वास्तविक संख्या रेखा पर हर बिंदु किसे दर्शाता है?
Every point on the real number line represents what?
#real numbers
#number line
#class 9
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A एक वास्तविक संख्या / A real number
B केवल प्राकृतिक संख्या / Only natural number
C केवल पूर्णांक / Only integer
D अपरिभाषित संख्या / Undefined number
Explanation opens after your attempt
Correct Answer
A. एक वास्तविक संख्या / A real number
Step 1
Concept
Each point on the real number line represents a real number. Understanding the number line helps in comparison.
Step 2
Why this answer is correct
The correct answer is A. एक वास्तविक संख्या / A real number. Each point on the real number line represents a real number. Understanding the number line helps in comparison.
Step 3
Exam Tip
वास्तविक संख्या रेखा का प्रत्येक बिंदु एक वास्तविक संख्या को दर्शाता है। संख्या रेखा समझना तुलना में मदद करता है।
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कौन सा विकल्प वास्तविक संख्या नहीं है?
Which option is not a real number?
#real numbers
#undefined
#denominator
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A ( -8 )
B \( \frac{6}{0} \)
C \( \sqrt{19} \)
D (0.45)
Explanation opens after your attempt
Correct Answer
B. \( \frac{6}{0} \)
Step 1
Concept
\( \frac{6}{0} \) is undefined because the denominator is zero. A real number must be defined.
Step 2
Why this answer is correct
The correct answer is B. \( \frac{6}{0} \). \( \frac{6}{0} \) is undefined because the denominator is zero. A real number must be defined.
Step 3
Exam Tip
\( \frac{6}{0} \) परिभाषित नहीं है क्योंकि हर शून्य है। वास्तविक संख्या हमेशा परिभाषित होनी चाहिए।
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\( \sqrt{81} \) किसके बराबर है?
What is \( \sqrt{81} \) equal to?
#real numbers
#square root
#perfect square
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A (8)
B (9)
C (18)
D (81)
Explanation opens after your attempt
Step 1
Concept
Since \(9^2=81\), \( \sqrt{81}=9 \). Identify square roots of perfect squares quickly.
Step 2
Why this answer is correct
The correct answer is B. (9). Since \(9^2=81\), \( \sqrt{81}=9 \). Identify square roots of perfect squares quickly.
Step 3
Exam Tip
\(9^2=81\) इसलिए \( \sqrt{81}=9 \)। पूर्ण वर्गों के वर्गमूल जल्दी पहचानें।
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\( \sqrt{20} \) किस दो पूर्णांकों के बीच है?
Between which two integers does \( \sqrt{20} \) lie?
#real numbers
#estimation
#square root
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A (2) और (3) / (2) and (3)
B (3) और (4) / (3) and (4)
C (4) और (5) / (4) and (5)
D (5) और (6) / (5) and (6)
Explanation opens after your attempt
Correct Answer
C. (4) और (5) / (4) and (5)
Step 1
Concept
\(4^2=16\) and \(5^2=25\), so \( \sqrt{20} \) lies between (4) and (5). Estimate using squares.
Step 2
Why this answer is correct
The correct answer is C. (4) और (5) / (4) and (5). \(4^2=16\) and \(5^2=25\), so \( \sqrt{20} \) lies between (4) and (5). Estimate using squares.
Step 3
Exam Tip
\(4^2=16\) और \(5^2=25\) है इसलिए \( \sqrt{20} \) (4) और (5) के बीच है। वर्गों से अनुमान लगाएँ।
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(0.125) किस प्रकार की वास्तविक संख्या है?
What type of real number is (0.125)?
#real numbers
#terminating decimal
#rational
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A अपरिमेय संख्या / Irrational number
B परिमेय संख्या / Rational number
C अपरिभाषित संख्या / Undefined number
D केवल पूर्णांक / Only integer
Explanation opens after your attempt
Correct Answer
B. परिमेय संख्या / Rational number
Step 1
Concept
(0.125) is a terminating decimal, so it is rational. A terminating decimal can be changed into a fraction.
Step 2
Why this answer is correct
The correct answer is B. परिमेय संख्या / Rational number. (0.125) is a terminating decimal, so it is rational. A terminating decimal can be changed into a fraction.
Step 3
Exam Tip
(0.125) समाप्त दशमलव है इसलिए यह परिमेय संख्या है। समाप्त दशमलव को भिन्न में बदला जा सकता है।
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(0.1010010001...) यदि कोई आवर्ती पैटर्न नहीं रखता है तो यह क्या है?
If (0.1010010001...) has no repeating pattern, what is it?
#real numbers
#irrational decimal
#non repeating
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A परिमेय संख्या / Rational number
B पूर्णांक / Integer
C अपरिमेय वास्तविक संख्या / Irrational real number
D प्राकृतिक संख्या / Natural number
Explanation opens after your attempt
Correct Answer
C. अपरिमेय वास्तविक संख्या / Irrational real number
Step 1
Concept
A non-terminating and non-repeating decimal is irrational. Such decimals also lie on the real number line.
Step 2
Why this answer is correct
The correct answer is C. अपरिमेय वास्तविक संख्या / Irrational real number. A non-terminating and non-repeating decimal is irrational. Such decimals also lie on the real number line.
Step 3
Exam Tip
असमाप्त और अनावर्ती दशमलव अपरिमेय होता है। ऐसे दशमलव भी वास्तविक संख्या रेखा पर आते हैं।
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कौन सी संख्या परिमेय और वास्तविक दोनों है?
Which number is both rational and real?
