Past Questions — 2025

A URL (Uniform Resource Locator) is a standardized naming convention used to identify and locate a specific resource (such as an HTML page, an image, a PDF, or a video) on the internet. It consists of several parts: the protocol (e.g., http, https), the domain name (e.g., www.example.com), and often a path to a specific file or directory. Why other options are incorrect: - Option (a): A browser is a software application (like Chrome or Firefox); it is not identified by a URL. - Option (b): While a URL points to a resource hosted on a server, the 'linking' process (mapping a domain to an IP address) is handled by the DNS (Domain Name System), not the URL itself. - Option (d): Server configuration involves settings like memory allocation, security rules, and software versions, which are managed via configuration files (e.g., .htaccess or nginx.conf), not by the URL.

Software is generally divided into two main categories: System Software and Application Software. 1. **Application Software** is designed to carry out specific tasks for the end-user. Examples include word processors (Microsoft Word), web browsers (Google Chrome), spreadsheets (Excel), and media players. Its primary role is to provide functionality that allows users to accomplish a particular goal. 2. **System Software** (such as the Operating System) is designed to manage the computer's hardware and provide a platform for application software to run. Evaluating the options: - **Option a (To manage hardware):** This is the role of System Software/Operating Systems. - **Option b (To perform specific tasks for users):** This is the correct definition of Application Software. - **Option c (To control system resources):** This is the role of the Operating System (a type of system software). - **Option d (To execute system commands):** This is typically handled by the Command Line Interface (CLI) or the OS kernel, which are parts of system software.

To find the gain or loss percentage, we need to compare the Cost Price (CP) and Selling Price (SP) for the same number of articles. Step 1: Find the Cost Price (CP) of one article. CP of 15 articles = ₹ 20 CP of 1 article = 20 / 15 = ₹ 4/3 Step 2: Find the Selling Price (SP) of one article. SP of 10 articles = ₹ 15 SP of 1 article = 15 / 10 = ₹ 3/2 Step 3: Determine if there is a gain or loss. Since SP (3/2 = 1.5) is greater than CP (4/3 ≈ 1.33), there is a gain. Step 4: Calculate the Gain per article. Gain = SP - CP Gain = (3/2) - (4/3) To subtract, find a common denominator (6): Gain = (9/6) - (8/6) = 1/6 Step 5: Calculate the Gain Percentage. Gain % = (Gain / CP) × 100 Gain % = ((1/6) / (4/3)) × 100 Gain % = (1/6 × 3/4) × 100 Gain % = (3/24) × 100 Gain % = (1/8) × 100 Gain % = 12.5% Alternative Method (LCM Method): Assume the person bought a number of articles equal to the LCM of 15 and 10, which is 30. CP of 30 articles = (20 / 15) * 30 = ₹ 40 SP of 30 articles = (15 / 10) * 30 = ₹ 45 Profit = 45 - 40 = ₹ 5 Profit % = (5 / 40) * 100 = (1 / 8) * 100 = 12.5%.

Step-by-step solution: 1. Let the present age of the boy be 9x and the present age of the girl be 10x (based on the ratio 9:10). 2. According to the problem, after 4 years, their ages will be (9x + 4) and (10x + 4) respectively. 3. The ratio of their ages after 4 years is given as 11:12. We can set up the equation: (9x + 4) / (10x + 4) = 11 / 12 4. Cross-multiply to solve for x: 12(9x + 4) = 11(10x + 4) 108x + 48 = 110x + 44 5. Rearrange the terms to isolate x: 110x - 108x = 48 - 44 2x = 4 x = 2 6. Now, find the girl's present age: Girl's present age = 10x = 10 * 2 = 20 years. Verification: Boy's present age = 9 * 2 = 18 years. After 4 years: Boy = 22, Girl = 24. Ratio = 22:24 = 11:12. This matches the given condition. Comparing with options: a. 18 years (This is the boy's age) b. 19 years (Incorrect) c. 20 years (Correct) d. 21 years (Incorrect)

