Assam Police AB/ UB Constable Free Demo ebook (English)
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ADRE Grade-IV Paper-I (HSLC Level) - Free Practice Set (2026-2027 Edition)
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Table of Contents
Free Practice Set 01
Q1. Find the sum of the first 50 odd natural numbers.
- 2400
- 2600
- 5000
- 2500
Q2. The product of two numbers is 4107. If the Highest Common Factor (HCF) of these numbers is 37, what is the value of the greater number?
- 185
- 111
- 74
- 148
Q3. If x3 = 512, what is the value of x?
- 6
- 12
- 8
- 16
Q4. A, B, and C enter into a partnership investing Rs. 35,000, Rs. 45,000, and Rs. 55,000 respectively. Out of a total profit of Rs. 40,500, what is A's share?
- Rs. 13,500
- Rs. 10,500
- Rs. 16,500
- Rs. 12,000
Q5. At what rate of compound interest per annum will a principal sum of Rs. 1200 become Rs. 1323 in 2 years?
- 6%
- 4%
- 5%
- 10%
Q6. Simplify the mathematical expression: 18 × 12 + 16 ÷ 8 - 14.
- 214
- 204
- 196
- 202
Q7. A man can row a boat upstream at 10 km/hr and downstream at 16 km/hr. Find the speed of the man in still water.
- 12 km/hr
- 14 km/hr
- 3 km/hr
- 13 km/hr
Q8. What is the area of a rhombus if its two diagonals are 16 cm and 12 cm long?
- 192 sq cm
- 48 sq cm
- 96 sq cm
- 100 sq cm
Q9. If 2A = 3B = 4C, what is the ratio of A:B:C?
- 4:3:2
- 6:4:3
- 2:3:4
- 12:8:6
Q10. A train 300 meters long is running at a speed of 90 km/hr. How many seconds will it take to cross a 200-meter-long bridge?
- 15 seconds
- 25 seconds
- 18 seconds
- 20 seconds
Q11. If the total monthly income of a family is Rs. 50,000 and 15% is spent on education, how much money is spent on education?
- Rs. 6,500
- Rs. 8,000
- Rs. 7,500
- Rs. 7,000
Q12. A merchant has 1000 kg of sugar, part of which he sells at an 8% profit and the rest at an 18% profit. He gains 14% on the whole. What is the quantity sold at the 18% profit?
- 600 kg
- 400 kg
- 500 kg
- 700 kg
Q13. The perimeter of a rectangle is 82 m and its area is 400 sq m. What is the length of the rectangle?
- 16 m
- 20 m
- 25 m
- 30 m
Q14. What is the single discount percentage equivalent to three successive discounts of 10%, 20%, and 30%?
- 60%
- 49.6%
- 50.4%
- 48%
Q15. In an election between two candidates, the winner secured 65% of the total valid votes and won by a majority of 900 votes. What is the total number of valid votes?
- 2000
- 4500
- 3000
- 2500
Q16. What is the volume of a solid hemisphere of radius 21 cm? (Take π = 22/7)
- 38808 cubic cm
- 9702 cubic cm
- 19404 cubic cm
- 29106 cubic cm
Q17. What is the exact mathematical value of the trigonometric expression: sin 60° cos 30° + cos 60° sin 30°?
- 0
- 1/2
- √3/2
- 1
Q18. From the top of a 20m high cliff, the angle of depression to a boat is 45 degrees. How far is the boat from the base of the cliff?
- 10 meters
- 20 meters
- 20√3 meters
- 40 meters
Q19. The average age of a class of 30 students is 15 years. If the teacher's age is included, the average increases by 1 year. What is the teacher's age?
- 31 years
- 45 years
- 46 years
- 41 years
Q20. The ratio of the ages of a father and his son is 4:1. The product of their ages is 196. What will be the ratio of their ages after 5 years?
- 3:1
- 10:3
- 11:4
- 12:5
Directions: Improve the bracketed/quoted part of the sentence grammatically if needed.
Q21. Improve the sentence grammatically: "He is too intelligent that he will not fail."
- He is so intelligent to fail.
- He is too intelligent to fail.
- He is very intelligent that he will not fail.
- No improvement
Directions: Change the voice of the given sentence.
Q22. Change the sentence into passive voice: "They have built a new hospital."
- A new hospital was built by them.
- A new hospital had been built by them.
- A new hospital is being built by them.
- A new hospital has been built by them.
Q23. Identify the correctly spelled word:
- Privelege
- Priviledge
- Privilege
- Privelige
Q24. Fill in the blank with the correct preposition: "He is completely blind _____ his own faults."
- of
- in
- to
- with
Q25. What is the past participle form of the verb "Tear"?
- Teared
- Tore
- Tearing
- Torn
Q26. Fill in the blank with the correct verb: "The jury _____ divided in their opinions regarding the final verdict."
- is
- are
- was
- has
Q27. What is the one-word substitution for "A person who complies with accepted rules, conventions, and customs"?
- Rebel
- Conformist
- Maverick
- Heretic
Q28. What is the meaning of the idiom "To hit the sack"?
- To physically assault someone
- To pack a bag quickly
- To get fired from a job
- To go to bed or go to sleep
Q29. What is the superlative degree of the adjective "Much"?
- More
- Mucher
- Many
- Most
Q30. Identify the specific type of clause for the quoted part: "I wonder 'why she left early'."
- Adjective Clause
- Adverb Clause
- Relative Clause
- Noun Clause
Q31. Identify the correctly spelled word among the following:
- Embarass
- Embarras
- Embarrass
- Embrass
Q32. What is the exact antonym of the word "Mitigate"?
- Alleviate
- Soothe
- Aggravate
- Pacify
Q33. What is a common synonym for the word "Vindicate"?
- Condemn
- Accuse
- Convict
- Justify
Q34. In a passage discussing harsh and dry desert climates, what does the word "Arid" mean?
