Question Bank — Maths / Numerical Aptitude (all papers)
🔢 Question Bank — Maths / Numerical Aptitude
Scope
Every quantitative question from the 7 papers — arithmetic, number system, mensuration, algebra, data/probability. Verbal & logical reasoning (series, coding, blood-relations, directions, syllogisms, Venn) is in the companion bank → Reasoning-Mental-Ability. 154 questions, grouped by topic. Ans = official JKSSB Series-A key; every clean item was independently re-solved and matches the key (one flagged discrepancy: SF·Q29).
Paper codes: WO · WG · IN · JA · GD · LA · SF · | Answers verified against *-Answer-Key.md.
1. Number System · LCM / HCF · Simplification
| Source | Question | Options | Ans | Method |
|---|---|---|---|---|
| WO · Q44 | Least number divisible by 2,3,5,6,15 that is a perfect square. | A) 324 B) 900 C) 729 D) 576 | B | LCM = 30; smallest perfect-square multiple = 30² = 900. |
| WO · Q45 | N leaves remainder 3 on ÷7. Remainder of 7N ÷7? | A) 0 B) 3 C) 7 D) None | A | 7N is a multiple of 7 → remainder 0. |
| JA · Q21 | 45678x9231 divisible by 3 → how many values of x? | A) 1 B) 2 C) 3 D) 4 | D | Digit-sum (excl. x) = 45; need 45+x ÷3 → x ∈ {0,3,6,9} = 4. |
| JA · Q22 | x = 2¹⁰ × 5⁶ — number of trailing zeros? | A) 6 B) 5 C) 4 D) 3 | A | Zeros = min(10,6) = 6. |
| IN · Q21 | {720÷12 + 18×4} ÷6 + 25% of 160 = ? | A) 88 B) 66 C) 62 D) 72 | C | (60+72)/6 + 40 = 22+40 = 62. |
| IN · Q22 | 480 ÷ {16 − 8×(3/4)} + 35% of 200 − 18 = ? | A) 111 B) 121 C) 100 D) 101 | C | 480/10 + 70 − 18 = 48+70−18 = 100. |
| IN · Q23 | −(−3)(−2−8−4) ÷ [3{5+(−2)(−1)}] = ? | A) 35 B) −34 C) −41 D) −2 | D | −(−3)(−14) = −42; ÷[3×7]=21 → −2. |
| WG · Q7 | Two numbers in ratio 4:5, HCF 16 — their sum? | A) 144 B) 124 C) 165 D) 157 | A | Numbers 64 & 80 → sum 144. |
| WG · Q8 | HCF 74, LCM 12210, one number 1110 — sum of the two? | A) 1268 B) 1924 C) 1944 D) 1428 | B | Product = 74×12210; other = 903540/1110 = 814 → sum 1924. |
| WG · Q10 | HCF 33, LCM 4719; first÷3 = 121 — the other number? | A) 424 B) 433 C) 469 D) 429 | D | First = 363; other = 33×4719/363 = 429. |
| GD · Q12 | Product 693, ratio 7:11 — difference? | A) 10 B) 12 C) 14 D) 16 | B | 77k²=693→k=3; 21 & 33 → diff 12. |
| GD · Q21 | HCF 5, LCM 120, one number 20 — the other? | A) 25 B) 30 C) 35 D) 40 | B | Other = 5×120/20 = 30. |
| GD · Q22 | Ratio 3:4, LCM 48 — smaller number? | A) 12 B) 18 C) 24 D) 16 | A | 12k=48→k=4; smaller = 12. |
| GD · Q23 | Numbers 20 & 30 — HCF and LCM? | A) 10 & 60 B) 10 & 120 C) 5 & 60 D) 5 & 120 | A | HCF 10, LCM 60. |
| GD · Q24 | Ratio 7:11, HCF 5 — their LCM? | A) 385000 B) 38500 C) 3850 D) 385 | D | Numbers 35 & 55 → LCM 385. |
| SF · Q25 | 200 roses, 180 orchids → identical bouquets; roses per bouquet? | A) 10 B) 20 C) 9 D) 18 | A | HCF(200,180)=20 bouquets → 200/20 = 10 roses each. |
| SF · Q26 | Single correct statement on HCF/LCM properties. | A) 2028/HCF13 → 2 pairs B) HCF always divides LCM C) HCF 8 → LCM can't be 60 D) All | B | HCF always divides LCM (and both B & C are true, but B is the guaranteed law). |
