MP Police Constable Mock Test 8 — 100 MCQs in Exam Pattern

Panini is credited with writing the foundational treatise of Sanskrit grammar, the Ashtadhyayi.

This is Article 20(2), the double jeopardy clause.

The words are “prosecuted and punished”.

Both must happen before the second trial is barred.

Santosh Yadav is the first woman in the world to have summited Mount Everest twice, first in May 1992 and again in May 1993.

Wheat needs cool winters and moderate water, and concentrates in the Indo-Gangetic Plains.

Gandhinagar is the capital. It is a planned city near Ahmedabad. Ahmedabad is the largest city but not the capital.

The Khilafat Movement protested British treatment of the Ottoman Caliph after World War I, since Indian Muslims saw the Caliph as the symbolic head of the global Muslim community. The Treaty of Sèvres (1920) threatened to dismantle the Caliphate entirely.

Sikkim is the answer. Sikkim decided to go organic in 2003 and reached full organic status at the end of December 2015. The Prime Minister announced it at Gangtok on 18 January 2016. Memory hook: 2003 plan, 2016 announcement.

The correct answer is Param Vir Chakra, Maha Vir Chakra, Vir Chakra. The three wartime awards rank in that order. The Param Vir Chakra is the highest. The Vir Chakra is the third.

The other orders put the Maha Vir Chakra or Vir Chakra first. That is wrong. The Param Vir Chakra always comes first.

Memory hook: Param, Maha, Vir: big, bigger, brave.

The Intergovernmental Committee inscribed it at its 16th session in Paris in December 2021. PIB reported it on 15 December 2021.

The answer is Gargi. She asked him a chain of questions on what holds up the world. The text records that the Brahmanas gave her leave for two more questions. Memory hook: Gargi asked, was warned, asked again.

The answer is the Lok Sabha. Article 75(3) says the Council of Ministers is collectively responsible to the House of the People. Why the others fail: the President acts on ministerial advice. The Rajya Sabha and the Court do not hold ministers to account in this way. Memory hook: responsibility to the lower House makes a system parliamentary.

These lacustrine terraces of the Kashmir Valley are called Karewas, locally known as ‘Vudr.’

Chhattisgarh was carved out of Madhya Pradesh on 1 November 2000. Raipur is its capital.

Chewang Norphel is known as the ‘Ice Man of Ladakh.’

French aviator is the answer. He was a pioneer of aviation and a war hero. Paris named its new tennis stadium after him in 1928. Memory hook: Garros = aviator, 1928 stadium.

PM-KISAN was launched in February 2019, with payments made effective retroactively from 1 December 2018.

India’s Standard Meridian, 82.5°E longitude, passes through Mirzapur in Uttar Pradesh.

El Niño occurs when the central and eastern Pacific, off Peru, warms up more than usual.

DRDO was founded in 1958. It was formed to give India an in-house defence research arm.

The correct answer is 8. The golds came in 1928, 1932, 1936, 1948, 1952, 1956, 1964 and 1980. That is a record in Olympic hockey.

The answer is West Bengal. The Ministry of Home Affairs lists eight North Eastern states, and West Bengal is not among them.

The answer is Kangchenjunga. It is 8,586 metres tall. Only Everest and K2 are taller. Why the others fail: Lhotse and Makalu are lower. Nanda Devi is far lower, though it lies wholly in India. Memory hook: Everest, K2, Kangchenjunga.

Kurma, the tortoise, supports Mount Mandara so that the gods and demons can churn the ocean for amrit.

The answer is Khangchendzonga National Park. It was inscribed in 2016. It meets both cultural and natural criteria. Why the others fail: Kaziranga, Nanda Devi and the Sundarbans are natural sites. Memory hook: Sikkim’s peak is both nature and sacred.

This question came in an RPSC College Lecturer (Drawing-II) paper dated 28 June 2016. Anish Kapoor, a Turner Prize winner, designed the Orbit.

The ‘Vedatrayi’ (three Vedas) comprises the Rigveda, Samaveda, and Yajurveda, with the Atharvaveda added later as a fourth.

