कौन-सा कथन वास्तविक संख्याओं के बारे में सही है?
Which statement about real numbers is correct?
#number-systems
#real-numbers
#irrational-numbers
A हर वास्तविक संख्या परिमेय होती है / Every real number is rational
B हर अपरिमेय संख्या वास्तविक संख्या होती है / Every irrational number is a real number
C हर वास्तविक संख्या पूर्णांक होती है / Every real number is an integer
D हर परिमेय संख्या अपरिमेय होती है / Every rational number is irrational
Explanation opens after your attempt
Correct Answer
B. हर अपरिमेय संख्या वास्तविक संख्या होती है / Every irrational number is a real number
Step 1
Concept
Real numbers include both rational and irrational numbers. Therefore every irrational number is real.
Step 2
Why this answer is correct
The correct answer is B. हर अपरिमेय संख्या वास्तविक संख्या होती है / Every irrational number is a real number. Real numbers include both rational and irrational numbers. Therefore every irrational number is real.
Step 3
Exam Tip
वास्तविक संख्याओं में परिमेय और अपरिमेय दोनों शामिल होते हैं। इसलिए हर अपरिमेय संख्या वास्तविक है।
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यदि \(a=\sqrt{6}\) और \(b=\sqrt{24}\), तो (b) किसके बराबर है?
If \(a=\sqrt{6}\) and \(b=\sqrt{24}\), then what is (b) equal to?
#number-systems
#surds
#comparison
A (2a)
B (3a)
C (4a)
D \(\frac{a}{2}\)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{24}=\sqrt{4\times6}=2\sqrt{6}=2a\). Identify the common surd.
Step 2
Why this answer is correct
The correct answer is A. (2a). \(\sqrt{24}=\sqrt{4\times6}=2\sqrt{6}=2a\). Identify the common surd.
Step 3
Exam Tip
\(\sqrt{24}=\sqrt{4\times6}=2\sqrt{6}=2a\)। समान करणी को पहचानें।
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\(\frac{3}{2^4\times5^2}\) को दशमलव में बदलने पर कितने दशमलव स्थान होंगे?
How many decimal places will \(\frac{3}{2^4\times5^2}\) have when converted into decimal?
#number-systems
#terminating-decimal
#place-value
A (2)
B (4)
C (6)
D (8)
Explanation opens after your attempt
Step 1
Concept
The highest power of (2) in the denominator is (4). After making \(5^2\) into \(5^4\), the decimal has (4) places.
Step 2
Why this answer is correct
The correct answer is B. (4). The highest power of (2) in the denominator is (4). After making \(5^2\) into \(5^4\), the decimal has (4) places.
Step 3
Exam Tip
हर में (2) की अधिकतम घात (4) है। \(5^2\) को \(5^4\) बनाने के बाद दशमलव (4) स्थानों तक होगा।
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कौन-सा विकल्प \(\sqrt{18}\) और (4) की तुलना सही करता है?
Which option correctly compares \(\sqrt{18}\) and (4)?
#number-systems
#square-root
#comparison
A \(\sqrt{18}<4\)
B \(\sqrt{18}=4\)
C \(\sqrt{18}>4\)
D तुलना संभव नहीं / Comparison is not possible
Explanation opens after your attempt
Correct Answer
C. \(\sqrt{18}>4\)
Step 1
Concept
Because \(18>16=4^2\), so \(\sqrt{18}>4\). Square both sides for comparison.
Step 2
Why this answer is correct
The correct answer is C. \(\sqrt{18}>4\). Because \(18>16=4^2\), so \(\sqrt{18}>4\). Square both sides for comparison.
Step 3
Exam Tip
क्योंकि \(18>16=4^2\), इसलिए \(\sqrt{18}>4\)। तुलना के लिए दोनों ओर वर्ग करें।
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कौन-सा विकल्प परिमेय और अपरिमेय संख्याओं के योग के बारे में सही है?
Which option is correct about the sum of a rational and an irrational number?
#number-systems
#irrational-numbers
#operations
A हमेशा परिमेय / Always rational
B हमेशा अपरिमेय / Always irrational
C हमेशा पूर्णांक / Always integer
D कभी परिभाषित नहीं / Never defined
Explanation opens after your attempt
Correct Answer
B. हमेशा अपरिमेय / Always irrational
Step 1
Concept
The sum of a rational and an irrational number is always irrational. Example is \(\sqrt{2}+3\).
Step 2
Why this answer is correct
The correct answer is B. हमेशा अपरिमेय / Always irrational. The sum of a rational and an irrational number is always irrational. Example is \(\sqrt{2}+3\).
Step 3
Exam Tip
परिमेय और अपरिमेय संख्या का योग हमेशा अपरिमेय होता है। उदाहरण \(\sqrt{2}+3\) है।
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\(\sqrt{45}+\sqrt{80}\) का सरलतम रूप क्या है?
What is the simplest form of \(\sqrt{45}+\sqrt{80}\)?
