HOME ACADEMY
Exam held on 25 oct 2026
General Awareness, Jammu & Kashmir GK, Reasoning, English and Mathematics
Instructions: Each question carries four options. Attempt all questions before checking the answer key and explanations provided at the end.
PART I: QUESTION PAPER
Section A: General Awareness and Science
Q1. Match the organisations in Column A with their member countries in Column B.
Column A: (i) SAARC (ii) ASEAN (iii) BRICS (iv) G-7
Column B: (a) India, Bangladesh, Nepal, Sri Lanka, Maldives, Bhutan, Afghanistan, Pakistan (b) Canada, France, Germany, Italy, Japan, United Kingdom, United States (c) Indonesia, Malaysia, Singapore, Thailand, Philippines, Brunei, Vietnam, Laos, Myanmar, Cambodia (d) Brazil, Russia, India, China, South Africa, Egypt, Ethiopia, Iran, United Arab Emirates, Indonesia
A) i-b, ii-a, iii-c, iv-d
B) i-b, ii-d, iii-a, iv-c
C) i-a, ii-c, iii-d, iv-b
D) i-b, ii-c, iii-d, iv-a
Q2. Which sport uses terms like Birdie, Eagle and Bogey?
A) Cricket
B) Golf
C) Baseball
D) Archery
Q3. Which of the following statements about India's Aditya-L1 mission are correct?
I. Aditya-L1 is India's first dedicated solar observatory mission.
II. It is positioned in a halo orbit around the Lagrangian point L1.
III. The mission studies the Sun's chromosphere and corona.
IV. Aditya-L1 was designed and developed by the UR Rao Satellite Centre.
A) Only I
B) Only II and III
C) Only I, II and IV
D) All of the above
Q4. Arrange the following in chronological order:
I. Establishment of Nuclear Power Corporation of India Limited (NPCIL)
II. Pokhran-I (Smiling Buddha)
III. Commissioning of Apsara reactor
IV. Formation of the Atomic Energy Commission
A) IV-III-II-I
B) III-I-II-IV
C) IV-II-III-I
D) III-IV-I-II
Q5. Match the Padma Bhushan 2026 awardees with their fields.
List I: (i) Alka Yagnik (ii) Dr. Nori Dattatreyudu (iii) Vellappally Natesan (iv) Vijay Amritraj
List II: (a) Public Affairs (b) Sports (c) Art (d) Medicine
A) i-c, ii-d, iii-a, iv-b
B) i-a, ii-d, iii-c, iv-b
C) i-c, ii-a, iii-d, iv-b
D) i-d, ii-c, iii-a, iv-b
Q6. Match the New Seven Wonders of the World with their countries.
List I: (i) Chichen Itza (ii) Petra (iii) Machu Picchu (iv) Colosseum
List II: (a) Jordan (b) Peru (c) Mexico (d) Italy
A) i-c, ii-a, iii-b, iv-d
B) i-a, ii-c, iii-d, iv-b
C) i-c, ii-b, iii-a, iv-d
D) i-d, ii-a, iii-b, iv-c
Q7. Which State–Thermal Power Plant pair is NOT correct?
A) Andhra Pradesh – Simhadri Super Thermal Power Plant
B) Bihar – Bhilai Power Plant
C) Gujarat – Mundra Thermal Power Plant
D) Madhya Pradesh – Vindhyachal Super Thermal Power Plant
Q8. Jammu and Kashmir formally became a Union Territory under the Jammu and Kashmir Reorganisation Act on:
A) 5 August 2019
B) 15 August 2019
C) 23 October 2019
D) 31 October 2019
Q9. Consider the following statements about Sheetal Devi.
I. She became the first female armless archer to win an individual gold medal at the 2025 World Para Archery Championships in Gwangju, South Korea.
II. She also secured silver in the women's team event and bronze in the mixed team event at the 2025 World Para Archery Championships.