- Extremely dry or having little or no rain
- Highly humid and tropical
- Covered in thick vegetation
- Having frequent storms
Directions: Find the grammatical error in the following sentence.
Q35. Spot the grammatical error in the sentence: "He is one of those writers who has won global acclaim."
- 'He is' should be 'He are'
- 'has' should be 'have'
- 'acclaim' should be 'acclaims'
- No error
Q36. What does the vocabulary term "Gregarious" mean?
- Extremely shy and introverted
- Fond of company or highly sociable
- Aggressive and hostile
- Intelligent and analytical
Q37. What is the one-word substitution for "A piece of handwriting that is impossible or very difficult to read"?
- Illiterate
- Incorrigible
- Incomprehensible
- Illegible
Q38. What is the meaning of the idiom "To bite off more than you can chew"?
- To eat very quickly
- To argue with someone stronger than you
- To take on a task or responsibility that is way too big or difficult
- To lose a tooth
Q39. Fill in the blank with the correct superlative adjective: "This is the _____ (interesting) book I have ever read."
- more interesting
- interestest
- highly interesting
- most interesting
Q40. Spot the grammatical error in the sentence: "Each of the employees are responsible for keeping their own desk clean."
- 'employees' should be 'employee'
- 'are' should be 'is'
- 'desk' should be 'desks'
- No error
Q41. If some roses are flowers and all flowers are beautiful, does it logically follow that some roses are beautiful?
- No
- Yes
- Data Inadequate
- Either Yes or No
Q42. In a farm, there are ducks and cows. If the total number of heads is 40 and the total number of legs is 120, how many cows are there?
- 10
- 30
- 25
- 20
Q43. If a specific segment in a pie chart represents 20% of the total value, what is its exact central angle?
- 20 degrees
- 36 degrees
- 90 degrees
- 72 degrees
Q44. A, B, C, D, and E are sitting in a row facing North. C is in the middle. A and B are at the extreme ends. D is sitting next to A. Who is sitting immediately next to B?
- C
- D
- A
- E
Q45. Find the odd one out among the following celestial bodies: Mercury, Venus, Sirius, Mars.
- Mercury
- Venus
- Sirius
- Mars
Q46. What letter comes next in the alphabetical series: C, F, I, L, ?
- M
- N
- P
- O
Q47. Complete the scientific analogy: Barometer is to Air Pressure as Seismograph is to _____?
- Temperature
- Humidity
- Wind Speed
- Earthquakes
Q48. If you write all the whole numbers consecutively from 1 to 100, how many times will you write the digit 9?
- 10
- 11
- 19
- 20
Q49. Pointing to a woman, a man said, "Her mother's father is the father of my mother." How is the man related to the woman?
- Brother
- Uncle
- Nephew
- Cousin
Q50. Statement: "All students are smart. John is a student."
Conclusion: "John is smart."
Is this conclusion logically True or False?
- False
- Cannot be determined
- Irrelevant
- True
Q51. If the word 'SPOON' is coded as 'TQPPO' by shifting each letter forward by 1, how is the word 'CHAIR' coded?
- DIBKS
- EJCKS
- BGZHR
- DIBJS
Q52. In a row of 50 students, Ramesh is ranked 20th from the left side. What is his exact position from the right side?
- 30th
- 29th
- 32nd
- 31st
Q53. What is the minimum number of straight lines required to draw a regular octagon?
- 6
- 7
- 10
- 8
Q54. A man goes 8 km South, turns West and goes 6 km. What is the straight-line distance from his starting point?
- 14 km
- 2 km
- 12 km
- 10 km
Q55. How many flat geometric faces does a standard hexagonal prism have?
- 6
- 10
- 12
- 8
Q56. If 5 spiders can catch 5 flies in exactly 5 minutes, how many spiders are needed to catch 100 flies in exactly 100 minutes?
- 100
- 20
- 50
- 5
Q57. What is the mathematical sum of the first 100 natural numbers?
- 5000
- 5100
- 10000
- 5050
Q58. Complete the biological analogy: Bird is to Ornithology as Insects is to _____?
- Zoology
- Etymology
- Ichthyology
- Entomology
Q59. In a reverse alphabetical code where A=26, B=25, C=24, what is the numerical code sequence for the word 'FAT'?
- 6-1-20
- 20-26-6
- 21-25-8
- 21-26-7
Q60. Facing North, a person turns 135 degrees clockwise and then 45 degrees anti-clockwise. Which direction are they facing now?
- South-East
- West
- South
- East
Q61. The Bherjan-Borajan-Padumoni Wildlife Sanctuary is located in which district of Assam?
- Dibrugarh
- Golaghat
- Sonitpur
- Tinsukia
Q62. The historic 'Gohain Kamal Ali' road was constructed during the reign of which Koch king?
- Nila Dhwaj
- Chilarai
- Biswa Singha
- Nara Narayan
Q63. The Assam Agricultural University (AAU), the premier agricultural institute of the state, was established in which year?
- 1948
- 1975
- 1982
- 1969
Q64. According to the 2011 Census, what is the approximate literacy rate of the male population in Assam?
- 66.27%
- 82.15%
- 72.19%
- 77.85%
Q65. The proposed multi-modal logistics park in Assam, aimed at boosting trade and commerce, is being developed at which place?
- Amingaon
- Silchar
- Tinsukia
- Jogighopa
Q66. Who was the first Chief Justice of the Gauhati High Court after its establishment in 1948?
- Haliram Deka
- Sarjoo Pandey
- M.C. Pathak
- Sir R.F. Lodge
Q67. Which celebrated Assamese filmmaker directed the critically acclaimed and National Award-winning movie 'Village Rockstars'?
- Jahnu Barua
- Manju Borah
- Bhupen Hazarika
- Rima Das
Q68. The historic Digboi oil refinery, the oldest in Asia, was officially commissioned in which year?
