📋 MOCK TEST – SET 31 🔥
WBSSC Group C (Clerk) — Advanced Level | Sets 31 onwards
Total: 60 Questions | GA: 20 | English: 10 | Reasoning: 10 | Arithmetic: 20 | Click option to check answer
SECTION A: GENERAL AWARENESS (Q.1–Q.20) — 20 Marks
Q.1. The ‘Swaran Singh Committee’ (1976) was constituted to recommend: Indian PolityHARD
Answer: (2) Fundamental Duties
The Swaran Singh Committee (1976) was set up during Emergency to recommend incorporation of Fundamental Duties in the Constitution. Led to 42nd Constitutional Amendment (1976) inserting Article 51-A with 10 Fundamental Duties in Part IV-A. An 11th duty was added by the 86th Amendment (2002).
The Swaran Singh Committee (1976) was set up during Emergency to recommend incorporation of Fundamental Duties in the Constitution. Led to 42nd Constitutional Amendment (1976) inserting Article 51-A with 10 Fundamental Duties in Part IV-A. An 11th duty was added by the 86th Amendment (2002).
Q.2. Under NEP 2020, the ‘School Quality Assessment and Accreditation Framework (SQAAF)’ is implemented by: NEP 2020HARD
Answer: (2) CBSE with State Boards/SCERTs
SQAAF developed by CBSE in collaboration with State/UT Boards and SCERTs. Assesses schools on 5 domains: Enabling Resources, Teaching-Learning and Assessment, Student Progression, Management and Leadership, and Beneficial Impact on Community. Self-evaluation and peer-evaluation model.
SQAAF developed by CBSE in collaboration with State/UT Boards and SCERTs. Assesses schools on 5 domains: Enabling Resources, Teaching-Learning and Assessment, Student Progression, Management and Leadership, and Beneficial Impact on Community. Self-evaluation and peer-evaluation model.
Q.3. Under NEP 2020, the ‘Vidya Pravesh’ programme is a: NEP 2020HARD
Answer: (2) 3-month play-based school preparation for Grade 1
Vidya Pravesh (2021): A 3-month play-based school preparation module for children entering Grade 1. Developed by NCERT under NEP 2020. Bridges gap between pre-school and formal schooling. Focuses on social-emotional skills, early literacy and numeracy.
Vidya Pravesh (2021): A 3-month play-based school preparation module for children entering Grade 1. Developed by NCERT under NEP 2020. Bridges gap between pre-school and formal schooling. Focuses on social-emotional skills, early literacy and numeracy.
Q.4. The ‘Sarthaq Guidelines’ (2021) issued under NEP 2020 stand for: NEP 2020HARD
Answer: (2) Students’ and Teachers’ Holistic Advancement through Quality Education
SARTHAQ = Students’ and Teachers’ Holistic Advancement through Quality Education. Issued by MoE in April 2021 as an implementation plan for NEP 2020 in school education. Provides action points, responsible agencies, and timelines for each NEP recommendation.
SARTHAQ = Students’ and Teachers’ Holistic Advancement through Quality Education. Issued by MoE in April 2021 as an implementation plan for NEP 2020 in school education. Provides action points, responsible agencies, and timelines for each NEP recommendation.
Q.5. The ‘Subsidiary Alliance’ system was devised by: Indian HistoryHARD
Answer: (2) Lord Wellesley
Subsidiary Alliance introduced by Lord Wellesley (1798). Indian rulers had to: (a) accept British troops, (b) pay for them or cede territory, (c) not ally with other powers, (d) accept a British Resident. First accepted by Nizam of Hyderabad (1798).
Subsidiary Alliance introduced by Lord Wellesley (1798). Indian rulers had to: (a) accept British troops, (b) pay for them or cede territory, (c) not ally with other powers, (d) accept a British Resident. First accepted by Nizam of Hyderabad (1798).
Q.6. The first session of the Indian Constituent Assembly was held on: Indian HistoryHARD
Answer: (2) 9 December 1946
The Constituent Assembly first met on 9 December 1946. Dr. Sachchidananda Sinha was temporary chairman. Dr. Rajendra Prasad elected permanent President on 11 December 1946. Constitution adopted 26 Nov 1949; enacted 26 Jan 1950. Total sessions: 11; took 2 years 11 months 18 days.
The Constituent Assembly first met on 9 December 1946. Dr. Sachchidananda Sinha was temporary chairman. Dr. Rajendra Prasad elected permanent President on 11 December 1946. Constitution adopted 26 Nov 1949; enacted 26 Jan 1950. Total sessions: 11; took 2 years 11 months 18 days.
