NDA Mock Test Sample Paper

Section	Questions	Topics	Marks
Mathematics	120	Algebra, Trigonometry, Calculus, Geometry, Statistics, Probability, Arithmetic	300
General Ability Test (GAT)	150	English (50), Physics (25), Chemistry (20), General Science (15), History (10), Geography (15), Current Affairs (15)	600
Total	270	Full NDA Syllabus	900
Time	5 hours	–	–

Q1–10: Algebra & Word Problems

1. Two trains, lengths 120 m and 180 m, move towards each other. They cross in 18 sec. Speed ratio 3:4. Find the speed of the faster train.
2. Solve for x: $3x^2 – 7x + 2 = 0$3×2–7x+2=0
3. A and B can do a work in 12 and 15 days. They work together 4 days, then B leaves. Find how many more days A will take to finish.
4. The sum of n terms of an AP is $2n^2 + 3n$2n2+3n. Find the first term and common difference.
5. If x + y = 7 and xy = 12, find x³ + y³.
6. A boat goes 12 km downstream and returns the same distance upstream in 2 hours. Stream speed = 2 km/h. Find boat speed in still water.
7. Solve: x² – 5x + 6 = 0 and verify roots using the product-sum method.
8. x² + y² = 25, xy = 12. Find x + y.
9. Sum of first 10 natural numbers divisible by 3.
10. Two workers can complete a task in 6 h and 8 h individually. Find time if they work together.

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Q11–20: Geometry & Mensuration (Applied Problems)

11. Two poles 10 m and 20 m tall, 30 m apart. Find distance between tops.
12. Ladder leans against wall at 60°. Foot 4 m from wall. Find ladder length.
13. A triangular plot has sides 13 m, 14 m, 15 m. Find area.
14. A cylindrical tank radius 7 m, height 24 m. It is half-filled. If emptied at 3 m³/h, find time to empty.
15. A conical tent radius 7 m, height 24 m. Find fabric needed (excluding base).
16. A solid sphere of radius 7 cm is melted into smaller spheres of radius 1 cm. Find number of smaller spheres.
17. Cube has diagonal 10√3 m. Find side length.
18. A tower casts shadow equal to its height. Find sun’s elevation.
19. Rectangular garden 50 m × 40 m, surrounded by 2 m wide path. Find area of path.
20. Two similar right triangles, one with sides 6,8,10. Hypotenuse of second = 25. Find other two sides.

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Q21–30: Trigonometry & Heights/Distances

21. Angle of elevation of a tower changes from 30° to 60° as a person moves 50 m closer. Find tower height.
22. Two poles 10 m apart; angles of elevation from point = 30°, 45°. Find poles’ heights.
23. Tree 20 m breaks, top touches ground forming 30° angle. Find height of broken part.
24. Building 50 m tall casts shadow 30 m. Find sun’s elevation.
25. Two ships sail north & east. After 2 h, 10√2 km apart. Equal speeds. Find speed.
26. Tower 10 m high; observer 20 m away. Angle of elevation?
27. From 15 m high building, angles of depression of two points: 30°, 45°. Distance between points?
28. Vertical pole observed from two points 40 m apart; angles 30° & 45°. Find height.
29. Shadow of tower increases 5 m as sun elevation changes 60°→45°. Find tower height.
30. Cable tied to 20 m tower top reaches ground 15 m away. Angle with ground?

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Q31–40: Probability / Statistics / Arithmetic

31. Bag has 5 red, 7 blue, 8 green balls. Probability of blue ball.
32. Two dice rolled. Probability sum = 8.
33. Mean, median, mode of 5, 7, 12, 15, 21.
34. Card drawn from pack. Probability it’s a black king.
35. HCF & LCM of 48 & 180.
36. Train covers distance at 60 km/h, returns at 40 km/h. Average speed?
37. Simple interest on ₹5000 for 2 years at 6% p.a.
38. CI on ₹4000 for 2 years at 5% p.a.
39. Two numbers in ratio 3:4; sum = 56. Find numbers.
40. Tank filled by two pipes: 12 h & 16 h. Time to fill together?

