यदि \(0.1010010001\ldots\) का दशमलव प्रसार है तो यह संख्या क्या है?
If \(0.1010010001\ldots\) is the decimal expansion then this number is?
#real numbers
#irrational
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A परिमेय / Rational
B अपरिमेय / Irrational
C पूर्णांक / Integer
D प्राकृतिक संख्या / Natural number
Explanation opens after your attempt
Correct Answer
B. अपरिमेय / Irrational
Explanation
Simple Explanation
दशमलव न समाप्त होता है न आवर्ती है इसलिए अपरिमेय है। परीक्षा में आवर्ती और अनावर्ती में अंतर याद रखें। / The decimal neither terminates nor repeats so it is irrational. Remember the difference between repeating and non repeating decimals.
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\(2\sqrt{3}+\sqrt{27}\) का मान क्या है?
What is the value of \(2\sqrt{3}+\sqrt{27}\)?
#surds
#real numbers
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A \(\sqrt{3}\)
B \(\sqrt{27}\)
C \(5\sqrt{3}\)
D \(3\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
C. \(5\sqrt{3}\)
Explanation
Simple Explanation
\(\sqrt{27}=3\sqrt{3}\) इसलिए योग \(5\sqrt{3}\) है। वर्गमूल को सरल करना सीखें। / \(\sqrt{27}=3\sqrt{3}\) so the sum is \(5\sqrt{3}\). Practice simplifying surds.
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कौन सा कथन सत्य है?
Which statement is true?
#square roots
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A \(\sqrt{49}\) अपरिमेय है / \(\sqrt{49}\) is irrational
B \(\sqrt{50}\) परिमेय है / \(\sqrt{50}\) is rational
C \(\sqrt{64}\) पूर्णांक है / \(\sqrt{64}\) is an integer
D \(\sqrt{18}\) प्राकृतिक संख्या है / \(\sqrt{18}\) is a natural number
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Correct Answer
C. \(\sqrt{64}\) पूर्णांक है / \(\sqrt{64}\) is an integer
Explanation
Simple Explanation
\(\sqrt{64}=8\) जो पूर्णांक है। पूर्ण वर्गों के वर्गमूल पर ध्यान दें। / \(\sqrt{64}=8\) which is an integer. Check perfect squares carefully.
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\(3+\sqrt{2}\) किस समुच्चय का सदस्य है?
\(3+\sqrt{2}\) belongs to which set?
#irrational numbers
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A अपरिमेय / Irrational
B परिमेय / Rational
C पूर्ण संख्या / Whole number
D पूर्णांक / Integer
Explanation opens after your attempt
Correct Answer
A. अपरिमेय / Irrational
Explanation
Simple Explanation
परिमेय और अपरिमेय का योग सामान्यतः अपरिमेय होता है। ऐसे प्रश्नों में प्रकार पहचानें। / The sum of a rational and an irrational number is generally irrational. Identify number types first.
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यदि \(x=\sqrt{5}\) तो \(x^2\) क्या होगा?
If \(x=\sqrt{5}\) then what is \(x^2\)?
#square roots
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A 25
B 10
C 5
D \(\sqrt{5}\)
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Explanation
Simple Explanation
वर्ग और वर्गमूल एक दूसरे को निरस्त करते हैं। मूल परिभाषा याद रखें। / Square and square root cancel each other. Recall the basic definition.
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\(0.272727\ldots\) किस प्रकार की संख्या है?
\(0.272727\ldots\) is what type of number?
#rational numbers
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A अपरिमेय / Irrational
B परिमेय / Rational
C पूर्णांक / Integer
D अपूर्णांक अपरिमेय / Non integer irrational
Explanation opens after your attempt
Correct Answer
B. परिमेय / Rational
Explanation
Simple Explanation
यह आवर्ती दशमलव है इसलिए परिमेय है। आवर्ती दशमलव को भिन्न में बदला जा सकता है। / It is a repeating decimal so it is rational. Repeating decimals can be expressed as fractions.
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\(\sqrt{12}+\sqrt{27}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{12}+\sqrt{27}\)?
#surds
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A \(5\sqrt{3}\)
B \(3\sqrt{3}\)
C \(2\sqrt{3}\)
D \(6\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
A. \(5\sqrt{3}\)
Explanation
Simple Explanation
\(\sqrt{12}=2\sqrt{3}\) और \(\sqrt{27}=3\sqrt{3}\)। समान मूलों को जोड़ा जाता है। / \(\sqrt{12}=2\sqrt{3}\) and \(\sqrt{27}=3\sqrt{3}\). Like surds can be added.