III. She won a gold medal at the 2024 Paris Paralympics.
IV. She received the Arjuna Award in 2024.
A) I, II and IV only
B) I, III and IV only
C) II, III and IV only
D) I, II and III only
Q10. As of 2002, the Constitution of Jammu and Kashmir contained:
A) 120 Sections and 10 Schedules
B) 158 Sections and 7 Schedules
C) 200 Sections and 8 Schedules
D) 395 Articles and 13 Schedules
Section B: Jammu and Kashmir General Knowledge
Q11. The Jammu region mainly experiences which type of climate?
A) Polar climate
B) Subtropical climate
C) Mediterranean climate
D) Tundra climate
Q12. Identify the crop based on the following statements.
I. It is a Rabi crop requiring cool and moist conditions initially and warm, dry weather at harvest.
II. It grows well in areas receiving approximately 50–70 cm of annual rainfall.
III. It is generally sown in August and harvested in March–April.
A) Rice
B) Wheat
C) Maize
D) Cotton
Q13. Which statements about the Banihal–Qazigund Road Tunnel are correct?
I. It is an 8.45 km single-tube tunnel on National Highway 144.
II. It connects Banihal and Qazigund, passing beneath the Pir Panjal Range.
III. It carries four lanes of traffic and is situated at an elevation of approximately 1,790 metres.
A) Only II
B) Only I and II
C) Only II and III
D) All of the above
Q14. Match the National Highways in Jammu and Kashmir with their descriptions.
List I: (i) NH-1 (ii) NH-44 (iii) NH-144A (iv) NH-444
List II: (a) Uri–Baramulla–Srinagar–Kargil–Leh route (b) Srinagar–Banihal–Jammu–Kathua route (c) Srinagar–Budgam–Pulwama–Shopian–Kulgam–Qazigund route (d) Jammu–Akhnoor–Nowshera–Rajouri–Poonch route
A) i-a, ii-b, iii-d, iv-c
B) i-a, ii-c, iii-d, iv-b
C) i-d, ii-b, iii-a, iv-c
D) i-c, ii-b, iii-a, iv-d
Q15. Which river originates from the Kailash Kund area in the Bhaderwah region of Doda district?
A) Marusudar
B) Ujh
C) Chenab
D) Tawi
Q16. Which tourist destination is NOT correctly matched with its location?
A) Betaab Valley – Anantnag district
B) Wular Lake – Bandipora district
C) Verinag – Kupwara district
D) Doodhpathri – Budgam district
Q17. Match the fauna of Jammu and Kashmir with their scientific names.
List I: (i) Musk Deer (ii) Markhor (iii) Hangul (iv) Himalayan Thar
List II: (a) Hemitragus jemlahicus (b) Capra falconeri (c) Moschus chrysogaster (d) Cervus elaphus hanglu
A) i-c, ii-b, iii-d, iv-a
B) i-d, ii-b, iii-c, iv-a
C) i-b, ii-c, iii-a, iv-d
D) i-a, ii-b, iii-c, iv-d
Section C: Reasoning and Mental Ability
Q18. Find the next number in the series:
2, 5, 13, 35, 97, ?
A) 250
B) 275
C) 300
D) 302
Q19. Find the next number in the series:
1, 2, 6, 21, 88, 445, ?
A) 2676
B) 2767
C) 2881
D) 2941
Q20. Find the next letter in the series:
A, B, D, H, P, F, ?
A) I
B) J
C) K
D) L
Q21. Find the next letter in the series:
B, E, J, M, Z, C, ?
A) F
B) G
C) I
D) J
Q22. If TABLE = UCEMG and CHAIR = DJDJT, then PENCIL = ?
A) QGQDKO
B) QFODJM
C) QHQDKN
D) QFODKN
Q23. A man starts facing North. He turns right 45°, left 135°, right 180°, left 225° and right 90°. Which direction is he finally facing?
A) North-East
B) North-West
C) South-East
D) South-West
Q24. A boy walks 16 km East, 12 km South, 20 km West, 8 km North, 12 km East and 4 km South. Find the shortest distance from his starting point.
A) (4\sqrt2) km
B) 4 km
C) (8\sqrt2) km
D) 8 km
Q25. A says: “B is the son of the only daughter of my mother's husband's father. C is the sister of B's father. D is the only son of C's mother's husband. D is A's father and A is the only child of D. E is the daughter of A.” How is B related to A?