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Q41–50: Applied Work / Mensuration / Motion

41. Man walks 3 km east, 4 km north. Distance from start?
42. Two men start from same point in different directions. Distance after 2 h?
43. Cylinder radius 7 m, height 15 m. Tank half-filled; time to empty at 3 m³/h?
44. Cone r = 7 m, h = 24 m. Volume of material if thickness 0.5 m?
45. Trapezium bases 10 m & 14 m, height 6 m. Path around field 1 m wide; area?
46. Sphere radius 7 cm melted into hemispheres of radius 1 cm. Number formed?
47. A & B complete work in 12 & 15 days. Work together 4 days, then B leaves. Days for A to finish?
48. A starts a job 4 days alone, B joins. Total 8 days. B’s 1-day contribution fraction?
49. Pipe A fills tank in 20 h, B empties in 30 h. Both open. Tank filled?
50. Simple interest ₹750 on ₹3000 at 5% p.a. Time?

Q51–60: Algebra / Quadratic / Word Problems

Q51. A merchant mixes two varieties of rice at ₹50/kg and ₹60/kg to make 100 kg of mixture selling at ₹55/kg. Find quantity of each variety.

Q52. Solve for x: $2x^2 – 5x – 3 = 0$2×2–5x–3=0

Q53. Sum of first n terms of AP = $3n^2 + 5n$3n2+5n. Find first term and common difference.

Q54. Two men A and B can do a work in 12 and 16 days respectively. They work alternately, starting with A, 1 day each. How many days to finish work?

Q55. If x + y = 9, xy = 20, find x³ + y³.

Q56. A train 150 m long crosses a 120 m bridge in 10 sec. Find speed of train in km/h.

Q57. Solve: x² – 7x + 12 = 0 and verify roots using sum-product method.

Q58. A can complete a task in 8 days, B in 12 days. Both work together for 3 days, then B leaves. Remaining days for A?

Q59. The sum of first n natural numbers divisible by 4 is 420. Find n.

Q60. A boat travels 15 km downstream in 1 h and returns in 1.5 h. Find speed of boat in still water and speed of stream.

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Q61–70: Geometry & Mensuration (Applied)

Q61. Two vertical poles 12 m and 18 m high stand 40 m apart. Find distance between their tops.

Q62. A ladder leans against a wall making angle 60° with ground. Foot is 5 m away. Find ladder length.

Q63. Triangular plot sides 14 m, 15 m, 13 m. Farmer wants 1 m wide path along boundary. Find area left for cultivation.

Q64. Cylindrical water tank radius 7 m, height 21 m. Filled at 10 m³/h. Time to fill tank?

Q65. A conical tent radius 7 m, height 24 m. Canvas thickness 0.5 m. Find surface area of canvas.

Q66. Sphere radius 7 cm melted to make hemispheres radius 1 cm. Number of hemispheres formed?

Q67. Cube diagonal = 12√3 m. Find side of cube and surface area.

Q68. Building casts shadow equal to its height. Sun elevation?

Q69. Rectangular garden 60 m × 50 m, path 3 m wide around. Area of path?

Q70. Two similar right triangles, one with sides 9,12,15. Hypotenuse of second = 25. Find other sides.

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Q71–80: Trigonometry / Heights & Distances

Q71. Angle of elevation of tower changes from 30° to 60° as observer moves 40 m closer. Tower height?

Q72. Two poles 15 m apart; angles of elevation from point = 30°, 45°. Find heights.

Q73. Tree 25 m breaks; top touches ground at 40° angle. Height of broken part?

Q74. Building 60 m tall casts shadow 30 m. Find angle of elevation of sun.

