UKPSC Prelims 2021 CSAT (Paper II) with Answers & Explanations

Explanation

The cost price of the item is calculated as 555 / 1.11 = 500. If the item is sold for 455, the loss is 500 - 455 = 45, which is a loss percentage of (45 / 500) * 100 = 9%.

Explanation

Rohit completes 1/t of the work in one hour. If he works for 1.5 (or 1 1/2) hours, the work completed is 3/(2t), making the unfinished part of the work equal to 1 - 3/(2t), which simplifies to (2t - 3)/(2t).

Explanation

The sequence alternates between single increasing letters (A, B, C, D) at positions 1, 4, 7, 10, and pairs of decreasing even-numbered letters (Z, X; V, T; R, P) at the remaining positions. Following this pattern, the ninth term is P (R - 2) and the tenth term is D (C + 1), which gives the missing terms as P, D.

Explanation

Assuming K represents division (due to a common typographical error where the division sign is replaced by a plus sign), the expression 30K2Q3J6T5 translates to 30 / 2 + 3 x 6 - 5. Following the BODMAS rule, this simplifies to 15 + 18 - 5, which equals 28.

Explanation

For any number p in the range 0 < p < 1, its reciprocal 1/p will always be greater than 1, and therefore greater than p itself. For example, if p = 0.5, then 1/p = 2, making the inequality p < 1/p (0.5 < 2) true.

Explanation

Let Varun's present age be x years. According to the given condition, his age after one year (x + 1) will be twice his age 12 years ago (x - 12), which gives the equation x + 1 = 2(x - 12). Solving this equation, we get x + 1 = 2x - 24, which simplifies to x = 25 years.

Explanation

Sumit's grandfather and Hemant's grandfather are brothers, which makes Sumit's father and Hemant's father first cousins. Therefore, Sumit and Hemant are second cousins, making Cousin the correct relationship.

Explanation

The total number of students is 60, and 15 of them chose football. To find the central angle for football in a pie chart, calculate the proportion of football students (15/60) and multiply it by the total degrees in a circle (360), which gives 90 degrees.

Explanation

Let the number of 1 rupee, 50 paise, and 25 paise coins be 2x, 3x, and 4x respectively. The total value is (2x * 1) + (3x * 0.5) + (4x * 0.25) = 4.5x rupees, which is equal to 180. Solving for x gives x = 40, so the number of 50 paise coins is 3 * 40 = 120.

Explanation

To find the year in which Christmas fell on Tuesday again, we calculate the number of odd days starting from December 25, 1979. The number of odd days between December 25 of consecutive years is 2 for leap years (1980 and 1984) and 1 for non-leap years. This gives 2 (for 1980) + 1 (1981) + 1 (1982) + 1 (1983) + 2 (1984) = 7 odd days, which equals exactly 1 week, making December 25, 1984 also a Tuesday.

Explanation

By setting up the equations based on the given conditions, let the fraction be x/y. The first condition gives (x - 5) / (y - 5) = 1/2, which simplifies to 2x - y = 5. The second condition gives (x + 2) / (y + 2) = 2/3, which simplifies to 3x - 2y = -2. Solving this system of linear equations yields x = 12 and y = 19, making the fraction 12/19.

Explanation

The coding pattern involves subtracting 5 from the alphabetical position of each letter. Applying this to CRANE, C (-5) is X, R (-5) is M, A (-5) is V, N (-5) is I, and E (-5) is Z, resulting in the code XMVIZ.

Explanation

A bag is normally used to carry books, and according to the given code, 'bag' is called 'dictionary'. Therefore, a dictionary is used to carry books.

Explanation

The question contains some OCR typographical errors where '+' and '÷' are represented as 't', and '÷' is represented as 'x'. Applying the correct mathematical operators, the mapping is: '÷' becomes '-', '+' becomes '×', '×' becomes '+', and '-' becomes '÷'. Substituting these into the expression gives 52 - 4 × 5 + 8 ÷ 2 = 52 - 20 + 4 = 36.