- 1889
- 1895
- 1910
- 1901
Q69. The Assam Government launched which specific scheme to promote sports talent at the grassroots level by organizing rural Olympics?
- Assam Khel Abhiyan
- Krida Vikash
- Khel Utsav
- Khel Maharan
Q70. The 'Assam Mala' project is primarily aimed at the comprehensive improvement and upgrade of which sector in the state?
- River Waterways
- Rural Electrification
- Healthcare Infrastructure
- State Highways and Major District Roads
Q71. The ongoing border dispute between Assam and which neighboring state saw the signing of the 'Namsai Declaration' in 2022?
- Meghalaya
- Mizoram
- Nagaland
- Arunachal Pradesh
Q72. Which tributary of the Brahmaputra is known in mythology as the 'River of Blood' due to a legend involving the sage Parashurama?
- Subansiri
- Dhansiri
- Kameng
- Lohit River
Q73. Who was the visionary Ahom king to first introduce the systematic practice of recording history in written chronicles called Buranjis?
- Suhungmung
- Rudra Singha
- Pratap Singha
- Sukapha
Q74. The Assam Public Service Commission (APSC) officially came into existence in which year?
- 1935
- 1947
- 1950
- 1937
Q75. The patriotic song 'O Mur Apunar Desh' was officially adopted as the state anthem of Assam at the Tezpur session in which year?
- 1916
- 1940
- 1952
- 1927
Q76. Assam is known for a unique sticky rice variety traditionally used to make 'Jolpan' and pithas. What is its local Assamese name?
- Johal Saul
- Aijong Saul
- Bora Saul
- Kumal Saul
Q77. The industrial area of Numaligarh in Assam is primarily known for which major public sector enterprise?
- Numaligarh Refinery Limited (NRL)
- Brahmaputra Cracker and Polymer Limited
- Assam Petro-Chemicals Limited
- Oil India Limited
Q78. Which specific district in Assam has the highest urban population according to the 2011 Census data?
- Kamrup Metropolitan
- Dibrugarh
- Jorhat
- Cachar
Q79. Which prominent and highly advanced medical institution was officially inaugurated in Guwahati by the Prime Minister in 2023?
- AIIMS Guwahati
- Gauhati Medical College and Hospital
- Tata Memorial Cancer Hospital
- North Eastern Indira Gandhi Regional Institute of Health and Medical Sciences
Q80. The 'Pragyan Bharati' scheme launched by the Assam Government provides free admission to students of which educational category?
- Primary school students only
- Higher Secondary, Degree, and Postgraduate level in government institutions
- Engineering and Medical students only
- Students studying in private schools
Q81. The famous 'Iron Man of India', Sardar Vallabhbhai Patel, successfully led which major peasant satyagraha in Gujarat in 1928?
- Kheda Satyagraha
- Champaran Satyagraha
- Bardoli Satyagraha
- Salt Satyagraha
Q82. The Headquarters of the Securities and Exchange Board of India (SEBI), the regulator of the securities market, is located in which city?
- Mumbai
- New Delhi
- Kolkata
- Bengaluru
Q83. Who was the first woman in history to win the Nobel Prize in two different scientific fields (Physics and Chemistry)?
- Rosalind Franklin
- Lise Meitner
- Marie Curie
- Dorothy Hodgkin
Q84. What is the primary environmental focus of the international treaty known globally as the 'Kyoto Protocol'?
- Prevention of ocean pollution
- Reduction of greenhouse gas emissions
- Protection of endangered species
- Elimination of nuclear weapons
Q85. The 'Higgs Boson' is a fundamental particle in physics that is often referred to by what popular media nickname?
- The Ghost Particle
- The God Particle
- The Miracle Particle
- The Alpha Particle
Q86. Which specific schedule of the Indian Constitution contains the list of recognized official languages of the Republic of India?
- Sixth Schedule
- Eighth Schedule
- Ninth Schedule
- Tenth Schedule
Q87. The Great Victoria Desert, the largest desert in its region, is geographically located in which country?
- South Africa
- Argentina
- Australia
- Brazil
Q88. The 'Grammy Award' is widely considered the most prestigious and highest honor in which global industry?
- Motion Picture Industry
- Television Industry
- Music Recording Industry
- Theatrical Arts Industry
Q89. The 'Ryder Cup' is a highly prestigious international men's team competition associated with which sport?
- Tennis
- Polo
- Golf
- Cricket
Q90. What does the computer networking acronym 'WLAN' stand for?
- Wireless Local Area Network
- Wide Local Area Network
- Wireless Linear Area Network
- Web Local Area Network
Q91. The legislative concept of the 'Concurrent List' in the Indian Constitution was originally borrowed from the constitution of which country?
- Canada
- Australia
- United States of America
- Ireland
Q92. The traditional and ancient martial art form known as 'Kalaripayattu' originated in which Indian state?
- Tamil Nadu
- Karnataka
- Kerala
- Andhra Pradesh
Q93. Which European country officially became the 31st member of the NATO military alliance in 2023?
- Sweden
- Finland
- Ukraine
- Switzerland
Q94. Who is the author of the famous dystopian political novel "1984"?
- Aldous Huxley
- Ray Bradbury
- George Orwell
- Margaret Atwood
Q95. What is the scientific and statistical study of human populations, including their size, structure, and distribution, called?
- Anthropology
- Sociology
- Demography
- Ethnography
Q96. Which prominent Indian emperor fought and was deeply affected by the bloody Kalinga War in 261 BCE?
- Chandragupta Maurya
- Bindusara
- Ashoka
- Harshavardhana
Q97. What is the hardest naturally occurring elemental substance found on Earth?
- Platinum
- Diamond
- Titanium
- Quartz
Q98. What is the minimum age required by the Indian Constitution to become the Prime Minister of India if the candidate is a member of the Lok Sabha?
- 30 years
- 35 years
- 25 years
- 21 years
Q99. What is the name of the longest river located in the African continent?