#real numbers
#rational
#class 9
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A \( \sqrt{15} \)
B \( \frac{-11}{6} \)
C \( \sqrt{21} \)
D असमाप्त अनावर्ती दशमलव / Non-terminating non-repeating decimal
Explanation opens after your attempt
Correct Answer
B. \( \frac{-11}{6} \)
Step 1
Concept
\( \frac{-11}{6} \) is a ratio of two integers with non-zero denominator. So it is a rational real number.
Step 2
Why this answer is correct
The correct answer is B. \( \frac{-11}{6} \). \( \frac{-11}{6} \) is a ratio of two integers with non-zero denominator. So it is a rational real number.
Step 3
Exam Tip
\( \frac{-11}{6} \) दो पूर्णांकों का अनुपात है और हर शून्य नहीं है। इसलिए यह परिमेय वास्तविक संख्या है।
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कौन सी संख्या अपरिमेय वास्तविक संख्या है?
Which number is an irrational real number?
#real numbers
#irrational
#square root
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A \( \frac{13}{5} \)
B ( -4 )
C \( \sqrt{17} \)
D (0.75)
Explanation opens after your attempt
Correct Answer
C. \( \sqrt{17} \)
Step 1
Concept
(17) is not a perfect square, so \( \sqrt{17} \) is irrational. Still, it is a real number.
Step 2
Why this answer is correct
The correct answer is C. \( \sqrt{17} \). (17) is not a perfect square, so \( \sqrt{17} \) is irrational. Still, it is a real number.
Step 3
Exam Tip
(17) पूर्ण वर्ग नहीं है इसलिए \( \sqrt{17} \) अपरिमेय है। फिर भी यह वास्तविक संख्या है।
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\( \sqrt{32} \) का सरल रूप क्या है?
What is the simplified form of \( \sqrt{32} \)?
#real numbers
#surd simplification
#radicals
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A \(2\sqrt{8}\)
B \(8\sqrt{2}\)
C \(4\sqrt{2}\)
D \(16\sqrt{2}\)
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Correct Answer
C. \(4\sqrt{2}\)
Step 1
Concept
Since \(32=16\times2\), \( \sqrt{32}=4\sqrt{2} \). Choose the largest perfect-square factor.
Step 2
Why this answer is correct
The correct answer is C. \(4\sqrt{2}\). Since \(32=16\times2\), \( \sqrt{32}=4\sqrt{2} \). Choose the largest perfect-square factor.
Step 3
Exam Tip
\(32=16\times2\) इसलिए \( \sqrt{32}=4\sqrt{2} \)। सबसे बड़ा पूर्ण वर्ग गुणनखंड चुनें।
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\( \sqrt{45} \) को सरल करने पर क्या मिलेगा?
What is obtained by simplifying \( \sqrt{45} \)?
#real numbers
#surd simplification
#class 9
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A \(3\sqrt{5}\)
B \(5\sqrt{3}\)
C \(9\sqrt{5}\)
D (15)
Explanation opens after your attempt
Correct Answer
A. \(3\sqrt{5}\)
Step 1
Concept
Since \(45=9\times5\), \( \sqrt{45}=3\sqrt{5} \). Take the perfect square outside the square root.
Step 2
Why this answer is correct
The correct answer is A. \(3\sqrt{5}\). Since \(45=9\times5\), \( \sqrt{45}=3\sqrt{5} \). Take the perfect square outside the square root.
Step 3
Exam Tip
\(45=9\times5\) इसलिए \( \sqrt{45}=3\sqrt{5} \)। वर्गमूल में पूर्ण वर्ग को बाहर निकालें।
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\( \sqrt{75} \) का सरल रूप कौन सा है?
Which is the simplified form of \( \sqrt{75} \)?
#real numbers
#radicals
#simplification
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A \(25\sqrt{3}\)
B \(5\sqrt{3}\)
C \(3\sqrt{5}\)
D \(15\sqrt{5}\)
Explanation opens after your attempt
Correct Answer
B. \(5\sqrt{3}\)
Step 1
Concept
Since \(75=25\times3\), \( \sqrt{75}=5\sqrt{3} \). Identifying perfect-square factors is important.
Step 2
Why this answer is correct
The correct answer is B. \(5\sqrt{3}\). Since \(75=25\times3\), \( \sqrt{75}=5\sqrt{3} \). Identifying perfect-square factors is important.
Step 3
Exam Tip
\(75=25\times3\) इसलिए \( \sqrt{75}=5\sqrt{3} \)। पूर्ण वर्ग गुणनखंड पहचानना जरूरी है।
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\( \sqrt{2}\times\sqrt{18} \) का मान क्या है?
What is the value of \( \sqrt{2}\times\sqrt{18} \)?
#real numbers
#surd multiplication
#square root
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A (6)
B \( \sqrt{20} \)
C \(2\sqrt{18}\)
D (9)
Explanation opens after your attempt
Step 1
Concept
\( \sqrt{2}\times\sqrt{18}=\sqrt{36}=6 \). In multiplication, multiply the numbers inside square roots.
Step 2
Why this answer is correct
The correct answer is A. (6). \( \sqrt{2}\times\sqrt{18}=\sqrt{36}=6 \). In multiplication, multiply the numbers inside square roots.
Step 3
Exam Tip
\( \sqrt{2}\times\sqrt{18}=\sqrt{36}=6 \)। गुणा में वर्गमूल के अंदर की संख्याएँ गुणा करें।
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\( \sqrt{48}\div\sqrt{3} \) का मान क्या है?
What is the value of \( \sqrt{48}\div\sqrt{3} \)?