A) Brother
B) Nephew
C) Cousin
D) Uncle
Q26. A can complete a piece of work in 8 days, B in 18 days and C in 24 days. All three start working together. After one day, A leaves. How many more days will B and C take to finish the remaining work?
A) 4 days
B) 5 days
C) 6 days
D) 8 days
Q27. A team of 15 workers can finish a project in 20 days. After 8 days, five workers leave. How many extra days will the remaining workers take to finish the project compared with the original schedule?
A) 6 days
B) 8 days
C) 12 days
D) 18 days
Q28. Two trains start simultaneously from stations 480 km apart and move towards each other. Train A travels 50% faster than Train B. They meet after 3 hours. After meeting, Train A reduces its speed by 50%, while Train B increases its speed by 50%. Find the sum of the times taken by both trains to reach their destinations after meeting.
A) 7 hours
B) 7.5 hours
C) 8 hours
D) 8.5 hours
**Q29. All engineers are intelligent. Some intelligent people are writers. No writer is dishonest.
Conclusions:
I. Some intelligent people are not dishonest.
II. Some engineers are not dishonest.
III. No engineer is dishonest.
A) Only I follows
B) Only II follows
C) Only I and II follow
D) Only III follows
Q30. Statement: Some books are novels. All novels are interesting. Which conclusion definitely follows?
A) Some books are interesting.
B) All books are interesting.
C) All interesting things are books.
D) Some interesting things are not novels.
Section D: English Language
Reading Comprehension for Questions 31 and 32
Read the passage and answer the questions.
Artificial Intelligence (AI) is rapidly transforming the global workplace. Unlike previous technological revolutions that mainly replaced physical labour, AI is reshaping cognitive and creative work as well. Tasks such as data analysis, content writing, customer service and even medical diagnosis are increasingly being handled by intelligent machines. This has sparked a worldwide debate about whether AI is a threat to human employment or an opportunity for a better future.
Experts argue that AI will eliminate certain repetitive and routine jobs while simultaneously creating new roles requiring critical thinking, emotional intelligence, creativity and ethical judgment. The key challenge for governments and institutions is to invest in reskilling and upskilling the workforce so that people can adapt to an AI-driven economy. Countries that treat AI as a partner rather than a replacement stand to gain the most. Ultimately, the impact of AI on work depends not only on the technology itself but also on the choices societies make in deploying it responsibly.
Q31. What is the key responsibility of governments in the age of AI, according to the passage?
A) Banning AI from workplaces to protect jobs
B) Allowing only large corporations to use AI
C) Slowing down AI research to prevent unemployment
D) Investing in reskilling and upskilling the workforce
Q32. Which attitude towards AI does the passage recommend that countries adopt?
A) View AI as a competitor that must be controlled strictly
B) Avoid AI adoption until its effects are fully understood
C) Use AI only in sectors where human labour is unavailable
D) Treat AI as a partner rather than a replacement
Q33. Choose the option that identifies the error in the sentence: “The team of scientists have made a remarkable discovery that will change our understanding of the universe.”
A) “discovery” should be “discoveries”
B) “have made” should be “has made”
C) “will change” should be “would change”
D) “understanding of” should be “understanding”
Q34. Arrange the following sentences in the correct order.
P. Soon, dark clouds covered the sky.
Q. We decided to postpone the picnic.
R. The weather was pleasant in the morning.
S. Heavy rain started within a few minutes.
A) Q-R-P-S
B) R-P-S-Q
C) R-S-Q-P
D) Q-R-S-P
Q35. Convert the sentence from indirect speech to direct speech: “The teacher warned the students that they must not waste their time.”
A) The teacher said, “You must not waste your time.”
B) The teacher said to students, “They must not waste their time.”
C) The teacher warned the students, “We must not waste our time.”
D) The teacher said to the students, “You must not waste your time.”
Q36. Fill in the blank with the most suitable modal: “She has been studying all week. She _____ be exhausted by now.”