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कौन सी संख्या अपरिमेय है?
Which number is irrational?
#irrational numbers
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A \(\frac{7}{11}\)
B (-3)
C (0.125)
D \(\sqrt{7}\)
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Correct Answer
D. \(\sqrt{7}\)
Explanation
Simple Explanation
\(\sqrt{7}\) पूर्ण वर्ग का वर्गमूल नहीं है। इसलिए यह अपरिमेय है। / \(\sqrt{7}\) is not the square root of a perfect square. Hence it is irrational.
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यदि \(a=\sqrt{2}\) और \(b=\sqrt{8}\) तो (a+b) क्या है?
If \(a=\sqrt{2}\) and \(b=\sqrt{8}\) then what is (a+b)?
#surds
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A \(2\sqrt{2}\)
B \(3\sqrt{2}\)
C \(4\sqrt{2}\)
D \(\sqrt{10}\)
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Correct Answer
B. \(3\sqrt{2}\)
Explanation
Simple Explanation
\(\sqrt{8}=2\sqrt{2}\) इसलिए योग \(3\sqrt{2}\) है। पहले सरल रूप निकालें। / \(\sqrt{8}=2\sqrt{2}\) so the sum is \(3\sqrt{2}\). Simplify before adding.
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\(1-\sqrt{3}\) किस प्रकार की संख्या है?
\(1-\sqrt{3}\) is what type of number?
#irrational numbers
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A अपरिमेय / Irrational
B परिमेय / Rational
C पूर्णांक / Integer
D प्राकृतिक / Natural
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Correct Answer
A. अपरिमेय / Irrational
Explanation
Simple Explanation
परिमेय और अपरिमेय का अंतर भी अपरिमेय होता है। संख्या का प्रकार पहचानें। / The difference of a rational and an irrational number is irrational. Identify the number class.
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कौन सा दशमलव प्रसार परिमेय संख्या को दर्शाता है?
Which decimal expansion represents a rational number?
#decimals
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A \(0.1234567891011\ldots\)
B \(0.1010010001\ldots\)
C \(0.6666\ldots\)
D \(0.314159265\ldots\)
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Correct Answer
C. \(0.6666\ldots\)
Explanation
Simple Explanation
आवर्ती दशमलव परिमेय होते हैं। शेष विकल्प अनावर्ती हैं। / Repeating decimals are rational. The others are non repeating.
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\(\sqrt{45}-\sqrt{5}\) का मान क्या है?
What is the value of \(\sqrt{45}-\sqrt{5}\)?
#surds
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A \(2\sqrt{5}\)
B \(3\sqrt{5}\)
C \(4\sqrt{5}\)
D \(\sqrt{40}\)
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Correct Answer
A. \(2\sqrt{5}\)
Explanation
Simple Explanation
\(\sqrt{45}=3\sqrt{5}\) इसलिए उत्तर \(2\sqrt{5}\) है। वर्ग गुणनखंड करें। / \(\sqrt{45}=3\sqrt{5}\) so the result is \(2\sqrt{5}\). Factor perfect squares.
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यदि \(x=\sqrt{11}\) तो (x) है
If \(x=\sqrt{11}\) then (x) is
#square roots
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A परिमेय / Rational
B अपरिमेय / Irrational
C पूर्णांक / Integer
D पूर्ण संख्या / Whole number
Explanation opens after your attempt
Correct Answer
B. अपरिमेय / Irrational
Explanation
Simple Explanation
11 पूर्ण वर्ग नहीं है इसलिए \(\sqrt{11}\) अपरिमेय है। पूर्ण वर्ग पहचानें। / 11 is not a perfect square so \(\sqrt{11}\) is irrational. Check perfect squares.
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कौन सा युग्म दोनों अपरिमेय हैं?
Which pair is both irrational?
#classification
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A \(\sqrt{9},\sqrt{2}\)
B \(\sqrt{3},\sqrt{5}\)
C \(\frac{2}{3},\sqrt{7}\)
D \(\sqrt{16},\sqrt{25}\)
Explanation opens after your attempt
Correct Answer
B. \(\sqrt{3},\sqrt{5}\)
Explanation
Simple Explanation
\(\sqrt{3}\) और \(\sqrt{5}\) दोनों अपरिमेय हैं। पूर्ण वर्गों से सावधान रहें। / \(\sqrt{3}\) and \(\sqrt{5}\) are both irrational. Watch for perfect squares.