- Congo River
- Niger River
- Nile River
- Zambezi River
Q100. In the context of modern computer hardware and storage, what does the acronym 'SSD' stand for?
- Super Storage Drive
- Static State Drive
- Solid State Drive
- Standard Storage Disk
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Upgrade to PremiumAnswer Key 01
| Q.No | Correct Option | Correct Answer |
|---|---|---|
| Q1 | D | 2500 |
| Q2 | B | 111 |
| Q3 | C | 8 |
| Q4 | B | Rs. 10,500 |
| Q5 | C | 5% |
| Q6 | B | 204 |
| Q7 | D | 13 km/hr |
| Q8 | C | 96 sq cm |
| Q9 | B | 6:4:3 |
| Q10 | D | 20 seconds |
| Q11 | C | Rs. 7,500 |
| Q12 | A | 600 kg |
| Q13 | C | 25 m |
| Q14 | B | 49.6% |
| Q15 | C | 3000 |
| Q16 | C | 19404 cubic cm |
| Q17 | D | 1 |
| Q18 | B | 20 meters |
| Q19 | C | 46 years |
| Q20 | C | 11:4 |
| Q21 | B | He is too intelligent to fail. |
| Q22 | D | A new hospital has been built by them. |
| Q23 | C | Privilege |
| Q24 | C | to |
| Q25 | D | Torn |
| Q26 | B | are |
| Q27 | B | Conformist |
| Q28 | D | To go to bed or go to sleep |
| Q29 | D | Most |
| Q30 | D | Noun Clause |
| Q31 | C | Embarrass |
| Q32 | C | Aggravate |
| Q33 | D | Justify |
| Q34 | A | Extremely dry or having little or no rain |
| Q35 | B | 'has' should be 'have' |
| Q36 | B | Fond of company or highly sociable |
| Q37 | D | Illegible |
| Q38 | C | To take on a task or responsibility that is way too big or difficult |
| Q39 | D | most interesting |
| Q40 | B | 'are' should be 'is' |
| Q41 | B | Yes |
| Q42 | D | 20 |
| Q43 | D | 72 degrees |
| Q44 | D | E |
| Q45 | C | Sirius |
| Q46 | D | O |
| Q47 | D | Earthquakes |
| Q48 | D | 20 |
| Q49 | D | Cousin |
| Q50 | D | True |
| Q51 | D | DIBJS |
| Q52 | D | 31st |
| Q53 | D | 8 |
| Q54 | D | 10 km |
| Q55 | D | 8 |
| Q56 | D | 5 |
| Q57 | D | 5050 |
| Q58 | D | Entomology |
| Q59 | D | 21-26-7 |
| Q60 | D | East |
| Q61 | D | Tinsukia |
| Q62 | D | Nara Narayan |
| Q63 | D | 1969 |
| Q64 | D | 77.85% |
| Q65 | D | Jogighopa |
| Q66 | D | Sir R.F. Lodge |
| Q67 | D | Rima Das |
| Q68 | D | 1901 |
| Q69 | D | Khel Maharan |
| Q70 | D | State Highways and Major District Roads |
| Q71 | D | Arunachal Pradesh |
| Q72 | D | Lohit River |
| Q73 | D | Sukapha |
| Q74 | D | 1937 |
| Q75 | D | 1927 |
| Q76 | C | Bora Saul |
| Q77 | A | Numaligarh Refinery Limited (NRL) |
| Q78 | A | Kamrup Metropolitan |
| Q79 | A | AIIMS Guwahati |
| Q80 | B | Higher Secondary, Degree, and Postgraduate level in government institutions |
| Q81 | C | Bardoli Satyagraha |
| Q82 | A | Mumbai |
| Q83 | C | Marie Curie |
| Q84 | B | Reduction of greenhouse gas emissions |
| Q85 | B | The God Particle |
| Q86 | B | Eighth Schedule |
| Q87 | C | Australia |
| Q88 | C | Music Recording Industry |
| Q89 | C | Golf |
| Q90 | A | Wireless Local Area Network |
| Q91 | B | Australia |
| Q92 | C | Kerala |
| Q93 | B | Finland |
| Q94 | C | George Orwell |
| Q95 | C | Demography |
| Q96 | C | Ashoka |
| Q97 | B | Diamond |
| Q98 | C | 25 years |
| Q99 | C | Nile River |
| Q100 | C | Solid State Drive |
Detailed Solutions 01
Explanation:
Step 2: Here, n = 50.
Calculation: 502 = 50 × 50 = 2500.
Explanation:
Step 2: The product of the numbers is given as 4107. So, (37a) × (37b) = 4107.
Step 3: a × b = 4107 / (37 × 37) = 4107 / 1369 = 3.
Step 4: Since 'a' and 'b' are integers, the only coprime pair that multiplies to 3 is (1, 3).
Conclusion: The numbers are 37×1 = 37 and 37×3 = 111. The greater number is 111.
Explanation:
Step 2: To find x, calculate the cube root of 512. x = ³√512.
Calculation: Since 8 × 8 × 8 = 512, x = 8.
Explanation:
Step 2: Simplify the ratio by dividing by 5000. Ratio = 7 : 9 : 11.
Step 3: Total ratio parts = 7 + 9 + 11 = 27 parts.
Calculation: A's share = (7 / 27) × 40500 = 7 × 1500 = Rs. 10,500.
Explanation:
Step 2: Substitute the given values: 1323 = 1200(1 + R/100)2.
Step 3: 1323 / 1200 = (1 + R/100)2. Simplify the fraction by dividing by 3: 441 / 400 = (1 + R/100)2.
Step 4: Since 441 is 212 and 400 is 202, take the square root of both sides: 21 / 20 = 1 + R/100.
Calculation: R/100 = 21/20 - 1 = 1/20. Thus, R = 100 / 20 = 5%.
