of a book, it is the outer casing. A window is primarily composed of panes, just as a book is primarily composed of pages.
- d. Shelf: A shelf is where a book is stored (Location), not a part of the book itself.
Therefore, 'Page' is the most accurate analogy.
The cost of a pineapple is Rs.7 whereas a watermelon costs Rs.5. A man spends a total of Rs.38 on these fruits. The number of whole pineapples that the man purchases is:
A)
2
B)
3
C)
4
D)
Data inadequate
Let the number of pineapples be 'p' and the number of watermelons be 'w'. Both p and w must be non-negative integers because the question specifies 'whole' fruits.
The cost equation is: 7p + 5w = 38.
We can solve this by testing integer values for p:
1. If p = 1: 7(1) + 5w = 38 => 5w = 31 (Not divisible by 5)
2. If p = 2: 7(2) + 5w = 38 => 14 + 5w = 38 => 5w = 24 (Not divisible by 5)
3. If p = 3: 7(3) + 5w = 38 => 21 + 5w = 38 => 5w = 17 (Not divisible by 5)
4. If p = 4: 7(4) + 5w = 38 => 28 + 5w = 38 => 5w = 10 => w = 2 (Valid integer solution)
5. If p = 5: 7(5) + 5w = 38 => 35 + 5w = 38 => 5w = 3 (Not divisible by 5)
6. If p = 6: 7(6) = 42, which exceeds the total budget of 38.
Therefore, the only possible number of whole pineapples the man could have purchased is 4 (with 2 watermelons).
The top of a 21m high tower makes an angle of elevation of 60° with the bottom of an electric pole and an angle of elevation of 30° with the top of the pole. What is the height of the electric pole?
A)
14m
B)
16m
C)
7m
D)
8m
Let the height of the tower be $H = 21\text{ m}$, the height of the electric pole be $h$, and the horizontal distance between them be $d$.
1. From the bottom of the pole, the angle of elevation to the top of the tower is $60^\circ$:
$$\tan(60^\circ) = \frac{H}{d} \implies \sqrt{3} = \frac{21}{d} \implies d = \frac{21}{\sqrt{3}} = 7\sqrt{3}\text{ m}$$
2. From the top of the pole, the angle of elevation to the top of the tower is $30^\circ$:
$$\tan(30^\circ) = \frac{H - h}{d} \implies \frac{1}{\sqrt{3}} = \frac{21 - h}{7\sqrt{3}}$$
3. Solving for $h$:
$$21 - h = 7 \implies h = 14\text{ m}$$
Thus, the height of the electric pole is $14\text{ m}$ (Option a). Other options like 7m (Option c), 16m (Option b), and 8m (Option d) are mathematically incorrect as they do not satisfy these trigonometric relations.
A cube has six different symbols drawn over its six faces. The symbols are star, circle, triangle, rectangle, cross and arrow. Three different positions of the cube are shown in the three given figures. Which symbol is opposite to the rectangle?
A)
Triangle
B)
Star
C)
Arrow
D)
Circle
To find the symbol opposite to the rectangle, we can apply the standard rules of a cube/dice using the three given positions:
1. **Comparing Figure 1 and Figure 2**:
- Both figures share two common symbols: **Star** and **Triangle**.
- According to the rule of cubes, when two faces are common, the remaining third faces on both positions are opposite to each other.
- Therefore, **Circle** is opposite to **Cross** (Circle ↔ Cross).
2. **Comparing Figure 2 and Figure 3**:
- Both figures share two common symbols: **Star** and **Cross**.
- Therefore, the remaining third faces must be opposite to each other.
- This means **Triangle** is opposite to **Arrow** (Triangle ↔ Arrow).
3. **Finding the remaining opposite pair**:
- Since Circle is opposite to Cross, and Triangle is opposite to Arrow, the only remaining pair of symbols must be opposite to each other.
- Thus, **Star** is opposite to **Rectangle** (Star ↔ Rectangle).
**Why other options are incorrect**:
- **a (Triangle)**: It is opposite to the Arrow.
- **c (Arrow)**: It is opposite to the Triangle.
- **d (Circle)**: It is opposite to the Cross.
The device that connects multiple networks and determines the best path for data packets is called:
A)
Hub
B)
Switch
C)
Repeater
D)
Router
The correct answer is a Router. Here is the step-by-step breakdown:
1. **Router (Correct):** A router is a Layer 3 (Network Layer) device in the OSI model. Its primary function is to connect different networks (e.g., connecting a home local area network to the internet). It uses a routing table and routing protocols to determine the 'best path' (most efficient route) for data packets to travel from the source to the destination based on IP addresses.
2. **Hub (Incorrect):** A hub is a Layer 1 (Physical Layer) device. It is a non-intelligent device that simply broadcasts incoming data packets to all connected ports, regardless of the destination. It does not determine paths or connect different networks.
3. **Switch (Incorrect):** A switch is primarily a Layer 2 (Data Link Layer) device. While it is smarter than a hub (it sends data only to the specific device using MAC addresses), it is used to connect devices within a single local area network (LAN), not to connect multiple different networks or determine the best path across them.
4. **Repeater (Incorrect):** A repeater is a Layer 1 device used to regenerate or amplify a signal to allow it to travel longer distances without degradation. It does not perform any routing or path determination.