Q.7. ‘Jaldapara National Park’ in West Bengal is primarily known for: West BengalHARD
Answer: (2) Indian One-Horned Rhinoceros
Jaldapara National Park (Alipurduar district, WB) has the largest rhino population in West Bengal. Located in the Dooars along the Torsa River. Also home to elephants, leopards, bison. Upgraded from sanctuary to national park in 2012.
Jaldapara National Park (Alipurduar district, WB) has the largest rhino population in West Bengal. Located in the Dooars along the Torsa River. Also home to elephants, leopards, bison. Upgraded from sanctuary to national park in 2012.
Q.8. ‘Tyndall Effect’ is the scattering of light by: ScienceHARD
Answer: (2) Colloidal particles
Tyndall Effect = scattering of a light beam by colloidal particles, making the path visible. True solutions do NOT show this effect (particles too small). Examples: milk, starch solution, fog. Named after John Tyndall (1869).
Tyndall Effect = scattering of a light beam by colloidal particles, making the path visible. True solutions do NOT show this effect (particles too small). Examples: milk, starch solution, fog. Named after John Tyndall (1869).
Q.9. The ‘Ilbert Bill Controversy’ (1883) was related to: Indian HistoryHARD
Answer: (2) Indian judges trying European subjects
Ilbert Bill (1883) by Viceroy Ripon: proposed allowing Indian district magistrates to try European British subjects. Fierce European opposition forced a compromise. Ironically united Indians against racism → contributed to the birth of INC (1885).
Ilbert Bill (1883) by Viceroy Ripon: proposed allowing Indian district magistrates to try European British subjects. Fierce European opposition forced a compromise. Ironically united Indians against racism → contributed to the birth of INC (1885).
Q.10. The ‘UDAN Scheme’ (Ude Desh ka Aam Nagrik) is aimed at: Current AffairsHARD
Answer: (2) Affordable air travel via unserved airports
UDAN (Regional Connectivity Scheme) launched 2016. Caps airfare (~₹2,500 for 1-hour flight). Airlines receive Viability Gap Funding (VGF). 4th phase extended to seaplanes and helicopters. Over 500 routes and 70+ airports operationalised.
UDAN (Regional Connectivity Scheme) launched 2016. Caps airfare (~₹2,500 for 1-hour flight). Airlines receive Viability Gap Funding (VGF). 4th phase extended to seaplanes and helicopters. Over 500 routes and 70+ airports operationalised.
Q.11. Which Article grants the President the power to grant pardons, reprieves, respites, or remissions of punishment? Indian PolityHARD
Answer: (2) Article 72
Article 72: President’s pardoning power. Covers: offences against Union law, court-martial cases, death sentence. Types: Pardon, Reprieve, Respite, Remission, Commutation. Governor has similar power under Article 161 (except court-martial and death penalty — only President).
Article 72: President’s pardoning power. Covers: offences against Union law, court-martial cases, death sentence. Types: Pardon, Reprieve, Respite, Remission, Commutation. Governor has similar power under Article 161 (except court-martial and death penalty — only President).
Q.12. The ‘Rarh’ region of West Bengal refers to: West BengalHARD
Answer: (2) Laterite upland west of Bhagirathi
Rarh = undulating laterite upland of WB to the west of the Bhagirathi. Covers Birbhum, Bankura, Puruliya, parts of Burdwan and Medinipur. Red laterite soil, low rainfall. Bishnupur (terracotta temples) is in this region.
Rarh = undulating laterite upland of WB to the west of the Bhagirathi. Covers Birbhum, Bankura, Puruliya, parts of Burdwan and Medinipur. Red laterite soil, low rainfall. Bishnupur (terracotta temples) is in this region.
Q.13. India’s AI language model work for Indian languages is primarily associated with which institution? Current AffairsHARD
Answer: (2) IIT Madras (AI4Bharat)
AI4Bharat (IIT Madras) developed open-source AI language models for Indian languages — IndicBERT, IndicTrans2 (translation), IndicWhisper (speech). Government partnered with IIT Madras for BharatGen (India’s own LLM) under MeitY.
AI4Bharat (IIT Madras) developed open-source AI language models for Indian languages — IndicBERT, IndicTrans2 (translation), IndicWhisper (speech). Government partnered with IIT Madras for BharatGen (India’s own LLM) under MeitY.
Q.14. The ‘National Commission for Scheduled Castes’ is established under which Article? Indian PolityHARD
Answer: (2) Article 338
Article 338: National Commission for Scheduled Castes (NCSC). A constitutional body. 89th Amendment (2003) bifurcated the earlier combined SC/ST Commission — creating separate NCSC (Art. 338) and NCST (Art. 338-A).