Bhagwan Ahir was the chief organiser of the Chauri Chaura incident, on 4 February 1922.

Mawsynram, in Meghalaya’s East Khasi Hills, holds the Guinness World Record for the highest average annual rainfall, about 11,871 mm.

The award, presented by France Football magazine, recognises the year’s best male and female footballers.

Ashoka’s roughly 33 surviving inscriptions fall into four groups: Major Rock Edicts, Minor Rock Edicts, Major Pillar Edicts, and Minor Pillar Edicts.

Substitute the real operations: − becomes ×, × becomes +, + becomes ÷, and ÷ becomes −. The expression becomes: (9 × 3) + 8 ÷ 4 − 6. Solve the bracket first. 9 × 3 = 27. The expression is now: 27 + 8 ÷ 4 − 6. Division comes next. 8 ÷ 4 = 2. Working left to right, 27 + 2 = 29, then 29 − 6 = 23. So the value of the expression is 23.

This sequence follows how milk is traditionally processed into ghee. Milk is the raw starting material from the animal. Milk is set with a culture and turns into curd. Curd is churned to separate out butter. Butter is then heated slowly to produce ghee. So the order is Milk, Curd, Butter, Ghee, matching option D.

The operations alternate between multiplying by 2 and adding 3. Check: 4×2=8, 8+3=11, 11×2=22, 22+3=25, 25×2=50, 50+3=53. The next operation in turn is multiply by 2. So 53×2 gives 106.

In FISH, each letter is shifted back by 2 places: F-2=D, I-2=G, S-2=Q, H-2=F, giving DGQF, which matches. So the rule is: shift every letter back by 2 places. Apply the same rule to HORSE: H-2=F, O-2=M, R-2=P, S-2=Q, E-2=C. So the answer is FMPQC.

After the swap, Simran sits in Naveen’s old seat. That seat’s rank from the left was fixed at 16, Naveen’s original rank. We’re told this same seat is now 20th from the right. Total = rank from left + rank from right − 1 = 16 + 20 − 1 = 35. So the row has 35 students.

Look at Row 1. Multiply the first two numbers: 9 x 6 = 54. Divide that by 3: 54 / 3 = 18. This matches the third number shown. The rule is: third number = (first x second) divided by 3. Apply it to Row 2: 12 x 9 = 108. Divide by 3: 108 / 3 = 36.

Each term equals the sum of the two terms before it, minus 1. Check: 5+7-1=11, 7+11-1=17, 11+17-1=27, 17+27-1=43. The same rule gives the next term. So it is 27+43-1, which is 69.

Four cousins sit in a row of 4 positions, numbered 1 to 4 from the left. Aarav sits at the rightmost position, so Aarav is at position 4. Bina sits immediately to the left of Aarav, so Bina is at position 3. Only positions 1 and 2 remain, for Zoya and Chirag. Position 2 sits immediately next to Bina’s position 3. Zoya does not sit immediately next to Bina, so Zoya is not at position 2. So Zoya sits at position 1, and Chirag sits at position 2. The full row is: Zoya, Chirag, Bina, Aarav. In a row of four, second from the right is position 3. Bina is the one sitting at position 3. So Bina sits second from the right.

The cube has side 6, so it is cut into 6 x 6 x 6 = 216 unit cubes. Fully hidden cubes touch none of the outer faces. Their count is (N-2)^3, using N as the side length. Here N-2 = 6-2 = 4, so (N-2)^3 = 4^3 = 64. Face-center cubes, with one painted face, number 6 x (N-2)^2 = 6 x 16 = 96. Edge cubes, with two painted faces, number 12 x (N-2) = 12 x 4 = 48. The total of 216 unit cubes is not the number asked for here. The fully unpainted cubes number 64.

The Venn diagram shows how many people like Cricket, Football, and Hockey. Only Cricket: 22. Only Football: 17. Only Hockey: 13. Cricket and Football only: 9. Football and Hockey only: 6. Cricket and Hockey only: 5. All three: 4. This question asks for one region’s number directly, with no other region added. So the answer is 22.