#real numbers
#surd division
#class 9
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A (2)
B (4)
C (8)
D (16)
Explanation opens after your attempt
Step 1
Concept
\( \frac{\sqrt{48}}{\sqrt{3}}=\sqrt{16}=4 \). In division of square roots, divide the numbers inside.
Step 2
Why this answer is correct
The correct answer is B. (4). \( \frac{\sqrt{48}}{\sqrt{3}}=\sqrt{16}=4 \). In division of square roots, divide the numbers inside.
Step 3
Exam Tip
\( \frac{\sqrt{48}}{\sqrt{3}}=\sqrt{16}=4 \)। वर्गमूल के भाग में अंदर की संख्याओं का भाग लें।
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\(2\sqrt{5}+3\sqrt{5}\) का सरल रूप क्या है?
What is the simplified form of \(2\sqrt{5}+3\sqrt{5}\)?
#real numbers
#like surds
#addition
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A \(5\sqrt{5}\)
B \(6\sqrt{5}\)
C \(5\sqrt{10}\)
D \( \sqrt{25} \)
Explanation opens after your attempt
Correct Answer
A. \(5\sqrt{5}\)
Step 1
Concept
Coefficients of like surd terms are added. So \(2\sqrt{5}+3\sqrt{5}=5\sqrt{5}\).
Step 2
Why this answer is correct
The correct answer is A. \(5\sqrt{5}\). Coefficients of like surd terms are added. So \(2\sqrt{5}+3\sqrt{5}=5\sqrt{5}\).
Step 3
Exam Tip
समान करणी पदों के गुणांक जोड़े जाते हैं। इसलिए \(2\sqrt{5}+3\sqrt{5}=5\sqrt{5}\)।
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\(7\sqrt{3}-2\sqrt{3}\) का सरल रूप क्या है?
What is the simplified form of \(7\sqrt{3}-2\sqrt{3}\)?
#real numbers
#like surds
#subtraction
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A \(9\sqrt{3}\)
B \(5\sqrt{3}\)
C \(5\sqrt{6}\)
D \( \sqrt{21} \)
Explanation opens after your attempt
Correct Answer
B. \(5\sqrt{3}\)
Step 1
Concept
In like surd terms, coefficients are subtracted. Hence \(7\sqrt{3}-2\sqrt{3}=5\sqrt{3}\).
Step 2
Why this answer is correct
The correct answer is B. \(5\sqrt{3}\). In like surd terms, coefficients are subtracted. Hence \(7\sqrt{3}-2\sqrt{3}=5\sqrt{3}\).
Step 3
Exam Tip
समान करणी पदों में गुणांक घटते हैं। इसलिए \(7\sqrt{3}-2\sqrt{3}=5\sqrt{3}\)।
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\( \sqrt{27}+\sqrt{12} \) का सरल रूप क्या है?
What is the simplified form of \( \sqrt{27}+\sqrt{12} \)?
#real numbers
#surd addition
#simplification
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A \(5\sqrt{3}\)
B \( \sqrt{39} \)
C \(3\sqrt{15}\)
D (15)
Explanation opens after your attempt
Correct Answer
A. \(5\sqrt{3}\)
Step 1
Concept
\( \sqrt{27}=3\sqrt{3} \) and \( \sqrt{12}=2\sqrt{3} \). So the sum is \(5\sqrt{3}\).
Step 2
Why this answer is correct
The correct answer is A. \(5\sqrt{3}\). \( \sqrt{27}=3\sqrt{3} \) and \( \sqrt{12}=2\sqrt{3} \). So the sum is \(5\sqrt{3}\).
Step 3
Exam Tip
\( \sqrt{27}=3\sqrt{3} \) और \( \sqrt{12}=2\sqrt{3} \) हैं। इसलिए योग \(5\sqrt{3}\) है।
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कौन सा विकल्प सही है?
Which option is correct?
#real numbers
#square root
#common error
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A \( \sqrt{4}+\sqrt{9}=\sqrt{13} \)
B \( \sqrt{4}+\sqrt{9}=5 \)
C \( \sqrt{4}+\sqrt{9}=13 \)
D \( \sqrt{4}+\sqrt{9}=6 \)
Explanation opens after your attempt
Correct Answer
B. \( \sqrt{4}+\sqrt{9}=5 \)
Step 1
Concept
\( \sqrt{4}=2 \) and \( \sqrt{9}=3 \), so the sum is (5). Do not add square roots directly inside.
Step 2
Why this answer is correct
The correct answer is B. \( \sqrt{4}+\sqrt{9}=5 \). \( \sqrt{4}=2 \) and \( \sqrt{9}=3 \), so the sum is (5). Do not add square roots directly inside.
Step 3
Exam Tip
\( \sqrt{4}=2 \) और \( \sqrt{9}=3 \) इसलिए योग (5) है। वर्गमूलों को सीधे अंदर जोड़ना गलत है।
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\( \sqrt{5} \) का वर्ग क्या है?
What is the square of \( \sqrt{5} \)?
#real numbers
#square of square root
#class 9
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A \( \sqrt{25} \)
B (10)
C (5)
D (25)
Explanation opens after your attempt
Step 1
Concept
( \(\sqrt{5}\)2 =5 ). The square of the square root of a positive number gives the same number.
Step 2
Why this answer is correct
The correct answer is C. (5). ( \(\sqrt{5}\)2 =5 ). The square of the square root of a positive number gives the same number.
Step 3
Exam Tip
( \(\sqrt{5}\)2 =5 ) होता है। किसी धनात्मक संख्या के वर्गमूल का वर्ग वही संख्या देता है।
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\( \sqrt{14} \) किस दो पूर्णांकों के बीच स्थित है?
Between which two integers is \( \sqrt{14} \) located?