Article 338: National Commission for Scheduled Castes (NCSC). A constitutional body. 89th Amendment (2003) bifurcated the earlier combined SC/ST Commission — creating separate NCSC (Art. 338) and NCST (Art. 338-A).
Q.15. The ‘Charak Puja’ — a folk festival involving body-piercing rituals — is mainly observed on: West BengalHARD
Answer: (2) Chaitra Sankranti
Charak Puja (Nil Puja) observed on Chaitra Sankranti — last day of the Bengali year. Devotees undergo body piercing, fire walking, and hanging from a rotating pole. Primarily in rural WB: Bardhaman, Birbhum, Hooghly, Bankura.
Charak Puja (Nil Puja) observed on Chaitra Sankranti — last day of the Bengali year. Devotees undergo body piercing, fire walking, and hanging from a rotating pole. Primarily in rural WB: Bardhaman, Birbhum, Hooghly, Bankura.
Q.16. The ‘Pradhan Mantri Jan Dhan Yojana (PMJDY)’ was launched on: Current AffairsHARD
Answer: (2) 28 August 2014
PMJDY launched 28 August 2014. World’s largest financial inclusion programme. Zero-balance accounts, RuPay debit card, ₹2 lakh accident insurance, ₹30,000 life insurance, overdraft facility ₹10,000. Over 53 crore accounts opened as of 2024.
PMJDY launched 28 August 2014. World’s largest financial inclusion programme. Zero-balance accounts, RuPay debit card, ₹2 lakh accident insurance, ₹30,000 life insurance, overdraft facility ₹10,000. Over 53 crore accounts opened as of 2024.
Q.17. ‘Laughing Gas’ used as an anaesthetic is chemically: ScienceHARD
Answer: (2) Nitrous oxide (N₂O)
Laughing Gas = Nitrous oxide (N₂O). Used as anaesthetic/analgesic in dentistry and surgery. Causes euphoria. Discovered by Joseph Priestley (1772); named by Humphry Davy. Also used as propellant in whipped cream canisters. Greenhouse gas (298× CO₂ warming potential).
Laughing Gas = Nitrous oxide (N₂O). Used as anaesthetic/analgesic in dentistry and surgery. Causes euphoria. Discovered by Joseph Priestley (1772); named by Humphry Davy. Also used as propellant in whipped cream canisters. Greenhouse gas (298× CO₂ warming potential).
Q.18. ‘No-Confidence Motion’ against the Council of Ministers can be introduced in: Indian PolityHARD
Answer: (2) Lok Sabha only
Council of Ministers is collectively responsible to Lok Sabha (Article 75(3)). No-Confidence Motion only in Lok Sabha. Requires notice by 50 members; voted within 10 days. If passed, government must resign. Rajya Sabha has no such power.
Council of Ministers is collectively responsible to Lok Sabha (Article 75(3)). No-Confidence Motion only in Lok Sabha. Requires notice by 50 members; voted within 10 days. If passed, government must resign. Rajya Sabha has no such power.
Q.19. ‘Tusu Parab’ is a harvest festival celebrated primarily by which community in West Bengal? West BengalHARD
Answer: (2) Kurmi-Mahato and OBC communities of Jangalmahal
Tusu Parab: harvest festival during Makar Sankranti by Kurmi-Mahato communities of Puruliya, Bankura, West Medinipur, Jhargram. Young girls worship the Tusu deity, sing folk songs, and immerse idol in rivers. GI-tagged folk song genre.
Tusu Parab: harvest festival during Makar Sankranti by Kurmi-Mahato communities of Puruliya, Bankura, West Medinipur, Jhargram. Young girls worship the Tusu deity, sing folk songs, and immerse idol in rivers. GI-tagged folk song genre.
Q.20. The TATA–Powerchip semiconductor fab plant under India’s Semiconductor Mission is being set up in: Current AffairsHARD
Answer: (2) Dholera, Gujarat
Tata Electronics–Powerchip (PSMC) fab at Dholera Special Investment Region (DSIR), Gujarat. Approved 2024 under India Semiconductor Mission. 28nm node technology. Investment: ~₹91,000 crore. Micron’s ATMP plant in Sanand, Gujarat.
Tata Electronics–Powerchip (PSMC) fab at Dholera Special Investment Region (DSIR), Gujarat. Approved 2024 under India Semiconductor Mission. 28nm node technology. Investment: ~₹91,000 crore. Micron’s ATMP plant in Sanand, Gujarat.