Explanation

The cyclist starts at a point, goes 30 km North, 40 km East, 20 km South, and finally 40 km West. This places him 10 km North of his starting point, making the distance from the start exactly 10 km.

Explanation

By the principle of inclusion-exclusion, the total number of students is the sum of those playing each sport minus those playing two sports plus those playing all three: 33 = 20 + 25 + 18 - 15 - 12 - 10 + x. Solving for x gives 7, which represents the number of students who play all three games.

Explanation

The phrase "only daughter of your father" spoken to a woman refers to the woman herself. Since the person's mother is that only daughter, the woman is the mother of the person.

Explanation

The pattern is to divide the first number by the second number and find the sum of the digits of the resulting quotient. For 246 and 2, 246 divided by 2 is 123, and the sum of its digits (1 + 2 + 3) is 6; for 870 and 3, 870 divided by 3 is 290, and the sum of its digits (2 + 9 + 0) is 11. Following this, 735 divided by 5 is 147, and the sum of its digits (1 + 4 + 7) is 12.

Explanation

Truth and falsity are properties that belong exclusively to propositions, which are statements that make assertions about reality and can either correspond to facts (true) or not (false). In contrast, arguments are evaluated in terms of being valid or invalid, rather than true or false.

Explanation

In options b, c, and d, the first word represents a venue or space where the entities denoted by the second word are typically located or found. Option a does not follow this pattern, as planets are not found inside or on the Moon.

Explanation

The sequence consists of three parts in each term: a first number, a middle letter, and a last number. The first numbers increase by successive odd numbers (2 + 5 = 7, 7 + 7 = 14, 14 + 9 = 23, 23 + 11 = 34, 34 + 13 = 47), the middle letters go backward in alphabetical order (Z, Y, X, W, V, U), and the last numbers are consecutive odd numbers increasing by 2 (5, 7, 9, 11, 13, 15), which gives the next term as 47U15.

Explanation

In options a, b, and c, the product of the first two digits equals the third digit (1 x 2 = 2, 3 x 2 = 6, and 2 x 2 = 4), whereas option d does not follow this pattern (3 x 3 is 9, not 7). Additionally, 337 is the only odd and prime number among the options.

Explanation

For a number to be divisible by 8, the number formed by its last three digits must be divisible by 8. In 97468x4, the last three digits form the number 8x4, which is divisible by 8 when x is 2 (824 / 8 = 103) or 6 (864 / 8 = 108), making 2 the least value.

Explanation

The number A can be written as the product of its prime factors to find the total power of 3. Here, 81 is 3 raised to the power of 4, 117 is 9 times 13 (which contains 3 raised to the power of 2), 63 is 9 times 7 (which contains 3 raised to the power of 2), and 46 has no factor of 3. Adding the exponents of 3 gives 4 + 2 + 2 = 8, meaning the maximum value of b is 8.

Explanation

The numbers of the form 7k + 3 lying between 11 and 100 start from 17 (where k = 2) and end at 94 (where k = 13). The total number of such terms is calculated as 13 - 2 + 1 = 12.

Explanation

The pattern for both series is given by the formula: T(n) = T(n-1) + (n-1)^3 - S(n-1) where S is the sequence 0, 3, 10, 21, 36... (having a constant second difference of 4).

Applying this pattern to the second series starting with 5: T1 = 5 T2 = 5 + 1^3 - 0 = 6 a = 6 + 2^3 - 3 = 11 b = 11 + 3^3 - 10 = 28 c = 28 + 4^3 - 21 = 71 d = 71 + 5^3 - 36 = 160

Explanation

Since D is 0 and the digits are distinct, the sum of the units digits A + A must end in 0, which means A must be 5 (as A cannot be 0). Substituting A = 5 gives B = 9 and C = 2, which satisfies the addition 295 + 225 = 520.

