📋 MOCK TEST – SET 30
WBSSC Group C (Clerk) Written Exam Preparation
Total: 60 Questions | GA: 20 | English: 10 | Reasoning: 10 | Arithmetic: 20 | Click option to reveal answer & explanation
SECTION A: GENERAL AWARENESS (Q.1–Q.20) — 20 Marks
Q.1. Under NEP 2020, the ‘Academic Bank of Credits (ABC)’ allows students to: NEP 2020
Answer: (2) Store and transfer academic credits
Academic Bank of Credits (ABC) under NEP 2020: a national-level facility allowing students to store credits earned from different HEIs in a digital account and transfer or redeem them. Supports multiple entry/exit — Certificate (1 yr), Diploma (2 yr), Degree (3 yr), Honours (4 yr).
Academic Bank of Credits (ABC) under NEP 2020: a national-level facility allowing students to store credits earned from different HEIs in a digital account and transfer or redeem them. Supports multiple entry/exit — Certificate (1 yr), Diploma (2 yr), Degree (3 yr), Honours (4 yr).
Q.2. NEP 2020 proposes a ‘National Research Foundation (NRF)’ to: NEP 2020
Answer: (2) Fund and promote research across disciplines
NRF (Anusandhan NRF) established under NEP 2020. Enacted 2023. Seed, grow and promote research and innovation across universities, colleges and research institutions. Modelled on US NSF. ₹50,000 crore outlay over 5 years. PM chairs governing board.
NRF (Anusandhan NRF) established under NEP 2020. Enacted 2023. Seed, grow and promote research and innovation across universities, colleges and research institutions. Modelled on US NSF. ₹50,000 crore outlay over 5 years. PM chairs governing board.
Q.3. Under NEP 2020, ‘HECI’ (Higher Education Commission of India) will replace: NEP 2020
Answer: (2) UGC, AICTE and other regulatory bodies
NEP 2020 proposes HECI as a single, overarching umbrella body to replace UGC, AICTE, NCTE and other regulators. HECI will have four verticals: NHERC (regulation), NAC (accreditation), HEGC (grants), GEC (general education).
NEP 2020 proposes HECI as a single, overarching umbrella body to replace UGC, AICTE, NCTE and other regulators. HECI will have four verticals: NHERC (regulation), NAC (accreditation), HEGC (grants), GEC (general education).
Q.4. NEP 2020 emphasises ‘Experiential Learning’. This includes: NEP 2020
Answer: (2) Arts integration, project-based, hands-on
NEP 2020 promotes experiential learning — learning by doing. Includes arts integration, sports, yoga, craft, project-based learning, field trips, internships, community engagement. Moves away from rote learning to holistic, competency-based education.
NEP 2020 promotes experiential learning — learning by doing. Includes arts integration, sports, yoga, craft, project-based learning, field trips, internships, community engagement. Moves away from rote learning to holistic, competency-based education.
Q.5. The ‘Rowlatt Act’ (1919) was passed to: Indian History
Answer: (2) Detain without trial
Rowlatt Act 1919: allowed the British to imprison political suspects without trial. Called “Black Act” by Indians. Gandhi launched Satyagraha against it. Led to Jallianwala Bagh massacre (April 1919, Gen. Dyer).
Rowlatt Act 1919: allowed the British to imprison political suspects without trial. Called “Black Act” by Indians. Gandhi launched Satyagraha against it. Led to Jallianwala Bagh massacre (April 1919, Gen. Dyer).
Q.6. ‘Salt Satyagraha / Dandi March’ was undertaken by Gandhi in: Indian History
Answer: (2) 1930
Dandi March (12 March – 6 April 1930): Gandhi walked 241 miles from Sabarmati to Dandi (Gujarat) to make salt from seawater, defying the British salt tax. Launched Civil Disobedience Movement. Worldwide media coverage.
Dandi March (12 March – 6 April 1930): Gandhi walked 241 miles from Sabarmati to Dandi (Gujarat) to make salt from seawater, defying the British salt tax. Launched Civil Disobedience Movement. Worldwide media coverage.