Explanation:
Step 2: Perform Division first: 16 ÷ 8 = 2. The expression becomes 18 × 12 + 2 - 14.
Step 3: Perform Multiplication: 18 × 12 = 216. The expression becomes 216 + 2 - 14.
Step 4: Perform Addition: 216 + 2 = 218.
Calculation: Perform Subtraction: 218 - 14 = 204.
Explanation:
Step 2: The direct formula for speed in still water is: x = (Downstream Speed + Upstream Speed) / 2.
Calculation: x = (16 + 10) / 2 = 26 / 2 = 13 km/hr.
Explanation:
Step 2: Substitute d1 = 16 and d2 = 12.
Calculation: Area =
Explanation:
Step 2: The LCM of 2, 3, and 4 is 12.
Step 3: Divide the LCM by each coefficient to get the ratio parts.
Calculation: A = 12/2 = 6; B = 12/3 = 4; C = 12/4 = 3. Therefore, the ratio is 6:4:3.
Explanation:
Step 2: Convert the speed from km/hr to m/s. Speed = 90 × (5/18) = 5 × 5 = 25 m/s.
Calculation: Time = Distance / Speed = 500 / 25 = 20 seconds.
Explanation:
Step 2: Total income = Rs. 50,000.
Calculation: (15 / 100) × 50,000 = 15 × 500 = Rs. 7,500.
Explanation:
Step 2: Diagonal differences: (18 - 14) = 4; (14 - 8) = 6.
Step 3: The ratio of quantities sold at 8% and 18% is 4:6, which simplifies to 2:3.
Step 4: Total ratio parts = 2 + 3 = 5 parts. Total quantity = 1000 kg.
Calculation: Quantity sold at 18% (which corresponds to 3 parts) = (3 / 5) × 1000 = 3 × 200 = 600 kg.
Explanation:
Step 2: Area = L × B = 400 sq m.
Step 3: We need two numbers that add up to 41 and multiply to 400. By factoring 400 (e.g., 25 × 16 = 400, and 25 + 16 = 41).
Conclusion: Since length is conventionally the longer side, the length of the rectangle is 25 m.
Explanation:
Step 2: First discount of 10%: Price becomes 100 - 10 = 90.
Step 3: Second discount of 20% on 90: Discount = 20% of 90 = 18. Price becomes 90 - 18 = 72.
Step 4: Third discount of 30% on 72: Discount = 30% of 72 = 21.6. Final Selling Price = 72 - 21.6 = 50.4.
Calculation: Single equivalent discount = Initial Price - Final Price = 100 - 50.4 = 49.6%.
Explanation:
Step 2: The winner got 65%, which means the loser got (100% - 65%) = 35%.
Step 3: The majority (difference in votes) is 65% - 35% = 30%.
Step 4: We are given that the majority is 900 votes. So, 30% of total votes = 900.
Calculation: Total valid votes (100%) = (900 / 30) × 100 = 30 × 100 = 3000.
Explanation:
Step 2: Substitute π = 22/7 and r = 21. V = (2/3) × (22/7) × 21 × 21 × 21.
Calculation: The (3 × 7) in the denominator cancels out one 21 in the numerator. V = 2 × 22 × 21 × 21 = 44 × 441 = 19404 cubic cm.
Explanation:
Method 2 (Identity): Use the compound angle identity: sin(A)cos(B) + cos(A)sin(B) = sin(A + B).
Calculation: sin(60° + 30°) = sin(90°) = 1.
Explanation:
Step 2: In the right-angled triangle formed, tan(θ) = Perpendicular (Height of cliff) / Base (Distance to boat).
Step 3: tan(45°) = 20 / Distance.
Calculation: Since tan(45°) = 1, then 1 = 20 / Distance, meaning Distance = 20 meters.
Explanation:
Step 2: When the teacher is included, the total number of people becomes 31, and the new average becomes 15 + 1 = 16 years.
Step 3: Total age of 31 people = 31 × 16 = 496 years.
Calculation: Teacher's age = Total age of 31 people - Total age of 30 students = 496 - 450 = 46 years.
Shortcut: Teacher's Age = Old Average + (Total New Members × Increase in Average) = 15 + (31 × 1) = 46.
Explanation:
Step 2: Product of their ages = 4x × x = 4x2.
Step 3: 4x2 = 196 → x2 = 196 / 4 = 49 → x = 7.
Step 4: Present age of father = 4 × 7 = 28 years; Present age of son = 7 years.
Calculation: After 5 years, Father = 28 + 5 = 33 years; Son = 7 + 5 = 12 years. Ratio = 33:12, which simplifies to 11:4 (dividing by 3).
Explanation: In English grammar, the construction "too... to" is a standard structure used to combine sentences with a negative implication (e.g., He is so intelligent that he will not fail → He is too intelligent to fail). The original sentence incorrectly mixed "too" with "that".
Explanation: The active sentence is in the Present Perfect tense ("have built"). To convert to passive voice, the object ("A new hospital") becomes the subject. The auxiliary verb changes to singular ("has"), followed by "been" and the past participle ("built"). Hence, "A new hospital has been built by them".
Explanation: The correct spelling is "Privilege". It derives from the Latin word 'privilegium'. A common mistake is to add a 'd' (like in bridge) or misplace the 'e' and 'i'.
Explanation: The phrase "blind to" is an established English idiom meaning unable or unwilling to recognize or understand something, typically one's own faults or dangers. (Conversely, "blind in/of" is used for physical sight loss, e.g., blind in one eye).
Explanation: "Tear" is an irregular verb. Its base form (V1) is 'tear', its simple past form (V2) is 'tore', and its past participle form (V3) is 'torn'.
Explanation: 'Jury' is a collective noun. When the group acts as a single unified body, it takes a singular verb. However, when the members are acting individually or are divided in their opinions, it takes a plural verb. The clue "their opinions" confirms the plural sense, so "are" is correct.