Step-by-step calculation: 1. Find the total Marked Price (MP) of the books: There are 10 books, and each is priced at ₹ 300. Total MP = 10 × 300 = ₹ 3,000. 2. Identify the Selling Price (SP): The books are sold for a total of ₹ 2,500. 3. Calculate the Discount amount: Discount = Total MP - Total SP = 3,000 - 2,500 = ₹ 500. 4. Calculate the Discount Percentage: Discount % = (Discount / Total MP) × 100 Discount % = (500 / 3,000) × 100 Discount % = (1 / 6) × 100 = 100/6 % = 50/3 %. 5. Convert the improper fraction to a mixed fraction: 50 ÷ 3 = 16 with a remainder of 2. Therefore, 50/3% = 16 2/3%. Comparing with options: - Option (a) 16 2/3% matches our calculation. - Option (b) 17 1/2% is incorrect. - Option (c) 3 1/3% is incorrect. - Option (d) 0% is incorrect as there is a clear difference between MP and SP.

Step-by-step calculation: 1. **Identify given values**: - Curved Surface Area (CSA) = 5544 cm² - Diameter (d) = 42 cm - Radius (r) = Diameter / 2 = 42 / 2 = 21 cm 2. **Formula for Total Surface Area (TSA)**: The Total Surface Area of a cone is the sum of its Curved Surface Area and the area of its circular base. TSA = CSA + Base Area TSA = πrl + πr² 3. **Calculate the Base Area**: Base Area = πr² Using π ≈ 22/7: Base Area = (22/7) * 21 * 21 Base Area = 22 * 3 * 21 Base Area = 66 * 21 = 1386 cm² 4. **Calculate Total Surface Area**: TSA = 5544 cm² (given CSA) + 1386 cm² (calculated Base Area) TSA = 6930 cm² **Analysis of Options**: None of the provided options (a. 27720, b. 25530, c. 27270, d. 22770) match the mathematically correct answer of 6930 cm². The options provided in the prompt appear to be incorrect or belong to a different problem. However, based on the provided data, the absolute correct answer is 6930 cm².

Let the height of the tower be 'h' and the length of the shadow when the altitude is 60° be 'x'. 1. When the altitude of the sun is 60°: tan(60°) = height / shadow √3 = h / x h = x√3 --- (Equation 1) 2. When the altitude of the sun is 30°: The shadow length increases by 30m, so the shadow is (x + 30). tan(30°) = height / shadow 1/√3 = h / (x + 30) h = (x + 30) / √3 --- (Equation 2) 3. Equating the two expressions for h: x√3 = (x + 30) / √3 Multiply both sides by √3: x(√3 * √3) = x + 30 3x = x + 30 2x = 30 x = 15m 4. Substitute x back into Equation 1 to find the height (h): h = 15 * √3 = 15√3 m. Therefore, the height of the tower is 15√3 m. Note: Options (a) and (c) are identical in the provided list; both represent the correct numerical value.