Explanation

Hiring Mayank for a role like production or finance where hard work is highly valued, while keeping him away from marketing roles that require fluent English, is the most pragmatic and balanced managerial decision. This approach utilizes his strengths while ensuring that job requirements are properly met.

Explanation

Let the larger number be x and the smaller number be y. Subtracting half of the smaller number (y/2) from both gives the resulting numbers as (x - y/2) and (y/2). Since the larger resulting number is three times the smaller, we have x - y/2 = 3(y/2), which simplifies to x = 2y, giving a ratio of 2:1.

Explanation

The statement proposes mid-day meals as a means to increase school attendance, which directly assumes that the meals will attract children to school (Assumption I). Furthermore, this initiative implicitly assumes that children who lack proper nutrition or good food at home will be motivated to attend school for the meals (Assumption II). Therefore, both assumptions I and II are implicit.

Explanation

The total monthly household expenditure is the sum of all items, which is 4500 + 1800 + 650 + 2400 = 9350. The percentage portion represented by rent is calculated as (1800 / 9350) * 100, which equals approximately 19.25%.

Explanation

Based on the given information, if we assume a standard total of 100 children, there are 40 girls and 60 boys. Since 50 children are of medium height and 20 of them are boys (one third of 60), there are 30 girls of medium height, leaving 10 girls who are either tall or short. Since we cannot distinguish between tall and short girls with the given data, the exact number of tall girls cannot be determined.

Explanation

The pattern followed in each transition is +2, -2, -2 for the positional values of the letters. Applying this to PKI, we get P (+2) = R, K (-2) = I, and I (-2) = G, which gives RIG.

Explanation

The 21st letter from the right corresponds to the 6th letter from the left, which is F. The 16th letter from the left is P. The letter midway between the 6th (F) and 16th (P) positions is the 11th letter, which is K.

Explanation

There are exactly 3 pairs of letters (P-R, E-L, and A-B) in the word 'IMPERISHABLE' that have the same number of letters between them in the word as in the alphabetical sequence, in the same order.

Explanation

The number of days between August 15, 1988, and August 15, 1989, is 365 days, which equals 52 weeks and 1 odd day because 1989 is an ordinary year. Therefore, Independence Day in 1989 was celebrated one day later than in 1988, which is Thursday.

Explanation

By comparing the letter positions in the words BAKE (5796) and FIRE (3146), we can determine the individual codes for the letters: F is 3, E is 6, A is 7, and R is 4. Combining these gives the code for FEAR as 3674, which corresponds to option D.

Explanation

Comparing the statements 'you are good' (256) and 'good and bad' (358), the common word 'good' is coded as 5. Comparing 'we are bad' (637) and 'good and bad' (358), the common word 'bad' is coded as 3. Therefore, in the phrase 'good and bad' represented by 358, the remaining word 'and' must be coded as 8.

Explanation

Converting the fractions into decimals gives 4/5 = 0.8, 2/3 ≈ 0.67, 1/2 = 0.5, and 3/8 = 0.375. Arranging them from largest to smallest results in 4/5, 2/3, 1/2, 3/8, which corresponds to option a.

Explanation

The volume of a sphere is proportional to the cube of its radius. Therefore, if the ratio of the radii of two spheres is 1 : 2, the ratio of their volumes is (1)^3 : (2)^3, which equals 1 : 8.

Explanation

Deer, Horse, and Giraffe are all herbivorous animals, whereas a Jackal is a carnivorous (or omnivorous) animal, making it the odd one out.

Explanation

By facing his home, the boy's forward steps are towards home and his backward steps are towards the school. Since he takes two steps backward for every one step forward, his net movement will be in the backward direction, which leads him to the school.

Explanation

According to the statements, Roshan, Mohan, and Rohan are all studying Geometry, as mentioned in statements 3 and 4. Sohan is only studying Physics, Chemistry, and English, making him the only one who is not studying Geometry.