A) Can
B) Must
C) May
D) Would
Q37. Fill in the blanks with the most appropriate modals: “The roads are slippery after the rain. You _____ drive carefully, and you _____ avoid using your phone while driving.”
A) Can; could
B) May; should
C) Ought to; could
D) Should; must
Q38. Fill in the blanks with the most appropriate articles: “My father is _____ honest man and _____ university professor.”
A) An; a
B) A; the
C) An; the
D) A; a
Q39. Identify the sentence with the correct use of articles.
A) She plays a piano beautifully.
B) She bought a umbrella from the market.
C) I saw an one-eyed man near the park.
D) He is the best player in the team.
Reading Comprehension for Questions 40–43
Read the passage and answer the questions.
Last Sunday, Riya and her brother Rohan decided to visit the old library in (1) _____ neighbourhood. They had heard that the library (2) _____ a rare collection of books on Indian history. When they arrived, the librarian, who was already busy arranging shelves, greeted (3) _____ warmly. Riya picked up a book about the (4) _____ of India's freedom struggle. The (5) _____ of knowledge she gained that day was truly priceless. “I (6) _____ this place again next week,” she whispered to Rohan. Outside, they could (7) _____ the sound of children playing, and the (8) _____ weather made everything feel perfect. Both of them left the library feeling inspired and grateful.
Q40. Fill blanks (1) and (3) with the most appropriate pronouns.
A) His; their
B) Her; them
C) Their; them
D) Our; they
Q41. Fill blanks (2) and (6) with the most appropriate verb forms.
A) Has; visited
B) Has; will visit
C) Had; will visit
D) Has; would visit
Q42. Fill blanks (4) and (7) with the appropriate homophones.
A) Tail; hear
B) Tale; hear
C) Tail; here
D) Tale; here
Q43. Fill blanks (5) and (8) with the most appropriate phrases.
A) Wealth; cold and windy
B) Amount; hot and humid
C) Lack; warm and sunny
D) Wealth; cool and breezy
Q44. Which sentence contains a noun clause?
A) The girl who won the prize is my sister.
B) He ran fast but missed the bus.
C) I believe that honesty is the best policy.
D) She smiled when she saw him.
Q45. Which sentence uses the apostrophe correctly?
A) The dog wagged it's tail happily.
B) Its' a beautiful morning today.
C) The childrens' playground was repaired.
D) Riya's handwriting is the neatest in the entire class.
Q46. The synonym of “Eloquent” is:
A) Halting
B) Maundering
C) Articulate
D) Stuttering
Q47. The antonym of “Benevolent” is:
A) Sympathetic
B) Philanthropic
C) Altruistic
D) Malevolent
Q48. Fill in the blanks: “The school bus remained _____ for an hour while the students rushed to buy _____ from the nearby shop.”
A) Stationary; stationery
B) Stationery; stationary
C) Stationery; stationery
D) Stationary; stationary
Section E: Mathematics and Quantitative Aptitude
Q49. In a GP, the first term is (a) and the common ratio is (r). The sum of the first two terms is 18, and the sum of the second and third terms is 54. Find (2(a+r)).
A) 6
B) 9
C) 12
D) 15
Q50. The simple interest on a sum for 3 years is equal to the compound interest on the same sum for 2 years at the same annual rate. Find the rate of interest.
A) 50%
B) 75%
C) 100%
D) Cannot be determined
Q51. A sum of money amounts to ₹13,310 after 3 years and ₹16,105.10 after 5 years at compound interest, compounded annually. Find the original principal.
A) ₹10,000
B) ₹11,000
C) ₹11,500
D) ₹12,500
Q52. A trader buys pens and notebooks for ₹1,800. He sells all the pens at a profit of 20% and all the notebooks at a loss of 10%. If his overall profit is ₹60, find the cost price of the notebooks.
A) ₹750
B) ₹800
C) ₹900
D) ₹1,000
Q53. A dealer sells two articles for ₹960 each. He makes a profit of (x%) on one article and a loss of (x%) on the other. The overall transaction results in a loss of ₹40. If (x=100/k), find (k).