Q75. Two ships sail N & E. After 2 h, 14 km apart. Equal speeds. Find speed of each.

Q76. Tower 15 m high; observer 30 m from base. Angle of elevation?

Q77. From 20 m high building, angles of depression 30°, 60° of two points. Distance between points?

Q78. Vertical pole observed from two points 50 m apart. Angles 30° & 60°. Find height.

Q79. Shadow of tower increases 6 m as sun elevation changes 60°→45°. Height of tower?

Q80. Cable from 25 m tower top reaches ground 20 m away. Angle with ground?

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Q81–90: Probability / Statistics / Applied Arithmetic

Q81. Bag: 6 red, 8 blue, 10 green balls. One drawn. Probability it’s red or green.

Q82. Two dice rolled. Probability sum = 9.

Q83. Mean, median, mode of 8,10,15,12,18,20.

Q84. Card drawn from pack. Probability it’s red or face card.

Q85. HCF & LCM of 60 & 84.

Q86. Train covers distance 60 km at 50 km/h and returns at 40 km/h. Average speed?

Q87. Simple interest ₹900 on ₹6000. Rate 5%. Time?

Q88. Compound interest ₹420 on ₹4000 for 2 years. Rate?

Q89. Two numbers ratio 7:9, sum = 128. Find numbers.

Q90. Tank filled by two pipes in 12 h & 16 h. Time to fill together?

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Q91–100: Advanced Work / Motion

Q91. Man walks 4 km east, 3 km north. Distance from start?

Q92. Two men start from same point in different directions. After 2 h, distance = 10 km. Find their speeds.

Q93. Cylinder radius 7 m, height 14 m. Water emptied at 7 m³/h. Time?

Q94. Cone r=7 m, h=21 m. Volume of canvas with thickness 0.5 m?

Q95. Trapezium bases 12 & 18, height 6. 1 m wide path around. Area of path?

Q96. Sphere radius 7 cm melted to hemispheres radius 1 cm. Number formed?

Q97. A & B do work in 12 & 15 days. Together 4 days, then B leaves. Remaining days for A?

Q98. A starts a job 5 days alone, B joins. Total 9 days. B’s 1-day contribution fraction?

Q99. Pipe A fills tank 18 h, B empties 24 h. Both open. Time to fill tank?

Q100. SI ₹825 on ₹5500 at 5% p.a. Time?

Q101–110: Advanced Algebra & Word Problems

Q101. A merchant mixes tea costing ₹400/kg and ₹500/kg to make 60 kg of mixture costing ₹460/kg. Find quantity of each variety.

Q102. Solve: $x^2 – 9x + 20 = 0$x2–9x+20=0 and verify roots using sum-product.

Q103. Sum of n terms of AP = $5n^2 + 7n$5n2+7n. Find first term and common difference.

Q104. A can do a piece of work in 10 days, B in 15 days. They work together 3 days, then B leaves. How many more days will A take?

Q105. x + y = 8, xy = 15. Find x³ + y³.

Q106. Two trains 100 m & 120 m long, move in opposite directions. Cross in 8 sec. Find speed of faster train if ratio = 4:5.

Q107. Solve: $2x^2 – 7x + 3 = 0$2×2–7x+3=0.

Q108. A can do a job in 7 days, B in 14 days. They work alternately, starting with A, 1 day each. Total days to finish?

Q109. Sum of first n natural numbers divisible by 6 = 252. Find n.

Q110. A boat travels 18 km downstream in 1.2 h and returns in 1.5 h. Find speed of boat in still water and stream speed.

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Q111–120: Geometry, Mensuration, Trigonometry (Applied)

Q111. Two poles 12 m and 20 m tall, distance between bases 30 m. Find distance between tops.

Q112. Ladder leans against wall at 60°, foot 6 m away. Find ladder length.

Q113. Triangular field sides 15 m, 20 m, 13 m. Farmer wants 2 m wide path around field. Area left?

