Detailed Solutions: Simplification
Simplification is one of the most important topics in Mathematics for Class 6–10, SSC, Banking, Railway, NDA, and other competitive exams. It tests a student’s ability to solve expressions using BODMAS rule, fractions, decimals, and brackets quickly and accurately.
Here, you will find the Top 10 Important Simplification Questions with Answers that are frequently asked in exams.
What is Simplification in Mathematics?
Simplification is the process of reducing a mathematical expression into its simplest form using the BODMAS rule
(Brackets, Orders, Division, Multiplication, Addition, Subtraction).
It is widely used in:
Arithmetic
Algebra
Competitive exam problem-solving
Question: 1
\( 7 – [4 – \{3- (3 – 5 + 4)\}] \) सरल करें ।
[A] 10 [B] 4
[C] 6 [D] 7
⚡Solution:
Answer (b): BODMAS नियम का पालन करते हुए हल करें ।
=\( 7 – [4 – \{3- (3 – 5 + 4)\}] \)
=\( 7 – [4 – \{3- (-2 + 4)\}] \)
=\( 7 – [4 – \{3- (2)\}] \)
=\( 7 – [4 – \{3 – 2\}] \)
=\( 7 – [4 – \{1\}] \)
=\( 7 – [4 – 1] \)
=\( 7 – [3] \)
=\( 7 – 3 \)
=\( 4 \)
Question: 2
\( (7)^3 – (5)^3 – (2)^3 – 3×7×5×2 \) का मान ज्ञात करें ।
[A] 1 [B] 17
[C] 0 [D] 210
⚡Solution:
Answer (c) : सर्वसमिका प्रयोग करें ।
यदि \( a + b + c \) = 0 तब \( (a)^3 + (b)^3 + (c)^3 = 3abc \)
\(\Rightarrow \) \( (7)^3 – (5)^3 – (2)^3 – 3×7×5×2 \)
\(\Rightarrow \)\( \{ (7)^3 – (5)^3 – (2)^3 \} – 3×7×5×2 \)
\(\Rightarrow \) \( \{3×7×(-5)×(-2) \} – 3×7×5×2 \)
\(\Rightarrow \) \(3×7×5×2 – 3×7×5×2 \)
\(\Rightarrow \) 0
Question: 3
Evaluate: \(45 + 3 \times (12 \div 4) – 8\) का मान ज्ञात करें ।
[A] 45 [B] 50
[C] 46 [D] 48
⚡Solution:
Answer (c) : 46
- Solve the bracket: \(12 \div 4 = 3\)
- Multiply:\( 3 \times 3 = 9\)
- Add and Subtract: 45 + 9 – 8 = 46
Question: 4
Evaluate: \(15 – [8 + \{12 – (6 – 3)\}] \)का मान ज्ञात करें ।
[A] 15 [B] 17
[C] 0 [D] -2
⚡Solution:
Answer (d) : -2
- Inner bracket: 6 – 3 = 3
- Curly bracket: 12 – 3 = 9
- Square bracket: 8 + 9 = 17
- Final calculation: 15 – 17 = -2
Question: 5
Evaluate: \(\sqrt{144} + 15^2 – 100 \) का मान ज्ञात करें ।
[A] 125 [B] 137
[C] 100 [D] 225
⚡Solution:
Answer (b) : 137
- Square root: \(\sqrt{144} = 12\)
- Square:\( 15^2 = 225 \)
- Combine: 12 + 225 – 100 = 137
Question: 6
Evaluate:\( (18 \times 2) \div 4 + 2^3 – 5\) का मान ज्ञात करें ।
[A] 12 [B] 17
[C] 20 [D] 18
⚡Solution:
Answer (a) : 12
- Bracket: \(18 \times 2 = 36\)
- Exponent: \(2^3 = 8\)
- Division: \(36 \div 4 = 9\)
- Addition/Subtraction: 9 + 8 – 5 = 12
Question: 7
Evaluate: \(1.25 \times 8 + 4.5 \div 0.5 – 2.5\) का मान ज्ञात करें ।
[A] 15.5 [B] 17.5
[C] 16.5 [D] 20
⚡Solution:
Answer (c) : 16.5
- Multiplication: \(1.25 \times 8 = 10\)
- Division: \(4.5 \div 0.5\) is the same as \(45 \div 5 = 9\)
- Combine: 10 + 9 – 2.5 = 19 – 2.5 = 16.5
Why Simplification Questions Are Important for Exams
- Used in almost every maths question
- Saves time in SSC, Banking, and Railway exams
- Improves accuracy and speed
- Helps in solving fractions, algebra, and percentage
Conclusion
Practicing Simplification important questions daily will improve your calculation speed and confidence in exams. Mastering this topic gives you a strong base for all other mathematics chapters.