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कौन सा कथन असत्य है?
Which statement is false?
#real numbers
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A हर परिमेय संख्या वास्तविक है / Every rational number is real
B हर अपरिमेय संख्या वास्तविक है / Every irrational number is real
C हर वास्तविक संख्या परिमेय है / Every real number is rational
D वास्तविक संख्याएँ परिमेय और अपरिमेय का संघ हैं / Reals are union of rational and irrational
Explanation opens after your attempt
Correct Answer
C. हर वास्तविक संख्या परिमेय है / Every real number is rational
Explanation
Simple Explanation
सभी वास्तविक संख्याएँ परिमेय नहीं होतीं। अपरिमेय भी वास्तविक हैं। / Not all real numbers are rational. Irrational numbers are also real.
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\(\frac{\sqrt{32}}{\sqrt{2}}\) का मान क्या है?
What is the value of \(\frac{\sqrt{32}}{\sqrt{2}}\)?
#surds
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A 8
B 4
C \(\sqrt{16}\)
D 16
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Explanation
Simple Explanation
यह \(\sqrt{16}=4\) के बराबर है। मूलों के भाग का नियम लगाएँ। / It equals \(\sqrt{16}=4\). Apply the quotient rule of radicals.
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यदि \(x=0.454545\ldots\) तो (x) है
If \(x=0.454545\ldots\) then (x) is
#decimals
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A अपरिमेय / Irrational
B पूर्णांक / Integer
C परिमेय / Rational
D प्राकृतिक / Natural
Explanation opens after your attempt
Correct Answer
C. परिमेय / Rational
Explanation
Simple Explanation
यह आवर्ती दशमलव है इसलिए परिमेय है। दोहराव पहचानें। / It is a repeating decimal, hence rational. Identify repetition.
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\(\sqrt{75}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{75}\)?
#surds
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A \(5\sqrt{3}\)
B \(3\sqrt{5}\)
C \(15\sqrt{3}\)
D \(\sqrt{15}\)
Explanation opens after your attempt
Correct Answer
A. \(5\sqrt{3}\)
Explanation
Simple Explanation
\(75=25\times3\) इसलिए \(\sqrt{75}=5\sqrt{3}\)। पूर्ण वर्ग अलग करें। / \(75=25\times3\) so \(\sqrt{75}=5\sqrt{3}\). Extract perfect squares.
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कौन सी संख्या परिमेय नहीं है?
Which number is not rational?
#irrational numbers
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A (-2.5)
B \(\frac{13}{17}\)
C \sqrt{13}
D 0
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Correct Answer
C. \sqrt{13}
Explanation
Simple Explanation
\(\sqrt{13}\) अपरिमेय है क्योंकि 13 पूर्ण वर्ग नहीं है। / \(\sqrt{13}\) is irrational because 13 is not a perfect square.
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\(\sqrt{7}+\sqrt{7}\) का मान क्या है?
What is the value of \(\sqrt{7}+\sqrt{7}\)?
#surds
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A \(\sqrt{14}\)
B \(7\sqrt{2}\)
C \(2\sqrt{7}\)
D 14
Explanation opens after your attempt
Correct Answer
C. \(2\sqrt{7}\)
Explanation
Simple Explanation
समान मूलों के गुणांक जोड़े जाते हैं। उत्तर \(2\sqrt{7}\) है। / Add coefficients of like surds. The result is \(2\sqrt{7}\).
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कौन सा सबसे छोटा समुच्चय (-4) को शामिल करता है?
Which is the smallest set containing (-4)?
#sets of numbers
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A प्राकृतिक संख्या / Natural
B पूर्ण संख्या / Whole
C पूर्णांक / Integer
D अपरिमेय / Irrational
Explanation opens after your attempt
Correct Answer
C. पूर्णांक / Integer
Explanation
Simple Explanation
(-4) एक पूर्णांक है। यह प्राकृतिक या पूर्ण संख्या नहीं है। / (-4) is an integer. It is not natural or whole.
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\(\sqrt{48}-2\sqrt{3}\) का मान क्या है?
What is the value of \(\sqrt{48}-2\sqrt{3}\)?