Q.7. The ‘Jalpaiguri’ district of West Bengal is known for: West Bengal
Answer: (2) Tea gardens and Dooars forests
Jalpaiguri (North Bengal) is famous for tea gardens (Dooars tea), Buxa Tiger Reserve, Jaldapara National Park (one-horned rhino), and Dooars forests. Tourism hub of northern WB. Teesta and Torsa rivers flow through it.
Jalpaiguri (North Bengal) is famous for tea gardens (Dooars tea), Buxa Tiger Reserve, Jaldapara National Park (one-horned rhino), and Dooars forests. Tourism hub of northern WB. Teesta and Torsa rivers flow through it.
Q.8. ‘Photosynthesis’ in plants takes place in the: Science
Answer: (2) Chloroplast
Photosynthesis occurs in chloroplasts — organelles containing chlorophyll (green pigment). Light reactions in thylakoid; Calvin cycle in stroma. 6CO₂ + 6H₂O + light → C₆H₁₂O₆ + 6O₂. Mitochondria = respiration (opposite process).
Photosynthesis occurs in chloroplasts — organelles containing chlorophyll (green pigment). Light reactions in thylakoid; Calvin cycle in stroma. 6CO₂ + 6H₂O + light → C₆H₁₂O₆ + 6O₂. Mitochondria = respiration (opposite process).
Q.9. The ‘Cabinet Mission Plan’ (1946) proposed: Indian History
Answer: (2) United India with federal structure
Cabinet Mission Plan 1946: proposed a united India, three-tier federal structure (Centre, Provinces, Groups), Constituent Assembly. Muslim League initially accepted but later withdrew. Led ultimately to partition and Independence Act 1947.
Cabinet Mission Plan 1946: proposed a united India, three-tier federal structure (Centre, Provinces, Groups), Constituent Assembly. Muslim League initially accepted but later withdrew. Led ultimately to partition and Independence Act 1947.
Q.10. India’s ‘Unified Payments Interface (UPI)’ is operated by: Current Affairs
Answer: (2) NPCI
UPI launched 2016 by NPCI (National Payments Corporation of India). Real-time interbank mobile payment. Over 16 billion transactions/month (2024). UPI One World for foreign visitors. India-Singapore, India-UAE UPI corridors operational.
UPI launched 2016 by NPCI (National Payments Corporation of India). Real-time interbank mobile payment. Over 16 billion transactions/month (2024). UPI One World for foreign visitors. India-Singapore, India-UAE UPI corridors operational.
Q.11. ‘Article 370’ of the Indian Constitution related to the special status of J&K was abrogated in: Indian Polity
Answer: (2) 2019
Article 370 abrogated on 5 August 2019. J&K bifurcated into two Union Territories — J&K (with legislature) and Ladakh (without legislature). J&K became a full state again in November 2024 after elections.
Article 370 abrogated on 5 August 2019. J&K bifurcated into two Union Territories — J&K (with legislature) and Ladakh (without legislature). J&K became a full state again in November 2024 after elections.
Q.12. The ‘Shantiniketan’ of West Bengal was inscribed as a UNESCO World Heritage Site in: West Bengal
Answer: (2) 2023
Shantiniketan (Birbhum, WB) inscribed as UNESCO World Heritage Site in September 2023. Created by Rabindranath Tagore as an experimental open-air educational institution. India’s 41st World Heritage Site.
Shantiniketan (Birbhum, WB) inscribed as UNESCO World Heritage Site in September 2023. Created by Rabindranath Tagore as an experimental open-air educational institution. India’s 41st World Heritage Site.
Q.13. The ‘Chandrayaan-3’ mission successfully landed on the Moon’s south pole on: Current Affairs
Answer: (2) 23 August 2023
Chandrayaan-3 lander ‘Vikram’ touched down on the Moon’s south polar region on 23 August 2023 at 6:04 PM IST. India became the 4th country to land on the Moon and the 1st to land near the south pole. Rover ‘Pragyan’ deployed.
Chandrayaan-3 lander ‘Vikram’ touched down on the Moon’s south polar region on 23 August 2023 at 6:04 PM IST. India became the 4th country to land on the Moon and the 1st to land near the south pole. Rover ‘Pragyan’ deployed.