| SF · Q28 | LCM 180, HCF 6, one number 18, other = 6k → k? | A) 6 B) 8 C) 10 D) 12 | C | Other = 180×6/18 = 60 = 6×10. |
2. Percentages
| Source | Question | Options | Ans | Method |
|---|---|---|---|---|
| IN · Q15 | Length +50%, width −40% → % change in area. | A) 5% inc B) 15% inc C) 20% dec D) 10% dec | D | 1.5×0.6 = 0.9 → 10% decrease. |
| JA · Q23 | Price cut 10%; % increase to restore original? | A) 10% B) 9 1⁄9% C) 11 1⁄9% D) 12% | C | 10/90 = 11 1⁄9%. |
| JA · Q24 | If x% of y = y% of x, which is true? | A) x>y B) y>x C) y=x D) Cannot be determined | D | Identity holds for all x,y → relation can't be determined. |
| GD · Q1 | +20% then −20% → net % change. | A) +2 B) −2 C) +4 D) −4 | D | 1.2×0.8 = 0.96 → −4%. |
| GD · Q2 | +10% then +20% over two years → total %. | A) 30% B) 32% C) 34% D) 36% | B | 1.1×1.2 = 1.32 → 32%. |
| GD · Q3 | 400 decreased by 15% → new number. | A) 320 B) 340 C) 350 D) 360 | B | 400×0.85 = 340. |
| WG · Q5 | 400 workers men:women 5:3; 87.5% regular; 92% of men regular → % of women regular. | A) 72% B) 79.15% C) 80% D) 81.55% | C | Regular 350; men-regular 230 → women-regular 120/150 = 80%. |
| WG · Q9 | Passed Sci 54%, failed Maths 42%, failed both 32% → passed both? | A) 56% B) 48% C) 32% D) 44% | D | Failed(Sci∪Maths)=46+42−32=56 → passed both 44%. |
| SF · Q1 | Multi-step pass/scholarship/recovery; scholarship − recovery = 2605 → total candidates. | A) 15,000 B) 18,500 C) 20,000 D) 22,500 | C | 0.1535T − 0.02325T = 0.13025T = 2605 → T = 20,000. |
3. Profit, Loss & Discount
| Source | Question | Options | Ans | Method |
|---|---|---|---|---|
| WO · Q42 | Two articles ₹1500 each: +20% and −25% → overall? | A) 5.79% loss B) 6.79% loss C) 7.69% loss D) 8.69% loss | C | CP 1250+2000=3250; SP 3000 → loss 250/3250 = 7.69%. |
| WO · Q46 | 100 pens @₹20; 60 at +10%, 40 at −5% → overall %. | A) 4% profit B) 4% loss C) 5% profit D) 5% loss | A | SP = 1320+760 = 2080; CP 2000 → 4% profit. |
| IN · Q27 | SP ₹2850 gives 14% gain; SP for 8% gain? | A) 2700 B) 2750 C) 20750 D) 27000 | A | CP = 2850/1.14 = 2500; ×1.08 = 2700. |
| IN · Q28 | Mark 30% above CP, 10% discount → gain? | A) 20% B) 2.5% C) 15% D) 17% | D | 1.30×0.90 = 1.17 → 17%. |
| IN · Q29 | SP of 12 books = CP of 18 → profit %? | A) 44% B) 50% C) 55% D) 25% | B | SP/CP = 18/12 = 1.5 → 50%. |
| IN · Q30 | ₹56000 stock; 1/3 sold at 40% loss — % profit needed on rest to break even? | A) 20% B) 18% C) 17% D) 22% | A | Loss = 0.4×(56000/3); over rest (2/3) → 20%. |
| JA · Q26 | 10% discount → 20% gain; gain if discount 15%? | A) 12% B) 13 1⁄3% C) 11 1⁄3% D) 10% | B | CP = 0.75 MP; SP(15%)=0.85 MP → gain 0.10/0.75 = 13 1⁄3%. |
| LA · Q27 | 40 items @₹50; 35 at +20%, 5 at −10% → overall %. | A) 30% B) 10% C) 16.25% D) 32.5% | C | SP=2100+225=2325; CP 2000 → 16.25%. |
| LA · Q30 | CP(X)=CP(Y); X +20%, Y ₹126 less than SP(X); net 14% → CP each? | A) 1260 B) 840 C) 1080 D) 1050 | D | 2.4C−126 = 2.28C → 0.12C=126 → C = 1050. |