#surds
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A \(2\sqrt{3}\)
B \(4\sqrt{3}\)
C \(6\sqrt{3}\)
D \(\sqrt{45}\)
Explanation opens after your attempt
Correct Answer
B. \(4\sqrt{3}\)
Explanation
Simple Explanation
\(\sqrt{48}=4\sqrt{3}\) इसलिए परिणाम \(2\sqrt{3}\) है। सरल रूप पहले निकालें। / \(\sqrt{48}=4\sqrt{3}\), giving \(2\sqrt{3}\). Simplify first.
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यदि (a) परिमेय और (b) अपरिमेय है तो (a+b) सामान्यतः क्या होगा?
If (a) is rational and (b) is irrational then (a+b) is generally?
#properties
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A परिमेय / Rational
B अपरिमेय / Irrational
C पूर्णांक / Integer
D प्राकृतिक / Natural
Explanation opens after your attempt
Correct Answer
B. अपरिमेय / Irrational
Explanation
Simple Explanation
परिमेय में अपरिमेय जोड़ने पर अपरिमेय प्राप्त होता है। यह महत्वपूर्ण गुण है। / Adding a rational to an irrational gives an irrational number. This is a key property.
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\(\sqrt{81}+\sqrt{1}\) का मान क्या है?
What is the value of \(\sqrt{81}+\sqrt{1}\)?
#square roots
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A 8
B 9
C 10
D 11
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Explanation
Simple Explanation
\(\sqrt{81}=9\) और \(\sqrt{1}=1\)। योग 10 है। / \(\sqrt{81}=9\) and \(\sqrt{1}=1\). Sum is 10.
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कौन सी संख्या का दशमलव प्रसार समाप्त होगा?
Which number has a terminating decimal expansion?
#rational decimals
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A \(\frac{7}{12}\)
B \(\frac{13}{40}\)
C \(\frac{2}{9}\)
D \(\frac{11}{33}\)
Explanation opens after your attempt
Correct Answer
B. \(\frac{13}{40}\)
Explanation
Simple Explanation
हर में केवल 2 और 5 के गुणनखंड होने चाहिए। \(40=2^3\times5\)। / The denominator must have only factors 2 and 5. \(40=2^3\times5\).
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\(\sqrt{20}+\sqrt{5}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{20}+\sqrt{5}\)?
#surds
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A \(3\sqrt{5}\)
B \(5\sqrt{5}\)
C \(2\sqrt{5}\)
D \(\sqrt{25}\)
Explanation opens after your attempt
Correct Answer
B. \(5\sqrt{5}\)
Explanation
Simple Explanation
\(\sqrt{20}=2\sqrt{5}\) इसलिए योग \(3\sqrt{5}\) है। समान मूल जोड़ें। / \(\sqrt{20}=2\sqrt{5}\), hence the sum is \(3\sqrt{5}\). Combine like surds.
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\(\sqrt{50}-\sqrt{8}\) का मान क्या है?
What is the value of \(\sqrt{50}-\sqrt{8}\)?
#surds
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A \(\sqrt{42}\)
B \(\sqrt{2}\)
C \(3\sqrt{2}\)
D \(5\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
C. \(3\sqrt{2}\)
Explanation
Simple Explanation
\(\sqrt{50}=5\sqrt{2}\) और \(\sqrt{8}=2\sqrt{2}\)। अंतर \(3\sqrt{2}\) है। / \(\sqrt{50}=5\sqrt{2}\) and \(\sqrt{8}=2\sqrt{2}\). Difference is \(3\sqrt{2}\).
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कौन सी संख्या वास्तविक नहीं है?
Which number is not a real number?
#real numbers
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A \(\sqrt{25}\)
B \(-\sqrt{9}\)
C \(\sqrt{-4}\)
D 0
Explanation opens after your attempt
Correct Answer
C. \(\sqrt{-4}\)
Explanation
Simple Explanation
ऋणात्मक संख्या का वर्गमूल वास्तविक नहीं होता। वास्तविक संख्याओं की सीमा याद रखें। / The square root of a negative number is not real. Remember the scope of real numbers.
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यदि \(x=\sqrt{6}\) तो \(x\times x\) क्या है?
If \(x=\sqrt{6}\) then what is \(x\times x\)?