Step-by-step solution: 1. Let the initial salaries of Remi and Sawmi be 2x and 3x respectively, based on the given ratio 2:3. 2. According to the problem, both salaries are increased by ₹ 4000. The new salaries are (2x + 4000) and (3x + 4000). 3. The new ratio is given as 40:57. We can set up the following equation: (2x + 4000) / (3x + 4000) = 40 / 57 4. Cross-multiply to solve for x: 57 * (2x + 4000) = 40 * (3x + 4000) 114x + 228,000 = 120x + 160,000 5. Rearrange the terms to isolate x: 228,000 - 160,000 = 120x - 114x 68,000 = 6x x = 68,000 / 6 x = 11,333.33... 6. Now, calculate Sawmi's initial salary (3x): Sawmi's Salary = 3 * (68,000 / 6) = 68,000 / 2 = ₹ 34,000. 7. However, the question asks for Sawmi's salary. Usually, in such competitive exam contexts, if the options don't match the 'initial' salary, we check for the 'new' salary after the increase: New Salary = 34,000 + 4,000 = ₹ 38,000 (This matches option a). Wait, let's re-verify the calculation. If Sawmi's initial salary was 34,000 and Remi's was 22,666.66, the ratio is 2:3. New salaries: Remi = 26,666.66, Sawmi = 38,000. Ratio: 26,666.66 / 38,000 = 0.7017. Target ratio: 40/57 = 0.70175. Let's re-read the options. If the answer is ₹ 46,800 (Option b): If Sawmi's new salary = 46,800, then initial = 42,800. If Sawmi's initial = 46,800, then new = 50,800. Let's test Option b (₹ 46,800) as the initial salary: If Sawmi = 46,800 (3x), then x = 15,600. Remi = 2x = 31,200. New Remi = 31,200 + 4,000 = 35,200. New Sawmi = 46,800 + 4,000 = 50,800. Ratio = 35,200 / 50,800 = 352 / 508 = 88 / 127 (Not 40/57). Let's re-calculate the equation: 114x + 228,000 = 120x + 160,000 6x = 68,000 3x = 34,000. Sawmi's initial salary = 34,000. Sawmi's new salary = 38,000. Given the options provided in the prompt, Option (a) ₹ 38,000 matches the salary after the increase. However, if the question intended a different ratio or value, we must check the options again. If we assume the ratio was meant to be different or there is a typo in the question's provided options vs the math, based on the provided numbers, 38,000 is the only mathematically reachable figure. Correction: Let's check if Sawmi's salary is the 'new' salary. If New Sawmi = 38,000, then Initial Sawmi = 34,000. Initial Remi = (2/3)*34,000 = 22,666.66. New Remi = 26,666.66. Ratio = 26,666.66 / 38,000 = 40/57. This confirms Option (a) is the New Salary. Wait, looking at the options again, if the answer is (b) 46,800, let's reverse engineer: (2x+4000)/(3x+4000) = 40/57 57(2x+4000) = 40(3x+4000) 114x + 228000 = 120x + 160000 6x = 68000 3x = 34000. New salary = 38000. There might be a typo in the provided options or the question's ratio. But based on the calculation, 38,000 is the correct result for the new salary. If the question asks for 'Sawmi's salary' and 38,000 is an option, it refers to the salary after the increase.

Let the time spent travelling on the bicycle be 't' hours. Since the total time taken is 9 hours, the time spent travelling on foot must be (9 - t) hours. We know that Distance = Speed × Time. 1. Distance travelled on bicycle = 9 km/hr × t = 9t km 2. Distance travelled on foot = 4 km/hr × (9 - t) = (36 - 4t) km The total distance travelled is given as 61 km. Therefore: 9t + (36 - 4t) = 61 5t + 36 = 61 5t = 61 - 36 5t = 25 t = 5 hours Now, we calculate the distance travelled on the bicycle: Distance = 9 km/hr × 5 hours = 45 km. Verification: Distance on foot = 4 km/hr × (9 - 5) = 4 × 4 = 16 km. Total distance = 45 km + 16 km = 61 km. This matches the question statement. Comparing with options: a. 40km (Incorrect) b. 36km (Incorrect) c. 30km (Incorrect) d. 45km (Correct)

To find the volume of a room (which is typically a rectangular prism or cuboid), the formula used is: Volume = Base Area × Height. Given: 1. Base Area = 16 m² 2. Height = 3 m Calculation: Volume = 16 m² × 3 m = 48 m³. Analysis of options: - Option (a) 16m: Incorrect value and incorrect unit (length instead of volume). - Option (b) 48m³: Correct value and correct unit (cubic meters). - Option (c) 54m: Incorrect value and incorrect unit. - Option (d) 66m³: Incorrect value.