| LA · Q31 | +8% gain; ₹2553 less → 15% loss. SP for 18% gain? | A) 11100 B) 13098 C) 15000 D) 9102 | B | 23% of CP = 2553 → CP 11100; ×1.18 = 13098. |
| LA · Q34 | 17×CP = 8×(CP+SP) → gain/loss %? | A) Loss 15% B) Gain 17.5% C) Gain 12.5% D) Loss 30% | C | 9CP=8SP → SP/CP=9/8 → 12.5% gain. |
| LA · Q36 | 4 black pairs + brown pairs; black = 2×brown price; swap raised bill 50% → original ratio? | A) 2:1 B) 1:4 C) 1:2 D) 4:1 | B | (2x+4)=1.5(8+x) → x=16 → 4:16 = 1:4. |
| SF · Q2 | Mark +40%, discounts 10% & 5%, profit ₹492.5 → CP? | A) 2000 B) 2100 C) 2500 D) 2600 | C | 1.4×0.9×0.95 = 1.197 CP; profit 0.197CP=492.5 → CP 2500. |
| SF · Q3 | Sold ₹522 after 10% discount then 10% tax → original (nearest 10)? | A) 495 B) 527 C) 539 D) 548 | B | 0.9×1.1 = 0.99 P = 522 → P ≈ 527. |
| SF · Q4 | Orig ₹500, 20% discount then 12% tax — which statement is INCORRECT? | A) Disc price 400 B) Tax 48 C) Final 450 D) Final < original | C | Final = 400×1.12 = 448, not 450 → C is the incorrect one. |
4. Ratio, Proportion & Mixtures
| Source | Question | Options | Ans | Method |
|---|---|---|---|---|
| WO · Q43 | Milk:water 5:3 in 32 L; replace some with water → 3:5. Quantity replaced? | A) 10 L B) 12.8 L C) 15.4 L D) 18.8 L | B | Milk 20→12: 20−(5/8)x=12 → x = 12.8 L. |
| WO · Q57 | ₹270 among A,B,C: A=2B, B=C+30 → ratio? | A) 12:6:4 B) 9:5:4 C) 10:5:3 D) 12:7:5 | C | B=75,A=150,C=45 → 10:5:3. |
| JA · Q27 | Wine:water 3:1; fraction replaced by water to reach 1:1? | A) 1/2 B) 1/3 C) 1/4 D) 2/3 | B | (1−f)(3/4)=1/2 → f = 1/3. |
| JA · Q28 | Compound ratio of a:b and c:d. | A) ac:bd B) ab:cd C) ad:bc D) abc:bcd | A | Multiply antecedents/consequents → ac:bd. |
| GD · Q13 | a:b=4:7, b:c=14:15 → a:c? | A) 8:15 B) 3:15 C) 2:3 D) 8:20 | A | 4:7 = 8:14; with 14:15 → 8:15. |
| GD · Q14 | Boys:girls 5:6; +5 boys → 10:11. Girls? | A) 30 B) 66 C) 54 D) 33 | B | (5k+5)/6k=10/11 → k=11 → girls 66. |
| WG · Q3 | Ratio 2:11, difference 81 → smaller number. | A) 19 B) 18 C) 27 D) 16 | B | 9k=81→k=9; smaller 2×9 = 18. |
| WG · Q4 | Product = 10 + 5×sum, ratio 5:6 → the numbers. | A) 10 & 12 B) 12 & 18 C) 22 & 9 D) 25 & 29 | A | 6k²−11k−2=0 → k=2 → 10 & 12. |
| WG · Q11 | Income A:B=5:7; A saves 4000, B 5000; A-spend = ⅔ B-spend → combined income? | A) 22200 B) 24000 C) 22800 D) 46800 | B | 5x−4000=⅔(7x−5000) → x=2000 → 10000+14000 = 24000. |
| IN · Q80 | ₹12,00,000 in 2:3:5; returns +10%, +20%, −10% → overall? | A) 3% loss B) 3% profit C) 3.6% profit D) 3.6% loss | B | +24000+72000−60000 = +36000 = 3% profit. |
| SF · Q13 | Match ratios (sub-duplicate 25:36, duplicate 3:4, reciprocal 5:7, compound 2:3 & 9:4). | A) i-d,ii-a,iii-b,iv-c B) i-b,ii-c,iii-a,iv-d C) i-c,ii-d,iii-a,iv-b D) i-c,ii-a,iii-d,iv-b | D | 5:6, 9:16, 7:5, 3:2 → i-c, ii-a, iii-d, iv-b. |
| SF · Q14 | Componendo & Dividendo of a:b=c:d. | A) (a+b):(a−b)=(c+d):(c−d) B) (a−b):(a+b)=(c+d):(c−d) C) (a+c):(b+d)=(a−c):(b−d) D) (a+b):c=(b+d):a | A | Standard C&D form → A. |
| SF · Q15 | Price ∝ weight²; 5-unit bar ₹25000 breaks 2:3 → value lost? | A) 5000 B) 12000 C) 13000 D) 14000 | B | k=1000; new value 1000(4+9)=13000 → loss 12000. |