Statement 1 says all granules are particles. Statement 2 says some particles are crystals. The shared term ‘particles’ is not fully pinned down in either statement. We only know granules sit somewhere inside particles. We only know some particles, not necessarily the granule ones, are crystals. The crystal-particles could easily be a completely different set from the granules. So conclusion I, some granules are crystals, is not guaranteed. Conclusion II says the same thing in reverse, so it fails for the same reason. Neither conclusion is forced true by the statements. The correct answer is: neither conclusion I nor II follows.

Five neighbours sit in a row of 5 positions, numbered 1 to 5 from the left. Varun sits exactly in the middle, so Varun is at position 3. Yash sits at the leftmost position, so Yash is at position 1. Uday sits immediately to the right of Varun, so Uday is at position 4. Only positions 2 and 5 remain, for Wasim and Tarun. Wasim does not sit at the rightmost position, so Wasim is not at position 5. So Wasim sits at position 2, and Tarun sits at position 5. The full row is: Yash, Wasim, Varun, Uday, Tarun. Yash is at position 1, and Uday is at position 4. Positions 2 and 3 sit between them, held by Wasim and Varun. So exactly 2 people sit between Yash and Uday.

Each term is 3 times the term before it. Check: 3×3=9, 9×3=27, 27×3=81, 81×3=243. The pattern holds throughout. So the next term is 243×3, which is 729.

The gap between terms itself grows: +4, then +6, then +8, then +10. Each gap is 2 more than the last one. The next gap should be +12. So the next term is 33+12, which is 45.

The given set is (5, 9, 13). Check the gap between the first two numbers: 9 – 5 = 4. Now check the gap between the last two numbers: 13 – 9 = 4. Both gaps are equal. So the rule is: the three numbers rise by the same fixed gap each time. Test (6, 10, 16): the gaps are 10 – 6 = 4, and 16 – 10 = 6. These gaps differ, so it fails. Test (11, 15, 20): the gaps are 15 – 11 = 4, and 20 – 15 = 5. These gaps differ, so it fails. Test (10, 14, 18): the gaps are 14 – 10 = 4, and 18 – 14 = 4. These gaps match, so it works. Test (2, 6, 9): the gaps are 6 – 2 = 4, and 9 – 6 = 3. These gaps differ, so it fails. Only (10, 14, 18) follows the rule. So the answer is (10, 14, 18).

Devendra is the father of Ritika, so Ritika is Devendra’s daughter. Kamla is the wife of Devendra, so Kamla is Ritika’s mother. Ritika is the wife of Sanjay, so Sanjay is Ritika’s husband. Sanjay’s own mother, Vimla, does not change this relationship. Kamla is the mother of Sanjay’s wife. A wife’s mother is called a mother-in-law. So Kamla is related to Sanjay as his mother-in-law.

The given pair is 4 : 64. Check the cube of 4: 4 x 4 x 4 = 64, which matches. So the rule is: the second number is the cube of the first. Apply the same rule to 5: 5 x 5 x 5 = 125. So the answer is 125.

Each term is the sum of the two terms before it. Check: 2+3=5, 3+5=8, 5+8=13, 8+13=21. The same rule gives the next term. So it is 13+21, which is 34.

After the swap, Isha sits in Rakesh’s old seat. That seat’s rank from the right end was fixed at 11. New rank from left = total − rank from right + 1. New rank from left = 42 − 11 + 1 = 32. So Isha’s new rank from the left is 32nd.

Take point A as the origin (0,0). Facing North, Sarita walks 8 km to (0,8). She turns right, so she now faces East. She walks 8 km east to (8,8). She turns right again, so she now faces South. She walks 8 km south to (8,0). Point B is (8,0). This is 8 km east of A, with no north-south offset. So point B is due East of point A.

Statement 1 says all rivets are fasteners. Statement 2 says all bolts are fasteners. Here ‘fasteners’ is the shared term, but it sits as the predicate in both statements. This is different from a chain, and it proves nothing about rivets and bolts directly. Rivets and bolts could be two completely separate groups inside fasteners, with no overlap at all. So conclusion I, some rivets are bolts, is not guaranteed. Conclusion II claims all bolts are rivets, an even stronger, unsupported claim. Both conclusions rely on a connection the statements never actually make. This is a classic trap: sharing one larger category does not link two smaller groups. The correct answer is: neither conclusion I nor II follows.