To solve this puzzle, we map the friends to their colors and professions based on the given clues: 1. **Rosy**: Likes Yellow and is a Student (Given in clue 1). 2. **Mary**: Likes Purple (Given in clue 3). She is not a Teacher (Given in clue 3). 3. **Andy**: Likes Blue (Given in clue 3). Clue 4 states the Inspector likes Blue, so Andy is the Inspector. 4. **Lily**: Likes Brown (Given in clue 4). 5. **Daisy**: The only person left. The only color left is Green (since Yellow, Purple, Blue, and Brown are taken). Therefore, Daisy likes Green. Clue 2 states the Librarian likes Green, so Daisy is the Librarian. Now let's determine the remaining professions (Teacher and Principal) for Mary and Lily: - Mary is not a Teacher (Clue 3), so Mary must be the Principal. - Lily is the only one left to be the Teacher. Summary Table: - Rosy: Yellow | Student - Mary: Purple | Principal - Andy: Blue | Inspector - Lily: Brown | Teacher - Daisy: Green | Librarian Evaluating the options: - a. Andy - Inspector: Correct pair. - b. Purple - Principal: Correct pair (Mary likes Purple and is the Principal). - c. Daisy - Green: Correct pair. - d. Rosy - Teacher: Wrong pair. Rosy is a Student, not a Teacher.

Option B is correct: 144.

Digital citizenship refers to the responsible, ethical, and safe use of technology. 1. Option (b) 'Respecting others’ privacy online' is a core pillar of digital citizenship. It involves understanding boundaries, obtaining consent before sharing others' information, and maintaining confidentiality, which fosters a safe and respectful digital community. 2. Option (a) 'Sharing false information' (misinformation/disinformation) is irresponsible as it can lead to panic, confusion, and social harm. 3. Option (c) 'Cyberbullying' is a violation of digital ethics and is often illegal, involving the harassment of individuals via digital platforms. 4. Option (d) 'Piracy' is the unauthorized use or reproduction of copyrighted material, which is an illegal act and a breach of intellectual property rights. Therefore, only option (b) represents a positive and responsible behavior in the digital world.

To find the percentage change in the area of a square when its sides are increased, we can use two methods: the formula method or the assumption method. Method 1: Using the Successive Percentage Formula When two dimensions of a shape (like length and width of a rectangle or sides of a square) are increased, the net percentage change in area is given by the formula: Net % Change = a + b + (ab / 100) Here, a = 25% and b = 25% (since it is a square, both sides increase by the same percentage). Net % Change = 25 + 25 + (25 * 25 / 100) Net % Change = 50 + (625 / 100) Net % Change = 50 + 6.25 = 56.25% Method 2: Assumption Method 1. Let the original side of the square be 10 units. 2. Original Area = side * side = 10 * 10 = 100 sq units. 3. The side is increased by 25%. New side = 10 + (25% of 10) = 10 + 2.5 = 12.5 units. 4. New Area = 12.5 * 12.5 = 156.25 sq units. 5. Increase in Area = New Area - Original Area = 156.25 - 100 = 56.25 sq units. 6. Percentage Increase = (Increase / Original Area) * 100 = (56.25 / 100) * 100 = 56.25%. Comparing this result to the options: - Option (a) 65.25% is incorrect. - Option (b) 56.25% is correct. - Option (c) 65% is incorrect. - Option (d) 56% is incorrect.

Step-by-step solution: 1. **Identify given values and unify units**: - Radius of sphere ($R$) = 2.1 dm = 21 cm. - Length (height) of cylinder ($h$) = 7 cm. 2. **Calculate Volume of the Sphere**: - Volume of sphere = $\frac{4}{3} \pi R^3$ - Volume = $\frac{4}{3} \pi (21)^3$ cm³. 3. **Find the radius of the cylinder ($r$)**: - Since the sphere is converted into a cylinder, their volumes are equal. - Volume of cylinder = $\pi r^2 h$ - $\pi r^2 (7) = \frac{4}{3} \pi (21)^3$ - $r^2 = \frac{4 \times 21 \times 21 \times 21}{3 \times 7}$ - $r^2 = 4 \times 21 \times 21 = (2 \times 21)^2 = 42^2$ - $r = 42$ cm. 4. **Calculate Total Surface Area (TSA) of the Sphere**: - $TSA_{sphere} = 4 \pi R^2 = 4 \pi (21)^2 = 4 \pi (441) = 1764\pi$ cm². 5. **Calculate Total Surface Area (TSA) of the Cylinder (Rod)**: - $TSA_{cylinder} = 2\pi r(r + h)$ - $TSA_{cylinder} = 2\pi (42)(42 + 7) = 2\pi (42)(49)$ - $TSA_{cylinder} = 84 \times 49 \pi = 4116\pi$ cm². 6. **Calculate the Ratio**: - Ratio = $\frac{TSA_{cylinder}}{TSA_{sphere}} = \frac{4116\pi}{1764\pi}$ - Dividing both by 588: $4116 / 588 = 7$ and $1764 / 588 = 3$. - Ratio = 7:3. Therefore, the correct option is (d) 7:3.

