Question 1/11
Medium Mathematics
Chapter 2: Polynomials Irrational numbers and real numbers Class 10 Level 27
यदि कोई दशमलव अनंत और आवर्ती है तो वह किस प्रकार की संख्या है?
If a decimal is non terminating and repeating, what type of number is it?
#repeating-decimal
#rational-number
#concept
A परिमेय संख्या / Rational number
B अपरिमेय संख्या / Irrational number
C अवास्तविक संख्या / Non real number
D केवल पूर्णांक / Integer only
Explanation opens after your attempt
Correct Answer
A. परिमेय संख्या / Rational number
Step 1
Concept
A non terminating repeating decimal is rational. Do not call it irrational only because it is infinite.
Step 2
Why this answer is correct
The correct answer is A. परिमेय संख्या / Rational number. A non terminating repeating decimal is rational. Do not call it irrational only because it is infinite.
Step 3
Exam Tip
अनंत आवर्ती दशमलव परिमेय होता है। केवल अनंत देखकर उसे अपरिमेय न मानें।
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Question 2/11
Medium Mathematics
Chapter 2: Polynomials Irrational numbers and real numbers Class 10 Level 27
कौन सा विकल्प \(0.\overline{09}\) की प्रकृति सही बताता है?
Which option correctly describes the nature of \(0.\overline{09}\)?
#bar-decimal
#repeating-decimal
#rational
A परिमेय संख्या / Rational number
B अपरिमेय संख्या / Irrational number
C अवास्तविक संख्या / Non real number
D पूर्णांक / Integer
Explanation opens after your attempt
Correct Answer
A. परिमेय संख्या / Rational number
Step 1
Concept
The bar shows repetition of (09). Every recurring decimal is rational.
Step 2
Why this answer is correct
The correct answer is A. परिमेय संख्या / Rational number. The bar shows repetition of (09). Every recurring decimal is rational.
Step 3
Exam Tip
ऊपर की रेखा (09) के आवर्तन को बताती है। हर आवर्ती दशमलव परिमेय होता है।
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Question 3/11
Medium Mathematics
Chapter 2: Polynomials Irrational numbers and real numbers Class 10 Level 26
कौन सा विकल्प \(0.\overline{123}\) की प्रकृति सही बताता है?
Which option correctly describes the nature of \(0.\overline{123}\)?
#bar-decimal
#repeating-decimal
#rational
A परिमेय संख्या / Rational number
B अपरिमेय संख्या / Irrational number
C अवास्तविक संख्या / Non real number
D पूर्णांक / Integer
Explanation opens after your attempt
Correct Answer
A. परिमेय संख्या / Rational number
Step 1
Concept
The bar shows repetition of (123). A repeating decimal is rational.
Step 2
Why this answer is correct
The correct answer is A. परिमेय संख्या / Rational number. The bar shows repetition of (123). A repeating decimal is rational.
Step 3
Exam Tip
ऊपर की रेखा (123) के आवर्तन को बताती है। आवर्ती दशमलव परिमेय होता है।
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Question 4/11
Medium Mathematics
Chapter 2: Polynomials Irrational numbers and real numbers Class 10 Level 25
यदि \(x=0.\overline{12}\) है तो (x) किस प्रकार की संख्या है?
If \(x=0.\overline{12}\), what type of number is (x)?
#bar-decimal
#repeating-decimal
#rational
A परिमेय संख्या / Rational number
B अपरिमेय संख्या / Irrational number
C अवास्तविक संख्या / Non real number
D पूर्णांक / Integer
Explanation opens after your attempt
Correct Answer
A. परिमेय संख्या / Rational number
Step 1
Concept
The bar shows that (12) repeats. A repeating decimal is rational.
Step 2
Why this answer is correct
The correct answer is A. परिमेय संख्या / Rational number. The bar shows that (12) repeats. A repeating decimal is rational.
Step 3
Exam Tip
ऊपर की रेखा बताती है कि (12) दोहरता है। आवर्ती दशमलव परिमेय होता है।
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Question 5/11
Medium Mathematics
Chapter 2: Polynomials Irrational numbers and real numbers Class 10 Level 25
कौन सा विकल्प अनंत आवर्ती दशमलव है?
Which option is a non terminating repeating decimal?
#decimal-expansion
#repeating-decimal
#rational
A (1.272727...)
B (1.270270027...)
C (1.27)
D \(\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. (1.272727...)
Step 1
Concept
The block (27) repeats so it is a repeating decimal. A repeating decimal is rational.
Step 2
Why this answer is correct
The correct answer is A. (1.272727...). The block (27) repeats so it is a repeating decimal. A repeating decimal is rational.
Step 3
Exam Tip
(27) बार बार दोहर रहा है इसलिए यह आवर्ती दशमलव है। आवर्ती दशमलव परिमेय होता है।
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Question 6/11
Easy Mathematics
Chapter 2: Polynomials Irrational numbers and real numbers Class 10 Level 27
कौन सा विकल्प अनंत लेकिन आवर्ती दशमलव है?
Which option is a non terminating but repeating decimal?
#repeating-decimal
#rational-numbers
#decimal
A (4.565656...)
B (4.567891011...)
C (4.56)
D \(\sqrt{4}\)
Explanation opens after your attempt
Correct Answer
A. (4.565656...)
Step 1
Concept
The block (56) repeats so it is a repeating decimal. A repeating decimal is rational.
Step 2
Why this answer is correct
The correct answer is A. (4.565656...). The block (56) repeats so it is a repeating decimal. A repeating decimal is rational.