Each group is 3 letters in a row. The starting letter moves ahead by 5 places each time. B is 2nd, G is 7th, L is 12th, so the next start is 12+5=17, which is Q. The next group is Q, R, S in a row: QRS.

Take point A as the origin (0,0). Kavita walks 20 km north to (0,20). She turns right, faces East, and walks 14 km to (14,20). She turns right again, faces South, and walks 6 km to (14,14). Point B is (14,14). Point B is 14 km east and 14 km north of A, so point B lies North-East of point A. The question asks the reverse: where is A from B. The reverse of North-East is South-West. So point A is South-West of point B.

Take 20 May 2025 as the known reference day, a Tuesday. The span from 20 May 2025 to 20 May 2026 passes through February 2026. The year 2026 does not divide evenly by 4, so it is not a leap year. February 2026 has only 28 days, so no extra day is added. The full span is therefore a normal 365 days. Divide 365 by 7. That gives 52 full weeks, with a remainder of 1 day. Move 1 day forward from Tuesday. Tuesday plus 1 is Wednesday. So 20 May 2026 falls on a Wednesday.

Compare the input with Step 1. amber moves to the front of the line. It is the next word in alphabetical order in the input. Compare Step 1 with Step 2. coral moves to the front next. So the rule is: each step moves the next word in alphabetical order to the front of the line. Every number is left alone. It only shifts position as the words move around it. This rule fits every step shown above. Apply the same rule forward to reach Step 3. By Step 3, the front block holds 3 words, in this order: amber, coral, violet. So the answer is: amber coral violet 47 22.

Seven employees sit in a row of 7 positions, numbered 1 to 7 from the left. Zainab sits exactly in the middle, so Zainab is at position 4. Yogesh sits immediately to the right of Zainab, so Yogesh is at position 5. Abhishek sits immediately to the left of Zainab, so Abhishek is at position 3. Vikas sits at the leftmost position, so Vikas is at position 1. Dinesh sits at the rightmost position, so Dinesh is at position 7. Only positions 2 and 6 are left, for Chandni and Bhavesh. Bhavesh does not sit immediately next to Vikas. The only position next to Vikas is position 2. So Bhavesh cannot be at position 2. This means Bhavesh sits at position 6, and Chandni sits at position 2. The full row is: Vikas, Chandni, Abhishek, Zainab, Yogesh, Bhavesh, Dinesh. Bhavesh is at position 6, and position 7 is immediately to his right. Dinesh is the one sitting at position 7. So Dinesh sits immediately to the right of Bhavesh.

Compare the input with Step 1. Two moves happen together in each step. The next largest number goes to the front: that is 91. At the same time, the next word in reverse alphabetical order goes to the end: that is cumin. In Step 2, 58 moves to the front and clove moves to the end, together. So the rule is: each step sends the next number to the front and the next word to the end, at the same time. This rule fits every step shown above. Apply the same rule forward to reach Step 3. By Step 3, the front holds 91, 58, 23. The end holds cumin, clove, anise. So the answer is: 91 58 23 cumin clove anise.

Kiran is the mother of Neha, so Neha is Kiran’s daughter. Kiran is the sister of Ramesh, so they share the same parents. Ramesh is the father of Ojas, so Ojas is Ramesh’s son. Neha’s mother and Ojas’s father are siblings. Children of siblings are cousins to each other. So Neha is related to Ojas as his cousin.

The given set is (3, 2, 16). Square the first number: 3 x 3 = 9. Now double that square: 9 x 2 = 18. Then subtract the second number: 18 – 2 = 16. This matches. So the rule is: third number = (2 x first squared) minus second number. Test (2, 1, 8): 2 squared is 4, doubled is 8, and 8 – 1 = 7, not 8. This fails. Test (5, 3, 45): 5 squared is 25, doubled is 50, and 50 – 3 = 47, not 45. This fails. Test (4, 5, 27): 4 squared is 16, doubled is 32, and 32 – 5 = 27. This matches, so it works. Test (6, 10, 64): 6 squared is 36, doubled is 72, and 72 – 10 = 62, not 64. This fails. Only (4, 5, 27) follows the rule. So the answer is (4, 5, 27).