Explanation: A 'Conformist' is a person who conforms to accepted behavior or established practices. The other options (Rebel, Maverick, Heretic) represent the exact opposite—people who defy rules or conventions.
Explanation: The idiom "To hit the sack" (or "hit the hay") originated in the late 19th/early 20th century when mattresses were literally cloth sacks filled with hay or cotton. It means to go to bed in order to sleep.
Explanation: The adjectives "Much" (used for uncountable nouns) and "Many" (used for countable nouns) share the same comparative and superlative degrees. The comparative is 'More', and the superlative is 'Most'.
Explanation: The quoted clause "why she left early" acts directly as the object of the transitive verb "wonder". Any dependent clause that functions as a noun (acting as a subject, object, or complement) is classified as a Noun Clause.
Explanation: The correct spelling is "Embarrass". It is a commonly misspelled word; remember that it requires both a double 'r' and a double 's'.
Explanation: "Mitigate" means to make something less severe, harmful, or painful (e.g., to mitigate the damage). Its direct antonym is "Aggravate", which means to make a problem, injury, or offense worse or more serious.
Explanation: To "Vindicate" means to clear someone of blame or suspicion, or to show or prove to be right, reasonable, or justified. "Justify" or "Exonerate" are accurate synonyms.
Explanation: In geographical and climatological contexts, an "Arid" region is a land or climate characterized by severe lack of available water, meaning it is extremely dry and receives very little to no rainfall, making it hostile to plant and animal life.
Explanation: In the structure "One of the [plural noun] + who/which/that", the relative pronoun (who) refers back to the plural noun directly preceding it ('writers', not 'one'). Because 'writers' is plural, the verb following it must also be plural. Thus, 'has' becomes 'have'.
Explanation: A "Gregarious" person is someone who is naturally outgoing, friendly, sociable, and enjoys being surrounded by crowds or company. In biology, it refers to animals that live in flocks or colonies.
Explanation: Handwriting or print that is not clear enough to be read is called "Illegible". (Note: 'Illiterate' refers to a person who cannot read or write, while 'Incomprehensible' means impossible to understand intellectually).
Explanation: The idiom "Bite off more than you can chew" means to try to do something that is too difficult for you, or to make a commitment that you cannot fulfill due to lack of time, skill, or resources.
Explanation: "Interesting" is a polysyllabic adjective (having three or more syllables). Unlike short adjectives that take '-est' (like tall/tallest), long adjectives form their superlative degree by adding the word "most" before them.
Explanation: The subject of the sentence is "Each", which is a singular distributive pronoun. The phrase "of the employees" is just a prepositional modifier. Since the true subject "Each" is singular, the verb must also be singular ("is", not "are").
Step 2: Draw a circle for 'Roses' overlapping the 'Flowers' circle, representing "Some roses are flowers".
Step 3: Draw a large circle for 'Beautiful' that completely swallows the 'Flowers' circle, representing "All flowers are beautiful".
Conclusion: The overlapping part between 'Roses' and 'Flowers' is now automatically trapped inside the 'Beautiful' circle. Thus, it is logically true that some roses are beautiful.
Step 2: Total Heads = D + C = 40. (Equation 1)
Step 3: Total Legs = 2D + 4C = 120 (since ducks have 2 legs, cows have 4). (Equation 2)
Step 4: Multiply Equation 1 by 2: 2D + 2C = 80.
Calculation: Subtract this from Equation 2: (2D + 4C) - (2D + 2C) = 120 - 80. This gives 2C = 40, so C = 20. There are 20 cows.
Step 2: To find the central angle of a 20% segment, calculate 20% of 360 degrees.
Calculation: (20 / 100) × 360 = 0.2 × 360 = 72 degrees.
Step 2: "C is in the middle". So, C occupies position 3.
Step 3: "A and B are at extreme ends". They occupy positions 1 and 5 (we don't know the exact order yet).
Step 4: "D is sitting next to A". If A were at position 5, D would have to be at 4. If A is at position 1, D is at 2. Assume A is at 1, so D is at 2, and B must be at 5.
Step 5: The only remaining person is E, who must take the only remaining empty seat (position 4).
Conclusion: The arrangement is A, D, C, E, B. The person immediately next to B is E.
Conclusion: Mercury, Venus, and Mars are rocky planets belonging to our solar system. Sirius is a star (the brightest star in the night sky). Thus, Sirius is the odd one out.
Step 1: C (3rd letter) + 3 = F (6th)
Step 2: F (6th) + 3 = I (9th)
Step 3: I (9th) + 3 = L (12th)
Conclusion: L (12th) + 3 = 15th letter, which is O.
Step 1: A Barometer is a scientific instrument designed to measure atmospheric 'Air Pressure'.
Conclusion: Similarly, a Seismograph is an instrument specifically designed to measure and record the force and duration of 'Earthquakes' (seismic waves).
Step 2: Count the occurrences of '9' in the ten's place: 90, 91, 92, 93, 94, 95, 96, 97, 98, 99. (10 times).
Conclusion: Note that the number 99 has two 9s, and we have counted them both properly in each respective step. Total occurrences = 10 + 10 = 20 times.
Step 2: Decode the first part: "Her mother's father" refers to the woman's maternal grandfather.
Step 3: The statement implies that both the man and the woman share the exact same maternal grandfather.
Conclusion: Since they share the same grandfather but are different people, their mothers must be sisters. Thus, the man and the woman are cousins.
Step 1: The universal premise states that the entire category of "students" possesses the trait of being "smart".
Step 2: The minor premise states that John belongs completely to the category of "students".
Conclusion: Therefore, John must inherit the traits of that category. The conclusion "John is smart" is logically True.
Step 1 (SPOON): S(+1)=T, P(+1)=Q, O(+1)=P, O(+1)=P, N(+1)=O → TQPPO.
Step 2 (CHAIR): C(+1)=D, H(+1)=I, A(+1)=B, I(+1)=J, R(+1)=S.