SECTION B: GENERAL ENGLISH (Q.21–Q.30) — 10 Marks
Q.21. Choose the correct synonym of ‘OBSTREPEROUS’: HARD
Answer: (2) Noisy and difficult to control
Obstreperous = noisy, boisterous, difficult to control. Synonyms: Unruly, Turbulent, Vociferous, Clamorous. Antonym: Docile, Quiet. “The obstreperous crowd refused to disperse.”
Obstreperous = noisy, boisterous, difficult to control. Synonyms: Unruly, Turbulent, Vociferous, Clamorous. Antonym: Docile, Quiet. “The obstreperous crowd refused to disperse.”
Q.22. Choose the correct antonym of ‘SANGUINE’: HARD
Answer: (2) Pessimistic
Sanguine = optimistic, especially in difficulty. Antonyms: Pessimistic, Despondent, Gloomy, Cynical. Do not confuse with “sanguinary” (bloodthirsty).
Sanguine = optimistic, especially in difficulty. Antonyms: Pessimistic, Despondent, Gloomy, Cynical. Do not confuse with “sanguinary” (bloodthirsty).
Q.23. Identify the correctly spelled word: HARD
Answer: (2) Entrepreneur
Entrepreneur — French origin. E-N-T-R-E-P-R-E-N-E-U-R. Note: ‘entre’ + ‘preneur’. Common traps: double ‘n’, missing ‘e’ in middle.
Entrepreneur — French origin. E-N-T-R-E-P-R-E-N-E-U-R. Note: ‘entre’ + ‘preneur’. Common traps: double ‘n’, missing ‘e’ in middle.
Q.24. Fill in the blank: The new policy is in sharp contrast ________ the previous one. HARD
Answer: (2) with
In contrast with is the preferred fixed phrase in formal English. “In contrast to” is also used but “with” follows the phrase “in sharp contrast” most idiomatically. Both (2) and (3) are acceptable; “with” is the standard exam answer.
In contrast with is the preferred fixed phrase in formal English. “In contrast to” is also used but “with” follows the phrase “in sharp contrast” most idiomatically. Both (2) and (3) are acceptable; “with” is the standard exam answer.
Q.25. Choose the sentence with CORRECT use of the Subjunctive Mood: HARD
Answer: (2) I wish she were here.
Subjunctive mood: after “wish”, “if only”, “as if” — use “were” (not “was”) for all persons. Similarly: “If I were you…” “It is essential that he be present.”
Subjunctive mood: after “wish”, “if only”, “as if” — use “were” (not “was”) for all persons. Similarly: “If I were you…” “It is essential that he be present.”
Q.26. “He tried to wriggle out of his responsibilities.” The underlined phrase means: HARD
Answer: (2) Avoid by clever manoeuvring
“Wriggle out of” = to escape or avoid responsibility by being clever or dishonest. “He always wriggles out of paying the bill.” Synonyms: Shirk, Dodge, Evade.
“Wriggle out of” = to escape or avoid responsibility by being clever or dishonest. “He always wriggles out of paying the bill.” Synonyms: Shirk, Dodge, Evade.
Q.27. Identify the error: “Being a rainy day, (A) / we decided (B) / to stay indoors (C) / and read books. (D)” HARD
Answer: (1) A — Dangling Participle
“Being a rainy day” is a dangling participle — appears to modify “we” but logically refers to “the day.” Correct: “It being a rainy day, we decided to stay indoors.” OR “As it was a rainy day…”
“Being a rainy day” is a dangling participle — appears to modify “we” but logically refers to “the day.” Correct: “It being a rainy day, we decided to stay indoors.” OR “As it was a rainy day…”
Q.28. Change to Passive Voice: “Who taught you English?” HARD
Answer: (2) By whom were you taught English?
“Who” (subject) → “By whom.” “taught” → “were taught.” “You” becomes subject. Pattern: By whom + was/were + subject + past participle + object?
“Who” (subject) → “By whom.” “taught” → “were taught.” “You” becomes subject. Pattern: By whom + was/were + subject + past participle + object?
Q.29. One word substitution: A government by the people, of the people, for the people. HARD
Answer: (2) Democracy
Democracy = government by the people (Lincoln’s phrase). Autocracy = single ruler; Oligarchy = small group; Theocracy = religious authority; Plutocracy = wealthy class.
Democracy = government by the people (Lincoln’s phrase). Autocracy = single ruler; Oligarchy = small group; Theocracy = religious authority; Plutocracy = wealthy class.
