RIMC Entrance Exam 2026 Complete Preparation Hub
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Practice Papers (Mock Set 1)
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This original RIMC Entrance Exam 2026 Mathematics Mock Test 1 is specially designed for students preparing for admission to Class VIII at Rashtriya Indian Military College (RIMC), Dehradun for the July 2027 term. Aligned with the official National Testing Agency (NTA) pen-paper descriptive format, this paper carries 30 Questions worth 200 Marks to be solved in 90 Minutes. Each question includes an interactive Toggle Answer Sheet & Step-by-Step Solution.
📝 RIMC Mathematics Mock Test 1 – Highlights & Instructions
| Particular | Details |
|---|---|
| Subject Paper | Mathematics |
| Mock Test Series Number | Mock Test 1 |
| Target Level | RIMC Class 8 Entrance Examination (July 2027 Term) |
| Total Number of Questions | 30 Questions (Descriptive) |
| Maximum Marks | 200 Marks |
| Suggested Time Limit | 90 Minutes (1 Hour 30 Mins) |
| Answer Key Feature | Interactive Toggle Answer Sheet Included |
| Calculator Usage | Strictly Not Allowed |
Student Exam Instructions:
- Attempt all 30 questions sequentially on paper before toggling solutions.
- Show complete calculation steps, formulas, and reasoning for every question.
- Write final answers clearly with appropriate SI/everyday units (e.g., cm, m², ₹, kg, km/h).
- Do not use calculators, mobile phones, or digital aids.
- Use the Toggle Answer Sheet below each question to verify your working.
Section A – Basic & Conceptual Mathematics
Questions 1–10 | 4 Marks Each | Total: 40 MarksQ1. Number System (4 Marks)
Find the HCF and LCM of 24, 36, and 60. Show all important prime factorisation steps.
Toggle Solution & Working
Step-by-Step Solution:
• Prime factorisation of 24 = 2³ × 3
• Prime factorisation of 36 = 2² × 3²
• Prime factorisation of 60 = 2² × 3 × 5
• HCF = Product of lowest powers of common factors = 2² × 3 = 4 × 3 = 12.
• LCM = Product of highest powers of all factors = 2³ × 3² × 5 = 8 × 9 × 5 = 360.
Q2. Fractions (4 Marks)
Simplify: 3/4 + 5/6 - 2/3. Give your answer in the simplest fraction form.
Toggle Solution & Working
Step-by-Step Solution:
• Denominators are 4, 6, and 3. LCM(4, 6, 3) = 12.
• Convert fractions: 3/4 = 9/12, 5/6 = 10/12, 2/3 = 8/12.
• Expression = (9 + 10 - 8) / 12 = 11/12.
Q3. Decimals (4 Marks)
A student bought 2.75 kg rice, 1.85 kg wheat, and 0.65 kg pulses. Find the total weight of all the items purchased.
Toggle Solution & Working
Step-by-Step Solution:
• Weight of rice = 2.75 kg
• Weight of wheat = 1.85 kg
• Weight of pulses = 0.65 kg
• Total Weight = 2.75 + 1.85 + 0.65 = 5.25 kg.
Q4. Ratio (4 Marks)
The ratio of boys to girls in a class is 5 : 3. If there are 40 boys, find: (i) Number of girls, (ii) Total number of students in the class.
Toggle Solution & Working
Step-by-Step Solution:
• Ratio = 5 : 3. Let boys = 5x and girls = 3x.
• Given 5x = 40 ⟹ x = 8.
• (i) Number of girls = 3x = 3 × 8 = 24 girls.
• (ii) Total students = 40 + 24 = 64 students.
Q5. Percentage (4 Marks)
A school has 800 students. If 35% of the students are girls, find: (i) Number of girls, (ii) Number of boys.
Toggle Solution & Working
Step-by-Step Solution:
• Total students = 800.
• (i) Number of girls = 35% of 800 = (35 / 100) × 800 = 280 girls.
• (ii) Number of boys = 800 - 280 = 520 boys.
Q6. Average (4 Marks)
Find the average of the following numbers: 18, 24, 15, 27, 21, and 33.
Toggle Solution & Working
Step-by-Step Solution:
• Sum of numbers = 18 + 24 + 15 + 27 + 21 + 33 = 138.
• Total count = 6.
• Average = 138 / 6 = 23.
Q7. Simplification (4 Marks)
Simplify: 48 ÷ 6 + 7 × 3 - 5. Clearly show the BODMAS order of operations.
Toggle Solution & Working
Step-by-Step Solution:
• Step 1 (Division): 48 ÷ 6 = 8.
• Step 2 (Multiplication): 7 × 3 = 21.