| SF · Q16 | If x/a=y/b=z/c=k, then (bx+cy+az)/k = ? | A) 0 B) abc C) a+b+c D) ab+bc+ac | D | =ab+bc+ca → ab+bc+ac. |
5. Averages
| Source | Question | Options | Ans | Method |
|---|---|---|---|---|
| WO · Q41 | 12 students avg 20; 3 join → avg +1. Avg of the 3 new? | A) 22 B) 23 C) 24 D) 25 | D | 15×21 − 12×20 = 315−240 = 75 → 75/3 = 25. |
| WG · Q22 | 40 students avg 45; 25 wrongly 35 (twice), 38 wrongly 32 (once) → correct avg. | A) 44.65 B) 38 C) 48.27 D) 49.80 | A | 1800 − 20 + 6 = 1786 → 44.65. |
| WG · Q23 | Avg 50 over 40; drop highest & lowest → 38 avg 48; H−L=172. Highest? | A) 114 B) 131 C) 125 D) 174 | D | H+L=2000−1824=176; with H−L=172 → H = 174. |
| WG · Q24 | 8 members, top 85; if top were 92 avg would be 84 → team total? | A) 679 B) 665 C) 666 D) 657 | B | 8×84=672; actual = 672−7 = 665. |
| WG · Q17 | Avg age of 3 = 21; x:y=1:2, y:z=1:3 → value of y. | A) 13 B) 14 C) 21 D) 7 | B | Ratio 1:2:6 (9 parts)=63 → part 7 → y=2×7 = 14. |
| GD · Q4 | Avg of 10 = 15; 36 read as 26 → correct avg. | A) 14 B) 16 C) 18 D) 20 | B | 150 + 10 = 160 → 16. |
| GD · Q5 | Avg of 30 numbers = 20 and 20 numbers = 30 → combined avg. | A) 20 B) 22 C) 24 D) 26 | C | (600+600)/50 = 24. |
| GD · Q6 | Avg of 6 consecutive even numbers = 25 → smallest & largest. | A) 18,28 B) 20,30 C) 22,32 D) 24,34 | B | 20,22,24,26,28,30 → 20 & 30. |
| GD · Q7 | Average of first n natural numbers. | A) 2n+1 B) (2n+1)/2 C) n+1 D) (n+1)/2 | D | Sum n(n+1)/2 ÷ n = (n+1)/2. |
| SF · Q5 | 10 students avg 72; remove one 90 and one 60 → new avg. | A) 71.2 B) 72.5 C) 73.4 D) 74.6 | A | (720−150)/8 = 570/8 = 71.25 ≈ 71.2. |
| SF · Q6 | 12 students avg 68; 96 recorded as 72 → correct avg. | A) 70 B) 71.33 C) 72.5 D) 73.4 | A | 816 + 24 = 840 → 70. |
| SF · Q7 | 20 students avg 75; 5 absent; 4 re-scored 85; final avg 77 → 5th's marks. (wording ambiguous) | A) 80 B) 85 C) 87 D) 89 | B | Per key = 85. (Straight totals 20×77 − 15×75 − 4×85 give 75, so the item's phrasing is loose.) |
| SF · Q8 | Multi-step (remove top 25%, add 10 @40, correct 100→80), final avg 50 → original n. | A) 36 B) 40 C) 44 D) 48 | D | Set up equation across all changes → n = 48. |
| SF · Q19 | 5-member board avg 25; D(30) replaced by F → avg 24; B=C−5, A=F+2, E=B → age of E. | A) 20 B) 21 C) 25 D) 27 | B | New total 120; F = 25; solve chain → E = 21. |
6. Ages
| Source | Question | Options | Ans | Method |
|---|---|---|---|---|
| WG · Q6 | A:B = 5:7; 5 yr ago 5:8 → present ages. | A) 22 & 36 B) 15 & 21 C) 25 & 42 D) 10 & 13 | B | (5x−5)/(7x−5)=5/8 → x=3 → 15 & 21. |
| WG · Q16 | 13 yr ago father = 3×brother; 5 yr hence = 2×; I'm twice brother's age → my age. | A) 62 B) 63 C) 92 D) 15 | A | brother 31 → me 2×31 = 62. |
| GD · Q15 | A:B = 7:9; after 4 yr → 9:11. A's present age? | A) 28 B) 35 C) 21 D) 14 | D | (7x+4)/(9x+4)=9/11 → x=2 → A = 14. |
| GD · Q16 | Father+son = 50; 5 yr ago father = 4×son → son's age. | A) 10 B) 12 C) 13 D) 14 | C | f=4s−15, f+s=50 → s = 13. |
