Hi readers, While we are practicing simplification, we should have knowledge about some basic formulas, some previously defined results and the Rule for BODMAS. Here we are providing those basics with some problems.

BASIC FORMULAE

1. (a + b)² = a² + b² + 2ab
2. (a – b)² = a² + b² – 2ab
3. (a + b)² – (a – b)² = 4ab
4. (a + b)² + (a – b)² = 2 (a² + b²)
5. (a² – b²) = (a + b) (a – b)
6. (a + b + c)²= a² + b² + c² + 2 (ab + bc + ca)
7. (a³ + b³) = (a +b) (a² – ab + b²)
8. (a³ – b³) = (a – b) (a²+ ab + b²)
9. (a³ + b³ + c³ -3abc) = (a + b + c) (a² + b² + c² – ab – bc – ca)
10. If a + b + c = 0, then a³ + b³ + c³ = 3abc.

SOME IMPORTANT RESULTS 

(i) (1 + 2 + 3 +…. + n) =n(n+1)/2
(ii) (1² + 2² + 3² + … + n²) = n (n+1)(2n+1)/6
(iii) (1³ + 2³ + 3³ + … + n³) =n²(n+1)²

BODMAS

This rule is used to execute the operations in the correct sequence,then only we can find the correct answer for the given expression.

B-Brackets
O-Of
D-Division
M-Multiplication
A-Addition
S-Subtraction

Problems

1. 95% of 75% of 4860 – 45% of 55%of 5550=?

1)1890.135

2) 2089.125

3) 1889.135

4) 2910.235

2. 937+23.124-32.768-38.439=?

1)1.874

2)1.934

3)1.854

4) 1.826

3. 497÷7×91÷13+√38.44+³√9.261 =?

1)500.3

2) 505.3

3) 675.3

4) 513.3

4. 3640÷14×16+340=?

1)0.70

2)3525

3)9600

4) None of these

5.Find the value of     

1) 320

2)230

3)430

4) None of these

6. Find the value of (1- 1/3 ) (1- 1/4 ) (1- 1/5 )….. (1- 1/100 )

1) 1/25

2) 1/100

3) 1/50

4) None of these

7. 32.05% of 259.99 = ?
1) 92

2) 88

3) 78

4) 83

8. 25.05 × 123.95 + 388.999 × 15.001 = ?
1) 900

2) 8950

3) 8935

4) 8975

9. (15.01)² × 730 = ?

1) 6125

2) 6225

3) 6200

4) 6075

10. 42% of ? = 4116

1) 9400

2) 9600

3) 9800

4) 10200