Q.30. Spot the error: “The data (A) / collected from the survey (B) / are being (C) / analysed carefully. (D)” HARD
Answer: (4) No error
“Data” is technically plural of “datum” → plural verb “are being” is grammatically correct in formal/academic English. “The data are being analysed” ✓. In exam context (formal grammar): no error.
“Data” is technically plural of “datum” → plural verb “are being” is grammatically correct in formal/academic English. “The data are being analysed” ✓. In exam context (formal grammar): no error.
SECTION C: LOGICAL REASONING (Q.31–Q.40) — 10 Marks
Q.31. Six people A, B, C, D, E, F sit in a row facing North. D sits 3rd from left. B sits immediate right of D. A sits at an extreme end. F is between A and D. E is not adjacent to B. Who sits 2nd from the right? HARD
Answer: (1) C
D=3rd from left. B=4th (immediate right of D). A at extreme end → A=1st. F between A(1) and D(3) → F=2nd. Arrangement so far: A(1),F(2),D(3),B(4). Remaining: C and E for positions 5 and 6. E not adjacent to B(4) → E≠5th → E=6th, C=5th. Final: A(1),F(2),D(3),B(4),C(5),E(6). 2nd from right = position 5 = C.
D=3rd from left. B=4th (immediate right of D). A at extreme end → A=1st. F between A(1) and D(3) → F=2nd. Arrangement so far: A(1),F(2),D(3),B(4). Remaining: C and E for positions 5 and 6. E not adjacent to B(4) → E≠5th → E=6th, C=5th. Final: A(1),F(2),D(3),B(4),C(5),E(6). 2nd from right = position 5 = C.
Q.32. Complete the series: 3, 7, 13, 21, 31, 43, ___ HARD
Answer: (2) 57
Differences: +4, +6, +8, +10, +12, +14. Pattern: even numbers increasing by 2 each time. 43+14 = 57.
Differences: +4, +6, +8, +10, +12, +14. Pattern: even numbers increasing by 2 each time. 43+14 = 57.
Q.33. In a code, P=4, Q=8, R=18, S=24. Using the same pattern, what is T? HARD
Answer: (2) 40
Pattern using position×2: T is the 20th letter. 20×2 = 40. Consistent with P(16)→… Using differences: 4,8,18,24,40 → gaps 4,10,6,16 — or simply T=20th letter × 2 = 40 fits best among options.
Pattern using position×2: T is the 20th letter. 20×2 = 40. Consistent with P(16)→… Using differences: 4,8,18,24,40 → gaps 4,10,6,16 — or simply T=20th letter × 2 = 40 fits best among options.
Q.34. Statements: All politicians are liars. Some liars are actors. All actors are rich.
Conclusions: I. Some politicians are rich. II. Some actors are liars. III. Some rich are liars. HARD
Conclusions: I. Some politicians are rich. II. Some actors are liars. III. Some rich are liars. HARD
Answer: (2) Only II and III follow
II: “Some liars are actors” → convert → Some actors are liars ✓. III: “Some liars are actors” + “All actors are rich” → Some liars are rich → Some rich are liars ✓. I: Cannot conclude politicians∩rich (undistributed middle). ✗. Answer: II and III.
II: “Some liars are actors” → convert → Some actors are liars ✓. III: “Some liars are actors” + “All actors are rich” → Some liars are rich → Some rich are liars ✓. I: Cannot conclude politicians∩rich (undistributed middle). ✗. Answer: II and III.
Q.35. A is the son of B. B is the sister of C. C is married to D. D is the father of E. E is the sister of F. How is A related to F? HARD
Answer: (2) Cousin
A’s mother=B. B’s brother=C. C’s wife=D. C and D’s children=E and F. B and C are siblings → B’s child (A) and C’s children (E,F) are cousins.
A’s mother=B. B’s brother=C. C’s wife=D. C and D’s children=E and F. B and C are siblings → B’s child (A) and C’s children (E,F) are cousins.
Q.36. 5 friends P, Q, R, S, T sit around a circular table. P is 2nd to the left of Q. T is not adjacent to Q. R is immediate right of T. S is between R and P. Who is immediate left of Q? HARD
Answer: (2) S
Arrangement (clockwise): Q(1), S(2), P(3), T(4), R(5). P is 2nd left of Q ✓ (Q→R→P going left = positions 5,4,3 → P=3rd). R is immediate right of T ✓ (T=4, R=5). S between R(5) and P(3) → S=pos2 ✓. T not adjacent Q(1): T=pos4, adjacent to 3 and 5 — not adjacent to 1 ✓. Immediate left of Q (anticlockwise) = position 2 = S.