#number-systems
#surds
#addition
A \(7\sqrt{5}\)
B \(8\sqrt{5}\)
C \(9\sqrt{5}\)
D \(10\sqrt{5}\)
Explanation opens after your attempt
Correct Answer
A. \(7\sqrt{5}\)
Step 1
Concept
\(\sqrt{45}=3\sqrt{5}\) and \(\sqrt{80}=4\sqrt{5}\). The sum is \(7\sqrt{5}\).
Step 2
Why this answer is correct
The correct answer is A. \(7\sqrt{5}\). \(\sqrt{45}=3\sqrt{5}\) and \(\sqrt{80}=4\sqrt{5}\). The sum is \(7\sqrt{5}\).
Step 3
Exam Tip
\(\sqrt{45}=3\sqrt{5}\) और \(\sqrt{80}=4\sqrt{5}\)। योग \(7\sqrt{5}\) है।
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कौन-सी संख्या \(\frac{p}{q}\) रूप में लिखी जा सकती है, जहाँ (p) और (q) पूर्णांक हैं और \(q\ne0\)?
Which number can be written in the form \(\frac{p}{q}\), where (p) and (q) are integers and \(q\ne0\)?
#number-systems
#rational-numbers
#recurring-decimal
A \(\sqrt{11}\)
B \(\pi\)
C \(0.\overline{37}\)
D \(\sqrt{13}\)
Explanation opens after your attempt
Correct Answer
C. \(0.\overline{37}\)
Step 1
Concept
A recurring decimal is rational. Therefore \(0.\overline{37}\) can be written in \(\frac{p}{q}\) form.
Step 2
Why this answer is correct
The correct answer is C. \(0.\overline{37}\). A recurring decimal is rational. Therefore \(0.\overline{37}\) can be written in \(\frac{p}{q}\) form.
Step 3
Exam Tip
आवर्ती दशमलव परिमेय होता है। इसलिए \(0.\overline{37}\) को \(\frac{p}{q}\) रूप में लिखा जा सकता है।
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\(\sqrt{7}\) को संख्या रेखा पर रखने से पहले कौन-सा अंतराल पहचानना चाहिए?
Which interval should be identified before placing \(\sqrt{7}\) on the number line?
#number-systems
#number-line
#square-roots
A \(1<\sqrt{7}<2\)
B \(2<\sqrt{7}<3\)
C \(3<\sqrt{7}<4\)
D \(4<\sqrt{7}<5\)
Explanation opens after your attempt
Correct Answer
B. \(2<\sqrt{7}<3\)
Step 1
Concept
Because \(2^2<7<3^2\). Therefore \(\sqrt{7}\) lies between (2) and (3).
Step 2
Why this answer is correct
The correct answer is B. \(2<\sqrt{7}<3\). Because \(2^2<7<3^2\). Therefore \(\sqrt{7}\) lies between (2) and (3).
Step 3
Exam Tip
क्योंकि \(2^2<7<3^2\) है। इसलिए \(\sqrt{7}\) (2) और (3) के बीच होगा।
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यदि (x=0.101001000100001...) है, तो (x) किस प्रकार की संख्या है?
If (x=0.101001000100001...), what type of number is (x)?
#number-systems
#irrational-numbers
#non-recurring-decimal
A परिमेय क्योंकि दशमलव सांत है / Rational because the decimal terminates
B परिमेय क्योंकि दशमलव आवर्ती है / Rational because the decimal recurs
C अपरिमेय क्योंकि दशमलव असांत अनावर्ती है / Irrational because the decimal is non-terminating non-recurring
D पूर्णांक क्योंकि इसमें केवल (0) और (1) हैं / Integer because it has only (0) and (1)
Explanation opens after your attempt
Correct Answer
C. अपरिमेय क्योंकि दशमलव असांत अनावर्ती है / Irrational because the decimal is non-terminating non-recurring
Step 1
Concept
The decimal continues and has no fixed repetition. Such decimals are irrational.
Step 2
Why this answer is correct
The correct answer is C. अपरिमेय क्योंकि दशमलव असांत अनावर्ती है / Irrational because the decimal is non-terminating non-recurring. The decimal continues and has no fixed repetition. Such decimals are irrational.
Step 3
Exam Tip
दशमलव चलता रहता है और कोई निश्चित आवृत्ति नहीं है। ऐसे दशमलव अपरिमेय होते हैं।
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\(\frac{17}{125}\) का दशमलव प्रसार कैसा होगा?
What type of decimal expansion will \(\frac{17}{125}\) have?
#number-systems
#terminating-decimal
#rational-numbers
A सांत / Terminating
B असांत आवर्ती / Non-terminating recurring
C असांत अनावर्ती / Non-terminating non-recurring
D अपरिमेय / Irrational
Explanation opens after your attempt
Correct Answer
A. सांत / Terminating
Step 1
Concept
\(125=5^3\), so the denominator has only (5). The decimal will terminate.
Step 2
Why this answer is correct
The correct answer is A. सांत / Terminating. \(125=5^3\), so the denominator has only (5). The decimal will terminate.
Step 3
Exam Tip
\(125=5^3\), इसलिए हर में केवल (5) है। दशमलव सांत होगा।
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