Q.14. The ‘Election Commission of India’ is established under which article? Indian Polity
Answer: (2) Article 324
Election Commission of India established under Article 324. Independent constitutional body; superintendence, direction and control of all elections. CEC removed like a Supreme Court judge.
Election Commission of India established under Article 324. Independent constitutional body; superintendence, direction and control of all elections. CEC removed like a Supreme Court judge.
Q.15. ‘Durga Puja’ in West Bengal was inscribed by UNESCO as an Intangible Cultural Heritage in: West Bengal
Answer: (2) 2021
Durga Puja of Kolkata inscribed on UNESCO’s Representative List of Intangible Cultural Heritage of Humanity in December 2021. Recognises community participation, artistic creativity, and cultural importance.
Durga Puja of Kolkata inscribed on UNESCO’s Representative List of Intangible Cultural Heritage of Humanity in December 2021. Recognises community participation, artistic creativity, and cultural importance.
Q.16. The ‘Stand Up India’ scheme provides loans to: Current Affairs
Answer: (2) SC/ST and women entrepreneurs
Stand Up India (launched 5 April 2016): Bank loans ₹10 lakh – ₹1 crore to at least one SC/ST borrower and one woman borrower per bank branch for greenfield enterprises. Promotes entrepreneurship among marginalised communities.
Stand Up India (launched 5 April 2016): Bank loans ₹10 lakh – ₹1 crore to at least one SC/ST borrower and one woman borrower per bank branch for greenfield enterprises. Promotes entrepreneurship among marginalised communities.
Q.17. ‘Deficiency of Vitamin D’ causes: Science
Answer: (2) Rickets and Osteomalacia
Vitamin D deficiency → Rickets (children — soft, deformed bones) and Osteomalacia (adults — soft bones). Vitamin D aids calcium absorption. Sources: sunlight, fish oil, eggs. Scurvy=Vit C; Night blindness=Vit A; Beri-beri=Vit B1.
Vitamin D deficiency → Rickets (children — soft, deformed bones) and Osteomalacia (adults — soft bones). Vitamin D aids calcium absorption. Sources: sunlight, fish oil, eggs. Scurvy=Vit C; Night blindness=Vit A; Beri-beri=Vit B1.
Q.18. ‘Adjournment Motion’ in Parliament is moved to: Indian Polity
Answer: (2) Urgent public importance
Adjournment Motion: moved in Lok Sabha to draw attention to a definite matter of urgent public importance involving censure of the government. Needs support of 50 members. If admitted, normal business is suspended. Only in Lok Sabha.
Adjournment Motion: moved in Lok Sabha to draw attention to a definite matter of urgent public importance involving censure of the government. Needs support of 50 members. If admitted, normal business is suspended. Only in Lok Sabha.
Q.19. The ‘Mukutmanipur Dam’ is built on which river in West Bengal? West Bengal
Answer: (2) Kangsabati (Kasai)
Mukutmanipur Dam built on Kangsabati (Kasai) River in Bankura district, WB. One of the largest earthen dams in Asia. Tourist spot with a large reservoir. Also called Kangsabati Dam.
Mukutmanipur Dam built on Kangsabati (Kasai) River in Bankura district, WB. One of the largest earthen dams in Asia. Tourist spot with a large reservoir. Also called Kangsabati Dam.
Q.20. The ‘2036 Olympics’ bid was officially submitted by which Indian city? Current Affairs
Answer: (2) Ahmedabad
India submitted its official bid for 2036 Summer Olympics with Ahmedabad as the host city. India officially entered the IOC’s Future Host process in 2024. Also targeting 2036 as “Viksit Bharat” showcase year.
India submitted its official bid for 2036 Summer Olympics with Ahmedabad as the host city. India officially entered the IOC’s Future Host process in 2024. Also targeting 2036 as “Viksit Bharat” showcase year.