To find the missing number in the sequence 7, 26, 63, 124, 215, 342, (...), we look for a mathematical pattern relating the numbers. Observation: - The first number is 7, which is close to 8 (2³). - The second number is 26, which is close to 27 (3³). - The third number is 63, which is close to 64 (4³). - The fourth number is 124, which is close to 125 (5³). - The fifth number is 215, which is close to 216 (6³). - The sixth number is 342, which is close to 343 (7³). The pattern is clearly (n³ - 1), starting from n = 2: 1. 2³ - 1 = 8 - 1 = 7 2. 3³ - 1 = 27 - 1 = 26 3. 4³ - 1 = 64 - 1 = 63 4. 5³ - 1 = 125 - 1 = 124 5. 6³ - 1 = 216 - 1 = 215 6. 7³ - 1 = 343 - 1 = 342 Following this pattern, the next number (the 7th term) should be based on n = 8: 7. 8³ - 1 = 512 - 1 = 511 Comparing this result to the options: a. 391 (Incorrect) b. 421 (Incorrect) c. 481 (Incorrect) d. 511 (Correct)

Step-by-step calculation: 1. Calculate 60% of 90: (60/100) * 90 = 0.6 * 90 = 54. 2. Calculate 5% of 20: (5/100) * 20 = 0.05 * 20 = 1. 3. Find the difference to determine how much greater the first value is than the second: 54 - 1 = 53. Reviewing the provided options: a. 12 b. 23 c. 30 d. 38 None of the provided options match the mathematically correct answer of 53. There may be a typo in the question's options provided in the prompt.

Step-by-step solution: 1. **Determine A's efficiency**: A can complete the job in 15 days. Therefore, A's work rate (efficiency) is 1/15 of the job per day. 2. **Determine B's efficiency**: The problem states that B is twice as fast as A. This means B's efficiency is 2 times that of A. B's efficiency = 2 * (1/15) = 2/15 of the job per day. 3. **Calculate combined efficiency**: When A and B work together, their combined work rate is the sum of their individual rates. Combined rate = (1/15) + (2/15) = 3/15. 4. **Simplify the combined rate**: 3/15 simplifies to 1/5 of the job per day. 5. **Calculate total days**: The time taken to complete the job is the reciprocal of the combined work rate. Time = 1 / (1/5) = 5 days. Comparing with options: - a. 3 days: Incorrect. - b. 8 days: Incorrect. - c. 10 days: Incorrect. - d. 5 days: Correct.

In a pie chart, the full circle represents 100% and the total central angle is 360°. So the central angle for any sector is: central angle = (percentage share / 100) × 360° From the pie-chart, cement corresponds to 20% of the total expenditure. Therefore: central angle = (20/100) × 360° = 72° So the correct option is (d) 72°. Why the other options are incorrect: - (a) 60° would correspond to 16.67% of the total, not 20%. - (b) 62° does not match any standard percentage sector here. - (c) 70° would correspond to 19.44%, which is not the given share. Hence, the correct answer is 72°.

From the bar graph, take the numbers of girls and boys for the years 2021, 2022, 2023 and 2024. Let the totals be: - Girls = G2021 + G2022 + G2023 + G2024 - Boys = B2021 + B2022 + B2023 + B2024 The ratio of the average number of girls to the average number of boys for 2021–2024 is (G2021 + G2022 + G2023 + G2024)/4 : (B2021 + B2022 + B2023 + B2024)/4 The 4 cancels, so this is simply: Total girls : Total boys Reading the values from the bar graph and adding them gives: - Total girls = 44 - Total boys = 52 So the required ratio is: 44 : 52 = 11 : 13 Therefore, the correct option is (a) 11:13. Why the others are incorrect: - (b) 13:11 is the reverse of the correct ratio. - (c) 11:15 does not match the totals from the graph. - (d) 15:11 is also the reverse/mismatched ratio and not supported by the data.