A) 3
B) 7
C) 8
D) 9
Q54. A solid sphere of radius (R) is melted and recast into (n) identical smaller spheres. If the total surface area of all the smaller spheres is five times the surface area of the original sphere, find (n).
A) 25
B) 64
C) 125
D) 216
Q55. A solid sphere is melted and recast into a cylinder. The cylinder is then melted and recast into identical cones, each having the same base radius as the cylinder and a height equal to one-third of the cylinder's height. How many cones are formed?
A) 2
B) 3
C) 6
D) 9
Q56. Three metallic spheres with radii 2 cm, 3 cm and 5 cm are melted and recast into a solid cube. Find the edge length of the cube, rounded to the nearest whole number.
A) 3 cm
B) 5 cm
C) 7 cm
D) 9 cm
PART II: ANSWER KEY AND SOLUTIONS
Section A: General Awareness and Science
Q1. Correct answer: C. SAARC corresponds to group (a), ASEAN to (c), BRICS to (d), and G-7 to (b).
Q2. Correct answer: B. Birdie, eagle and bogey are scoring terms in golf. A birdie is one stroke below par, an eagle is two below par, and a bogey is one above par.
Q3. Intended answer: D. Aditya-L1 is India's first dedicated solar observatory mission and operates in a halo orbit around the Sun–Earth L1 point. Its instruments investigate solar phenomena, including the chromosphere and corona. The wording about spacecraft development should be checked against the official ISRO mission documentation.
Q4. Correct answer: A. The chronological sequence is Atomic Energy Commission (1948), Apsara reactor (1956), Pokhran-I (1974), and NPCIL (1987).
Q5. Intended answer: A. The proposed matching is Alka Yagnik—Art, Nori Dattatreyudu—Medicine, Vellappally Natesan—Public Affairs, and Vijay Amritraj—Sports. Verify these award categories against the official 2026 Padma Awards notification before using this question for current-affairs revision.
Q6. Correct answer: A. Chichen Itza is in Mexico, Petra in Jordan, Machu Picchu in Peru, and the Colosseum in Italy.
Q7. Correct answer: B. Bhilai is in Chhattisgarh, not Bihar. The other listed plant-state pairs are correct.
Q8. Correct answer: D. The Jammu and Kashmir Reorganisation Act, 2019, came into effect on 31 October 2019, creating the Union Territories of Jammu and Kashmir and Ladakh.
Q9. No correct option as written. Statement III is false because Sheetal Devi won bronze in the mixed team compound event at the 2024 Paris Paralympics, not gold. Her Arjuna Award was part of the 2023 National Sports Awards, presented in January 2024. The question's intended statements I and II need independent verification against the 2025 championship results, and no option lists I and II alone.
Q10. Intended answer: B. The former Constitution of Jammu and Kashmir is commonly described as containing 158 Articles and 7 Schedules. The option incorrectly says “Sections”; it should say “Articles.”
Section B: Jammu and Kashmir General Knowledge
Q11. Correct answer: B. The Jammu plains generally experience a subtropical climate, with hot summers, monsoon rainfall and relatively cool winters. Mountainous areas have different climatic conditions.
Q12. Intended answer: B. Wheat is a Rabi crop requiring cool growing conditions and warmer, dry weather for ripening. However, the statement that it is generally sown in August is incorrect for the usual wheat season in northern India. The question needs correction.
Q13. Correct answer: C, as intended. Statement I is false because the Banihal–Qazigund tunnel is a twin-tube tunnel, not a single-tube tunnel, and it forms part of NH-44. Statements II and III are intended to be correct.
Q14. Correct answer: A. The intended matches are NH-1 with the Uri–Leh route, NH-44 with the Srinagar–Jammu route, NH-144A with the Jammu–Poonch route, and NH-444 with the Srinagar–Qazigund route. For examination use, confirm the exact termini and highway descriptions from the current official road records.
Q15. Correct answer: D. The Tawi is associated with the Kailash Kund region near Bhaderwah and ultimately joins the Chenab River.
Q16. Correct answer: C. Verinag is in Anantnag district, not Kupwara district.
