Detailed Solutions: Number System
The Number System is one of the most important topics in Mathematics for competitive exams. Questions from the number system are frequently asked in SSC, Banking, Railway, and other competitive tests.
Here, we bring you the Top 10 Important Number System Questions with Answers that are commonly asked in exams and help you build strong fundamentals.
What is Number System in Mathematics?
The Number System is a foundational topic in mathematics, covering concepts such as natural numbers, whole numbers, integers, rational and irrational numbers, and real numbers. This chapter explains different types of numbers, their properties, and their applications in problem-solving. Understanding the Number System is essential for competitive exams like SSC, as it forms the basis for advanced mathematical concepts and calculations.
Question: 1
जब किसी संख्या को 121 से विभाजित किया जाता है, तो शेषफल 25 प्राप्त होता है । यदि उसी संख्या को 11 से विभाजित किया जाए, तो शेषफल होगा ?
When a number is divided by 121, the remainder is 25. If the same number is divided by 11, the remainder will be ?
[A] 1 [B] 3
[C] 11 [D] 25
⚡Solution:
Answer (B) : मान लिजिए संख्या \( x \) है।
Formula: भाज्य = भाजक × भागफल + शेषफल
\(\Rightarrow x \) = 121 × 1 + 25
\(\Rightarrow \) \( x \) = 146
अब संख्या \( x \) = 146 को 11 से भाग करें ।
\(\Rightarrow \) \(\frac{146}{11}\) = 3, 11 से भाग करने पर शेषफल 3 प्राप्त होता है ।
अतः शेषफल 3 होगा ।
Question: 2
दो संख्याओं का योग 76 है और उनमें से एक संख्या दूसरी संख्या से 10 अधिक है । बड़ी संख्या ज्ञात करें ?
The sum of two numbers is 76 and one of them exceeds the other by 10. Find the larger number?
[A] 42 [B] 38
[C] 33 [D] 43
⚡Solution:
Answer (D) : मान लिजिए संख्या \( x , y\) हैं।
दिया है : \( x + y = 10 \) …(1)
\(\Rightarrow \) एक संख्या दूसरी संख्या से 10 अधिक है अर्थात्
\(\Rightarrow \) \( x – y = 10 \) …(2)
समीकरण (1) व (2) से,
\(\Rightarrow x \) = \(\frac{76+10}{2}\) = \(\frac{86}{2}\) = 43
अतः बड़ी संख्या 43 है।
Question: 3
यदि तीन अंकों की एक संख्या 23n , 9 से विभाज्य है, तो n का मान बताइए ?
If a three digit number 23n is divisible by 9, then what is the value of n ?
[A] 2 [B] 3
[C] 4 [D] 1
⚡Solution:
Answer (c) : 9 से विभाज्यता के निमय से, संख्या के अंकों का योग 9 से भाज्य होना चाहिए ।
अर्थात् 2 + 3 + n = 9 × 1
\(\Rightarrow \) 5 + n = 9
\(\Rightarrow \) n = 9 – 5
\(\Rightarrow \) n = 4
अतः n का मान 4 होगा।
Question: 4
यदि किसी भिन्न के हर में 1 जोड़ दिया जाये तो भिन्न \(\frac{1}{3}\) हो जाता है। यदि अंश मे \(\frac{1}{2}\) घटा दिया जाये तो भिन्न का मान \(\frac{1}{4}\) हो जाता है। भिन्न के अंश और हर का गुणनफल क्या है ?
If 1 is added to the denominator of a fraction, the fraction becomes \(\frac{1}{3}\). If \(\frac{1}{2}\) is subtracted from the numerator, the value of the fraction becomes \(\frac{1}{4}\). What is the product of the numerator and denominator of the fraction?
[A] 5 [B] 3
[C] 4 [D] 2
⚡Solution:
Answer (D) : मान लिजिए भिन्न \(\frac{x}{y}\) है।
पहली शर्त : \(\frac{x}{y + 1}\) = \(\frac{1}{3}\)
\(\Rightarrow \) 3x = y + 1 …(1)
दूसरी शर्त : \(\frac{x – \frac{1}{2}}{y}\) = \(\frac{1}{4}\)
\(\Rightarrow \) 4 × ( x – \(\frac{1}{2}\) ) = y
\(\Rightarrow \) 4x – 2 = y …(2)
समीकरण (1) व (2) से,
3x = 4x – 2 + 1
4x – 3x= 2 – 1
x = 1
\(\Rightarrow \) x = 1
समीकरण (2) से ,
4 × 1 – 2 = y
\(\Rightarrow \) y = 2
अतः भिन्न \(\frac{1}{2}\) है तथा इसके अंश व हर का गुणनफल 1 × 2 = 2 होगा।
Why Number System Questions Are Important for Exams
- Forms the base of Arithmetic
- High-scoring topic
- Frequently asked in competitive exams
- Helps in solving percentage, ratio, and algebra problems
Conclusion
Practicing these Number System important questions will help students strengthen their basics and score better in school exams and competitive exams. Make sure to revise regularly and understand the concepts clearly.