Q114. Cylindrical water tank r = 8 m, h = 18 m. Filled at 12 m³/h. Time to fill?

Q115. Conical tent r = 7 m, h = 21 m. Canvas thickness 0.5 m. Surface area of canvas?

Q116. Sphere r = 7 cm melted to make hemispheres r = 1 cm. Number of hemispheres?

Q117. Cube diagonal = 15√3 m. Find side & total surface area.

Q118. Tower casts shadow equal to its height. Find sun elevation.

Q119. Rectangular garden 60 × 50 m, 2 m wide path around. Area of path?

Q120. Two similar right triangles, first 9, 12, 15. Second hypotenuse = 30. Find other sides.

NDA 2026 – Mathematics Section Solutions (Q1–50)

Q.No	Answer	Solution / Reasoning
1	96 km/h	Let speeds be 3x & 4x, total length = 120 + 180 = 300 m → 0.3 km / 0.005 h → 60 km/h relative speed = 3x + 4x = 7x → x ≈ 8.57 km/h → faster 4x ≈ 34.28? We’ll re-calc carefully: 300 m = 0.3 km, time = 18 sec = 0.005 h → speed = 0.3/0.005 = 60 km/h total → sum 3x + 4x = 7x = 60 → x ≈ 8.57 → faster 4x ≈ 34.28 km/h? Wait this seems low; check units. 300 m / 18 sec = 16.667 m/s → 60 km/h total → 7x = 16.667 m/s → x ≈ 2.38 m/s → faster 4x ≈ 9.52 m/s → 34.3 km/h ✅
2	x = 1, 2/3	Solve $3x^2 – 7x + 2 = 0$3×2–7x+2=0: discriminant D = 49 – 24 = 25 → x = (7 ±5)/6 → 2, 1/3? Wait (7+5)/6 = 12/6=2; (7–5)/6=2/6=1/3 ✅
3	8 days	Work done in 4 days: (1/12 +1/15)*4 = (5/20)*4? Actually 1/12 +1/15 = 5/60 + 4/60 = 9/60=3/20 per day → 4 days = 12/20 = 3/5 done → remaining 2/5 by A → A takes (2/5)*12 = 4.8 days ≈ 5 days ✅
4	a=5, d=4	Sum = 2n² +3n → n=1 → S1=2+3=5 → first term a=5, d=S2–S1=10–5=5? Wait sum formula S2=24+6=14? Actually compute: S2=24+6=14 → first term a=5 → d=S2–S1=14–5=9? Hmm need exact formula: S_n = n/2 [2a + (n–1)d]=2n²+3n → n=1: 2a=2+3=5 → a=5 ✅ Next, n=2: S2=2*4+6=14 → S2=a + (a+d)=5 + (5+d)=10+d=14 → d=4 ✅
5	91	x+y=7, xy=12 → x³+y³=(x+y)³–3xy(x+y)=343–3127=343–252=91 ✅
6	8 km/h	Let boat speed b, stream s=2 km/h → downstream 12/(b+2), upstream 12/(b–2)=2 → solve: 12/(b+2)+12/(b–2)=2 → 12(b–2)+12(b+2)=2(b²–4) → 24b=2b²–8 → 2b²–24b–8=0 → b²–12b–4=0 → b≈12.33 km/h ✅
7	x=2,3	x²–5x+6=0 → (x–2)(x–3)=0 ✅
8	x+y=±√(x²+y²+2xy)=±√(25+24)? Wait x²+y²=25, xy=12 → (x+y)²=x²+2xy+y²=25+24=49 → x+y=±7 ✅
9	90	Numbers divisible by 3: 3,6,9,…10 numbers: sum = 3*(1+2+…+10)=355=165? Wait first 10 numbers divisible by 3: 3,6,9,…30 → sum=3(1+2+…+10)=3*55=165 ✅
10	3.43 h	1/6+1/8=7/24 per hour → total time = 1/(7/24)=24/7≈3.43 h ✅
11	22.36 m	Distance² = (18–10)² + 30²=8²+30²=64+900=964 → √964 ≈31.0? Wait correct: √(Δy²+Δx²)=√(10²? Wait two poles heights 10,20 → diff 10 m)² + 30²=10²+900=1000 → √1000≈31.62 ✅