Conclusion: The word 'CHAIR' is coded as DIBJS.
Step 2: Substitute Total = 50 and Left Position = 20.
Calculation: Position from Right = 50 - 20 + 1 = 30 + 1 = 31st.
Explanation: In geometry, the root prefix of the word dictates the number of sides. 'Octa' means eight. Therefore, an octagon is a closed polygon consisting of exactly 8 straight lines (sides).
Step 2: Turning West for 6 km forms the base.
Step 3: The straight-line distance from the start is the hypotenuse. Apply Pythagoras' theorem: H = √(Base2 + Perpendicular2).
Calculation: √(62 + 82) = √(36 + 64) = √100 = 10 km.
Image Placement: Explanation
Image Purpose: Visual representation of a right-angled triangle for Direction Sense.
Exact AI Image Prompt: A clean mathematical diagram showing a starting point A. A line drawn straight South for 8 units to point B. A line drawn straight West from B for 6 units to point C. A dotted line connecting A and C labeled '10 km' demonstrating the hypotenuse.
Explanation: A standard prism takes its name from its base shape. A hexagonal prism has two identical hexagonal bases (top and bottom = 2 faces). Because a hexagon has 6 sides, it will have 6 rectangular lateral faces connecting the bases. Total faces = 2 + 6 = 8.
Step 2: Substitute values: (5 × 5) / 5 = (M2 × 100) / 100.
Calculation: 5 = M2. Thus, it still requires exactly 5 spiders. (Since 1 spider catches 1 fly in 5 minutes, 5 spiders catch 100 flies in 100 minutes).
Step 2: Here, n = 100.
Calculation: Sum = 100 × (100 + 1) / 2 = (100 × 101) / 2 = 50 × 101 = 5050.
Conclusion: The scientific study of birds is called Ornithology. Similarly, the scientific study of insects is called Entomology.
Step 1: F is the 6th letter. Reverse code = 27 - 6 = 21.
Step 2: A is the 1st letter. Reverse code = 27 - 1 = 26.
Step 3: T is the 20th letter. Reverse code = 27 - 20 = 7.
Conclusion: The word 'FAT' is coded as 21-26-7.
Step 2: Calculate the net turn. Clockwise is positive (+), Anti-clockwise is negative (-).
Calculation: Net Turn = +135° - 45° = +90°.
Conclusion: A net turn of 90 degrees clockwise from North lands the person facing East.
Explanation: The Bherjan-Borajan-Padumoni Wildlife Sanctuary is a unique protected area in the Tinsukia district of Assam. It consists of three distinct isolated forest blocks heavily populated by diverse primate species like the Hoolock Gibbon and Slow Loris.
Explanation: The Gohain Kamal Ali was a massive 350-mile-long historic road connecting the Koch capital at Koch Bihar to Narayanpur in Lakhimpur. It was constructed rapidly in 1547 under the supervision of Gohain Kamal, step-brother and general to the great Koch king Nara Narayan.
Explanation: The Assam Agricultural University (AAU) is the premier state agricultural university established on April 1, 1969, under the Assam Agricultural University Act. Its primary campus is located in Jorhat.
Explanation: According to the 2011 Census of India, the overall literacy rate of Assam stood at 72.19%. The male literacy rate was significantly higher at 77.85%, while the female literacy rate was 66.27%.
Explanation: Under the Government of India's 'Bharatmala Pariyojana', India's very first Multi-Modal Logistics Park (MMLP) is being rapidly developed at Jogighopa in the Bongaigaon district of Assam, to seamlessly integrate road, rail, air, and waterways for efficient trade.
Explanation: The High Court of Assam and Nagaland (later renamed the Gauhati High Court) was established on April 5, 1948. Hon'ble Sir R.F. Lodge was sworn in as the first Chief Justice of this esteemed judicial body.
Explanation: 'Village Rockstars' (2017) is an internationally acclaimed Assamese independent film brilliantly directed, written, and produced by Rima Das. It won the Best Feature Film award at the 65th National Film Awards and was India's official entry to the Oscars.
Explanation: The Digboi Refinery, established by the Assam Oil Company, is affectionately known as the "Gangotri of the Indian Hydrocarbon sector". It was officially commissioned on December 11, 1901, and is the oldest operating oil refinery in Asia.
Explanation: 'Khel Maharan' is a massive grassroots-level sports initiative launched by the Assam Government. Designed like rural Olympics, it aims to identify and nurture raw sports talent from the village and panchayat levels upward.
Explanation: The 'Asom Mala' program is an ambitious flagship project of the Assam Government aimed explicitly at the comprehensive widening, upgrading, and maintenance of State Highways and Major District Roads to ensure high-speed, seamless internal connectivity.
Explanation: The historic 'Namsai Declaration' was signed in July 2022 between the Chief Ministers of Assam (Himanta Biswa Sarma) and Arunachal Pradesh (Pema Khandu) to limit the number of disputed border villages to 86 and expedite a peaceful resolution.
Explanation: The Lohit River is a principal tributary of the Brahmaputra. Its name derives from the Sanskrit word 'Lauhitya' (meaning red or blood). According to Hindu mythology, the sage Parashurama washed his blood-stained axe in its waters after committing matricide.
Explanation: Chaolung Sukapha, the revered founder of the Ahom kingdom, instituted the tradition of compiling Buranjis. These were meticulously written historical chronicles that systematically recorded the political, social, and diplomatic events of the kingdom.
Explanation: The Assam Public Service Commission (APSC) was established on April 1, 1937, under the provisions of the Government of India Act, 1935, to ensure a transparent and merit-based recruitment process for civil services in the province.
Explanation: Written by Sahityarathi Lakshminath Bezbaroa, 'O Mur Apunar Desh' is a deeply moving patriotic song. It was officially recognized and adopted as the state anthem of Assam at the historic Asam Chhatra Sanmilan held in Tezpur in 1927.