The same letter ‘U’ shows up in both View 1 and View 2. In View 1, ‘U’ appears together with R and Q. In View 2, ‘U’ appears together with P and S. A cube face touches exactly four other faces, and never touches the one face opposite it. Between the two views, ‘U’ has now been seen next to four different faces. The one face never seen next to ‘U’ must be the face opposite it. That face is ‘T’, so the answer is T.

The given set is (2, 6, 18). Square the middle number: 6 x 6 = 36. Now multiply the first and third numbers: 2 x 18 = 36. Both results are equal. So the rule is: the middle number squared equals the first number times the third number. This means the three numbers form a rising chain with a fixed multiplying factor. Test (4, 8, 15): 8 squared is 64, but 4 x 15 = 60. These do not match, so it fails. Test (5, 15, 40): 15 squared is 225, but 5 x 40 = 200. These do not match, so it fails. Test (3, 12, 48): 12 squared is 144, and 3 x 48 = 144. These match, so it works. Test (2, 10, 51): 10 squared is 100, but 2 x 51 = 102. These do not match, so it fails. Only (3, 12, 48) follows the rule. So the answer is (3, 12, 48).

Statement 1 says all valves are pumps. Statement 2 says all pumps are engines. Chain these using the shared term pumps. Every valve is a pump, and every pump is an engine. So every valve is also an engine. This means valves sit inside engines, not outside them. Conclusion I claims all engines are valves. This reverses the chain illegally and does not follow. Conclusion II claims no engines are valves. But we just showed valves are inside engines, so some engines must be valves. Conclusion II directly contradicts this and does not follow either. The correct answer is: neither conclusion I nor II follows.

The cuboid measures 9 cm by 12 cm by 15 cm, and each small cube has side 3 cm. Along each edge, the number of small cubes is that edge’s length divided by 3. That gives 9/3 = 3, 12/3 = 4, and 15/3 = 5 small cubes along each direction. Multiply these three counts together for the total: 3 x 4 x 5 = 60. A common mistake is forgetting to divide the dimensions at all. That wrongly multiplies 9 x 12 x 15 to get 1620. Another mistake is dividing only two of the three dimensions by 3. The total number of small cubes is 60.

The cube has side 4, so it is cut into 4 x 4 x 4 = 64 unit cubes. Edge cubes touch exactly two outer faces. Their count is 12 x (N-2), using N as the side length. Here N-2 = 4-2 = 2. So edge cubes = 12 x 2 = 24. A common mistake is using (N-1) instead of (N-2) in the formula. That wrongly gives 12 x 3 = 36. Corner cubes always number 8, since every cube has 8 corners. The total number of unit cubes here is 64, not the answer to this question. The cubes with exactly two painted faces number 24.

The given pair is Skin : Sweat. The skin is an organ, and sweat is the substance it produces. We need a pair with the same organ-produces-substance link. Kidney : Filter names a function, not a substance, so it does not match. Lungs : Breathe and Heart : Beat also name actions, not substances. Liver : Bile fits the pattern: the liver is an organ, and bile is the substance it produces. So the answer is Liver : Bile.

A letter has the same water image only if it is symmetric top to bottom. The standard list is C, D, E, H, I, K, O, and X. The word ‘DECODE’ has 6 letters. Checking each one against that list gives a match every time it appears: D, E, C, O, D, E. That is 6 matching letters in total, so the answer is 6.

Take point Q as the origin (0,0). Farhan walks 10 km north to (0,10). He turns right, faces East, and walks 15 km to (15,10). He turns right again, faces South, and walks 4 km to (15,6). He turns right once more, faces West, and walks 9 km to (6,6). Point R is (6,6). This is 6 km east and 6 km north of Q. Equal east and north offsets mean point R lies exactly North-East of point Q.