• Step 3 (Addition & Subtraction): 8 + 21 - 5 = 29 - 5 = 24.
Q8. Unitary Method (4 Marks)
A shopkeeper sells 8 notebooks for ₹240. Find the cost of 15 notebooks.
Toggle Solution & Working
Step-by-Step Solution:
• Cost of 8 notebooks = ₹240.
• Cost of 1 notebook = 240 / 8 = ₹30.
• Cost of 15 notebooks = 15 × ₹30 = ₹450.
Q9. Profit and Loss (4 Marks)
A school bag was purchased for ₹800 and sold for ₹920. Find: (i) Profit amount, (ii) Profit percentage.
Toggle Solution & Working
Step-by-Step Solution:
• CP = ₹800, SP = ₹920.
• (i) Profit = SP - CP = 920 - 800 = ₹120.
• (ii) Profit % = (Profit / CP) × 100 = (120 / 800) × 100 = 15%.
Q10. Simple Interest (4 Marks)
Find the simple interest on ₹5,000 at 6% per annum for 2 years. Also find the total maturity amount.
Toggle Solution & Working
Step-by-Step Solution:
• P = ₹5000, R = 6%, T = 2 years.
• Simple Interest (SI) = (P × R × T) / 100 = (5000 × 6 × 2) / 100 = ₹600.
• Total Amount = P + SI = 5000 + 600 = ₹5,600.
Section B – Intermediate Mathematics
Questions 11–20 | 6 Marks Each | Total: 60 MarksQ11. Fractions & Application (6 Marks)
Rohan spent 2/5 of his money on books and 1/4 of his money on stationery. What fraction of his money is left?
Toggle Solution & Working
Step-by-Step Solution:
• Fraction spent = 2/5 + 1/4 = (8 + 5) / 20 = 13/20.
• Remaining fraction = 1 - 13/20 = 7/20.
Q12. Percentage (6 Marks)
A student scored: Mathematics: 72 out of 100, English: 64 out of 80, Science: 54 out of 75. Calculate the percentage obtained in each subject.
Toggle Solution & Working
Step-by-Step Solution:
• Mathematics % = (72 / 100) × 100 = 72%.
• English % = (64 / 80) × 100 = 80%.
• Science % = (54 / 75) × 100 = 72%.
Q13. Ratio and Proportion (6 Marks)
The ratio of the ages of A and B is 3 : 5. If the sum of their ages is 32 years, find their individual ages.
Toggle Solution & Working
Step-by-Step Solution:
• Let A's age = 3x and B's age = 5x. Total parts = 3x + 5x = 8x = 32 ⟹ x = 4.
• Age of A = 3 × 4 = 12 years.
• Age of B = 5 × 4 = 20 years.
Q14. Speed, Time and Distance (6 Marks)
A car travels at a speed of 45 km/h. How far will it travel in: (i) 2 hours?, (ii) 40 minutes? Show time conversion steps.
Toggle Solution & Working
Step-by-Step Solution:
• (i) In 2 hours: Distance = 45 × 2 = 90 km.
• (ii) 40 minutes = 40 / 60 = 2/3 hours. Distance = 45 × (2/3) = 30 km.
Q15. Time and Work (6 Marks)
A worker can complete a particular job in 12 days. Assuming equal daily work, what fraction of the work will be completed in: (i) 3 days?, (ii) 8 days?
Toggle Solution & Working
Step-by-Step Solution:
• Work done in 1 day = 1/12.
• (i) In 3 days = 3 × (1/12) = 1/4 of work.
• (ii) In 8 days = 8 × (1/12) = 2/3 of work.
Q16. Algebra (6 Marks)
Solve: 3x + 7 = 28. Then verify your answer by substituting the value of x back into the original equation.
Toggle Solution & Working
Step-by-Step Solution:
• 3x + 7 = 28 ⟹ 3x = 28 - 7 = 21 ⟹ x = 7.
• Verification: LHS = 3(7) + 7 = 21 + 7 = 28 = RHS. Verified!
Q17. Algebraic Simplification (6 Marks)
Simplify: 5(2x + 3) - 2(x + 4). Then find its numerical value when x = 4.
Toggle Solution & Working
Step-by-Step Solution:
• Expand: 10x + 15 - 2x - 8 = 8x + 7.
• Substitute x = 4: 8(4) + 7 = 32 + 7 = 39.
Q18. Geometry (6 Marks)
The three angles of a triangle are (2x)°, (3x)°, and (4x)°. Find: (i) The value of x, (ii) All three angles, (iii) The type of triangle according to its angles.
Toggle Solution & Working
Step-by-Step Solution:
• Sum of angles of a triangle = 180° ⟹ 2x + 3x + 4x = 9x = 180° ⟹ x = 20°.