| GD · Q17 | Father 40, son 10 → in how many years father = 3×son? | A) 10 B) 20 C) 15 D) 5 | D | 40+x = 3(10+x) → x = 5. |
| SF · Q17 | Match age-scenarios to present age of older person. | A) P1,Q2,R3,S4 B) P2,Q1,R3,S4 C) P2,Q3,R1,S4 D) P3,Q2,R4,S1 | C | Solve each → P-2, Q-3, R-1, S-4. |
| SF · Q18 | Kunal:Sagar 6 yr ago 6:5; 4 yr hence 11:10 → true statement. | A) Sagar 18 B) Sum 32 C) 6 yr ago Kunal 12 D) 2 yr ago 5:4 | C | Solving gives Kunal(−6)=12 → C. |
| SF · Q20 | Man's age = son²; 1 yr ago man = 8×son → man's present age (son = x). | A) 25 B) 36 C) 49 D) 64 | C | x²−1=8(x−1) → x=7 → man = 49. |
7. Time & Work · Pipes
| Source | Question | Options | Ans | Method |
|---|---|---|---|---|
| WO · Q47 | A 12 d, B 18 d together; A leaves after 3 d; C joins, B+C finish rest in 4 d; C alone = x. | A) 11.08 B) 11 C) 12.05 D) 12 | A | Work left after 3 d solved → C alone ≈ 11.08 days. |
| WO · Q48 | Pipes A 12 h, B 16 h fill; C empties in 24 h; all open → time. | A) 8 h B) 8 h 40 m C) 9 h D) 9 h 36 m | D | Net rate 1/12+1/16−1/24 = 5/48 → 9 h 36 m. |
| JA · Q29 | A 10, B 12, C 15; A leaves after 2 d, C after 2 more → total days. | A) 6 B) 6 2⁄5 C) 6 3⁄5 D) 6 1⁄2 | B | Done 4/5 in 4 d; rest 1/5 by B → +2 2⁄5 → 6 2⁄5 days. |
| JA · Q30 | A 15, B 25 together; B leaves 7 d before completion → total time. | A) 16 B) 14 C) 12 D) 10 | C | T/15 + (T−7)/25 = 1 → T = 12 days. |
| GD · Q8 | Man+woman 8 d; man alone 10 d → woman alone. | A) 20 B) 40 C) 50 D) 60 | B | 1/8 − 1/10 = 1/40 → 40 days. |
| GD · Q9 | A+B 10 d; A alone 30 d → B alone. | A) 10 B) 15 C) 20 D) 25 | B | 1/10 − 1/30 = 1/15 → 15 days. |
| GD · Q10 | A 18 d; B takes half of A → together. | A) 4 B) 8 C) 6 D) 12 | C | B=9; 1/18+1/9 = 1/6 → 6 days. |
| GD · Q11 | A 15, B 20; both work 4 d → fraction left. | A) 15/8 B) 8/15 C) 7/15 D) 15/7 | B | 4×(7/60)=28/60=7/15 done → left 8/15. |
| WG · Q18 | A+B together 3 d; B leaves after 2 d; finished 2 d later → time for the solo worker. | A) 12 B) 4.2 C) 6 D) 3.33 | C | Rest 1/3 in 2 d → rate 1/6 → 6 days. |
| WG · Q19 | A takes 50% more time than B; together 18 d → B alone. | A) 30 B) 25 C) 18 D) 42 | A | (5/3)/b = 1/18 → b = 30 days. |
| IN · Q76 | Pump speed ×9/7 fills 30 min earlier → original time. | A) 135 B) 140 C) 145 D) 150 | A | New time = 7/9 old; old×2/9 = 30 → 135 min. |
| SF · Q9 | A,B,C 25 d (eff 4:3:5); A leaves after 5 d, B +33.3%, C leaves d days early, done in 35 d → d. | A) 4 B) 5 C) 6 D) 8 | C | Work-balance equation → d = 6. |
| SF · Q10 | A = x days, B = x+5; together 6 d → x. | A) 12 B) 8 C) 10 D) 6 | C | x²−7x−30=0 → x = 10. |
8. Time, Speed & Distance (trains · boats)
| Source | Question | Options | Ans | Method |
|---|---|---|---|---|
| WO · Q59 | Boat 30 km down in 2 h, up in 3 h → time for 45 km down + 30 km up. | A) 5:30 h B) 5:45 h C) 7 h D) None | D | Down 15, up 10 → 3 h + 3 h = 6 h → None of these. |
| WO · Q60 | Train 120 m at 54 km/h; T1 = pole, T2 = 180 m platform → T2−T1. | A) 10 s B) 12 s C) 15 s D) 18 s | B | 15 m/s: T1=8 s, T2=20 s → 12 s. |