Q17. Correct answer: A. The intended matches are Musk Deer—Moschus chrysogaster, Markhor—Capra falconeri, Hangul—Cervus elaphus hanglu, and Himalayan Thar—Hemitragus jemlahicus.
Section C: Reasoning and Mental Ability
Q18. Correct answer: B (275). Multiply each term by 2 and add successive powers of 3: (2\times2+1=5), (5\times2+3=13), (13\times2+9=35), (35\times2+27=97). Therefore, (97\times2+81=275).
Q19. Correct answer: A (2676). The pattern is multiplication by successive integers followed by addition of the same integer: (1\times1+1=2), (2\times2+2=6), (6\times3+3=21), (21\times4+4=88), (88\times5+5=445). The next term is (445\times6+6=2676).
Q20. Correct answer: D (L), using the intended pattern. The letter positions double successively: 1, 2, 4, 8, 16, 32 and 64. Converting these positions cyclically within the alphabet gives A, B, D, H, P, F and L. The cyclic rule should be stated explicitly in a properly designed question.
Q21. No uniquely established answer. The supplied sequence does not provide a sufficiently clear, conventional rule to establish one option confidently. Option A (F) was the apparent intended answer, but it should not be treated as a verified solution without a defined pattern.
Q22. Correct answer: A (QGQDKO), using the intended rule. Apply repeating shifts of +1, +2 and +3 to PENCIL: P→Q, E→G, N→Q, C→D, I→K and L→O. However, the given TABLE and CHAIR examples do not consistently follow that same rule, so the question is internally defective.
Q23. Correct answer: B (North-West). The net turn is (45^\circ-135^\circ+180^\circ-225^\circ+90^\circ=-45^\circ). The person ends 45° anticlockwise from North, facing North-West.
Q24. Correct answer: C ((8\sqrt2) km). Net horizontal displacement is (16-20+12=8) km East. Net vertical displacement is (12-8+4=8) km South. Therefore, the shortest distance is (\sqrt{8^2+8^2}=8\sqrt2) km.
Q25. No reliable answer. The family relationships are contradictory or ambiguous when interpreted literally. Rewrite the family tree before assigning an answer.
Q26. Correct answer: D (8 days). The three workers complete (1/8+1/18+1/24=2/9) of the work in the first day. The remaining work is (7/9). B and C together complete (1/18+1/24=7/72) per day. Thus, ( (7/9)/(7/72)=8) more days.
Q27. Correct answer: A (6 extra days). Total work is (15\times20=300) worker-days. After 8 days, 120 worker-days have been completed, leaving 180 worker-days. Ten workers need 18 more days, whereas the original schedule required 12 more days. Extra time is (18-12=6) days.
Q28. Correct answer: A (7 hours). Combined initial speed is (480/3=160) km/h. If B's speed is (x), A's is (1.5x), so (2.5x=160), giving B = 64 km/h and A = 96 km/h. Before meeting, A covers 288 km and B covers 192 km. After meeting, A travels the remaining 192 km at 48 km/h in 4 hours; B travels 288 km at 96 km/h in 3 hours. Their times total 7 hours.
Q29. Correct answer: A (Only I follows). Some intelligent people are writers, and no writer is dishonest. Therefore, some intelligent people are not dishonest. The premises do not establish whether any engineers are writers, so conclusions II and III do not follow.
Q30. Correct answer: A. Some books are novels, and all novels are interesting. Therefore, at least some books are interesting.
Section D: English Language
Q31. Correct answer: D. The passage explicitly identifies investment in reskilling and upskilling as a key responsibility of governments and institutions.
Q32. Correct answer: D. The passage recommends treating AI as a partner rather than a replacement for human workers.
Q33. Correct answer: B. In the standard singular collective-noun construction, “team” takes “has made.” The corrected sentence is: “The team of scientists has made a remarkable discovery that will change our understanding of the universe.”
Q34. Correct answer: B. The logical sequence is R-P-S-Q: pleasant morning, dark clouds, heavy rain, and the decision to postpone the picnic.
Q35. Best available answer: D. The teacher is directly addressing the students, so “they/their” changes to “you/your.” A more precise conversion retaining the reporting verb is: “The teacher warned the students, ‘You must not waste your time.’”