#real numbers
#estimation
#number line
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A (1) और (2) / (1) and (2)
B (2) और (3) / (2) and (3)
C (3) और (4) / (3) and (4)
D (4) और (5) / (4) and (5)
Explanation opens after your attempt
Correct Answer
C. (3) और (4) / (3) and (4)
Step 1
Concept
\(3^2=9\) and \(4^2=16\), so \( \sqrt{14} \) lies between (3) and (4). Check the nearest perfect squares.
Step 2
Why this answer is correct
The correct answer is C. (3) और (4) / (3) and (4). \(3^2=9\) and \(4^2=16\), so \( \sqrt{14} \) lies between (3) and (4). Check the nearest perfect squares.
Step 3
Exam Tip
\(3^2=9\) और \(4^2=16\) है इसलिए \( \sqrt{14} \) (3) और (4) के बीच है। निकटतम पूर्ण वर्ग देखें।
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कौन सी संख्या (5) और (6) के बीच है?
Which number lies between (5) and (6)?
#real numbers
#square root interval
#estimation
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A \( \sqrt{24} \)
B \( \sqrt{30} \)
C \( \sqrt{37} \)
D \( \sqrt{50} \)
Explanation opens after your attempt
Correct Answer
B. \( \sqrt{30} \)
Step 1
Concept
\(5^2=25\) and \(6^2=36\), so \( \sqrt{30} \) lies between (5) and (6). Compare squares.
Step 2
Why this answer is correct
The correct answer is B. \( \sqrt{30} \). \(5^2=25\) and \(6^2=36\), so \( \sqrt{30} \) lies between (5) and (6). Compare squares.
Step 3
Exam Tip
\(5^2=25\) और \(6^2=36\) है इसलिए \( \sqrt{30} \) (5) और (6) के बीच है। वर्गों की तुलना करें।
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\( -\sqrt{9} \) का मान क्या है?
What is the value of \( -\sqrt{9} \)?
#real numbers
#negative square root
#value
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A (3)
B ( -3 )
C (9)
D ( -9 )
Explanation opens after your attempt
Step 1
Concept
\( \sqrt{9}=3 \), so \( -\sqrt{9}=-3 \). Apply the outside negative sign at the end.
Step 2
Why this answer is correct
The correct answer is B. ( -3 ). \( \sqrt{9}=3 \), so \( -\sqrt{9}=-3 \). Apply the outside negative sign at the end.
Step 3
Exam Tip
\( \sqrt{9}=3 \) है इसलिए \( -\sqrt{9}=-3 \)। बाहर का ऋण चिह्न अंत में लगाएँ।
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( | -12 | ) का मान क्या है?
What is the value of ( | -12 | )?
#real numbers
#absolute value
#distance
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A ( -12 )
B (0)
C (12)
D (24)
Explanation opens after your attempt
Step 1
Concept
Absolute value shows the distance of a number from (0). Therefore ( | -12 |=12 ).
Step 2
Why this answer is correct
The correct answer is C. (12). Absolute value shows the distance of a number from (0). Therefore ( | -12 |=12 ).
Step 3
Exam Tip
निरपेक्ष मान संख्या की (0) से दूरी बताता है। इसलिए ( | -12 |=12 )।
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( |4-9| ) का मान क्या है?
What is the value of ( |4-9| )?
#real numbers
#absolute value
#calculation
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A ( -5 )
B (5)
C (13)
D (0)
Explanation opens after your attempt
Step 1
Concept
(4-9=-5) and ( |-5|=5 ). Absolute value always gives distance.
Step 2
Why this answer is correct
The correct answer is B. (5). (4-9=-5) and ( |-5|=5 ). Absolute value always gives distance.
Step 3
Exam Tip
(4-9=-5) और ( |-5|=5 )। निरपेक्ष मान हमेशा दूरी देता है।
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वास्तविक संख्या ( -0.6 ) संख्या रेखा पर कहाँ है?
Where is the real number ( -0.6 ) on the number line?
#real numbers
#number line
#negative decimal
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A (0) और (1) के बीच / Between (0) and (1)
B ( -1 ) और (0) के बीच / Between ( -1 ) and (0)
C ( -2 ) और ( -1 ) के बीच / Between ( -2 ) and ( -1)
D (1) और (2) के बीच / Between (1) and (2)
Explanation opens after your attempt
Correct Answer
B. ( -1 ) और (0) के बीच / Between ( -1 ) and (0)
Step 1
Concept
( -0.6 ) is left of zero and right of ( -1 ). So it lies between ( -1 ) and (0).
Step 2
Why this answer is correct
The correct answer is B. ( -1 ) और (0) के बीच / Between ( -1 ) and (0). ( -0.6 ) is left of zero and right of ( -1 ). So it lies between ( -1 ) and (0).
Step 3
Exam Tip
( -0.6 ) शून्य से बाईं ओर और ( -1 ) से दाईं ओर है। इसलिए यह ( -1 ) और (0) के बीच है।
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(1.25) को भिन्न में बदलने पर क्या मिलेगा?
What is obtained by converting (1.25) into a fraction?
#real numbers
#decimal to fraction
#rational
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A \( \frac{5}{4} \)
B \( \frac{1}{25} \)
C \( \frac{25}{10} \)
D \( \frac{4}{5} \)
Explanation opens after your attempt
Correct Answer
A. \( \frac{5}{4} \)
Step 1
Concept
\(1.25=\frac{125}{100}=\frac{5}{4} \). Write terminating decimals using denominators that are powers of (10).
Step 2
Why this answer is correct
The correct answer is A. \( \frac{5}{4} \). \(1.25=\frac{125}{100}=\frac{5}{4} \). Write terminating decimals using denominators that are powers of (10).