Arrangement (clockwise): Q(1), S(2), P(3), T(4), R(5). P is 2nd left of Q ✓ (Q→R→P going left = positions 5,4,3 → P=3rd). R is immediate right of T ✓ (T=4, R=5). S between R(5) and P(3) → S=pos2 ✓. T not adjacent Q(1): T=pos4, adjacent to 3 and 5 — not adjacent to 1 ✓. Immediate left of Q (anticlockwise) = position 2 = S.
Q.37. A person starts from O, walks 6 km NE, then 6 km SE, then 6 km SW, then 6 km NW. Where does he end up? HARD
Answer: (1) Back at O
NE+SE = net East displacement; SW+NW = net West displacement of equal magnitude. Total displacement = zero. Returns to starting point O. (Equivalent to traversing a square rotated 45°.)
NE+SE = net East displacement; SW+NW = net West displacement of equal magnitude. Total displacement = zero. Returns to starting point O. (Equivalent to traversing a square rotated 45°.)
Q.38. In a mirror (horizontal flip) of the word ‘MAGNIFY’, which letter appears UNCHANGED? HARD
Answer: (2) A
In a vertical mirror (left-right flip), bilaterally symmetric letters look unchanged: A, H, I, M, O, T, U, V, W, X, Y. From MAGNIFY, A has perfect bilateral symmetry making it the clearest correct answer.
In a vertical mirror (left-right flip), bilaterally symmetric letters look unchanged: A, H, I, M, O, T, U, V, W, X, Y. From MAGNIFY, A has perfect bilateral symmetry making it the clearest correct answer.
Q.39. In a certain system: 4+3=25, 5+4=41, 7+2=53. Then 6+5=? HARD
Answer: (2) 61
Pattern: a²+b². 4²+3²=16+9=25✓; 5²+4²=25+16=41✓; 7²+2²=49+4=53✓. So 6²+5²=36+25=61✓.
Pattern: a²+b². 4²+3²=16+9=25✓; 5²+4²=25+16=41✓; 7²+2²=49+4=53✓. So 6²+5²=36+25=61✓.
Q.40. Assertion (A): The Rajya Sabha cannot be dissolved.
Reason (R): The Rajya Sabha is a permanent House because it represents the States. HARD
Reason (R): The Rajya Sabha is a permanent House because it represents the States. HARD
Answer: (1) Both true, R correctly explains A
A ✓: Rajya Sabha is permanent — cannot be dissolved. R ✓: Represents States/federal units; designed to be a continuing chamber (Article 83(1)). 1/3 members retire every 2 years. R correctly explains A.
A ✓: Rajya Sabha is permanent — cannot be dissolved. R ✓: Represents States/federal units; designed to be a continuing chamber (Article 83(1)). 1/3 members retire every 2 years. R correctly explains A.
SECTION D: ARITHMETIC (Q.41–Q.60) — 20 Marks
Q.41. Find the smallest number which when divided by 12, 15, 18 and 27 leaves remainder 8 in each case. HARD
Answer: (2) 548
LCM(12,15,18,27): 12=2²×3; 15=3×5; 18=2×3²; 27=3³. LCM=2²×3³×5=4×27×5=540. Required=540+8=548.
LCM(12,15,18,27): 12=2²×3; 15=3×5; 18=2×3²; 27=3³. LCM=2²×3³×5=4×27×5=540. Required=540+8=548.
Q.42. If x = 2 + √3, find the value of x² + 1/x². HARD
Answer: (2) 14
x=2+√3, 1/x=2−√3 (rationalise). x+1/x=4. x²+1/x²=(x+1/x)²−2=16−2=14.
x=2+√3, 1/x=2−√3 (rationalise). x+1/x=4. x²+1/x²=(x+1/x)²−2=16−2=14.
Q.43. A, B, C enter into a partnership. A invests ₹5,000 for 8 months, B invests ₹6,000 for 6 months, C invests ₹3,000 for 12 months. If total profit is ₹11,900, find B’s share. HARD
Answer: (4) ₹3,825
Effective investment: A=5000×8=40,000; B=6000×6=36,000; C=3000×12=36,000. Ratio=40:36:36=10:9:9. Total parts=28. B=(9/28)×11,900=107,100÷28=₹3,825.
Effective investment: A=5000×8=40,000; B=6000×6=36,000; C=3000×12=36,000. Ratio=40:36:36=10:9:9. Total parts=28. B=(9/28)×11,900=107,100÷28=₹3,825.
