Prepare for the Odisha Police Constable Recruitment 2026 with this Mathematics Formula Mind Map, specially designed for candidates practising arithmetic and quantitative aptitude for Odisha government recruitment examinations. This quick revision resource from MockTestOdisha.in helps aspirants revise important mathematical formulas in a simple, organized, and easy-to-remember format.
The mind map covers 10 essential topics: Cylinder Surface Area and Cost, BODMAS Simplification, Divisibility Rule of 11, Cube and Hemisphere Surface Area, Percentage, Speed, Distance and Time, Relative Speed, Simple Interest, Fractions and Percentages, and Age and Ratio Problems.
These formulas can help candidates strengthen their calculation skills and practise arithmetic questions more efficiently. The compact HTML layout makes revision convenient on desktop and mobile devices, whether you are studying at home or reviewing formulas before a mock test.
For Odisha Police Constable 2026 preparation, revise each formula carefully and practise MCQs based on the relevant syllabus and official examination pattern for your post. Focus on accurate calculations, proper unit conversions, percentage problems, time-and-distance questions, interest calculations, and ratio-based age problems. Regular practice can help improve speed, accuracy, and confidence.
Who can benefit from this formula mind map?
- Odisha Police Constable (Civil) 2026 aspirants
- Candidates preparing for other posts under the 2026 Combined Uniformed Services recruitment
- Students practising arithmetic and quantitative aptitude MCQs
- Aspirants looking for quick mathematics formula revision before mock tests
Visit MockTestOdisha.in for mathematics practice questions, answer keys, mock tests, and other competitive examination preparation resources.
Revise the formulas, practise topic-wise MCQs, and prepare systematically for Odisha Police Recruitment 2026. Always check the official notification for the specific post you are applying for.
📘 Short Note: Curved Surface Area of a Cylinder
1. Formula:
Curved Surface Area (CSA) = 2πrh
Where:
- r = Radius of the circular base
- h = Height of the cylinder
- π = 22/7 (approximate value)
2. Given:
- Radius (r) = 21 cm
- Height (h) = 10 cm
- Cost of coloring = ₹1.50 per cm²
3. Calculation:
CSA = 2 × 22/7 × 21 × 10
CSA = 1320 cm²
Total Cost = Surface Area × Cost per cm²
Total Cost = 1320 × ₹1.50 = ₹1,980
Remember: The curved surface area excludes the two circular bases. The total surface area of a closed cylinder is 2πr(h + r).
📘 Short Note: BODMAS Rule
1. What is BODMAS?
BODMAS helps us solve mathematical expressions in the correct order.
- B – Brackets
- O – Orders (powers and roots)
- D – Division
- M – Multiplication
- A – Addition
- S – Subtraction
2. Important Rule:
Division and multiplication have equal priority, so solve them from left to right. Addition and subtraction also have equal priority and are solved from left to right.
3. Given Expression:
18 + 3 × (24 ÷ 8 × 2) − 6
4. Step-by-Step Calculation:
Step 1: Solve the bracket from left to right.
24 ÷ 8 = 3
3 × 2 = 6
Step 2: Multiply.
18 + 3 × 6 − 6
18 + 18 − 6
Step 3: Perform addition and subtraction from left to right.
18 + 18 = 36
36 − 6 = 30
Correct Answer: 30
Remember: Multiplication does not always come before division. Both have equal priority, and the same left-to-right rule applies to addition and subtraction.
Question 3: Divisibility Rule of 11
Question: If the number 795P948 is divisible by 11, find the digit P.
📘 Rule: Divisibility by 11
A number is divisible by 11 if the difference between the sums of digits in alternate positions is 0 or a multiple of 11.
Formula:
Difference = Sum of digits in alternate positions − Sum of digits in the remaining positions
✏️ Step-by-Step Solution
Step 1: Write the number
795P948
Step 2: Add digits in alternate positions
First group: 8 + 9 + 5 + 7 = 29
Second group: 4 + P + 9 = 13 + P
Step 3: Find the difference
Difference = 29 − (13 + P)
Difference = 16 − P
Step 4: Apply the divisibility rule
Since P is a digit from 0 to 9, the value of 16 − P ranges from 7 to 16.
The only multiple of 11 in this range is 11.