Build the order from the given clues, highest to lowest. Naina beats Ritu but loses to Sohan, so Sohan is above Naina. Devraj beats Sohan, so Devraj is above Sohan. Priya sits below Naina but above Ritu. The full order is: Devraj, Sohan, Naina, Priya, Ritu. Devraj is highest, so Sohan holds the second-highest marks.

The cube has side 6, so N-2 = 6-2 = 4. Only the violet pair of faces can give a cube exactly one violet face. Each face in that pair contributes (N-2)^2 face-center cubes, so 4^2 = 16 cubes per face. Two faces share the violet color, so violet face-center cubes = 2 x 16 = 32. Forgetting to double for the second face wrongly gives just 16. All three colors together give 6 x (N-2)^2 = 6 x 16 = 96 one-face cubes in total. Corner cubes, unrelated to this count, always number 8. The cubes with exactly one violet face number 32.

The Venn diagram shows how many people like Physics, Chemistry, and Biology. Only Physics: 15. Only Chemistry: 19. Only Biology: 11. Physics and Chemistry only: 7. Chemistry and Biology only: 8. Physics and Biology only: 4. All three: 3. This is the number in the centre region, where all three circles overlap. So the answer is 3.

Archimedes is credited with first explaining the existence of buoyant force in fluids.

Radar systems rely on microwaves specifically, since their short wavelength allows precise detection and location of objects like aircraft and ships.

Communicable diseases are caused by pathogens, including bacteria, viruses, fungi, and parasites, and can spread between people.

The immune system defends the body against pathogens, including bacteria, viruses, and other harmful invaders.

Boiling simply turns liquid water into gaseous water vapour — the rising bubbles are not trapped air or decomposed gases, but water vapour itself.

Ordinary ionic salts actually have both high melting points and high boiling points, not a low melting point paired with a high boiling point.

Sliding along a straight incline is an example of rectilinear (straight-line) motion.

Red blood cells vastly outnumber both white blood cells and platelets in a normal blood sample.

Sound travels fastest in solids and slowest in gases, with liquids falling in between — not, as a common misconception might suggest, with gases faster than liquids.

Potential difference between two points is precisely defined as the work done per unit charge moved between them.

A raised, motionless hammer possesses potential energy due to its height, ready to convert to kinetic energy when released.

Transgenic organisms are genetically altered, but they CAN pose environmental hazards, making the second claim false.

Momentum is a vector quantity, unlike pressure, energy, and work, which are scalars.

Bats emit high-frequency sound waves, beyond the range of human hearing, called ultrasonic waves. These waves bounce off nearby objects and return as echoes, which bats use to build a picture of their surroundings. This technique, echolocation, lets bats navigate and hunt accurately even in complete darkness.

Quartz is silicon dioxide, and its crystal structure gives it useful piezoelectric properties, generating a voltage when mechanically stressed.

The pipe’s rate is 1/27 of the tank per hour. In 5 hours, it fills 5 x 1/27 = 5/27 of the tank. The greatest common factor of 5 and 27 is 1. Dividing numerator and denominator by 1 gives 5/27. So 5/27 of the tank is filled. Check: 5 x 27 = 135, and 27 x 5 = 135, equal as expected.

This canteen uses kg of rice at a constant daily rate. In 5 days it uses 139 kg of rice, so more days always means more kg of rice. Days and quantity are directly proportional here. Set up the proportion 5 : 55 :: 139 : x. So x = (55 x 139) / 5 = 1529 kg of rice. Check: 1529 x 5 = 7645, and 55 x 139 = 7645, which match.

Let radius = r = 105 cm and height = h = 10 cm. Volume of a cylinder = pi x r^2 x h. r^2 = 105 x 105 = 11025. Base area = pi x r^2 = (22/7) x 11025 = 34650 sq cm. Volume = base area x height = 34650 x 10 = 346500 cubic cm.

Let the number be 3525. We need 90% of 3525. By definition, 90% of 3525 = (90/100) x 3525. First multiply: 90 x 3525 = 317250. Then divide by 100: 317250/100 = 3172.5. Check: 90% of 3525 also equals 3525% of 90, i.e. (3525/100) x 90 = 3172.5.

