## Mathematics Formula for Competitive Exam

The mathematics formula is crucial for competitive exam success. In these exams, time management is everything. If you handle your time properly, you can achieve great results. While other subjects are important, securing a high score in maths can significantly impact your overall performance. Achieving high marks comes from consistent practice. The key is to solve your math problems accurately and promptly, which you can do by applying shortcut tricks.

## Key Mathematics Topics to Focus On

- Number sets
- Algebra
- Geometry
- Trigonometry
- Matrix and determinant
- Vectors
- Analytic Geometry
- Differential calculus
- Integral Calculus
- Differential Equations
- Series

### मैथ के फार्मूला – Math Formula Hindi

- (α+в)²= α²+2αв+в²
- (α+в)²= (α-в)²+4αв b
- (α-в)²= α²-2αв+в²
- (α-в)²= f(α+в)²-4αв
- α² + в²= (α+в)² – 2αв
- α² + в²= (α-в)² + 2αв
- α²-в² =(α + в)(α – в)
- 2(α² + в²) = (α+ в)² + (α – в)²
- 4αв = (α + в)² -(α-в)²
- αв ={(α+в)/2}²-{(α-в)/2}²
- (α + в + ¢)² = α² + в² + ¢² + 2(αв + в¢ + ¢α)
- (α + в)³ = α³ + 3α²в + 3αв² + в³
- (α + в)³ = α³ + в³ + 3αв(α + в)
- (α-в)³=α³-3α²в+3αв²-в³
- α³ + в³ = (α + в)(α² -αв + в²)
- α³ + в³ = (α+ в)³ -3αв(α+ в)
- α³ -в³ = (α -в)(α² + αв + в²)
- α³ -в³ = (α-в)³ + 3αв(α-в)

#### Speed, Distance & Time Formulas

- Speed = distance/time
- Time = distance/Speed
- Distance = Speed × Time
- Distance = Rate × Time
- Rate = Distance/Time
- Convert from kph (km/h) to mps (m/sec):

x km/hr = x * (5/18) m/sec - Convert from mps (m/sec) to kph (km/h):

x m/sec = x * (18/5) km/h - If the ratio of the speeds of A and B is a:b, then the ratio of the times taken by them to cover the same distance is 1/a:1/b or b:a.
- Suppose a person covers a certain distance at x km/hr and an equal distance at y km/hr. The average speed for the entire journey is: 2xy/(x + y).
- When speed is constant, the distance covered is directly proportional to the time taken. So, if Sa = Sb, then Da/Db = Ta/Tb.
- When time is constant, speed is directly proportional to the distance travelled. So, if Ta = Tb, then Sa/Sb = Da/Db.
- When the distance is constant, speed is inversely proportional to the time taken. If speed increases, time taken to cover the distance decreases. Therefore, if Da = Db, then Sa/Sb = Tb/Ta.
- If the speeds given are in Harmonic Progression (HP), then the corresponding times taken will be in Arithmetic Progression (AP).
- If the speeds given are in AP, then the corresponding times taken will be in HP.
- If two objects are moving in the same direction with speeds a and b, then their relative speed is |a-b|.
- If two objects are moving in opposite directions with speeds a and b, then their relative speed is (a+b).

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