Step 3
Exam Tip
\(1.25=\frac{125}{100}=\frac{5}{4} \)। समाप्त दशमलव को (10) की घात वाले हर से लिखें।
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(2.75) किस भिन्न के बराबर है?
Which fraction is equal to (2.75)?
#real numbers
#decimal conversion
#class 9
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A \( \frac{11}{4} \)
B \( \frac{7}{25} \)
C \( \frac{25}{11} \)
D \( \frac{4}{11} \)
Explanation opens after your attempt
Correct Answer
A. \( \frac{11}{4} \)
Step 1
Concept
\(2.75=\frac{275}{100}=\frac{11}{4} \). Convert the decimal into a fraction and simplify.
Step 2
Why this answer is correct
The correct answer is A. \( \frac{11}{4} \). \(2.75=\frac{275}{100}=\frac{11}{4} \). Convert the decimal into a fraction and simplify.
Step 3
Exam Tip
\(2.75=\frac{275}{100}=\frac{11}{4} \)। दशमलव को भिन्न में बदलकर सरल करें।
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\( \frac{7}{8} \) का दशमलव रूप क्या है?
What is the decimal form of \( \frac{7}{8} \)?
#real numbers
#fraction to decimal
#rational
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A (0.875)
B (0.78)
C (0.708)
D (1.875)
Explanation opens after your attempt
Correct Answer
A. (0.875)
Step 1
Concept
Dividing (7) by (8) gives (0.875). Use division to find decimal form.
Step 2
Why this answer is correct
The correct answer is A. (0.875). Dividing (7) by (8) gives (0.875). Use division to find decimal form.
Step 3
Exam Tip
(7) को (8) से भाग देने पर (0.875) मिलता है। भाग विधि से दशमलव रूप निकालें।
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\( \frac{9}{4} \) का दशमलव रूप क्या है?
What is the decimal form of \( \frac{9}{4} \)?
#real numbers
#decimal form
#fractions
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A (2.25)
B (0.94)
C (4.9)
D (1.25)
Explanation opens after your attempt
Step 1
Concept
\(9\div4=2.25\). Fractions with denominator (4) often give terminating decimals.
Step 2
Why this answer is correct
The correct answer is A. (2.25). \(9\div4=2.25\). Fractions with denominator (4) often give terminating decimals.
Step 3
Exam Tip
\(9\div4=2.25\) होता है। हर (4) वाले भिन्न अक्सर समाप्त दशमलव देते हैं।
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\(0.\overline{12}\) किस प्रकार की संख्या है?
What type of number is \(0.\overline{12}\)?
#real numbers
#repeating decimal
#rational
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A अपरिमेय संख्या / Irrational number
B परिमेय वास्तविक संख्या / Rational real number
C अपरिभाषित संख्या / Undefined number
D केवल पूर्णांक / Only integer
Explanation opens after your attempt
Correct Answer
B. परिमेय वास्तविक संख्या / Rational real number
Step 1
Concept
\(0.\overline{12}\) is a repeating decimal, so it is rational. Every rational number is also real.
Step 2
Why this answer is correct
The correct answer is B. परिमेय वास्तविक संख्या / Rational real number. \(0.\overline{12}\) is a repeating decimal, so it is rational. Every rational number is also real.
Step 3
Exam Tip
\(0.\overline{12}\) आवर्ती दशमलव है इसलिए यह परिमेय है। हर परिमेय संख्या वास्तविक भी होती है।
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किस विकल्प में केवल अपरिमेय वास्तविक संख्याएँ हैं?
Which option contains only irrational real numbers?
#real numbers
#irrational numbers
#classification
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A \( \sqrt{2} \) और \( \sqrt{8} \) / \( \sqrt{2} \) and \( \sqrt{8} \)
B (4) और \( \frac{3}{5} \) / (4) and \( \frac{3}{5} \)
C (0.5) और (2) / (0.5) and (2)
D \( \sqrt{16} \) और \( \sqrt{25} \) / \( \sqrt{16} \) and \( \sqrt{25} \)
Explanation opens after your attempt
Correct Answer
A. \( \sqrt{2} \) और \( \sqrt{8} \) / \( \sqrt{2} \) and \( \sqrt{8} \)
Step 1
Concept
\( \sqrt{2} \) and \( \sqrt{8}=2\sqrt{2} \) are both irrational. Square roots of perfect squares can be rational.
Step 2
Why this answer is correct
The correct answer is A. \( \sqrt{2} \) और \( \sqrt{8} \) / \( \sqrt{2} \) and \( \sqrt{8} \). \( \sqrt{2} \) and \( \sqrt{8}=2\sqrt{2} \) are both irrational. Square roots of perfect squares can be rational.
Step 3
Exam Tip
\( \sqrt{2} \) और \( \sqrt{8}=2\sqrt{2} \) दोनों अपरिमेय हैं। पूर्ण वर्ग के वर्गमूल परिमेय हो सकते हैं।
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किस विकल्प में केवल परिमेय वास्तविक संख्याएँ हैं?
Which option contains only rational real numbers?
#real numbers
#rational numbers
#classification
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A \( \sqrt{3} \) और (2) / \( \sqrt{3} \) and (2)
B ( -5 ) और (0.4) / ( -5 ) and (0.4)
C \( \sqrt{7} \) और \( \sqrt{11} \) / \( \sqrt{7} \) and \( \sqrt{11} \)
D \( \pi \) और (1) / \( \pi \) and (1)
Explanation opens after your attempt
Correct Answer
B. ( -5 ) और (0.4) / ( -5 ) and (0.4)
Step 1
Concept
( -5 ) is an integer and (0.4) is a terminating decimal. So both are rational real numbers.