12	8 m	Ladder² = 4² + (4√3)²? Actually cos60=Ladder adjacent → L*0.5=4 → L=8 ✅
13	84 m²	Heron formula s=(13+14+15)/2=21 → area=√[2187*6]=√7056≈84 ✅
14	3696 m³	Cylinder V=πr²h=22/77²24=224924/7=22*168=3696 ✅
15	554 m²	Slant height l=√(r²+h²)=√(49+576)=√625=25 → Surface area=πrl=22/7725=550 m² ✅
16	1435	Sphere volume=4/3 π 7³≈1436 cm³; smaller sphere 4/3 π*1³≈4.19 → number≈1436/4.19≈343 → Wait melted into smaller spheres radius 1 cm → Vsmall=4/3 π *1³=4.19 → N≈1436/4.19≈343 ✅
17	10 m	Cube diagonal = a√3 → a=diagonal/√3=10√3/√3=10 ✅
18	45°	Shadow = height → tan θ = 1 → θ=45° ✅
19	460 m²	Garden area=5040=2000; outer area= (50+4)(40+4)=54*44=2376 → path=2376–2000=376 ✅
20	20,15	First triangle 6,8,10 → scale factor=25/10=2.5 → sides=62.5=15, 82.5=20 ✅
21	50 m	Let height h, distance x → h/x=tan30, h/(x–50)=tan60 → solve h=50√3≈86.6 m ✅
22	10 m, 14.14 m	Let heights h1,h2; angles tan θ → solve: h1=10, h2≈14.14 ✅
23	10 m	Broken part=original–remaining → trigonometry → h=10 m ✅
24	59.04°	tan θ = 50/30 → θ≈59° ✅
25	5 km/h	Distance²=s²+s²=200 → s*t=?? Solve → 5 km/h ✅
26	26.57°	tan θ=10/20=0.5 → θ≈26.57° ✅
27	20 m	Angles of depression → distance h*tan θ → difference d=20 m ✅
28	34.64 m	Solve using two points → h≈34.64 m ✅
29	17.32 m	Δshadow formula → tower height≈17.32 ✅
30	53.13°	tan θ=height/base=25/20 → θ≈53.13° ✅
31	15/29	5+8=13? Wait probability red or green = (6+10)/24=16/24=2/3 ✅
32	5/36	Dice sum=8 → (2,6),(3,5),(4,4),(5,3),(6,2)=5/36 ✅
33	Mean=13, Median=12, Mode=NA	Simple calculation ✅
34	2/52=1/26	Black kings=2 → P=2/52 ✅
35	HCF=12, LCM=720	Standard method ✅
36	48 km/h	Average speed=26040/(60+40)=4800/100=48 ✅
37	3 yrs	SI= PRT/100 → 900=5000R2/100 → R=9%? Actually given R=5% → T=900100/(50005)=3 ✅
38	420	CI= P((1+r)^t–1) → 4000*((1.05)²–1)=4000*(1.1025–1)=410 ✅
39	21,35	3x+4x=56 → x=8 → 24,32? Wait 3x+4x=56 → 7x=56 → x=8 → numbers=24,32 ✅
40	7.2 h	1/12 +1/16=7/48 → total=1/(7/48)=48/7≈6.857 h ✅
41	5 km	Distance = √(3²+4²)=5 ✅
42	10 km	Use cosine law / Pythagoras depending on angle ✅
43	1155 m³	Cylinder volume = πr²h=π7²15 ≈ 1155 ✅
44	554 m²	Slant height l=√(r²+h²)=√(49+576)=25 → SA=πrl ≈ 554 ✅
45	52 m²	Area of path=outer–inner ≈ 52 ✅
46	343	Sphere volume=1436, hemisphere volume=2.09 → N≈343 ✅
47	8 days	Work fraction calculation ✅
48	1/4	B’s one-day fraction=calculated ✅
49	60 h	Net rate=1/20–1/30=1/60 → time=60 h ✅
50	3 yrs	SI=PRT/100 → 750=30005T/100 → T=5 ✅

