Past Questions

Step-by-step calculation: 1. The expression is 36/5 + 36/5 + 36/5 + 36/5. 2. Since all terms have the same denominator (5), we can simply add the numerators: (36 + 36 + 36 + 36) / 5. 3. This is equivalent to 4 * (36/5). 4. 4 * 36 = 144. 5. 144 / 5 = 28.8. Reviewing the provided options (a. 246, b. 266, c. 146, d. 166), none of the options match the mathematically correct result of 28.8. There appears to be a typographical error in the question's options or the expression provided. However, based on the arithmetic provided in the prompt, the value is 28.8.

Let's break down the relationships step-by-step: 1. A is the brother of B: This means A is Male. A and B are siblings. 2. B is the sister of C: This means B is Female. A, B, and C are all siblings. 3. C is the father of D: This means C is Male and is the parent of D. 4. Relationship between A and D: Since A is the brother of C, and C is the father of D, A is the paternal uncle of D. 5. Determining D's relation to A: The question asks how D is related to A. While we know A is the uncle, the gender of D is not mentioned in the problem statement. D could be the son of C (making D the nephew of A) or the daughter of C (making D the niece of A). Since the gender of D is unknown, we cannot determine if D is a nephew or a niece. Therefore, the relationship cannot be established.

To find the number of ways to arrange the letters of a word, we use the formula for permutations of a multiset: n! / (n1! * n2! * ... * nk!), where 'n' is the total number of letters and 'n1, n2, etc.' are the frequencies of the repeating letters. 1. Count the total number of letters in the word 'APPLE': A, P, P, L, E = 5 letters. So, n = 5. 2. Identify the repeating letters: The letter 'P' appears 2 times. All other letters (A, L, E) appear 1 time each. 3. Apply the formula: Number of arrangements = 5! / 2! 5! (5 factorial) = 5 × 4 × 3 × 2 × 1 = 120 2! (2 factorial) = 2 × 1 = 2 4. Calculate the final result: 120 / 2 = 60. Therefore, there are 60 distinct ways to arrange the letters of the word 'APPLE'. Comparison with options: - Option a (30) is incorrect. - Option b (60) is correct. - Option c (90) is incorrect. - Option d (120) is incorrect as it fails to account for the repetition of the letter 'P'.

This is an analogy question that tests the relationship between a whole and its constituent parts. 1. **Analyze the first pair:** A 'Window' is the whole object, and a 'pane' is a single sheet of glass that makes up a part of that window. Therefore, the relationship is 'Whole : Part'. 2. **Apply the relationship to the second pair:** We are looking for the part that makes up a 'Book'. 3. **Evaluate the options:** - (a) Novel: A novel is a type of book, not a part of a book (Category : Example). - (b) Page: A page is a single sheet of paper that makes up a part of a book. This matches the 'Whole : Part' relationship. - (c) Cover: While a cover is part of a book, a window is primarily composed of panes, just as a book is primarily composed of pages. The 'pane' is the repeating unit of the window, and the 'page' is the repeating unit of the book. - (d) Shelf: A shelf is where a book is stored, not a part of the book (Object : Location). Therefore, 'Page' is the most accurate analog to 'pane'.

Step-by-step solution: 1. **Determine combined efficiency**: A and B together can complete the whole work in 5 days. Therefore, their combined work rate (A + B) is 1/5 of the work per day. 2. **Analyze the remaining work**: The problem states that A left after 2/3 of the work was completed. The remaining work is: 1 - 2/3 = 1/3 of the total work. 3. **Calculate B's efficiency**: B completed this remaining 1/3 of the work in 3 days. Work rate of B = (Work done) / (Time taken) = (1/3) / 3 = 1/9 of the work per day. 4. **Calculate time for B to finish the whole work**: If B's rate is 1/9 per day, the time taken by B alone to complete the entire work (1 unit) is: Time = 1 / (1/9) = 9 days. Verification of options: - Option (a) 9 days: Matches our calculation. - Option (b) 6 days: Incorrect. - Option (c) 5 days: This is the combined time for A and B, not B alone. - Option (d) 3 days: This is the time B took to finish only the remaining 1/3 of the work.

Step-by-step solution: 1. Let the total amount of money given to the boys be 'B' and the total amount given to the girls be 'G'. 2. According to the problem, the ratio of the total money divided among boys and girls is B:G = 8:9. 3. Let the amount each individual boy or girl receives be 'x'. 4. The total amount for boys is (Number of boys) × (Amount per boy), so B = 48 * x. 5. The total amount for girls is (Number of girls) × (Amount per girl), so G = N * x (where N is the number of girls). 6. Substitute these into the ratio: (48 * x) / (N * x) = 8 / 9. 7. The 'x' cancels out: 48 / N = 8 / 9. 8. Cross-multiply to solve for N: 8 * N = 48 * 9. 9. N = (48 * 9) / 8. 10. N = 6 * 9 = 54. Therefore, the number of girls is 54. Option (c) is correct. Options (a), (b), and (d) are incorrect as they do not satisfy the given ratio when the individual amounts are equal.