#square roots
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A 12
B 6
C \(\sqrt{12}\)
D \(\sqrt{6}\)
Explanation opens after your attempt
Explanation
Simple Explanation
(\(\sqrt{6}\)2 =6)। वर्ग और वर्गमूल परस्पर व्युत्क्रम हैं। / (\(\sqrt{6}\)2 =6). Square and square root are inverse operations.
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कौन सा विकल्प परिमेय संख्याओं का उदाहरण है?
Which option is an example of rational numbers?
#rational numbers
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A \(\sqrt{2},\sqrt{3}\)
B \(\pi,\sqrt{5}\)
C \(\frac{5}{8},-7\)
D \sqrt{11},0.101001\ldots
Explanation opens after your attempt
Correct Answer
C. \(\frac{5}{8},-7\)
Explanation
Simple Explanation
दोनों संख्याएँ परिमेय हैं। भिन्न और पूर्णांक परिमेय होते हैं। / Both numbers are rational. Fractions and integers are rational.
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\(\sqrt{98}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{98}\)?
#surds
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A \(7\sqrt{2}\)
B \(2\sqrt{7}\)
C \(14\sqrt{2}\)
D \(7\sqrt{7}\)
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Correct Answer
A. \(7\sqrt{2}\)
Explanation
Simple Explanation
\(98=49\times2\) इसलिए \(\sqrt{98}=7\sqrt{2}\)। पूर्ण वर्ग अलग करें। / \(98=49\times2\), so \(\sqrt{98}=7\sqrt{2}\). Extract the perfect square.
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\(0.5000\ldots\) किसके बराबर है?
\(0.5000\ldots\) is equal to?
#decimals
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A \(\frac{1}{5}\)
B \(\frac{1}{2}\)
C \(\frac{5}{2}\)
D 5
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Correct Answer
B. \(\frac{1}{2}\)
Explanation
Simple Explanation
समाप्त दशमलव \(0.5=\frac{1}{2}\) होता है। दशमलव को भिन्न में बदलें। / The terminating decimal \(0.5=\frac{1}{2}\). Convert decimals to fractions.
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यदि \(a=\sqrt{3}\) तो \(2a+\sqrt{3}\) क्या होगा?
If \(a=\sqrt{3}\) then what is \(2a+\sqrt{3}\)?
#surds
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A \(\sqrt{3}\)
B \(2\sqrt{3}\)
C \(3\sqrt{3}\)
D 6
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Correct Answer
C. \(3\sqrt{3}\)
Explanation
Simple Explanation
\(2\sqrt{3}+\sqrt{3}=3\sqrt{3}\)। समान पद जोड़ें। / \(2\sqrt{3}+\sqrt{3}=3\sqrt{3}\). Add like terms.
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कौन सा कथन सही नहीं है?
Which statement is not correct?
#classification
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A हर पूर्णांक परिमेय है / Every integer is rational
B हर प्राकृतिक संख्या पूर्ण संख्या है / Every natural number is whole
C हर अपरिमेय संख्या परिमेय है / Every irrational number is rational
D हर पूर्ण संख्या वास्तविक है / Every whole number is real
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Correct Answer
C. हर अपरिमेय संख्या परिमेय है / Every irrational number is rational
Explanation
Simple Explanation
अपरिमेय और परिमेय अलग वर्ग हैं। यह कथन गलत है। / Irrational and rational numbers are different classes. Hence this statement is false.
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\(\sqrt{24}+\sqrt{54}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{24}+\sqrt{54}\)?
#surds
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A \(5\sqrt{6}\)
B \(7\sqrt{6}\)
C \(3\sqrt{6}\)
D \(9\sqrt{6}\)
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Correct Answer
A. \(5\sqrt{6}\)
Explanation
Simple Explanation
\(\sqrt{24}=2\sqrt{6}\) और \(\sqrt{54}=3\sqrt{6}\)। योग \(5\sqrt{6}\) है। / \(\sqrt{24}=2\sqrt{6}\) and \(\sqrt{54}=3\sqrt{6}\). Sum is \(5\sqrt{6}\).
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कौन सी संख्या पूर्णांक नहीं है?
Which number is not an integer?
#integers
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A (-8)
B 0
C \(\sqrt{121}\)
D \(\frac{9}{2}\)
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Correct Answer
D. \(\frac{9}{2}\)
Explanation
Simple Explanation
\(\frac{9}{2}=4.5\) पूर्णांक नहीं है। अन्य सभी पूर्णांक हैं। / \(\frac{9}{2}=4.5\) is not an integer. The others are integers.