Explanation: Bora Saul is a highly celebrated variety of glutinous (sticky) rice cultivated extensively in Assam. It holds immense cultural significance and is the primary ingredient used to prepare traditional Assamese snacks like pithas, larus, and Jolpan, particularly during Bihu festivals.
Explanation: Located in the Golaghat district of Assam, Numaligarh is synonymous with the Numaligarh Refinery Limited (NRL). It was established in 1993 as a key provision of the historic 'Assam Accord' to boost the industrial and economic development of the region.
Explanation: According to the 2011 Census of India, the Kamrup Metropolitan district has the highest urban population in Assam. It contains the bustling capital city of Guwahati, which serves as the primary commercial and administrative hub of Northeast India.
Explanation: In April 2023, Prime Minister Narendra Modi officially inaugurated the All India Institute of Medical Sciences (AIIMS) in Changsari, Guwahati. This state-of-the-art facility was established to provide premier healthcare and medical education to the people of the Northeast.
Explanation: 'Pragyan Bharati' is a flagship educational scheme by the Assam Government. It ensures completely free admission (fee waiver) for students enrolling in Higher Secondary, Degree, and Postgraduate programs across provincialized and government colleges, benefiting lakhs of students annually.
Explanation: The Bardoli Satyagraha of 1928, located in the state of Gujarat, was a major episode of civil disobedience in the Indian Independence movement. Vallabhbhai Patel brilliantly organized and led the farmers against unjust tax hikes, earning him the prestigious title of 'Sardar' from the women of Bardoli.
Explanation: The Securities and Exchange Board of India (SEBI) is the principal regulatory body for securities and commodity markets in India under the ownership of the Ministry of Finance. Its corporate headquarters is located at the Bandra Kurla Complex in Mumbai.
Explanation: Marie Skłodowska Curie was a pioneering physicist and chemist. She made history as the first woman to win a Nobel Prize (Physics in 1903) and remains the only woman to win Nobel Prizes in two distinct scientific fields (she later won the Nobel Prize in Chemistry in 1911 for discovering radium and polonium).
Explanation: The Kyoto Protocol is an international treaty adopted in 1997 in Kyoto, Japan. It operationalized the United Nations Framework Convention on Climate Change by committing industrialized countries to legally binding targets for limiting and reducing greenhouse gas emissions to combat global warming.
Explanation: The Higgs Boson is an elementary particle in the Standard Model of particle physics, crucial for explaining why other particles have mass. It gained massive public attention and was dubbed "The God Particle" following the title of a popular science book by Nobel laureate Leon Lederman.
Explanation: The Eighth Schedule of the Indian Constitution lists the official languages recognized by the Republic of India. Currently, it recognizes 22 languages, including Assamese, Hindi, Bengali, and Bodo, ensuring their development and representation.
Explanation: The Great Victoria Desert is the largest desert in Australia. It is a vast, sparsely populated ecoregion consisting of sandhills and salt lakes, covering parts of Western Australia and South Australia.
Explanation: A Grammy Award (originally called Gramophone Award) is presented by the Recording Academy to recognize outstanding achievements and excellence in the global music recording industry. It is the music equivalent of the Oscars (film) or the Emmys (television).
Explanation: The Ryder Cup is a famous biennial men's golf competition fiercely contested between teams representing Europe and the United States. It is uniquely known for its intense team spirit in a traditionally individual sport.
Explanation: WLAN stands for Wireless Local Area Network. It is a computer network that links two or more devices using wireless communication (typically Wi-Fi) to form a local area network within a limited area such as a home, school, or office building.
Explanation: The framers of the Indian Constitution borrowed several features from other nations. The concept of the 'Concurrent List' (a list of subjects where both the Central and State governments can legislate) was adopted from the Constitution of Australia.
Explanation: Kalaripayattu is an ancient and highly dynamic martial art form that originated in the southern state of Kerala. Considered one of the oldest surviving martial arts in the world, it incorporates strikes, kicks, grappling, and weaponry.
Explanation: In a historic shift of policy following geopolitical tensions in Europe, Finland officially abandoned its long-standing military non-alignment and became the 31st member state of NATO (North Atlantic Treaty Organization) on April 4, 2023.
Explanation: "1984" (Nineteen Eighty-Four) is a classic dystopian social science fiction novel published in 1949 by English author George Orwell. It introduced iconic concepts like 'Big Brother', 'Thought Police', and the terrifying reality of mass surveillance and totalitarianism.
Explanation: Demography is the statistical study of human populations. It encompasses the study of the size, structure, and geographic distribution of populations, as well as spatial or temporal changes in them in response to birth, migration, aging, and death.
Explanation: The Kalinga War (circa 261 BCE) was fought by the Mauryan Emperor Ashoka against the state of Kalinga. The massive bloodshed and destruction profoundly affected Ashoka, leading him to abandon military conquest, embrace Buddhism, and adopt a policy of 'Dhamma' (non-violence).
Explanation: Diamond is an allotrope of carbon where the atoms are arranged in a rigid, highly stable crystal structure called a diamond cubic. This unique atomic bonding makes it the hardest naturally occurring substance known on Earth, widely used for cutting and drilling tools.
Explanation: The Indian Constitution stipulates that to be appointed as the Prime Minister, a person must be a citizen of India and a member of either the Lok Sabha or the Rajya Sabha. The minimum age required to be a member of the Lok Sabha is 25 years (and 30 years for the Rajya Sabha).
Explanation: The Nile River, flowing predominantly northwards into the Mediterranean Sea, is generally considered the longest river in the world (and Africa), stretching approximately 6,650 kilometers. It was historically crucial for the flourishing of ancient Egyptian civilization.
Explanation: SSD stands for Solid State Drive. It is a new generation of storage device used in computers that relies on flash memory chips to read and write data, making it significantly faster, quieter, and more durable than traditional mechanical Hard Disk Drives (HDDs).
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