| WG · Q12 | 900 km in 11 h; 2/5 at 60 km/h → speed for rest. | A) 108 B) 77 C) 81 D) 93 | A | 360 km/60 = 6 h; 540 km in 5 h → 108 km/h. |
| WG · Q13 | 42 km in 5 h; walk 6, cycle 10 → distance walked. | A) 12 km B) 1.2 km C) 37 km D) 3.9 km | A | 6w+10(5−w)=42 → w=2 h → 12 km. |
| WG · Q14 | 30% @20, 60% @40, 10% @10 → average speed. | A) 25 B) 22 C) 12 D) 31 | A | 100/(1.5+1.5+1) = 25 km/h. |
| WG · Q15 | Half at 6, half at 3 → average speed. | A) 4 B) 4.5 C) 5.22 D) 4.87 | A | 2·6·3/9 = 4 km/h. |
| IN · Q77 | Boats A18, B24, C36; B starts 1 h after A; B & C overtake A together → C starts how long after B? | A) 1 h B) 2 h C) 3 h D) Can't say | A | Overtake at A's t=4 h; C needs 2 h travel → starts at t=2 = 1 h after B. |
| JA · Q38 | Speed → 4/5 of usual → 15 min late → actual time. | A) 45 B) 60 C) 30 D) 75 | B | Time ×5/4; extra 1/4·T = 15 → T = 60 min. |
| LA · Q55 | 50 km/h out, 40 km/h back → average speed. | A) 44.4 B) 46.4 C) 46.8 D) 48.6 | A | 2·50·40/90 = 44.4 km/h. |
| LA · Q56 | Speed +25% → 1 h less → original time. | A) 3 B) 4 C) 5 D) 6 | C | Time ×4/5 saves 1/5·T = 1 h → T = 5 h. |
| LA · Q57 | Trains 120 m & 180 m, opposite, 54 & 72 km/h → time to cross. | A) 12 s B) 9 s C) 15 s D) 20 s | B | Rel 126 km/h = 35 m/s; 300/35 ≈ 8.6 ≈ 9 s. |
| SF · Q11 | 60 km/h for 5 h; actual speed 50 → real time. | A) 4.5 B) 6 C) 5.5 D) 5 | B | Distance 300 km; 300/50 = 6 h. |
| SF · Q12 | +10 km/h saves 2 h; +20 km/h saves 3 h → distance S. | A) 60 B) 90 C) 120 D) 150 | C | Solve: U=20, T=6 → S = 120 km. |
9. Simple & Compound Interest
| Source | Question | Options | Ans | Method |
|---|---|---|---|---|
| IN · Q19 | SI–CI difference (2 yr, 4%) = ₹1 → sum. | A) 625 B) 635 C) 645 D) 655 | A | P(r/100)² = 1 → P×0.0016 = 1 → 625. |
| IN · Q20 | CI on ₹30000 at 7% = ₹4347 → period (yr). | A) 2.5 B) 2 C) 5 D) 4 | B | (1.07)ⁿ = 1.1449 = 1.07² → n = 2. |
| LA · Q28 | CI − SI (2 yr, 17%) = ₹433.50 → sum. | A) 12000 B) 15000 C) 25000 D) 20000 | B | P(0.17)² = 433.5 → P = 15,000. |
| LA · Q38 | CI (2 yr, 8%) = ₹6656 → SI on same sum. | A) 6224 B) 6400 C) 5600 D) 6336 | B | P = 40000; SI = 40000×0.08×2 = 6400. |
| LA · Q35 | ₹10000 loan paid ₹800/month in 15 instalments → rate of return. | A) 16% p.a. B) 18% C) 15% D) 17% | A | Interest ₹2000 on reducing balance → ≈ 16% p.a. |
10. Probability
| Source | Question | Options | Ans | Method |
|---|---|---|---|---|
| IN · Q24 | P(red card OR face card) from 52. | A) 13/15 B) 1/4 C) 29/52 D) 8/13 | D | (26+12−6)/52 = 32/52 = 8/13. |
| IN · Q25 | P(a sure event). | A) 1 B) 0.5 C) 0 D) 0.25 | A | Certain → 1. |
| IN · Q26 | P(number > 6 on a die). | A) 1 B) 0.5 C) 0 D) — | C | Impossible → 0. |
| WG · Q1 | 8% of liver patients are alcoholics; P(alc)=6%, P(liver)=12% → P(liver | alcoholic). | A) 0.16 B) 0.44 C) 0.016 D) 0.22 | A |
| WG · Q2 | Two dice, P(sum 7 or 11). | A) 1/5 B) 5/3 C) 3/7 D) 2/9 | D | (6+2)/36 = 2/9. |
| WG · Q20 | Tickets 1–20, P(multiple of 3 or 5). | A) 1/2 B) 5/3 C) 5/8 D) 9/20 | D | 6+4−1 = 9 → 9/20. |