Let's break down the family relationships step-by-step: 1. **Lura and Liani**: Lura is the only son of Liani. (Liani is the mother, Lura is the son). 2. **Liani and Lawma**: Liani is the only daughter of Lawma. (Lawma is the grandparent of Lura). 3. **Sawmi and Liani**: Sawmi is the daughter-in-law of Liani. Since Lura is the only son of Liani, Sawmi must be married to Lura. 4. **Sawmi and Lala**: Sawmi is the mother of Lala. Since Sawmi is married to Lura, Lura is the father of Lala. 5. **Lala and Liani**: Liani is the mother of Lura, and Lura is the father of Lala. Therefore, Lala is the child of Liani's son. In family tree terminology, the child of one's son is a grandchild. Since the options provide 'Grandson' and there is no 'Granddaughter' option, and typically in these reasoning problems, the relationship is determined by the generational gap, Lala is the grandson of Liani. - Option (a) Son: Incorrect. Lura is the son. - Option (c) Husband: Incorrect. Lura is the husband of Sawmi. - Option (b) Grandson: Correct. Lala is the child of Liani's son.

In Microsoft PowerPoint, there are two primary file extensions for presentations: .pptx and .ppsx. 1. .pptx (PowerPoint Presentation): This is the standard editable format. When you open a .pptx file, it opens in 'Edit Mode' (Normal View), allowing the user to modify slides, text, and layout. 2. .ppsx (PowerPoint Show): This is the 'PowerPoint Show' format. When a user double-clicks a .ppsx file, the application bypasses the editing interface and launches the presentation directly into 'Slide Show mode' (Full Screen). This is ideal for distributing presentations to audiences who should view the slides without accidentally altering the content. Analysis of options: - Option (a) is incorrect because that describes a .pptx file. - Option (b) is incorrect because .ppsx files fully support all animations and transitions. - Option (c) is incorrect because 'read-only' is a file permission setting, not a file format behavior. While the user cannot easily edit it by double-clicking, they can still open it in PowerPoint's edit mode via the 'Open' menu. - Option (d) is correct as it describes the primary function of the .ppsx extension.

Let the three numbers be represented as follows: 1. Let the smallest number be $x$. 2. According to the problem, the middle number is 2 more than the smallest number, so the middle number = $x + 2$. 3. The difference between the largest number and the smallest number is 6, so the largest number = $x + 6$. Given that the sum of these three numbers is 41, we can set up the following equation: $x + (x + 2) + (x + 6) = 41$ Combine like terms: $3x + 8 = 41$ Subtract 8 from both sides: $3x = 41 - 8$ $3x = 33$ Divide by 3: $x = 11$ Verification: Smallest number = 11 Middle number = 11 + 2 = 13 Largest number = 11 + 6 = 17 Sum = 11 + 13 + 17 = 41. The conditions are satisfied. Comparing with the options: a. 8: $8 + 10 + 14 = 32$ (Incorrect) b. 9: $9 + 11 + 15 = 35$ (Incorrect) c. 10: $10 + 12 + 16 = 38$ (Incorrect) d. 11: $11 + 13 + 17 = 41$ (Correct)

Step-by-step solution: 1. Let the Selling Price (SP) be denoted as 'S'. 2. According to the problem, the Loss is 1/3 of the selling price. Therefore, Loss = (1/3)S. 3. We know the formula for Cost Price (CP) when there is a loss: CP = Selling Price + Loss. 4. Substituting the values: CP = S + (1/3)S = (4/3)S. 5. The formula for Loss Percentage is: (Loss / Cost Price) × 100. 6. Substituting the values into the formula: Loss% = [(1/3)S / (4/3)S] × 100. 7. The 'S' and the denominators '3' cancel out: Loss% = (1/4) × 100 = 25%. Verification of options: - Option a (15%): Incorrect calculation. - Option b (20%): This would occur if the loss was 1/4 of the CP, not 1/3 of the SP. - Option c (30%): Incorrect calculation. - Option d (25%): Matches the derived result.

A URL (Uniform Resource Locator) consists of several parts. The initial part, 'https://', is known as the 'scheme' or 'protocol'. 1. **HTTPS** stands for Hypertext Transfer Protocol Secure. It is the standard protocol used to communicate securely between a web browser and a web server. The 'S' at the end indicates that the data is encrypted using SSL/TLS. 2. **Option b (The server address)** is incorrect because the server address (or hostname) follows the protocol (e.g., 'www.google.com'). 3. **Option c (The file location)** is incorrect because the file location or path follows the domain name (e.g., '/images/logo.png'). 4. **Option d (The search engine)** is incorrect because a search engine (like Google or Bing) is a service/website, not a component of the URL structure itself.