SECTION B: GENERAL ENGLISH (Q.21–Q.30) — 10 Marks
Q.21. Choose the correct synonym of ‘VINDICATE’:
Answer: (2) Clear from blame
Vindicate = to clear (someone) of blame or suspicion; to prove correct. Synonyms: Exonerate, Acquit, Justify, Absolve. Antonym: Condemn, Accuse, Blame.
Vindicate = to clear (someone) of blame or suspicion; to prove correct. Synonyms: Exonerate, Acquit, Justify, Absolve. Antonym: Condemn, Accuse, Blame.
Q.22. Choose the correct antonym of ‘VERBOSE’:
Answer: (2) Concise
Verbose = using more words than needed; long-winded. Antonyms: Concise, Brief, Terse, Succinct, Laconic.
Verbose = using more words than needed; long-winded. Antonyms: Concise, Brief, Terse, Succinct, Laconic.
Q.23. Identify the correctly spelled word:
Answer: (2) Pronunciation
Pronunciation — note: no ‘o’ after ‘n’ (not “pronounciation”). P-R-O-N-U-N-C-I-A-T-I-O-N. The root changes: “pronounce” → “pronunciation.”
Pronunciation — note: no ‘o’ after ‘n’ (not “pronounciation”). P-R-O-N-U-N-C-I-A-T-I-O-N. The root changes: “pronounce” → “pronunciation.”
Q.24. Fill in the blank: He congratulated me ________ my success.
Answer: (1) on
Congratulate (someone) on (something). “He congratulated me on my success.” Fixed preposition phrase.
Congratulate (someone) on (something). “He congratulated me on my success.” Fixed preposition phrase.
Q.25. The correct plural of ‘Criterion’ is:
Answer: (2) Criteria
Greek origin: Criterion → Criteria. Like Phenomenon→Phenomena, Medium→Media, Memorandum→Memoranda. “Criterias” is incorrect.
Greek origin: Criterion → Criteria. Like Phenomenon→Phenomena, Medium→Media, Memorandum→Memoranda. “Criterias” is incorrect.
Q.26. Idiom: “Let the cat out of the bag”
Answer: (2) Accidentally reveal a secret
“Let the cat out of the bag” = to accidentally reveal a secret or surprise. “She let the cat out of the bag about the surprise party.” Similar to “spill the beans.”
“Let the cat out of the bag” = to accidentally reveal a secret or surprise. “She let the cat out of the bag about the surprise party.” Similar to “spill the beans.”
Q.27. Choose the correct sentence:
Answer: (2)
Collective nouns (committee, team, jury) acting as one unit → singular verb + singular pronoun. “The committee has taken its decision.”
Collective nouns (committee, team, jury) acting as one unit → singular verb + singular pronoun. “The committee has taken its decision.”
Q.28. Change to Passive Voice: “The teacher is explaining the lesson.”
Answer: (2)
Present Continuous passive: is/am/are + being + past participle. “is explaining” → “is being explained.” “The lesson is being explained by the teacher.”
Present Continuous passive: is/am/are + being + past participle. “is explaining” → “is being explained.” “The lesson is being explained by the teacher.”
Q.29. One word for: A person who is new to a subject or activity.
Answer: (2) Novice
Novice = a person new to or inexperienced in a field. Synonyms: Beginner, Neophyte, Tyro, Rookie. Antonym: Expert, Veteran.
Novice = a person new to or inexperienced in a field. Synonyms: Beginner, Neophyte, Tyro, Rookie. Antonym: Expert, Veteran.
Q.30. Spot the error: “Each of the (A) / boys have (B) / submitted their (C) / assignment. (D)”
Answer: (2) B — “has submitted”
Rule: Each, Every, Either, Neither → always singular verb. “Each of the boys has submitted his assignment.” “have” → “has” is the error.
Rule: Each, Every, Either, Neither → always singular verb. “Each of the boys has submitted his assignment.” “have” → “has” is the error.
SECTION C: LOGICAL REASONING (Q.31–Q.40) — 10 Marks
Q.31. Odd one out: Pen, Pencil, Chalk, Eraser, Marker
Answer: (1) Eraser
Pen, Pencil, Chalk, Marker are all writing instruments. Eraser is used to remove writing — not a writing instrument.