Perimeter is the total length of the boundary. A rectangle has two sides of length l and two sides of length b. So perimeter = l + l + b + b = 2l + 2b = 2(l + b).

Let length = L = 51 m and breadth = B = 14 m. Perimeter of a rectangle = 2 x (L + B). L + B = 51 + 14 = 65. Perimeter = 2 x 65 = 130 m.

Reference date: 1 January 2057, given as a Monday. Target date: 1 January 2058, exactly one year later. An ordinary year has 365 days = 52 weeks + 1 odd day. A leap year has 366 days = 52 weeks + 2 odd days. 2057 is an ordinary year, so it contributes 1 odd day(s). So the day of the week shifts by 1 day(s) from Monday. Counting 1 day(s) forward from Monday lands on Tuesday. Check: 1 January 2058 is indeed a Tuesday.

When a bill is discounted before its due date, the banker deducts the banker’s discount upfront. The holder receives only the remaining amount, not the full face value. The face value (Amount) is Rs 10500. The rate is R = 20% per annum. The bill is discounted 9 months before it is due. First find B.D. = (Amount x R x 9)/1200 = 1890000/1200 = Rs 1575. Money received = Amount – B.D. = 10500 – 1575 = Rs 8925. Check: Rs 8925 plus the discount of Rs 1575 equals the face value, Rs 10500.

Let the cheaper price = Rs 17 per kg. Let the dearer price = Rs 54 per kg. Let the mean price of the mixture = Rs 53 per kg. By the rule of alligation, cheaper qty : dearer qty = (dearer price – mean price) : (mean price – cheaper price). Dearer price minus mean price = 54 – 53 = 1. Mean price minus cheaper price = 53 – 17 = 36. So the ratio is 1 : 36. Dividing both terms by their HCF 1 gives the simplest ratio 1 : 36. Check: mixing 1 part at Rs 17 with 36 parts at Rs 54 costs Rs 1961 for 37 parts. That is Rs 53 per kg, matching the given mean price of Rs 53.

Let the edge of the cube = a = 3 cm. Volume of a cube = a^3, edge multiplied by itself three times. So volume = 3 x 3 x 3. 3 x 3 = 9, and 9 x 3 = 27. So the volume is 27 cubic cm.

Let length = l = 18 m, breadth = b = 4 m, height = h = 12 m. Volume of a cuboid = length x breadth x height. So volume = 18 x 4 x 12. 18 x 4 = 72, and 72 x 12 = 864. So the volume is 864 cubic m.

Let area = A = 576 sq m. Side of a square = sqrt(A). So side = sqrt(576) = 24 m. Check: 24 x 24 = 576 sq m, which matches A.

Let S.I. = Rs 9450, Rate R = 15% per annum, Time T = 6 years. Formula: Principal P = (100 x S.I.)/(R x T). 100 x S.I. = 100 x 9450 = 945000. R x T = 15 x 6 = 90. P = 945000/90 = Rs 10500. Check: S.I. = (P x R x T)/100 = (10500 x 15 x 6)/100 = Rs 9450.

Let Principal P = Rs 8125, Rate R = 8% per annum, Time T = 2 years. Compounded annually, each year the amount is multiplied by (100+R)/100 = 27/25. After year 1, Amount = 8125 x 27/25 = Rs 8775. After year 2, Amount = 8775 x 27/25 = Rs 9477. So Amount after 2 years = Rs 9477. C.I. = Amount – Principal = 9477 – 8125 = Rs 1352. Check: Principal + C.I. = 8125 + 1352 = Rs 9477, which matches the Amount.

Let downstream speed = 9 km/hr and upstream speed = 3 km/hr. Downstream speed = B + S and upstream speed = B – S, where B is still-water speed and S is stream speed. Adding these two equations cancels S: (B+S) + (B-S) = 2B. So 9 + 3 = 2B, which gives 2B = 12. B = 12/2 = 6 km/hr. Check: this places B exactly halfway between the downstream speed 9 and the upstream speed 3.