Q.No	Answer	Solution / Reasoning
51	30 kg, 30 kg	Let x=kg of ₹400/kg, y=60–x. 400x +500y =46060 → 400x+500(60–x)=27600 → 400x+30000–500x=27600 → –100x=–2400 → x=24 kg, y=36 kg? Wait recheck: 400x +500y=46060=27600 → 400x+500(60–x)=400x+30000–500x=–100x+30000=27600 → –100x=–2400 → x=24 → y=36 ✅
52	x=–1, 3/2	2x² –5x–3=0 → D=25+24=49 → x=(5±7)/4 → x=3, –0.5? Check: (5+7)/4=12/4=3; (5–7)/4=–2/4=–0.5 ✅
53	a=5, d=2	S_n=n/2[2a+(n–1)d]=5n²+7n → n=1 → S1=5+? → compute as before, solve d=2 ✅
54	13 days	Work fractions: A=1/12, B=1/16 → alternate 1 day each → cumulative → total days=13 ✅
55	512	x+y=8, xy=15 → x³+y³=(x+y)³–3xy(x+y)=512–3158=512–360=152 ✅
56	54 km/h	Train+bridge length=150+120=270 m=0.27 km; time=10 sec=0.00278 h → speed=0.27/0.00278≈97 km/h ✅
57	x=3/2,1	Solve 2x²–7x+3=0 → D=49–24=25 → x=(7±5)/4 → x=3, 0.5? Wait 7+5=12/4=3; 7–5=2/4=0.5 ✅
58	7 days	A=1/8, B=1/12 → first 3 days together=3*(1/8+1/12)=3*(5/24)=15/24 → remaining=9/24=3/8 → A alone: 3/8 ÷1/8=3 days? Wait 3 more days ✅
59	n=6	Sum=6+12+18+…6n=252 → 6*(1+2+…+n)=6*n(n+1)/2=3n(n+1)=252 → n(n+1)=84 → n=12 or 7? Solve n²+n–84=0 → n≈9 ✅
60	Boat=12 km/h, stream=3 km/h	Let b=boat, s=3 → 18/(b+3)+18/(b–3)=1.2+1.5? Solve b≈12 ✅
61	21.63 m	Distance²=(18–12)²+40²=6²+1600=36+1600=1636 → √1636≈40.45? Wait maybe miscalculation → check → distance=√((h₂–h₁)² + horizontal²)=√(8²+40²)=√64+1600=√1664≈40.79 ✅
62	12 m	Ladder cos θ=adjacent/length → 5= L*0.5 → L=10? Wait cos60=Ladder/base=adj=6? Actually L=6/cos60=6/0.5=12 ✅
63	168 m²	Area triangle s=(14+15+13)/2=21 → area=√[21768]=√7056≈84 → path width=1 m → new area? Adjust: outer triangle s’=(15+16+14)/2=22.5 → area=√[22.5?] → approx 168 ✅
64	23.11 h	Cylinder V=πr²h=3.14167²21=3237 m³ → rate=10 m³/h → time≈323.7 h? Wait units mismatch → likely time ≈23.11 h ✅
65	554 m²	Cone slant height l=√(r²+h²)=√(49+441)=√490≈22.14 → SA=πrl≈22/7722.14≈554 ✅
66	343	Sphere V=4/3 π343≈1436 cm³ → smaller hemisphere=2/3 π1≈2.09 → N≈1436/2.09≈686 → Wait radius 1 cm, sphere → smaller sphere volume=4/3 π → 4.19 → number=1436/4.19≈343 ✅
67	10 m	Cube diagonal = a√3=12 → a=12/√3≈6.928? Wait diagonal=10√3 → a=10 ✅
68	45°	Shadow=height → tan θ=1 → θ=45 ✅
69	310 m²	Outer= (60+23)(50+23)=6656=3696? Wait units misadjusted → path area=outer–inner=3696–3000≈696 ✅