• Angles = 2(20) = 40°, 3(20) = 60°, 4(20) = 80°.
• Since all angles are less than 90°, it is an Acute-angled triangle.
Q19. Perimeter & Mensuration (6 Marks)
A rectangular playground is 45 m long and 28 m wide. Find: (i) Its perimeter, (ii) The total cost of fencing it at ₹35 per metre.
Toggle Solution & Working
Step-by-Step Solution:
• Length = 45 m, Width = 28 m.
• (i) Perimeter = 2 × (Length + Width) = 2 × (45 + 28) = 2 × 73 = 146 m.
• (ii) Cost of fencing = 146 × ₹35 = ₹5,110.
Q20. Area (6 Marks)
A rectangular field is 60 m long and 40 m wide. A square garden of side 20 m is made inside the field. Find the remaining area of the field.
Toggle Solution & Working
Step-by-Step Solution:
• Area of field = 60 × 40 = 2,400 m².
• Area of square garden = 20 × 20 = 400 m².
• Remaining Area = 2,400 - 400 = 2,000 m².
Section C – Advanced Application
Questions 21–25 | 10 Marks Each | Total: 50 MarksQ21. HCF, LCM & Application (10 Marks)
Three bells ring at intervals of 12 minutes, 18 minutes, and 24 minutes respectively. If they ring together at 8:00 AM, after how much time will they ring together again? At what exact time will this happen? Show complete method.
Toggle Solution & Working
Step-by-Step Solution:
• LCM of 12, 18, and 24: 12 = 2²×3, 18 = 2×3², 24 = 2³×3.
• LCM = 2³ × 3² = 8 × 9 = 72 minutes = 1 hour 12 minutes.
• Time = 8:00 AM + 1 hour 12 minutes = 9:12 AM.
Q22. Profit, Loss & Percentage (10 Marks)
A shopkeeper purchased a bicycle for ₹6,000. He marked its price at ₹7,500 and then gave a discount of 10%. Find: (i) Discount amount, (ii) Selling price, (iii) Profit amount, (iv) Profit percentage.
Toggle Solution & Working
Step-by-Step Solution:
• CP = ₹6000, MP = ₹7500.
• (i) Discount = 10% of 7500 = ₹750.
• (ii) Selling Price (SP) = 7500 - 750 = ₹6,750.
• (iii) Profit = SP - CP = 6750 - 6000 = ₹750.
• (iv) Profit % = (750 / 6000) × 100 = 12.5%.
Q23. Simple Interest (10 Marks)
A person deposited ₹8,000 at a rate of 5% per annum for 3 years. Find: (i) Simple Interest, (ii) Total Amount. If the same amount is deposited for 2 more years at the same rate, find the total interest for 5 years.
Toggle Solution & Working
Step-by-Step Solution:
• P = ₹8000, R = 5%, T1 = 3 yrs.
• (i) SI for 3 yrs = (8000 × 5 × 3) / 100 = ₹1,200.
• (ii) Total Amount after 3 yrs = 8000 + 1200 = ₹9,200.
• (iii) Total SI for 5 yrs = (8000 × 5 × 5) / 100 = ₹2,000.
Q24. Mensuration (Pathway Area) (10 Marks)
A rectangular swimming pool is 25 m long and 12 m wide. Around the outside of the pool, a pathway 2 m wide is constructed on all four sides. Find: (i) Length of outer rectangle, (ii) Width of outer rectangle, (iii) Area of outer rectangle, (iv) Area of swimming pool, (v) Area of pathway.
Toggle Solution & Working
Step-by-Step Solution:
• (i) Outer Length = 25 + 2 + 2 = 29 m.
• (ii) Outer Width = 12 + 2 + 2 = 16 m.
• (iii) Outer Area = 29 × 16 = 464 m².
• (iv) Pool Area = 25 × 12 = 300 m².
• (v) Pathway Area = Outer Area - Pool Area = 464 - 300 = 164 m².
Q25. Speed, Time & Distance (10 Marks)
A train travels 180 km in 3 hours. Find: (i) Its speed in km/h, (ii) Distance travelled at the same speed in 4 hours 30 minutes, (iii) Time required to travel 300 km. Show all calculations.
Toggle Solution & Working
Step-by-Step Solution:
• (i) Speed = 180 / 3 = 60 km/h.
• (ii) Distance in 4.5 hrs = 60 × 4.5 = 270 km.
• (iii) Time for 300 km = 300 / 60 = 5 hours.
Section D – RIMC Challenge Questions
Questions 26–30 | 10 Marks Each | Total: 50 MarksQ26. Fraction Challenge (10 Marks)
A water tank is 3/5 full. After 120 litres of water are added, the tank becomes 4/5 full. Find the total capacity of the water tank in litres.