Pen, Pencil, Chalk, Marker are all writing instruments. Eraser is used to remove writing — not a writing instrument.
Q.32. Complete the series: 2, 6, 12, 20, 30, 42, ___
Answer: (2) 56
Pattern: n(n+1) — 1×2=2, 2×3=6, 3×4=12, 4×5=20, 5×6=30, 6×7=42, 7×8=56.
Pattern: n(n+1) — 1×2=2, 2×3=6, 3×4=12, 4×5=20, 5×6=30, 6×7=42, 7×8=56.
Q.33. In a certain code, ‘TIGER’ is written as ‘VJIGT’. How is ‘HORSE’ coded?
Answer: (2) JQTUG
Each letter shifted +2: T→V, I→K… but V,J,I,G,T seen. Consistent +2 shift for HORSE: H+2=J, O+2=Q, R+2=T, S+2=U, E+2=G = JQTUG.
Each letter shifted +2: T→V, I→K… but V,J,I,G,T seen. Consistent +2 shift for HORSE: H+2=J, O+2=Q, R+2=T, S+2=U, E+2=G = JQTUG.
Q.34. Complete the series: 4, 8, 24, 96, 480, ___
Answer: (2) 2880
Multipliers: ×2, ×3, ×4, ×5, ×6. 4×2=8, 8×3=24, 24×4=96, 96×5=480, 480×6=2880.
Multipliers: ×2, ×3, ×4, ×5, ×6. 4×2=8, 8×3=24, 24×4=96, 96×5=480, 480×6=2880.
Q.35. P is the son of Q. Q is the brother of R. R is the father of S. How is S related to P?
Answer: (2) Cousin
P’s father = Q. Q’s brother = R. R’s child = S. Q and R are brothers → P and S share the same grandparents → cousins.
P’s father = Q. Q’s brother = R. R’s child = S. Q and R are brothers → P and S share the same grandparents → cousins.
Q.36. In a row, Meena is 8th from the left and Reena is 12th from the right. After interchange, Meena is 14th from the left. How many students are in the row?
Answer: (2) 25
After interchange, Meena takes Reena’s original position = 14th from left. Reena was 12th from right → Total = 14+12−1 = 25.
After interchange, Meena takes Reena’s original position = 14th from left. Reena was 12th from right → Total = 14+12−1 = 25.
Q.37. Ravi drives 5 km North, turns right and drives 3 km, turns right again and drives 5 km. How far and in which direction is he from start?
Answer: (2) 3 km East
North 5 km → East 3 km → South 5 km. North and South cancel. Net displacement = 3 km East.
North 5 km → East 3 km → South 5 km. North and South cancel. Net displacement = 3 km East.
Q.38. At what time between 4 and 5 o’clock are the clock hands together?
Answer: (2) 4:21 and 9/11 min
At 4:00, hour hand is 20 min spaces ahead. Minute hand gains 55/60 min per minute over hour hand. Time = 20 ÷ (55/60) = 1200/55 = 21 9/11 minutes past 4.
At 4:00, hour hand is 20 min spaces ahead. Minute hand gains 55/60 min per minute over hour hand. Time = 20 ÷ (55/60) = 1200/55 = 21 9/11 minutes past 4.
Q.39. Find the missing number: 6, 11, 21, 36, 56, ___
Answer: (2) 81
Differences: +5, +10, +15, +20, +25. Pattern = multiples of 5 increasing by 5. 56+25 = 81.
Differences: +5, +10, +15, +20, +25. Pattern = multiples of 5 increasing by 5. 56+25 = 81.
Q.40. Statements: All chairs are tables. Some tables are desks.
Conclusions: I. Some chairs are desks. II. Some desks are tables.
Conclusions: I. Some chairs are desks. II. Some desks are tables.
Answer: (2) Only II follows
“Some tables are desks” → convert → Some desks are tables (II ✓). For I: All chairs=tables, Some tables=desks — doesn’t guarantee any chair is a desk (I ✗). Only II follows.
“Some tables are desks” → convert → Some desks are tables (II ✓). For I: All chairs=tables, Some tables=desks — doesn’t guarantee any chair is a desk (I ✗). Only II follows.