Explanation

By substituting the symbols according to the given rules, option b becomes 5 * 2 + 1 = 3 * 4 - 1. Calculating both sides, we get 11 = 11, which is mathematically correct.

Explanation

Based on the conditions, Mohan is in the fifth position, meaning exactly four boys are older than him (occupying positions 1 to 4) and two are younger. Since Shyam is older than Prem, and Prem is not the youngest, Shyam, Ram, and Manohar must all be in the top four along with Vivek. Since Manohar cannot be the eldest, Vivek must be the oldest boy in the group.

Explanation

The coding pattern for 'REMOTE' to 'ROTEME' rearranges the letters from positions 1-2-3-4-5-6 to 1-4-5-2-3-6. Applying this same pattern to the word 'PICNIC' (1:P, 2:I, 3:C, 4:N, 5:I, 6:C) yields 'PNIICC' (with 'PNICC' being a minor typographical error in the question for 'PNIICC').

Explanation

Let B be the number of benches and S be the number of students. Based on the given conditions, we can set up the equations S = 4(B - 3) and S = 3B + 3. Solving these simultaneously gives B = 15 and S = 48, meaning the number of students in the class is 48.

Explanation

In 3 days, A and B together complete 15 units of the total 30 units of work, assuming total work is 30 units (with A's efficiency as 2 units/day and B's as 3 units/day). The remaining 15 units of work are completed by B alone at his efficiency of 3 units/day, which takes 5 days. Thus, B worked alone for 5 days.

Explanation

One truck carries 3 tons per day, which means it can carry 90 tons in 30 days. To carry a total of 540 tons in 30 days, the number of trucks required is 540 divided by 90, which equals 6 trucks.

Explanation

The first eleven natural numbers are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, and 11. The arithmetic mean of these numbers is their sum (66) divided by their total count (11), which equals 6.

Explanation

The pattern in the given equations is that the sum of the digits of the first number is multiplied by the sum of the digits of the second number. For 38 + 15, we get (3 + 8) * (1 + 5) = 11 * 6 = 66, and for 29 + 36, we get (2 + 9) * (3 + 6) = 11 * 9 = 99. Applying this pattern to 82 + 44, we get (8 + 2) * (4 + 4) = 10 * 8 = 80.

Explanation

Arranging the words alphabetically, the first letter of difference determines the order: Telegraph (fifth letter g) is first, followed by Telemark (fifth letter m). For the remaining words starting with Telep, the sixth letter determines the sequence: Telepathy (sixth letter a) comes first, followed by Telephone (sixth letter h), and then Teleprinter (sixth letter r), giving the final sequence as (i), (iv), (v), (ii), (iii).

Explanation

The perimeter of a rectangle is given by 2(a + b) = 36, which simplifies to a + b = 18, where a and b are positive integers representing the side lengths. The unique integer pairs (a, b) with a <= b that satisfy this equation are (1,17), (2,16), (3,15), (4,14), (5,13), (6,12), (7,11), (8,10), and (9,9). Since a square is a special type of rectangle, there are a total of 9 possible rectangles.

Explanation

The man starts by facing South. Turning 135 degrees anti-clockwise puts him in the North-East direction, and a subsequent 180-degree turn in the clockwise direction reverses his facing to the opposite direction, which is South-West.

Explanation

The number of smaller cubes with no face painted is given by the formula (n - 2)^3, where n is the ratio of the edge of the larger cube to the edge of the smaller cube. Here, n = 6 / 1 = 6, so the number of unpainted cubes is (6 - 2)^3 = 4^3 = 64.

Explanation

The statement Fortune favors the brave implies that to achieve success (fortune), one needs to be brave and take risks, which makes Conclusion I logically follow. Conclusion II is a completely different philosophical quote about cowards that cannot be derived from the given statement.