Therefore, 16 − P = 11
P = 16 − 11
P = 5
✅ Final Answer
Option (B): 5
💡 Quick Exam Tip
For divisibility by 11, alternate-position digit sums must have a difference of 0 or a multiple of 11. Remember to check that the missing digit is between 0 and 9.
Question 4: Cube with a Hemisphere on Top
Question: A hemisphere is placed on top of a cube of side 14 cm. Find the total exposed surface area of the solid.
📘 Important Formulas
1. Total surface area of a cube:
TSA = 6a²
2. Area of a circle:
Area = πr²
3. Curved surface area of a hemisphere:
CSA = 2πr²
✏️ Step-by-Step Solution
Step 1: Identify the given values
Side of cube (a) = 14 cm
The largest hemisphere that fits on the cube has diameter 14 cm.
Radius (r) = 14 ÷ 2 = 7 cm
Step 2: Calculate the surface area of the cube
Cube TSA = 6a²
= 6 × 14²
= 6 × 196
= 1176 cm²
Step 3: Calculate the exposed surface area
The circular base of the hemisphere covers a circular area on the top of the cube. Therefore, subtract that circle’s area and add the hemisphere’s curved surface area.
Formula:
Exposed area = 6a² − πr² + 2πr²
= 6a² + πr²
Step 4: Substitute the values
Exposed area = 1176 + (22/7 × 7 × 7)
= 1176 + 154
= 1330 cm²
✅ Final Answer
Option (C): 1330 cm²
💡 Quick Exam Tip
When a hemisphere is placed on a cube, do not count the circular base of the hemisphere as an exposed surface. Subtract the covered circle from the cube’s surface area and add the hemisphere’s curved surface area.
Question 5: Percentage Calculation
Question: 1/20 is what percentage of 2/80?
📘 Important Formula
Percentage = (Value ÷ Reference Value) × 100
When asked “A is what percentage of B?”, use:
Percentage = (A ÷ B) × 100
✏️ Step-by-Step Solution
Step 1: Identify the values
A = 1/20
B = 2/80
Step 2: Apply the formula
Required percentage = [(1/20) ÷ (2/80)] × 100
Step 3: Simplify the division
Dividing by a fraction means multiplying by its reciprocal.
= (1/20) × (80/2) × 100
= (1/20) × 40 × 100
= 2 × 100
= 200%
✅ Final Answer
Option (C): 200%
💡 Quick Exam Tip
Always divide the first quantity by the second quantity, then multiply by 100. The answer can be greater than 100% when the first quantity is larger than the second.
Question 6: Average Speed and Relative Time
Question: A vehicle travels 600 km. It covers the first 300 km at 40 km/h. If its average speed for the entire journey is 70 km/h, find its speed for the remaining 300 km.
📘 Important Formulas
1. Speed = Distance ÷ Time
2. Time = Distance ÷ Speed
3. Average Speed = Total Distance ÷ Total Time
Important: Average speed is not generally the simple average of two speeds. Calculate it using total distance divided by total time.
✏️ Step-by-Step Solution
Step 1: Identify the given values
Total distance = 600 km
First distance = 300 km
First speed = 40 km/h
Average speed = 70 km/h
Remaining distance = 600 − 300 = 300 km
Step 2: Calculate total journey time
Total time = Total distance ÷ Average speed
= 600 ÷ 70
= 60/7 hours
Step 3: Calculate the time taken for the first 300 km
Time = Distance ÷ Speed
= 300 ÷ 40
= 7.5 hours
= 15/2 hours
Step 4: Calculate the remaining time
Remaining time = Total time − First part time
= 60/7 − 15/2
= (120 − 105)/14
= 15/14 hours
Step 5: Calculate the remaining speed
Remaining speed = Remaining distance ÷ Remaining time
= 300 ÷ (15/14)
= 300 × 14/15
= 280 km/h
✅ Final Answer
Option (A): 280 km/h
💡 Quick Exam Tip
For journeys with different speeds, calculate the time for each part. Use the total distance and average speed to find total time, then subtract the known time to determine the remaining speed.
Question 7: Time and Distance — Police Chase
Question: A police officer travels at 120 km/h to catch a thief travelling at 100 km/h. If the thief is 5,000 metres ahead, how long will the police officer take to catch the thief?