Step 3
Exam Tip
(56) बार-बार दोहर रहा है इसलिए यह आवर्ती दशमलव है। आवर्ती दशमलव परिमेय होता है।
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Question 7/11
Easy Mathematics
Chapter 2: Polynomials Irrational numbers and real numbers Class 10 Level 26
\(2.\overline{18}\) किस प्रकार की संख्या है?
What type of number is \(2.\overline{18}\)?
#bar-decimal
#repeating-decimal
#rational
A परिमेय संख्या / Rational number
B अपरिमेय संख्या / Irrational number
C अवास्तविक संख्या / Non real number
D केवल पूर्णांक / Integer only
Explanation opens after your attempt
Correct Answer
A. परिमेय संख्या / Rational number
Step 1
Concept
The bar shows that (18) repeats. A repeating decimal is rational.
Step 2
Why this answer is correct
The correct answer is A. परिमेय संख्या / Rational number. The bar shows that (18) repeats. A repeating decimal is rational.
Step 3
Exam Tip
ऊपर की रेखा बताती है कि (18) दोहरता है। आवर्ती दशमलव परिमेय होता है।
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Question 8/11
Easy Mathematics
Chapter 2: Polynomials Irrational numbers and real numbers Class 10 Level 25
\(0.\overline{7}\) किस प्रकार की संख्या है?
What type of number is \(0.\overline{7}\)?
#repeating-decimal
#rational-number
#decimal
A परिमेय संख्या / Rational number
B अपरिमेय संख्या / Irrational number
C अवास्तविक संख्या / Non real number
D अपरिभाषित संख्या / Undefined number
Explanation opens after your attempt
Correct Answer
A. परिमेय संख्या / Rational number
Step 1
Concept
\(0.\overline{7}\) is a repeating decimal. Every repeating decimal is rational.
Step 2
Why this answer is correct
The correct answer is A. परिमेय संख्या / Rational number. \(0.\overline{7}\) is a repeating decimal. Every repeating decimal is rational.
Step 3
Exam Tip
\(0.\overline{7}\) आवर्ती दशमलव है। हर आवर्ती दशमलव परिमेय होता है।
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Question 9/11
Easy Mathematics
Chapter 2: Polynomials Irrational numbers and real numbers Class 10 Level 25
कौन सा दशमलव परिमेय संख्या दिखाता है?
Which decimal represents a rational number?
#repeating-decimal
#rational-numbers
#decimal
A (2.454545...)
B (1.010010001...)
C (3.14159265...) बिना आवर्तन / (3.14159265...) without repetition
D (0.1234567891011...)
Explanation opens after your attempt
Correct Answer
A. (2.454545...)
Step 1
Concept
The block (45) repeats so it is a repeating decimal. A repeating decimal is rational.
Step 2
Why this answer is correct
The correct answer is A. (2.454545...). The block (45) repeats so it is a repeating decimal. A repeating decimal is rational.
Step 3
Exam Tip
(45) बार-बार दोहर रहा है इसलिए यह आवर्ती दशमलव है। आवर्ती दशमलव परिमेय होता है।
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Question 10/11
Easy Mathematics
Chapter 2: Polynomials Irrational numbers and real numbers Class 10 Level 25
दशमलव (0.333...) किस प्रकार की संख्या है?
What type of number is the decimal (0.333...)?
#decimal-expansion
#rational-numbers
#repeating-decimal
A परिमेय संख्या / Rational number
B अपरिमेय संख्या / Irrational number
C अवास्तविक संख्या / Non real number
D न तो परिमेय न अपरिमेय / Neither rational nor irrational
Explanation opens after your attempt
Correct Answer
A. परिमेय संख्या / Rational number
Step 1
Concept
A repeating decimal is rational. It can be written as \(\frac{1}{3}\).
Step 2
Why this answer is correct
The correct answer is A. परिमेय संख्या / Rational number. A repeating decimal is rational. It can be written as \(\frac{1}{3}\).
Step 3
Exam Tip
दोहराने वाला दशमलव परिमेय होता है। इसे \(\frac{1}{3}\) लिखा जा सकता है।
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Question 11/11
Medium Mathematics
Chapter 1: Real Numbers 7: Decimal expansion of rational numbers Class 10 Level 21
किसी परिमेय संख्या का हर सरलतम रूप में \(2^3 \times 5^2 \times 7\) है। उसके दशमलव प्रसार के बारे में सही कथन चुनिए।
The denominator of a rational number in lowest form is \(2^3 \times 5^2 \times 7\). Choose the correct statement about its decimal expansion.
#real numbers
#decimal expansion
#rational numbers
#terminating decimal
#repeating decimal
A असांत आवर्ती / Non-terminating repeating
B सांत / Terminating
C असांत अनावर्ती / Non-terminating non-repeating
D पूर्णांक / Integer
Explanation opens after your attempt
Correct Answer
A. असांत आवर्ती / Non-terminating repeating
Step 1
Concept
A rational number has a terminating decimal only when the denominator in lowest form has prime factors only (2) and (5).
Step 2
Why this answer is correct
Here the denominator also contains (7), so the decimal will not terminate, but since the number is rational, it will repeat.
Step 3
Exam Tip
In exams, always reduce the fraction first and then check the prime factors of the denominator. चरण 1: परिमेय संख्या का दशमलव प्रसार तभी सांत होता है जब सरलतम रूप में हर के अभाज्य गुणनखंड केवल (2) और (5) हों। चरण 2: यहां हर में (7) भी है, इसलिए दशमलव प्रसार सांत नहीं होगा, पर परिमेय संख्या होने के कारण वह आवर्ती होगा। चरण 3: परीक्षा में पहले भिन्न को सरलतम रूप में जांचें, फिर हर के अभाज्य गुणनखंड देखें।
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