Q.44. A train of length 200 m at 54 km/h crosses another train of length 300 m coming from opposite direction at 36 km/h. Time taken: HARD
Answer: (2) 20 sec
Relative speed=54+36=90 km/h=25 m/s. Total length=200+300=500 m. Time=500÷25=20 sec.
Relative speed=54+36=90 km/h=25 m/s. Total length=200+300=500 m. Time=500÷25=20 sec.
Q.45. Find the value of: (1.5³ + 2.5³ + 3.0³) − 3 × 1.5 × 2.5 × 3.0 using the identity a³+b³+c³−3abc = (a+b+c)(a²+b²+c²−ab−bc−ca). HARD
Answer: (2) 12.25
a=1.5, b=2.5, c=3.0. a+b+c=7. a²+b²+c²=2.25+6.25+9=17.5. ab+bc+ca=3.75+7.5+4.5=15.75. (a²+b²+c²−ab−bc−ca)=1.75. Result=7×1.75=12.25. Verify: 1.5³+2.5³+3³−3(1.5)(2.5)(3)=3.375+15.625+27−33.75=46−33.75=12.25 ✓.
a=1.5, b=2.5, c=3.0. a+b+c=7. a²+b²+c²=2.25+6.25+9=17.5. ab+bc+ca=3.75+7.5+4.5=15.75. (a²+b²+c²−ab−bc−ca)=1.75. Result=7×1.75=12.25. Verify: 1.5³+2.5³+3³−3(1.5)(2.5)(3)=3.375+15.625+27−33.75=46−33.75=12.25 ✓.
Q.46. The average of 8 numbers is 20. If each number is multiplied by 3 and then 4 is added to each, the new average is: HARD
Answer: (2) 64
New average=3×old average+4=3×20+4=60+4=64.
New average=3×old average+4=3×20+4=60+4=64.
Q.47. A shopkeeper allows 25% discount on the marked price and still makes 20% profit. If his cost price is ₹480, what is the marked price? HARD
Answer: (2) ₹768
SP=480×1.2=576. SP=MP×0.75 → MP=576÷0.75=₹768.
SP=480×1.2=576. SP=MP×0.75 → MP=576÷0.75=₹768.
Q.48. Find the Compound Interest on ₹12,000 at 10% p.a. compounded half-yearly for 1 year. HARD
Answer: (2) ₹1,230
Half-yearly rate=5%, n=2 periods. A=12000×(1.05)²=12000×1.1025=13,230. CI=₹1,230.
Half-yearly rate=5%, n=2 periods. A=12000×(1.05)²=12000×1.1025=13,230. CI=₹1,230.
Q.49. Two vessels contain mixtures of milk and water: Vessel A has ratio 3:2; Vessel B has ratio 4:3. Both are mixed in equal quantities. Find milk to water ratio in the final mixture. HARD
Answer: (2) 41:29
Take 70 units each (LCM of 5 and 7). A(70): milk=42, water=28. B(70): milk=40, water=30. Total milk=82, water=58. Ratio=82:58=41:29.
Take 70 units each (LCM of 5 and 7). A(70): milk=42, water=28. B(70): milk=40, water=30. Total milk=82, water=58. Ratio=82:58=41:29.
Q.50. A hollow cylindrical pipe has outer radius 7 cm, inner radius 5 cm, length 20 cm. Find the volume of material used (π=22/7). HARD
Answer: (2) 1508.57 cm³
V=π(R²−r²)×h=(22/7)×(49−25)×20=(22/7)×24×20=(22×480)/7=10560/7=1508.57 cm³.
V=π(R²−r²)×h=(22/7)×(49−25)×20=(22/7)×24×20=(22×480)/7=10560/7=1508.57 cm³.
Q.51. A boat goes 48 km upstream in 8 hours and 50 km downstream in 5 hours. How long will it take to go 100 km in still water? HARD
Answer: (2) 12.5 hours
Upstream speed=48÷8=6 km/h. Downstream speed=50÷5=10 km/h. Still water speed=(6+10)÷2=8 km/h. Time=100÷8=12.5 hours.
Upstream speed=48÷8=6 km/h. Downstream speed=50÷5=10 km/h. Still water speed=(6+10)÷2=8 km/h. Time=100÷8=12.5 hours.
Q.52. The present ages of Arun and Barun are in ratio 4:5. Six years hence the ratio becomes 5:6. Find the sum of their present ages. HARD
Answer: (3) 54 years
Arun=4x, Barun=5x. (4x+6)/(5x+6)=5/6 → 24x+36=25x+30 → x=6. Arun=24, Barun=30. Sum=54 years.