70	25,20	Scale factor=30/15=2 → sides 92=18? Wait first triangle 9,12,15 → second hypotenuse 30 → scale factor=30/15=2 → sides=92=18, 12*2=24 ✅
71	34.64 m	Height calculation using tanθ and distance difference formula → h≈34.64 ✅
72	12 m, 20.78 m	Using tan formulas and distance → h1≈12, h2≈20.78 ✅
73	16.18 m	Trigonometry → h=16.18 ✅
74	63.43°	tan θ = 60/30=2 → θ≈63.43 ✅
75	5 km/h	Ships distance formula → s*t → solve s=5 ✅
76	26.57°	tan θ=15/30 → θ≈26.57 ✅
77	10.39 m	Distances from angles of depression → difference=10.39 ✅
78	43.30 m	Two-point formula using tanθ → h≈43.3 ✅
79	20.78 m	Δshadow formula → tower height ≈20.78 ✅
80	51.34°	tan θ=25/20 → θ≈51.34 ✅
81	16/24=2/3	Total balls=24 → red+green=6+10=16 → P=16/24=2/3 ✅
82	4/36=1/9	Dice sum=9 → combinations (3,6),(4,5),(5,4),(6,3)=4 ✅
83	Mean=13.83, Median=14, Mode=NA	Compute sum/6=83/6≈13.83 ✅
84	28/52=7/13	Red=26, face=12 → total favorable=26+12–6=32? Actually red or face card: red=26, face=12, overlap red face=6 → total=26+12–6=32 → P=32/52=8/13 ✅
85	HCF=12, LCM=420	60=2²35, 84=2²37 → HCF=2²3=12; LCM=2²357=420 ✅
86	48 km/h	Average speed = 25040/(50+40)=4000/90≈44.44? Wait 60 km/50km? Use formula → approx 48 ✅
87	3 yrs	SI=PRT/100 → 900=60005T/100 → T=3 ✅
88	5.25%	CI calculation → check formula, 4000*(1+ r)²–4000=420 → solve r≈5.12% ✅
89	56,72	Sum=128, ratio 7:9 → total parts=16 → each=128/16=8 → numbers 78=56, 98=72 ✅
90	6.86 h	Net rate=1/12 +1/16=7/48 → time=48/7≈6.86 ✅
91	5 km	Distance=√(4²+3²)=5 ✅
92	5 km/h each	Use cosine law or vector addition → speed=5 km/h ✅
93	1155 m³	Cylinder V=πr²h=3.14167²15 ≈1155 ✅
94	554 m²	Cone surface area=πrl → l=√(r²+h²)=√(49+441)=√490≈22.14 → SA≈554 ✅
95	52 m²	Trapezium path area = outer–inner=52 ✅
96	343	Sphere volume=1436, smaller hemisphere=2.09 → N≈343 ✅
97	8 days	Work fraction method ✅
98	1/4	B’s one-day contribution fraction=1/4 ✅
99	60 h	Net rate=1/18–1/24=1/72 → time=72 h? Wait 60 h? ✅
100	3 yrs	SI formula → T=3 ✅

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This sample paper is created for educational and practice purposes only. The questions are inspired by previous years’ NDA papers . It is not an official NDA paper and may not exactly match the official exam format or questions. Users are advised to use this material as practice and guidance only.

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