| WG · Q21 | 10 prizes, 25 blanks → P(prize). | A) 1/11 B) 2/15 C) 2/7 D) 1/14 | C | 10/35 = 2/7. |
| GD · Q18 | 3R,2B,5G → P(red). | A) 3/10 B) 1/2 C) 1/5 D) 2/5 | A | 3/10. |
| GD · Q19 | Die, P(even number > 2). | A) 1/2 B) 1/3 C) 1/6 D) 1/8 | B | {4,6} → 2/6 = 1/3. |
| GD · Q20 | Two coins, P(one head & one tail). | A) 1/4 B) 1/2 C) 3/4 D) 1 | B | 2/4 = 1/2. |
| LA · Q32 | Cards 1–100, P(perfect square). | A) 1/10 B) 1/100 C) 9/10 D) 90/100 | A | 10 squares → 1/10. |
| LA · Q40 | Die, P(3 or greater). | A) 1/2 B) 1/3 C) 1/4 D) 2/3 | D | {3,4,5,6} → 4/6 = 2/3. |
| SF · Q21 | Coin tossed 5× (+1/−1) → P(sum = +1). | A) 5/16 B) 5/32 C) 10/16 D) 2/3 | A | Need 3H2T = C(5,3)/32 = 10/32 = 5/16. |
| SF · Q22 | Die 3×, P(sum even | ≥ one 6, not all same). | A) 1/2 B) 3/5 C) 4/7 D) 5/9 | A |
| SF · Q23 | 4R,3B,3G, draw 3 → P(exactly two same colour). | A) 18/20 B) 13/45 C) 30/45 D) 13/20 | D | Favourable/120 → 13/20. |
| SF · Q24 | Pick 2 from {1..6} → P(sum prime). | A) 1/3 B) 2/5 C) 7/15 D) 8/15 | C | 7 prime-sum pairs of 15 → 7/15. |
11. Mensuration & Geometry
| Source | Question | Options | Ans | Method |
|---|---|---|---|---|
| IN · Q11 | Volume of a cuboid (l, b, h). | A) lbh B) lb+bh+hl C) 2(l+b)h D) 2(lb+bh+hl) | A | V = lbh. |
| IN · Q12 | Rhombus, diagonals 10 & 8.2 → area. | A) 82 B) 410 C) 41 D) 820 | C | ½·10·8.2 = 41 cm². |
| IN · Q13 | Circular pond circumference 22 km → diameter. | A) 15 B) 1.5 C) 0.7 D) 7 | D | 2·(22/7)r=22 → r=3.5 → d = 7 km. |
| IN · Q14 | Tyre radius 84 cm, 4 revolutions → distance. | A) 1056 B) 2112 C) 840 D) 1840 | B | 4·2π·84 = 2112 cm. |
| GD · Q25 | Wire square area 484 cm² reshaped to circle → circle area. | A) 44 B) 616 C) 308 D) 1232 | B | Perimeter 88 → r=14 → area 616 cm². |
| GD · Q26 | Circle circumference 88 m → radius. | A) 7 B) 14 C) 21 D) 28 | B | 2·(22/7)r=88 → 14 m. |
| GD · Q27 | Polygon with all sides & angles equal is ___. | A) Irregular B) Convex C) Regular D) Concave | C | Regular polygon. |
| GD · Q28 | Sum of interior angles of an n-sided polygon. | A) 180°(n−2) B) 90°(n−2) C) 180°(2n−2) D) 90°(2n−2) | A | (n−2)·180°. |
| LA · Q23 | Largest cone cut from a hemisphere → remaining as % of hemisphere. | A) 33.33% B) 50% C) 75% D) 66.66% | B | Cone (1/3)πr³ of hemisphere (2/3)πr³ → remaining 50%. |
| LA · Q25 | h+r = 46, TSA = 6072 (π=22/7) → volume. | A) 6072π B) 1085π C) 3036π D) 11025π | D | 2πr(h+r)=6072 → r=21, h=25 → V = 11025π. |
| LA · Q26 | Two cones (h 3.8 & 4.6, r 2.1) melted → sphere diameter. | A) 4.2 B) 1.4 C) 3.5 D) 6.3 | A | Vol sum → R=2.1 → d = 4.2 cm. |
| LA · Q33 | Sphere inscribed in cube; a = V(cube)/V(sphere), b = SA(sphere)/SA(cube) → ab. | A) 30/π B) 4 C) 36/π² D) 1 | D | (6/π)(π/6) = 1. |
| LA · Q37 | Cone fitted in cube (vol 343 cc) → cone volume. | A) 70 B) 80 C) 90 D) 60 | C | Side 7, r 3.5, h 7 → (1/3)π·12.25·7 ≈ 90 cc. |
| LA · Q39 | Box l:b:h = 3:2:4; paper @₹1.5/m² costs ₹1950 → 50% of volume. | A) 1500 B) 1750 C) 1800 D) 1600 | A | SA 1300 → 52k²=1300 → k=5; V=3000 → half 1500 m³. |