Step 2
Why this answer is correct
The correct answer is B. ( -5 ) और (0.4) / ( -5 ) and (0.4). ( -5 ) is an integer and (0.4) is a terminating decimal. So both are rational real numbers.
Step 3
Exam Tip
( -5 ) पूर्णांक है और (0.4) समाप्त दशमलव है। इसलिए दोनों परिमेय वास्तविक संख्याएँ हैं।
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\( \sqrt{2}+\sqrt{8} \) का सरल रूप क्या है?
What is the simplified form of \( \sqrt{2}+\sqrt{8} \)?
#real numbers
#surd addition
#like radicals
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A \(3\sqrt{2}\)
B \( \sqrt{10} \)
C \(2\sqrt{10}\)
D \(4\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. \(3\sqrt{2}\)
Step 1
Concept
\( \sqrt{8}=2\sqrt{2} \), so \( \sqrt{2}+2\sqrt{2}=3\sqrt{2} \). Simplify surds first.
Step 2
Why this answer is correct
The correct answer is A. \(3\sqrt{2}\). \( \sqrt{8}=2\sqrt{2} \), so \( \sqrt{2}+2\sqrt{2}=3\sqrt{2} \). Simplify surds first.
Step 3
Exam Tip
\( \sqrt{8}=2\sqrt{2} \) इसलिए \( \sqrt{2}+2\sqrt{2}=3\sqrt{2} \)। पहले करणी को सरल करें।
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\( \sqrt{50}-\sqrt{18} \) का सरल रूप क्या है?
What is the simplified form of \( \sqrt{50}-\sqrt{18} \)?
#real numbers
#surd subtraction
#simplification
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A \(2\sqrt{2}\)
B \(5\sqrt{2}\)
C \(8\sqrt{2}\)
D \( \sqrt{32} \)
Explanation opens after your attempt
Correct Answer
A. \(2\sqrt{2}\)
Step 1
Concept
\( \sqrt{50}=5\sqrt{2} \) and \( \sqrt{18}=3\sqrt{2} \). The difference is \(2\sqrt{2}\).
Step 2
Why this answer is correct
The correct answer is A. \(2\sqrt{2}\). \( \sqrt{50}=5\sqrt{2} \) and \( \sqrt{18}=3\sqrt{2} \). The difference is \(2\sqrt{2}\).
Step 3
Exam Tip
\( \sqrt{50}=5\sqrt{2} \) और \( \sqrt{18}=3\sqrt{2} \) हैं। अंतर \(2\sqrt{2}\) है।
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\( \frac{1}{\sqrt{5}} \) का हर परिमेय करने पर क्या मिलेगा?
What is obtained by rationalising the denominator of \( \frac{1}{\sqrt{5}} \)?
#real numbers
#rationalisation
#denominator
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A \( \frac{\sqrt{5}}{5} \)
B \( \sqrt{5} \)
C \( \frac{5}{\sqrt{5}} \)
D \( \frac{1}{5} \)
Explanation opens after your attempt
Correct Answer
A. \( \frac{\sqrt{5}}{5} \)
Step 1
Concept
Multiply numerator and denominator by \( \sqrt{5} \). This gives \( \frac{1}{\sqrt{5}}=\frac{\sqrt{5}}{5} \).
Step 2
Why this answer is correct
The correct answer is A. \( \frac{\sqrt{5}}{5} \). Multiply numerator and denominator by \( \sqrt{5} \). This gives \( \frac{1}{\sqrt{5}}=\frac{\sqrt{5}}{5} \).
Step 3
Exam Tip
अंश और हर को \( \sqrt{5} \) से गुणा करें। इससे \( \frac{1}{\sqrt{5}}=\frac{\sqrt{5}}{5} \) मिलता है।
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\( \frac{2}{\sqrt{3}} \) का परिमेय हर वाला रूप क्या है?
What is the form of \( \frac{2}{\sqrt{3}} \) with rational denominator?
#real numbers
#rationalisation
#surds
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A \( \frac{2\sqrt{3}}{3} \)
B \( \frac{\sqrt{3}}{2} \)
C \( \frac{2}{3} \)
D \(2\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
A. \( \frac{2\sqrt{3}}{3} \)
Step 1
Concept
To rationalise the denominator, multiply numerator and denominator by \( \sqrt{3} \). The answer is \( \frac{2\sqrt{3}}{3} \).
Step 2
Why this answer is correct
The correct answer is A. \( \frac{2\sqrt{3}}{3} \). To rationalise the denominator, multiply numerator and denominator by \( \sqrt{3} \). The answer is \( \frac{2\sqrt{3}}{3} \).
Step 3
Exam Tip
हर को परिमेय करने के लिए अंश और हर को \( \sqrt{3} \) से गुणा करें। उत्तर \( \frac{2\sqrt{3}}{3} \) है।
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\( \sqrt{2} \) और \( \sqrt{3} \) में कौन बड़ी है?
Which is greater between \( \sqrt{2} \) and \( \sqrt{3} \)?
#real numbers
#comparison
#square roots
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A \( \sqrt{2} \)
B \( \sqrt{3} \)
C दोनों बराबर / Both are equal
D दोनों वास्तविक नहीं हैं / Both are not real
Explanation opens after your attempt
Correct Answer
B. \( \sqrt{3} \)
Step 1
Concept
For positive numbers, the square root of the greater number is greater. Since (3>2), \( \sqrt{3}>\sqrt{2} \).