Explanation

The series is formed by pairs of numbers where the second number in each pair is the square of the first: (1, 1), (3, 9), (6, 36), (10, 100), and (15, 225). The first numbers of the pairs (1, 3, 6, 10, 15) increase by consecutive integers (+2, +3, +4, +5), making the missing term 15.

Explanation

By writing 9 as 3 squared, the given equation 9^x = 9 / 3^x can be rewritten in terms of base 3 as (3^2)^x * 3^x = 3^2. This simplifies to 3^(3x) = 3^2, which gives 3x = 2, and therefore x = 2/3.

Explanation

Let the third number A be 100, which makes B equal to 85 and C equal to 68. The difference between B and C is 17, and 17 as a percentage of B (85) is 20 percent. Therefore, C is 20 percent less than B.

Explanation

The numbers 22, 26, 34, and 46 when divided by 2 yield prime numbers (11, 13, 17, and 23 respectively), whereas 72 divided by 2 is 36, which is a composite number. Alternatively, the differences between consecutive terms (4, 8, 12) suggest the next term should be 46 + 16 = 62 instead of 72.

Explanation

The relationship between the first pair AE and DH is a shift of +3 positions for each letter, as A (+3) = D and E (+3) = H. Applying the same logic to JN, J (+3) = M and N (+3) = Q, which gives the pair MQ.

Explanation

The expression can be simplified by multiplying the exponents to get (0.000064)^(1/6). Since 0.000064 is equal to (0.2)^6, taking the sixth root yields 0.2, which corresponds to option B.

Explanation

The volume of a cube with edge length a is V = a^3, which gives the edge length a = V^(1/3). Since a cube has 12 edges, the total length of its edges is 12a = 12V^(1/3).

Explanation

The question contains a typographical error where "q" was misprinted as "p" in the main equation. By replacing "3p" with "3q" to make it mathematically consistent with the options, the equation can be simplified using the identity (a + b)(a - b) = a^2 - b^2 to yield 12xq = 8yp, which simplifies to x/y = 2p/3q.

Explanation

When the trains move in the same direction, the relative speed is the difference in their speeds. The total distance to be covered to completely pass each other is the sum of their lengths, which is 130m + 110m = 240m. Since it takes 1 minute (60 seconds) to pass each other in the same direction, the difference in their speeds is 240 meters divided by 60 seconds, which equals 4 m/sec.

Explanation

Using the compound interest formula A = P(1 + R/100)^t, we have 1331 = 1000(1.1)^t, which simplifies to 1.331 = (1.1)^t. Since 1.1 cubed is 1.331, the time required is 3 years.

Explanation

Self-directed learning is best described as active learning because the text emphasizes that individuals take the initiative in their own learning process rather than passively waiting to be taught.

Explanation

According to the text, the author refers to the modern environment as today's instructive environment, which makes self-directed learning essential. Therefore, option B is the correct answer.

Explanation

The passage explicitly states that one of the primary reasons for the need for self-directed learning is the convincing evidence that individuals who take the initiative in their learning process learn more things and learn better than those who wait to be taught. This directly supports the choice that self-directed learning helps people to learn more things and learn better.

Explanation

Autocracy is a system of government where supreme power is held by a single person. In contrast, plutocracy is rule by the wealthy, oligarchy is rule by a small group, and theocracy is rule by religious leaders.

Explanation

The passive form of "The Romans expected to conquer Carthrage" is correctly represented by "It was expected by the Romans that they would conquer Carthrage." This structure uses the dummy pronoun "it" as the subject, transforms the main verb to the passive "was expected", and expands the infinitive clause into a subordinate clause.

Explanation

The word competition refers to an event or contest in which people compete for supremacy or a prize. Among the given options, contest is the most accurate synonym as it also denotes a formal game, match, or struggle for victory.

Explanation

The word slumber means a state of sleep or to sleep peacefully. Therefore, sleep is the most appropriate synonym among the given options.