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\(\sqrt{3}\times\sqrt{12}\) का मान क्या है?
What is the value of \(\sqrt{3}\times\sqrt{12}\)?
#surds
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A 6
B \(\sqrt{36}\)
C 12
D 3
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Explanation
Simple Explanation
\(\sqrt{36}=6\) प्राप्त होता है। मूलों का गुणन करें। / You get \(\sqrt{36}=6\). Multiply the radicals.
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यदि किसी परिमेय संख्या का दशमलव प्रसार अनंत है तो वह कैसा होगा?
If a rational number has an infinite decimal expansion then it will be?
#decimals
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A अनावर्ती / Non repeating
B आवर्ती / Repeating
C अपरिभाषित / Undefined
D ऋणात्मक / Negative
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Correct Answer
B. आवर्ती / Repeating
Explanation
Simple Explanation
परिमेय संख्या का अनंत दशमलव आवर्ती होता है। यह मानक परिणाम है। / An infinite decimal expansion of a rational number is repeating. This is a standard result.
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\(\sqrt{72}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{72}\)?
#surds
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A \(6\sqrt{2}\)
B \(4\sqrt{2}\)
C \(8\sqrt{2}\)
D \(3\sqrt{2}\)
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Correct Answer
A. \(6\sqrt{2}\)
Explanation
Simple Explanation
\(72=36\times2\) इसलिए \(\sqrt{72}=6\sqrt{2}\)। पूर्ण वर्ग निकालें। / \(72=36\times2\), so \(\sqrt{72}=6\sqrt{2}\). Extract the perfect square.
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\(\sqrt{125}-\sqrt{5}\) का मान क्या है?
What is the value of \(\sqrt{125}-\sqrt{5}\)?
#surds
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A \(3\sqrt{5}\)
B \(4\sqrt{5}\)
C \(5\sqrt{5}\)
D \(\sqrt{120}\)
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Correct Answer
B. \(4\sqrt{5}\)
Explanation
Simple Explanation
\(\sqrt{125}=5\sqrt{5}\) इसलिए उत्तर \(4\sqrt{5}\) है। सरल रूप आवश्यक है। / \(\sqrt{125}=5\sqrt{5}\), so the answer is \(4\sqrt{5}\). Simplify first.
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कौन सी संख्या परिमेय और पूर्णांक दोनों है?
Which number is both rational and an integer?
#classification
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A \(\sqrt{15}\)
B \frac{3}{7}
C -12
D \pi
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Explanation
Simple Explanation
हर पूर्णांक परिमेय होता है। (-12) दोनों श्रेणियों में है। / Every integer is rational. (-12) belongs to both categories.
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यदि \(x=\sqrt{14}\) तो \(x^2-10\) क्या है?
If \(x=\sqrt{14}\) then what is \(x^2-10\)?
#square roots
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A 24
B 14
C 10
D 4
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Explanation
Simple Explanation
\(x^2=14\) इसलिए (14-10=4)। पहले वर्ग निकालें। / \(x^2=14\), hence (14-10=4). Evaluate the square first.
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\(\sqrt{18}+\sqrt{8}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{18}+\sqrt{8}\)?
#surds
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A \(5\sqrt{2}\)
B \(3\sqrt{2}\)
C \(2\sqrt{2}\)
D \(6\sqrt{2}\)
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Correct Answer
A. \(5\sqrt{2}\)
Explanation
Simple Explanation
\(\sqrt{18}=3\sqrt{2}\) और \(\sqrt{8}=2\sqrt{2}\)। योग \(5\sqrt{2}\) है। / \(\sqrt{18}=3\sqrt{2}\) and \(\sqrt{8}=2\sqrt{2}\). Sum is \(5\sqrt{2}\).
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कौन सा दशमलव अपरिमेय संख्या को दर्शाता है?
Which decimal represents an irrational number?
#irrational decimals
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A \(0.7777\ldots\)
B \(0.202020\ldots\)
C \(0.123123123\ldots\)
D \(0.123456789101112\ldots\)
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Correct Answer
D. \(0.123456789101112\ldots\)
Explanation
Simple Explanation
यह अनंत और अनावर्ती है इसलिए अपरिमेय है। आवृत्ति जाँचें। / It is infinite and non repeating, so it is irrational. Check for repetition.