Step 2
Why this answer is correct
The correct answer is B. \( \sqrt{3} \). For positive numbers, the square root of the greater number is greater. Since (3>2), \( \sqrt{3}>\sqrt{2} \).
Step 3
Exam Tip
धनात्मक संख्याओं में बड़ी संख्या का वर्गमूल बड़ा होता है। (3>2) इसलिए \( \sqrt{3}>\sqrt{2} \)।
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\( \sqrt{23} \) और (5) में कौन छोटी है?
Which is smaller between \( \sqrt{23} \) and (5)?
#real numbers
#ordering
#estimation
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A (5)
B दोनों बराबर / Both are equal
C \( \sqrt{23} \)
D निर्धारित नहीं / Cannot be determined
Explanation opens after your attempt
Correct Answer
C. \( \sqrt{23} \)
Step 1
Concept
\( \sqrt{23}<\sqrt{25}=5 \). Therefore \( \sqrt{23} \) is smaller.
Step 2
Why this answer is correct
The correct answer is C. \( \sqrt{23} \). \( \sqrt{23}<\sqrt{25}=5 \). Therefore \( \sqrt{23} \) is smaller.
Step 3
Exam Tip
\( \sqrt{23}<\sqrt{25}=5 \) है। इसलिए \( \sqrt{23} \) छोटी है।
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\( -\sqrt{5} \) और ( -2 ) में कौन बड़ी संख्या है?
Which is greater between \( -\sqrt{5} \) and ( -2 )?
#real numbers
#negative comparison
#number line
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A \( -\sqrt{5} \)
B ( -2 )
C दोनों बराबर / Both are equal
D दोनों धनात्मक / Both are positive
Explanation opens after your attempt
Step 1
Concept
\( \sqrt{5}\approx2.236 \), so \( -\sqrt{5}\approx -2.236 \). ( -2 ) is closer to zero, so it is greater.
Step 2
Why this answer is correct
The correct answer is B. ( -2 ). \( \sqrt{5}\approx2.236 \), so \( -\sqrt{5}\approx -2.236 \). ( -2 ) is closer to zero, so it is greater.
Step 3
Exam Tip
\( \sqrt{5}\approx2.236 \) इसलिए \( -\sqrt{5}\approx -2.236 \) है। ( -2 ) शून्य के अधिक निकट है इसलिए बड़ी है।
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\( \frac{3}{4} \) और \( \sqrt{1} \) में कौन बड़ी है?
Which is greater between \( \frac{3}{4} \) and \( \sqrt{1} \)?
#real numbers
#comparison
#rational
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A \( \frac{3}{4} \)
B \( \sqrt{1} \)
C दोनों बराबर / Both are equal
D निर्धारित नहीं / Cannot be determined
Explanation opens after your attempt
Correct Answer
B. \( \sqrt{1} \)
Step 1
Concept
\( \sqrt{1}=1 \) and \( \frac{3}{4}=0.75 \). Therefore \( \sqrt{1} \) is greater.
Step 2
Why this answer is correct
The correct answer is B. \( \sqrt{1} \). \( \sqrt{1}=1 \) and \( \frac{3}{4}=0.75 \). Therefore \( \sqrt{1} \) is greater.
Step 3
Exam Tip
\( \sqrt{1}=1 \) और \( \frac{3}{4}=0.75 \) है। इसलिए \( \sqrt{1} \) बड़ी है।
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किसी भी दो अलग-अलग वास्तविक संख्याओं के बीच कितनी परिमेय संख्याएँ होती हैं?
How many rational numbers are there between any two distinct real numbers?
#real numbers
#density
#rational numbers
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A केवल (1) / Only (1)
B केवल (2) / Only (2)
C अनंत / Infinitely many
D कोई नहीं / None
Explanation opens after your attempt
Correct Answer
C. अनंत / Infinitely many
Step 1
Concept
There are infinitely many rational numbers between two distinct real numbers. This is a simple form of the density property.
Step 2
Why this answer is correct
The correct answer is C. अनंत / Infinitely many. There are infinitely many rational numbers between two distinct real numbers. This is a simple form of the density property.
Step 3
Exam Tip
दो अलग-अलग वास्तविक संख्याओं के बीच अनंत परिमेय संख्याएँ होती हैं। यह घनत्व गुण का सरल रूप है।
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(1) और (2) के बीच एक अपरिमेय संख्या कौन सी है?
Which is an irrational number between (1) and (2)?
#real numbers
#irrational between
#number line
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A \( \frac{3}{2} \)
B \( \sqrt{2} \)
C (2)
D (1)
Explanation opens after your attempt
Correct Answer
B. \( \sqrt{2} \)
Step 1
Concept
\(1<\sqrt{2}<2\) and \( \sqrt{2} \) is irrational. Its position is found by comparing squares.
Step 2
Why this answer is correct
The correct answer is B. \( \sqrt{2} \). \(1<\sqrt{2}<2\) and \( \sqrt{2} \) is irrational. Its position is found by comparing squares.
Step 3
Exam Tip
\(1<\sqrt{2}<2\) और \( \sqrt{2} \) अपरिमेय है। वर्गों की तुलना से इसका स्थान पता चलता है।
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(2) और (3) के बीच एक अपरिमेय संख्या कौन सी है?
Which is an irrational number between (2) and (3)?
#real numbers
#irrational number
#interval
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A \( \sqrt{6} \)
B \( \frac{5}{2} \)
C (2.5)
D (3)
Explanation opens after your attempt
Correct Answer
A. \( \sqrt{6} \)
Step 1
Concept
Since \(2^2<6<3^2\), \( \sqrt{6} \) lies between (2) and (3). Since (6) is not a perfect square, it is irrational.