Toggle Solution & Working
Step-by-Step Solution:
• Difference in fraction = 4/5 - 3/5 = 1/5 of tank capacity.
• 1/5 of capacity = 120 litres ⟹ Total capacity = 120 × 5 = 600 litres.
Q27. Number Puzzle (10 Marks)
The sum of three consecutive natural numbers is 96. Find the three numbers. Then calculate their product.
Toggle Solution & Working
Step-by-Step Solution:
• Let numbers be x, x+1, x+2. Sum = 3x + 3 = 96 ⟹ 3x = 93 ⟹ x = 31.
• Numbers are 31, 32, 33.
• Product = 31 × 32 × 33 = 32,736.
Q28. Geometry Challenge (10 Marks)
A rectangular sheet is 30 cm long and 20 cm wide. A square of side 5 cm is cut from each of its four corners. Find: (i) Original area of the sheet, (ii) Total area removed, (iii) Remaining area of the sheet.
Toggle Solution & Working
Step-by-Step Solution:
• (i) Original Area = 30 × 20 = 600 cm².
• (ii) Area removed = 4 × (5 × 5) = 4 × 25 = 100 cm².
• (iii) Remaining Area = 600 - 100 = 500 cm².
Q29. Average Challenge (10 Marks)
The average age of 5 students is 12 years. When their teacher's age is included, the average age becomes 17 years. Find the teacher's age in years.
Toggle Solution & Working
Step-by-Step Solution:
• Sum of 5 students' ages = 5 × 12 = 60 years.
• Total sum with teacher (6 persons) = 6 × 17 = 102 years.
• Teacher's age = 102 - 60 = 42 years.
Q30. Mixed RIMC Challenge (10 Marks)
A student has ₹2,400. He spends 1/3 of the money on books and 25% of the original money on stationery. He then spends ₹300 on a school bag. Find: (i) Money spent on books, (ii) Money spent on stationery, (iii) Total money spent, (iv) Money remaining, (v) What percentage of the original money remains?
Toggle Solution & Working
Step-by-Step Solution:
• Total money = ₹2,400.
• (i) Books = 1/3 × 2400 = ₹800.
• (ii) Stationery = 25% of 2400 = ₹600.
• (iii) Total spent = 800 + 600 + 300 = ₹1,700.
• (iv) Money remaining = 2400 - 1700 = ₹700.
• (v) Remaining % = (700 / 2400) × 100 = 29.17%.
📊 RIMC Mathematics Mock Test 1 – Marks Distribution
| Section | Question Range | Marks Per Question | Total Section Marks |
|---|---|---|---|
| Section A (Basic & Conceptual) | Questions 1–10 | 4 Marks | 40 Marks |
| Section B (Intermediate) | Questions 11–20 | 6 Marks | 60 Marks |
| Section C (Advanced Application) | Questions 21–25 | 10 Marks | 50 Marks |
| Section D (RIMC Challenge) | Questions 26–30 | 10 Marks | 50 Marks |
| Total Aggregate | 30 Questions | — | 200 Marks |
🎯 Suggested 90-Minute Time Management Strategy
To ensure full completion of all 30 descriptive questions within the 90-minute limit, follow this time allocation plan:
| Time Window | Target Activity | Suggested Focus |
|---|---|---|
| 0–20 Mins | Questions 1–10 (Section A) | Solve basic 4-mark questions rapidly with accurate steps. |
| 20–45 Mins | Questions 11–20 (Section B) | Solve intermediate 6-mark word problems and algebra. |
| 45–70 Mins | Questions 21–25 (Section C) | Solve 10-mark multi-step applications carefully. |
| 70–85 Mins | Questions 26–30 (Section D) | Tackle high-level challenge problems and word puzzles. |
| 85–90 Mins | Final Checking & Verification | Verify calculation steps, SI units, and final answer highlights. |
Official Direct Links & Portals
| Official Resource | Direct Access Link |
|---|---|
| NTA RIMCEE Official Portal | Visit NTA RIMCEE Portal |
| NTA Official Documents & Bulletin | Download NTA Bulletin |
Frequently Asked Questions (FAQs)
1. How do I open the step-by-step solutions in this Mock Test?
Click or tap on the blue 'View Answer & Solution' toggle button underneath any question to instantly expand the complete step-by-step working and final answer.
2. Are calculators allowed in RIMC Mathematics exam?
No. Calculators are strictly prohibited in the RIMC entrance examination. All calculations must be performed manually.
3. How many marks are required to pass RIMC Mathematics?
Candidates must score a minimum of 50% marks (100 out of 200 Marks) in Mathematics to qualify for the next stage.