To find what percent one number is of another, we use the formula: (Part / Whole) × 100. Step 1: Identify the 'Part' and the 'Whole'. Part = 35 Whole = 70 Step 2: Set up the fraction: 35 / 70. Step 3: Simplify the fraction: 35/70 = 1/2. Step 4: Convert the fraction to a percentage: (1/2) × 100 = 50%. Reviewing the provided options: a. 40% b. 30% c. 20% d. 10% None of the provided options (a, b, c, or d) are correct, as the mathematically accurate answer is 50%.

In Microsoft PowerPoint, the shortcut Ctrl+D is specifically designed to 'Duplicate' the selected object or slide. When a slide is selected in the Slide Navigation pane, pressing Ctrl+D immediately creates an exact copy of that slide directly below it. Analysis of other options: - a. Ctrl+C: This is the 'Copy' command. It places the slide on the clipboard but does not create a duplicate until a 'Paste' command is issued. - b. Ctrl+X: This is the 'Cut' command. It removes the slide from its current position and places it on the clipboard. - c. Ctrl+V: This is the 'Paste' command. It inserts the content currently held on the clipboard into the presentation.

Step-by-step reasoning: 1. Ethernet networks have evolved through several physical media. Early Ethernet (10Base2, 10Base5) used coaxial cables, but these are now obsolete for general LANs. 2. Modern Ethernet standards (such as 10BASE-T, 100BASE-TX, 1000BASE-T) primarily utilize Twisted Pair cabling, specifically Unshielded Twisted Pair (UTP) categories like Cat5e, Cat6, and Cat6a. 3. Twisted pair is preferred for most modern local area networks (LANs) because it is cost-effective, flexible, and easy to install. 4. While Fiber optic cable (Option b) is used for high-speed backbones and long distances, it is not the 'most common' cable for general end-user device connectivity in a standard Ethernet network. 5. Shielded cable (Option d) is a specific type of twisted pair (STP) used in high-interference environments, but the general category is 'Twisted pair'. Therefore, Twisted pair cable is the most accurate answer for the majority of modern Ethernet deployments.

To find the time required for the investment to yield the given interest, we use the Simple Interest (SI) formula: Formula: SI = (P × R × T) / 100 Given values: - Principal (P) = ₹ 600 - Simple Interest (SI) = ₹ 108 - Rate of Interest (R) = 9% per annum - Time (T) = ? Rearranging the formula to solve for T: T = (SI × 100) / (P × R) Substituting the values: T = (108 × 100) / (600 × 9) T = 10800 / 5400 T = 2 years Verification of options: - Option (a) 4 years: Interest would be (600 * 9 * 4)/100 = ₹ 216 (Incorrect) - Option (b) 3 years: Interest would be (600 * 9 * 3)/100 = ₹ 162 (Incorrect) - Option (c) 2 years: Interest is (600 * 9 * 2)/100 = ₹ 108 (Correct) - Option (d) 1 year: Interest would be (600 * 9 * 1)/100 = ₹ 54 (Incorrect)

Step-by-step solution: 1. **Identify the given ratio**: The ratio of Cost Price (CP) to Selling Price (SP) is given as 20 : 23. 2. **Assign values**: Let the Cost Price (CP) be 20 units and the Selling Price (SP) be 23 units. 3. **Calculate Profit**: Profit = Selling Price - Cost Price = 23 - 20 = 3 units. 4. **Calculate Profit Percentage**: The formula for profit percentage is (Profit / Cost Price) × 100. Profit % = (3 / 20) × 100 5. **Simplify**: 3 × (100 / 20) = 3 × 5 = 15%. Verification of options: - Option (a) 10% is incorrect as it would require a profit of 2 units (22/20). - Option (b) 15% is correct. - Option (c) 20% is incorrect as it would require a profit of 4 units (24/20). - Option (d) 25% is incorrect as it would require a profit of 5 units (25/20).