Q36. Correct answer: B (Must). “Must” expresses a strong logical deduction: studying all week suggests that she is probably exhausted.
Q37. Correct answer: D (Should; must). “Should” gives advice to drive carefully, while “must” expresses a strong obligation to avoid phone use while driving.
Q38. Correct answer: A (An; a). “Honest” begins with a vowel sound because the h is silent. “University” begins with the consonant sound /juː/, so “a university professor” is correct.
Q39. Correct answer: D. “The best player” uses the definite article with a superlative adjective. The other sentences have errors: “play the piano,” “an umbrella,” and “a one-eyed man.”
Q40. Correct answer: C (Their; them). “Their neighbourhood” refers to Riya and Rohan, and “greeted them warmly” correctly uses the object pronoun.
Q41. Correct answer: B (Has; will visit). “The library has a rare collection” states a present fact, and “I will visit this place again next week” expresses a future intention.
Q42. Correct answer: B (Tale; hear). “Tale” means a story, while “hear” means to perceive sound.
Q43. Correct answer: D (Wealth; cool and breezy). “A wealth of knowledge” is an idiomatic expression, and “cool and breezy weather” fits the positive tone of the passage.
Q44. Correct answer: C. In “I believe that honesty is the best policy,” the clause “that honesty is the best policy” acts as the object of the verb “believe.”
Q45. Correct answer: D. “Riya's” correctly uses an apostrophe to indicate possession. “It's” means “it is” or “it has”; “its” is possessive. The correct plural possessive of “children” is “children's.”
Q46. Correct answer: C (Articulate). Eloquent means fluent, expressive and persuasive in speech or writing.
Q47. Correct answer: D (Malevolent). Benevolent means kind or well-meaning; malevolent means wishing harm to others.
Q48. Correct answer: A (Stationary; stationery). “Stationary” means not moving, whereas “stationery” means writing materials.
Section E: Mathematics and Quantitative Aptitude
Q49. Correct answer: D (15).
Given (a+ar=18) and (ar+ar^2=54).
Factor the second equation:
Since (a+ar=18), we get (18r=54), so (r=3).
Then (a(1+3)=18), giving (a=4.5).
Therefore,
Q50. Correct answer: C (100%).
Let the principal be (P) and the annual rate in decimal form be (i).
Simple interest for 3 years is (3Pi). Compound interest for 2 years is (P=P(2i+i^2)).
Equating the two gives (3Pi=P(2i+i^2)). For a positive rate, (i=1), or 100% per annum.
Q51. Correct answer: A (₹10,000).
The ratio of the 5-year amount to the 3-year amount represents compound growth over two years:
Therefore, ((1+r)^2=1.21), so (1+r=1.1) and the annual rate is 10%.
Q52. Correct answer: D (₹1,000).
Let the cost of pens be (x) and the cost of notebooks be (y).
Overall profit gives (0.20x-0.10y=60), or (2x-y=600).
Substituting (y=1800-x) gives (3x=2400), so (x=800). Hence, the cost of notebooks is (1800-800=₹1,000).
Q53. Correct answer: B (7).
The total selling price is ₹1,920. Since the overall loss is ₹40, the total cost price is ₹1,960.
For equal selling prices with equal percentage profit and loss:
Solving gives (x^2/10000=1/49), so (x=100/7). Since (x=100/k), (k=7).
Q54. Correct answer: C (125).
Conservation of volume gives (nr^3=R^3), where (r) is the radius of each smaller sphere.
The surface-area condition is (nr^2=5R^2).
Dividing the two relations gives (r=R/5). Substituting into the volume equation gives:
Therefore, (n=125).
Q55. Correct answer: D (9).
Cylinder volume is (\pi r^2h).
Each cone has base radius (r) and height (h/3), so its volume is:
Each cone has one-ninth of the cylinder's volume. Therefore, 9 cones are formed.
Q56. Correct answer: D (9 cm).
The total volume of the three spheres is:
If the cube's edge is (a), then (a^3=670.21), giving (a\approx8.75) cm. Rounded to the nearest whole number, the edge is 9 cm.