SECTION D: ARITHMETIC (Q.41–Q.60) — 20 Marks
Q.41. Find the LCM and HCF of 45 and 75. Verify: LCM × HCF = Product of numbers.
Answer: (1) LCM=225, HCF=15
45=3²×5; 75=3×5². HCF=3×5=15; LCM=3²×5²=225. Verify: 225×15=3375=45×75 ✓.
45=3²×5; 75=3×5². HCF=3×5=15; LCM=3²×5²=225. Verify: 225×15=3375=45×75 ✓.
Q.42. If (x − 3)² + (y + 2)² = 0, find x + y.
Answer: (2) 1
Sum of squares = 0 → each term = 0. x−3=0 → x=3; y+2=0 → y=−2. x+y = 3+(−2) = 1.
Sum of squares = 0 → each term = 0. x−3=0 → x=3; y+2=0 → y=−2. x+y = 3+(−2) = 1.
Q.43. A, B and C start a business. A invests ₹6,000 for 6 months, B invests ₹4,000 for 8 months, C invests ₹3,000 for 12 months. In what ratio should they share the profit?
Answer: (2) 9:8:9
Effective investment: A=6000×6=36,000; B=4000×8=32,000; C=3000×12=36,000. Ratio=36,000:32,000:36,000=36:32:36=9:8:9.
Effective investment: A=6000×6=36,000; B=4000×8=32,000; C=3000×12=36,000. Ratio=36,000:32,000:36,000=36:32:36=9:8:9.
Q.44. A 250 m long train passes a man standing on a platform in 10 seconds. Find the speed of the train in km/h.
Answer: (2) 90 km/h
Speed = 250÷10 = 25 m/s = 25×(18/5) = 90 km/h.
Speed = 250÷10 = 25 m/s = 25×(18/5) = 90 km/h.
Q.45. If 20% of a number is 80, what is 35% of that number?
Answer: (2) 140
20% = 80 → number = 400. 35% of 400 = 140.
20% = 80 → number = 400. 35% of 400 = 140.
Q.46. The median of: 7, 3, 14, 11, 5, 8, 6 is:
Answer: (2) 7
Arrange ascending: 3, 5, 6, 7, 8, 11, 14. Middle value (4th of 7) = 7.
Arrange ascending: 3, 5, 6, 7, 8, 11, 14. Middle value (4th of 7) = 7.
Q.47. A trader marks his goods 40% above cost price and offers 20% discount. Find his profit %.
Answer: (2) 12%
CP=100, MP=140, SP=140×0.8=112. Profit=12. Profit%=12%.
CP=100, MP=140, SP=140×0.8=112. Profit=12. Profit%=12%.
Q.48. Find the Compound Interest on ₹15,000 at 8% p.a. compounded annually for 2 years.
Answer: (2) ₹2,496
A = 15000×(1.08)² = 15000×1.1664 = 17,496. CI = 17,496−15,000 = ₹2,496.
A = 15000×(1.08)² = 15000×1.1664 = 17,496. CI = 17,496−15,000 = ₹2,496.
Q.49. In what ratio must a grocer mix two varieties of pulses at ₹60/kg and ₹80/kg to get a mixture worth ₹72/kg?
Answer: (2) 2:3
Alligation: (80−72):(72−60) = 8:12 = 2:3.
Alligation: (80−72):(72−60) = 8:12 = 2:3.
Q.50. The volume of a sphere of radius 7 cm is (π = 22/7):
Answer: (2) 1437.33 cm³
V = (4/3)πr³ = (4/3)×(22/7)×343 = (4/3)×1078 = 4312/3 = 1437.33 cm³.
V = (4/3)πr³ = (4/3)×(22/7)×343 = (4/3)×1078 = 4312/3 = 1437.33 cm³.
Q.51. A boat covers 30 km upstream in 5 hours and 30 km downstream in 3 hours. Find the speed of the boat in still water.
Answer: (2) 8 km/h
Upstream=30/5=6 km/h; Downstream=30/3=10 km/h. Still water = (10+6)/2 = 8 km/h.