The relationship in the original pair is 'dwelling : inhabitant', as an aerie is the nest or home of an eagle. Option 'd' (house : person) perfectly mirrors this relationship, as a house is the dwelling of a person. Option 'a' is incorrect because a capital is an administrative center, not a literal home. Option 'b' represents a prey-predator relationship between two animals. Option 'c' represents a part-to-whole or synonymous relationship, as a unit is a type of apartment.

Step-by-step solution: 1. Let the two numbers be represented as 4x and 5x, where 'x' is a common multiplier based on the given ratio 4 : 5. 2. According to the problem, the product of these two numbers is 980. Therefore, we can set up the equation: (4x) * (5x) = 980. 3. Simplify the equation: 20x² = 980. 4. Divide both sides by 20: x² = 980 / 20 = 49. 5. Take the square root of both sides: x = √49 = 7. 6. Now, find the two numbers: - Smaller number = 4x = 4 * 7 = 28 - Larger number = 5x = 5 * 7 = 35 7. The question asks for the larger number, which is 35. Verification of options: - Option (a) 20: Incorrect. - Option (b) 28: This is the smaller number, not the larger one. - Option (c) 35: Correct. - Option (d) 42: Incorrect.

By analyzing the different positions of the cube: 1. From the first position, the symbols adjacent to the 'Triangle' are 'Circle' and 'Star'. 2. From the second position, the symbols adjacent to the 'Triangle' are 'Cross' and 'Arrow'. 3. Since a face on a cube can have at most four adjacent faces, the four faces adjacent to 'Triangle' are 'Circle', 'Star', 'Cross', and 'Arrow'. 4. The only remaining symbol that must be opposite to the 'Triangle' is the 'Rectangle'. Therefore, the symbol opposite to the 'Rectangle' is the 'Triangle' (Option a). Other options ('Star', 'Arrow', and 'Circle') are incorrect because they are adjacent to the 'Triangle' and have different opposite faces.

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.

Step-by-step solution: 1. Let the three numbers be represented as 3x, 2x, and 5x, based on the given ratio 3:2:5. 2. According to the problem, the sum of their squares is 1862. Therefore, we set up the equation: (3x)² + (2x)² + (5x)² = 1862 3. Calculate the squares: 9x² + 4x² + 25x² = 1862 4. Combine the like terms: 38x² = 1862 5. Solve for x²: x² = 1862 / 38 x² = 49 6. Find the value of x: x = √49 = 7 7. Now, find the three numbers: First number = 3x = 3 * 7 = 21 Second number = 2x = 2 * 7 = 14 Third number = 5x = 5 * 7 = 35 8. The question asks for the smallest number, which is 14. Verification of options: - Option (a) 14: Correct (Smallest number). - Option (b) 21: Incorrect (This is the middle number). - Option (c) 35: Incorrect (This is the largest number). - Option (d) 7: Incorrect (This is the common ratio multiplier 'x', not one of the numbers).

To find the selling price after two successive discounts, we apply the discounts one after the other on the remaining balance. Step 1: Calculate the price after the first discount of 10%. First Discount = 10% of Rs. 500 = (10/100) * 500 = Rs. 50. Price after 1st discount = 500 - 50 = Rs. 450. Step 2: Calculate the price after the second discount of 10% (applied to the new price). Second Discount = 10% of Rs. 450 = (10/100) * 450 = Rs. 45. Final Selling Price = 450 - 45 = Rs. 405. Alternative Method (Formula): Selling Price = Marked Price * (1 - d1/100) * (1 - d2/100) Selling Price = 500 * (1 - 10/100) * (1 - 10/100) Selling Price = 500 * 0.9 * 0.9 Selling Price = 500 * 0.81 = Rs. 405. Analysis of options: - Option (a) Rs. 400 is incorrect; this would be the result if a single 20% discount was applied (500 - 100). - Option (b) Rs. 405 is correct. - Option (c) Rs. 410 and (d) Rs. 415 are mathematically incorrect based on the given percentages.

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.

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 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.

Step-by-step reasoning: 1. The standard English alphabet consists of 26 letters: A(1), B(2), C(3), D(4), E(5), F(6), G(7), H(8), I(9), J(10), K(11), L(12), M(13), N(14), O(15), P(16), Q(17), R(18), S(19), T(20), U(21), V(22), W(23), X(24), Y(25), Z(26). 2. The problem states that letters are switched in pairs: (1st, 2nd), (3rd, 4th), (5th, 6th), and so on. 3. This means for any pair (n, n+1) where n is odd, the letters swap positions. 4. We are looking for the 20th letter from the left in this new series. 5. Since 20 is an even number, it is the second member of the pair (19, 20). 6. According to the switching rule, the 19th letter and the 20th letter swap places. 7. In the original alphabet, the 19th letter is 'S' and the 20th letter is 'T'. 8. After swapping, the 19th position is occupied by 'T' and the 20th position is occupied by 'S'. 9. Therefore, the 20th letter from the left in the new series is 'S'.

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).

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 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).