Explanation

According to the given passage, "किसी राष्ट्र की सम्प्रता का मूल्यांकन हम उसकी संस्कृति के आधार पर कर सकते हैं" which translates to "we can evaluate the civilization of any nation on the basis of its culture". Therefore, option d (संस्कृति) is the correct answer.

Explanation

The passage explicitly states "यों तो संस्कृति और सम्प्रता में घनिष्ठ सम्बन्ध है", which means there is a close relationship between culture (संस्कृति) and "samprata" (सम्प्रता). Therefore, option b is the correct answer.

Explanation

दिए गए गद्यांश के अनुसार, संस्कृति मानव जीवन को श्रेष्ठ एवं उन्नत बनाने की साधनाओं का नाम है। यह वाक्य गद्यांश में स्पष्ट रूप से उल्लेखित है, इसलिए विकल्प C सही उत्तर है।

Explanation

गद्यांश की अंतिम पंक्ति के अनुसार, प्रकृति का मानव जीवन को प्रभावित करने में बड़ा महत्त्वपूर्ण हाथ रहता है। इसलिए विकल्प C (प्रकृति का) सही उत्तर है।

Explanation

'सांस्कृतिक' शब्द का निर्माण 'संस्कृति' मूल शब्द में 'इक' प्रत्यय लगाने से हुआ है। जब 'संस्कृति' में 'इक' प्रत्यय जुड़ता है, तो आदि स्वर 'अ' का 'आ' हो जाता है, जिससे यह शब्द 'सांस्कृतिक' बनता है।

Explanation

The word 'विरासत' is of Arabic origin (wirāsat) and has been assimilated into the Hindi language, which makes it a foreign loanword or 'विदेशी' शब्द. Therefore, it belongs to the विदेशी category.

Explanation

The word 'vibhooti' means wealth, greatness, or ash, and is not a synonym for 'pragati' (progress). The other options, 'unnati', 'abhyudaya', and 'utthan', all mean progress, rise, or development.

Explanation

मर्त्य का अर्थ मरणशील या मानव होता है, जो दिए गए विकल्पों में मानव का सबसे उपयुक्त पर्यायवाची है। अन्य विकल्प जैसे अमर्त्य (देवता), अज (अजन्मा/ब्रह्मा), और माधव (कृष्ण) मानव के पर्यायवाची नहीं हैं।

Explanation

अंश के अनुसार, संस्कृति मानव जीवन को श्रेष्ठ और उन्नत बनाने की साधनाओं का नाम है और सभ्यता (पाठ में 'सम्प्रता' मुद्रित) उन साधनाओं के फलस्वरूप प्राप्त हुई 'जीवन प्रणाली' का नाम है। इसलिए, 'सभ्यता' का अर्थ 'जीवन प्रणाली' है।

Explanation

मूल्यांकन का सही सन्धि-विच्छेद मूल्य + अंकन है। यहाँ दीर्घ स्वर सन्धि का नियम लागू होता है, जिसमें अ + अ मिलकर आ हो जाता है।

Explanation

The antonym of the word महत्वपूर्ण (meaning important or significant) is महत्वहीन (meaning unimportant or insignificant). Therefore, option B is the correct opposite word.

Explanation

इस गद्यांश में मुख्य रूप से सभ्यता और संस्कृति के बीच के संबंध, अंतर और मानव जीवन में उनके महत्व को परिभाषित किया गया है। इसलिए, इस गद्यांश का सबसे उपयुक्त शीर्षक सभ्यता और संस्कृति है।

Explanation

अंश के अनुसार, प्रत्येक राष्ट्र की अपनी एक सांस्कृतिक धरोहर होती है जिसके बल पर वह प्रगति के पथ पर अग्रसर होता रहता है। इसलिए विकल्प C (सांस्कृतिक धरोहर) सही उत्तर है।