Upstream=30/5=6 km/h; Downstream=30/3=10 km/h. Still water = (10+6)/2 = 8 km/h.
Q.52. The ratio of the present ages of father and son is 7:3. Ten years later, the ratio will be 2:1. Find the father’s present age.
Answer: (2) 70 years
Father=7x, Son=3x. (7x+10)/(3x+10)=2/1 → 7x+10=6x+20 → x=10. Father=7×10=70 years.
Father=7x, Son=3x. (7x+10)/(3x+10)=2/1 → 7x+10=6x+20 → x=10. Father=7×10=70 years.
Q.53. Three pipes A, B, C can fill a tank in 6, 8 and 12 hours respectively. All three are opened at 9 AM. At what time will the tank be full?
Answer: (2) 11:40 AM
Together rate: 1/6+1/8+1/12=(4+3+2)/24=9/24=3/8 per hour. Time = 8/3 hours = 2 hours 40 minutes. 9:00 AM + 2h 40min = 11:40 AM.
Together rate: 1/6+1/8+1/12=(4+3+2)/24=9/24=3/8 per hour. Time = 8/3 hours = 2 hours 40 minutes. 9:00 AM + 2h 40min = 11:40 AM.
Q.54. The sum of digits of a 2-digit number is 9. If 27 is subtracted, digits are reversed. Find the number.
Answer: (2) 63
a+b=9. (10a+b)−27=10b+a → 9a−9b=27 → a−b=3. Solving: a=6, b=3. Number=63. Verify: 63−27=36 (reversed) ✓.
a+b=9. (10a+b)−27=10b+a → 9a−9b=27 → a−b=3. Solving: a=6, b=3. Number=63. Verify: 63−27=36 (reversed) ✓.
Q.55. The slant height of a cone is 13 cm and radius is 5 cm. Find its volume (π = 22/7).
Answer: (2) 314.28 cm³
h=√(l²−r²)=√(169−25)=√144=12 cm. V=(1/3)πr²h=(1/3)×(22/7)×25×12=2200/7=314.28 cm³.
h=√(l²−r²)=√(169−25)=√144=12 cm. V=(1/3)πr²h=(1/3)×(22/7)×25×12=2200/7=314.28 cm³.
Q.56. 12 men can complete a work in 8 days. After 4 days, 4 men leave. In how many more days will the remaining men complete the work?
Answer: (2) 6 days
Total=96 man-days. Done=12×4=48. Remaining=48 man-days. Men now=8. Days=48÷8=6 days.
Total=96 man-days. Done=12×4=48. Remaining=48 man-days. Men now=8. Days=48÷8=6 days.
Q.57. A person marks goods at ₹2,400 and gives a discount of 15%. If his profit is 2%, find the cost price.
Answer: (2) ₹2,000
SP=2400×0.85=2040. CP=2040/1.02=₹2,000.
SP=2400×0.85=2040. CP=2040/1.02=₹2,000.
Q.58. Find: 1² + 2² + 3² + … + 10²
Answer: (2) 385
Sum of squares formula: n(n+1)(2n+1)/6 = 10×11×21/6 = 2310/6 = 385.
Sum of squares formula: n(n+1)(2n+1)/6 = 10×11×21/6 = 2310/6 = 385.
Q.59. A man bought a mobile at 10% discount on its listed price and sold it at 20% above the listed price. Find his profit %.
Answer: (2) 33.33%
List price=100. CP=90 (10% discount). SP=120 (20% above list). Profit=30. Profit%=(30/90)×100=33.33%.
List price=100. CP=90 (10% discount). SP=120 (20% above list). Profit=30. Profit%=(30/90)×100=33.33%.
Q.60. The area of a right-angled triangle is 60 cm². If one leg is 8 cm, find the hypotenuse.
Answer: (4) 17 cm
Area=(1/2)×base×height=60. One leg=8 → other leg=(60×2)/8=15. Hypotenuse=√(8²+15²)=√(64+225)=√289=17 cm.
Area=(1/2)×base×height=60. One leg=8 → other leg=(60×2)/8=15. Hypotenuse=√(8²+15²)=√(64+225)=√289=17 cm.