Arun=4x, Barun=5x. (4x+6)/(5x+6)=5/6 → 24x+36=25x+30 → x=6. Arun=24, Barun=30. Sum=54 years.
Q.53. A cistern is 1/4 full at 6 AM. Pipe A fills it in 4 hrs, Pipe B in 6 hrs, Pipe C (outlet) empties it in 3 hrs. All three opened. When will it be half full? HARD
Answer: (2) 9:00 AM
Net rate=1/4+1/6−1/3=(3+2−4)/12=1/12 per hour. Need to fill from 1/4 to 1/2 = 1/4 more. Time=(1/4)÷(1/12)=3 hours. Start 6 AM + 3 hrs = 9:00 AM.
Net rate=1/4+1/6−1/3=(3+2−4)/12=1/12 per hour. Need to fill from 1/4 to 1/2 = 1/4 more. Time=(1/4)÷(1/12)=3 hours. Start 6 AM + 3 hrs = 9:00 AM.
Q.54. A number when divided by 6 leaves remainder 3, when divided by 9 leaves remainder 6, when divided by 15 leaves remainder 12. Find the least such number. HARD
Answer: (1) 87
Observe: each divisor exceeds its remainder by 3 (6−3=3, 9−6=3, 15−12=3). LCM(6,9,15)=90. Required=90−3=87. Verify: 87÷6=14 R3✓; 87÷9=9 R6✓; 87÷15=5 R12✓.
Observe: each divisor exceeds its remainder by 3 (6−3=3, 9−6=3, 15−12=3). LCM(6,9,15)=90. Required=90−3=87. Verify: 87÷6=14 R3✓; 87÷9=9 R6✓; 87÷15=5 R12✓.
Q.55. A sphere is melted and recast into a cone of same radius (r=6 cm). Find the height of the cone. HARD
Answer: (2) 24 cm
Volume of sphere=(4/3)πr³. Volume of cone=(1/3)πr²h. Equal: (4/3)πr³=(1/3)πr²h → h=4r=4×6=24 cm.
Volume of sphere=(4/3)πr³. Volume of cone=(1/3)πr²h. Equal: (4/3)πr³=(1/3)πr²h → h=4r=4×6=24 cm.
Q.56. Taps A (fills in 10 hr), B (fills in 15 hr) together fill in 6 hr. Tap C is an outlet. A+B+C together fill in 8 hr. Find C’s emptying time. HARD
Answer: (2) 24 hours
A+B rate=1/10+1/15=1/6. A+B+C rate=1/8. C’s rate=1/8−1/6=(3−4)/24=−1/24. C empties in 24 hours.
A+B rate=1/10+1/15=1/6. A+B+C rate=1/8. C’s rate=1/8−1/6=(3−4)/24=−1/24. C empties in 24 hours.
Q.57. A trader sells 8 articles for the same price as he buys 10 articles. Find profit or loss %. HARD
Answer: (2) 25% profit
CP of 8=8k; SP of 8=10k. Profit=2k. Profit%=(2k/8k)×100=25%.
CP of 8=8k; SP of 8=10k. Profit=2k. Profit%=(2k/8k)×100=25%.
Q.58. The digit at units place of 7¹⁰⁵ is: HARD
Answer: (2) 7
Units digit of powers of 7: cycle of 4 → 7,9,3,1. 105÷4=26 remainder 1. Units digit same as 7¹ = 7.
Units digit of powers of 7: cycle of 4 → 7,9,3,1. 105÷4=26 remainder 1. Units digit same as 7¹ = 7.
Q.59. A man rows upstream 16 km in 4 hours. Ratio of still water speed to stream speed is 3:1. Find time to row 30 km downstream. HARD
Answer: (2) 3.75 hours
Upstream=16/4=4 km/h. Still=3k, stream=k → upstream=2k=4 → k=2. Still=6, stream=2. Downstream=6+2=8 km/h. Time=30/8=3.75 hours.
Upstream=16/4=4 km/h. Still=3k, stream=k → upstream=2k=4 → k=2. Still=6, stream=2. Downstream=6+2=8 km/h. Time=30/8=3.75 hours.
Q.60. In an examination, 65% passed in English, 55% passed in Maths, and 15% failed in both. What % passed in both? HARD
Answer: (2) 35%
Passed in at least one=100−15=85%. P(E∪M)=P(E)+P(M)−P(E∩M) → 85=65+55−P(E∩M) → P(E∩M)=35%.
Passed in at least one=100−15=85%. P(E∪M)=P(E)+P(M)−P(E∩M) → 85=65+55−P(E∩M) → P(E∩M)=35%.