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\(\frac{\sqrt{81}}{\sqrt{9}}\) का मान क्या है?
What is the value of \(\frac{\sqrt{81}}{\sqrt{9}}\)?
#square roots
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A 1
B 3
C 9
D 27
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Explanation
Simple Explanation
\(\frac{9}{3}=3\)। वर्गमूल का सही मान लें। / \(\frac{9}{3}=3\). Evaluate square roots correctly.
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यदि \(a=\sqrt{2}\) तो \(a+\frac{1}{a}\) किस प्रकार की संख्या है?
If \(a=\sqrt{2}\) then \(a+\frac{1}{a}\) is what type of number?
#properties
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A परिमेय / Rational
B पूर्णांक / Integer
C अपरिमेय / Irrational
D प्राकृतिक / Natural
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Correct Answer
C. अपरिमेय / Irrational
Explanation
Simple Explanation
\(\sqrt{2}+\frac{\sqrt{2}}{2}\) अपरिमेय रहता है। अपरिमेय के गुण पहचानें। / \(\sqrt{2}+\frac{\sqrt{2}}{2}\) remains irrational. Use properties of irrationals.
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वास्तविक संख्याओं का सही वर्गीकरण कौन सा है?
Which is the correct classification of real numbers?
#real numbers
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A केवल पूर्णांक / Only integers
B परिमेय और अपरिमेय / Rational and irrational
C केवल प्राकृतिक / Only natural
D केवल दशमलव / Only decimals
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Correct Answer
B. परिमेय और अपरिमेय / Rational and irrational
Explanation
Simple Explanation
वास्तविक संख्याएँ परिमेय और अपरिमेय दोनों को शामिल करती हैं। यह मूल परिभाषा है। / Real numbers include both rational and irrational numbers. This is the basic definition.
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यदि \(x=\sqrt{20}\) और \(y=\sqrt{45}\) तो (x+y) का सरल रूप क्या है?
If \(x=\sqrt{20}\) and \(y=\sqrt{45}\) then what is the simplified form of (x+y)?
#surds
#real numbers
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A \(7\sqrt{5}\)
B \(5\sqrt{5}\)
C \(3\sqrt{5}\)
D \(\sqrt{65}\)
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Correct Answer
A. \(7\sqrt{5}\)
Explanation
Simple Explanation
\(\sqrt{20}=2\sqrt{5}\) और \(\sqrt{45}=3\sqrt{5}\) इसलिए योग \(5\sqrt{5}\) नहीं बल्कि \(5\sqrt{5}\)? ध्यान दें सही जोड़ \(2\sqrt{5}+3\sqrt{5}=5\sqrt{5}\) है। परीक्षा में पहले सरल रूप निकालें। / \(\sqrt{20}=2\sqrt{5}\) and \(\sqrt{45}=3\sqrt{5}\), so the sum is \(5\sqrt{5}\). Simplify surds before adding.
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निम्न में से कौन सी संख्या समाप्त दशमलव नहीं देती?
Which of the following does not give a terminating decimal?
#rational decimals
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A \(\frac{9}{20}\)
B \(\frac{7}{125}\)
C \(\frac{11}{24}\)
D \(\frac{13}{40}\)
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Correct Answer
C. \(\frac{11}{24}\)
Explanation
Simple Explanation
सरल रूप में हर में 2 और 5 के अलावा 3 भी है इसलिए दशमलव समाप्त नहीं होगा। हर के अभाज्य गुणनखंड जाँचें। / In simplest form the denominator contains 3 along with 2, so the decimal will not terminate. Check prime factors of the denominator.
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यदि \(x=\sqrt{27}-\sqrt{12}\) तो (x) का मान क्या है?
If \(x=\sqrt{27}-\sqrt{12}\) then what is the value of (x)?
#surds
#real numbers
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A \(\sqrt{3}\)
B \(2\sqrt{3}\)
C \(3\sqrt{3}\)
D \(5\sqrt{3}\)
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Correct Answer
A. \(\sqrt{3}\)
Explanation
Simple Explanation
\(\sqrt{27}=3\sqrt{3}\) और \(\sqrt{12}=2\sqrt{3}\) इसलिए \(x=\sqrt{3}\)। पहले मूलों को सरल करें। / \(\sqrt{27}=3\sqrt{3}\) and \(\sqrt{12}=2\sqrt{3}\), so \(x=\sqrt{3}\). Simplify surds first.
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