📘 Important Formulas
1. Relative Speed (same direction):
Relative Speed = Faster Speed − Slower Speed
2. Time = Distance ÷ Speed
✏️ Step-by-Step Solution
Step 1: Identify the given values
Police speed = 120 km/h
Thief speed = 100 km/h
Distance between them = 5,000 metres
Step 2: Convert metres into kilometres
1 kilometre = 1,000 metres
Distance = 5,000 ÷ 1,000
= 5 km
Step 3: Calculate relative speed
Since both are moving in the same direction:
Relative speed = 120 − 100
= 20 km/h
Step 4: Calculate the catching time
Time = Distance ÷ Relative speed
= 5 ÷ 20 hours
= 1/4 hour
Step 5: Convert hours into minutes
Time = 1/4 × 60 minutes
= 15 minutes
✅ Final Answer
Option (C): 15 minutes
💡 Quick Exam Tip
When two objects move in the same direction, subtract their speeds to find relative speed. When they move in opposite directions towards each other, add their speeds.
Question 8: Simple Interest and Principal
Question: For 3 years, the simple interest at a rate 4% higher than the original rate is ₹360 more. Find the principal amount.
📘 Important Formulas
Simple Interest (SI) = (P × R × T) ÷ 100
Where:
- P = Principal amount
- R = Annual rate of interest
- T = Time in years
Difference in interest = (P × Difference in rate × T) ÷ 100
✏️ Step-by-Step Solution
Step 1: Identify the given values
Time (T) = 3 years
Difference in rate = 4%
Difference in simple interest = ₹360
Step 2: Apply the formula
Difference in SI = (P × Difference in rate × T) ÷ 100
360 = (P × 4 × 3) ÷ 100
Step 3: Simplify the equation
360 = 12P ÷ 100
360 × 100 = 12P
36,000 = 12P
P = 36,000 ÷ 12
P = ₹3,000
✅ Final Answer
Option (B): ₹3,000
💡 Quick Exam Tip
When the difference between two simple-interest amounts is given, use the difference between the interest rates. You do not need to calculate the two interest amounts separately.
Question 9: Percentage and Fractions
Question: 50% of 20% of 2/3 of a number is 686. Find the number.
📘 Important Rules and Formulas
1. Percentage to fraction:
50% = 50/100 = 1/2
20% = 20/100 = 1/5
2. Percentage of a quantity:
x% of a number = (x/100) × Number
3. Remember: The word “of” generally means multiplication in percentage and fraction problems.
✏️ Step-by-Step Solution
Step 1: Assume the number is x.
According to the question:
50% × 20% × 2/3 × x = 686
Step 2: Convert percentages into fractions.
(1/2) × (1/5) × (2/3) × x = 686
Step 3: Simplify the fractions.
(1 × 1 × 2)/(2 × 5 × 3) × x = 686
2/30 × x = 686
x/15 = 686
Step 4: Find x.
x = 686 × 15
x = 10,290
✅ Final Answer
Option (B): 10,290
💡 Quick Exam Tip
Convert percentages into fractions first. Multiply the fractions, simplify, and then solve for the unknown number. This often makes calculations faster and reduces errors.
Question 10: Ratio of Present Ages
Question: The present ages of Anu and Bina are in the ratio 4:5. After 6 years, their ages will be in the ratio 5:6. Find Bina’s present age.
📘 Important Rules and Formulas
1. Ratio method:
If two ages are in the ratio a:b, their ages can be represented as ax and bx.
2. Age after a given number of years:
Future age = Present age + Number of years
3. Ratio formula:
Ratio = First quantity ÷ Second quantity
✏️ Step-by-Step Solution
Step 1: Represent the present ages.
Let Anu’s present age = 4x years
Let Bina’s present age = 5x years
Step 2: Calculate their ages after 6 years.
Anu’s age = 4x + 6
Bina’s age = 5x + 6
Step 3: Apply the future-age ratio.
(4x + 6)/(5x + 6) = 5/6
Step 4: Cross-multiply.
6(4x + 6) = 5(5x + 6)
24x + 36 = 25x + 30
Step 5: Solve for x.
36 − 30 = 25x − 24x
x = 6
Step 6: Find Bina’s present age.
Bina’s present age = 5x
= 5 × 6
= 30 years
✅ Final Answer
Option (C): 30 years
💡 Quick Exam Tip
In age-ratio problems, represent present ages using a common variable. Add the given number of years to both ages, form the new ratio equation, and solve by cross-multiplication.