| SF · Q29 | Sphere melted into n spheres; relate Σ small SA (s) to big SA (S). | A) s=S B) s=n^⅓·S C) s=n^⅔·S D) s=n·S | C ⚠ | Volume conservation gives r=R·n^(−⅓) → s = n^⅓·S, i.e. option B is mathematically correct; official key marks C (likely a key error). |
| SF · Q30 | Rocket (cone on cylinder) — correct statement about the orange (cone) painted area. | A) CSA of cone B) CSA + base of cone C) CSA + (cone base − cylinder base) D) CSA cone + CSA cylinder | C | Visible cone area = CSA + exposed ring (cone base − cylinder base) → C. |
| SF · Q31 | Same rocket → cost of painting orange part (₹0.1/mm²), in terms of π. | A) 870π B) 8700π C) 2025π D) 202.5π | A | Orange area × 0.1 → 870π. |
| SF · Q32 | Cylinder & sphere, equal radius & equal TSA → V(cyl):V(sphere). | A) 3:4 B) 2:3 C) 9:8 D) 3:2 | A | Equal TSA → h=r; πr³ : (4/3)πr³ = 3:4. |
12. Algebra · Equations · AP
| Source | Question | Options | Ans | Method |
|---|---|---|---|---|
| WO · Q58 | x+y=14, x−y=4 → x·y. | A) 54 B) 45 C) 36 D) 63 | B | x=9, y=5 → 45. |
| IN · Q16 | Nature of solutions of 3x − 11y = 10. | A) Unique B) Two C) Infinitely many D) None | C | One linear equation, two variables → infinitely many. |
| IN · Q17 | (3,4) on 3y = kx + 7 → k. | A) 4/5 B) 5/3 C) 4/3 D) 4/7 | B | 12 = 3k+7 → k = 5/3. |
| IN · Q18 | x + 2y = 2 cuts the y-axis at. | A) (1,0) B) (2,0) C) (0,1) D) (0,2) | C | x=0 → y=1 → (0,1). |
| LA · Q21 | AP: (3rd+4th)=19, (1st+7th)=22 → 9th term. | A) 16 B) 17 C) 15 D) 26 | D | d=3, a=2 → a+8d = 26. |
| LA · Q22 | Which is true: √5+√3 vs √6+√2? | A) √5+√3 > √6+√2 B) < C) = D) product = 1 | A | Squares: 8+2√15 > 8+2√12 → A. |
| LA · Q24 | Minimum of x²+4xy+6y²−4y+4. | A) −4 B) 0 C) 2 D) 4 | C | (x+2y)² + 2(y−1)² + 2 → min 2. |
| LA · Q29 | AM = 41, GM = 9 → a possible value of X. | A) 125 B) 81 C) 49 D) 25 | B | x+y=82, xy=81 → {1,81} → 81. |
| SF · Q27 | LCM = 3x³+18x²+30x+12, HCF = x+2, one = x+2; other = k(x²+ax+b) → a+b. | A) 3 B) 4 C) 5 D) 6 | D | Product = HCF·LCM → other = 3(x²+4x+2) → a+b = 4+2 = 6. |
📊 Topic distribution
| # | Topic | Q |
|---|---|---|
| 1 | Number System · LCM/HCF · Simplification | 18 |
| 2 | Percentages | 10 |
| 3 | Profit, Loss & Discount | 14 |
| 4 | Ratio, Proportion & Mixtures | 14 |
| 5 | Averages | 14 |
| 6 | Ages | 8 |
| 7 | Time & Work · Pipes | 13 |
| 8 | Time, Speed & Distance | 13 |
| 9 | Simple & Compound Interest | 5 |
| 10 | Probability | 16 |
| 11 | Mensuration & Geometry | 18 |
| 12 | Algebra · Equations · AP | 9 |
| Total | ~152 |
FAA focus — where the marks cluster
Across all 7 papers the quantitative section is dominated by Percentages / Profit-Loss, Ratio & Averages, Time-Work-Speed, and Mensuration. For FAA (which adds heavier Maths/Stats), nail the CI–SI shortcut [P(r/100)² for the 2-yr difference], average-correction (add/subtract the error), mixture replacement [(1−f) rule], and cone/sphere/cylinder volume-surface formulas — these recur almost every paper. Companion: verbal & logical reasoning → Reasoning-Mental-Ability.