Step 2
Why this answer is correct
The correct answer is A. \( \sqrt{6} \). Since \(2^2<6<3^2\), \( \sqrt{6} \) lies between (2) and (3). Since (6) is not a perfect square, it is irrational.
Step 3
Exam Tip
\(2^2<6<3^2\) इसलिए \( \sqrt{6} \) (2) और (3) के बीच है। (6) पूर्ण वर्ग नहीं है इसलिए यह अपरिमेय है।
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\( \sqrt{0.04} \) का मान क्या है?
What is the value of \( \sqrt{0.04} \)?
#real numbers
#decimal square root
#class 9
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A (0.02)
B (0.2)
C (2)
D (0.4)
Explanation opens after your attempt
Step 1
Concept
\(0.2^2=0.04\), so \( \sqrt{0.04}=0.2 \). Be careful with place value in decimal square roots.
Step 2
Why this answer is correct
The correct answer is B. (0.2). \(0.2^2=0.04\), so \( \sqrt{0.04}=0.2 \). Be careful with place value in decimal square roots.
Step 3
Exam Tip
\(0.2^2=0.04\) इसलिए \( \sqrt{0.04}=0.2 \)। दशमलव के वर्गमूल में स्थान मान ध्यान रखें।
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\( \sqrt{0.25} \) का मान क्या है?
What is the value of \( \sqrt{0.25} \)?
#real numbers
#decimal square root
#perfect square
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A (0.5)
B (0.05)
C (2.5)
D (5)
Explanation opens after your attempt
Step 1
Concept
\(0.5^2=0.25\), so \( \sqrt{0.25}=0.5 \). You can check a square root by squaring it.
Step 2
Why this answer is correct
The correct answer is A. (0.5). \(0.5^2=0.25\), so \( \sqrt{0.25}=0.5 \). You can check a square root by squaring it.
Step 3
Exam Tip
\(0.5^2=0.25\) इसलिए \( \sqrt{0.25}=0.5 \)। वर्गमूल के लिए वर्ग करके जाँच सकते हैं।
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\( \sqrt{\frac{49}{64}} \) का मान क्या है?
What is the value of \( \sqrt{\frac{49}{64}} \)?
#real numbers
#fraction square root
#class 9
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A \( \frac{7}{8} \)
B \( \frac{49}{8} \)
C \( \frac{8}{7} \)
D \( \frac{7}{64} \)
Explanation opens after your attempt
Correct Answer
A. \( \frac{7}{8} \)
Step 1
Concept
Take square roots of numerator and denominator separately. \( \sqrt{\frac{49}{64}}=\frac{7}{8} \).
Step 2
Why this answer is correct
The correct answer is A. \( \frac{7}{8} \). Take square roots of numerator and denominator separately. \( \sqrt{\frac{49}{64}}=\frac{7}{8} \).
Step 3
Exam Tip
अंश और हर के अलग-अलग वर्गमूल लें। \( \sqrt{\frac{49}{64}}=\frac{7}{8} \)।
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\( \sqrt{\frac{16}{81}} \) किसके बराबर है?
What is \( \sqrt{\frac{16}{81}} \) equal to?
#real numbers
#square root fraction
#perfect squares
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A \( \frac{4}{9} \)
B \( \frac{8}{9} \)
C \( \frac{16}{9} \)
D \( \frac{4}{81} \)
Explanation opens after your attempt
Correct Answer
A. \( \frac{4}{9} \)
Step 1
Concept
\( \sqrt{16}=4 \) and \( \sqrt{81}=9 \). Therefore the answer is \( \frac{4}{9} \).
Step 2
Why this answer is correct
The correct answer is A. \( \frac{4}{9} \). \( \sqrt{16}=4 \) and \( \sqrt{81}=9 \). Therefore the answer is \( \frac{4}{9} \).
Step 3
Exam Tip
\( \sqrt{16}=4 \) और \( \sqrt{81}=9 \) है। इसलिए उत्तर \( \frac{4}{9} \) है।
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( \(2+\sqrt{3}\) ) किस प्रकार की संख्या है?
What type of number is ( \(2+\sqrt{3}\) )?
#real numbers
#irrational sum
#classification
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A परिमेय संख्या / Rational number
B अपरिमेय वास्तविक संख्या / Irrational real number
C पूर्णांक / Integer
D प्राकृतिक संख्या / Natural number
Explanation opens after your attempt
Correct Answer
B. अपरिमेय वास्तविक संख्या / Irrational real number
Step 1
Concept
Adding irrational \( \sqrt{3} \) to rational (2) gives an irrational number. It is also a real number.
Step 2
Why this answer is correct
The correct answer is B. अपरिमेय वास्तविक संख्या / Irrational real number. Adding irrational \( \sqrt{3} \) to rational (2) gives an irrational number. It is also a real number.
Step 3
Exam Tip
परिमेय (2) में अपरिमेय \( \sqrt{3} \) जोड़ने पर अपरिमेय संख्या मिलती है। यह वास्तविक संख्या भी है।
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( \(5-\sqrt{2}\) ) किस प्रकार की संख्या है?
What type of number is ( \(5-\sqrt{2}\) )?
#real numbers
#irrational difference
#class 9
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A अपरिमेय वास्तविक संख्या / Irrational real number
B परिमेय संख्या / Rational number
C पूर्ण संख्या / Whole number
D शून्य / Zero
Explanation opens after your attempt
Correct Answer
A. अपरिमेय वास्तविक संख्या / Irrational real number
Step 1
Concept
Subtracting an irrational number from a rational number gives an irrational result. Thus \(5-\sqrt{2}\) is an irrational real number.
Step 2
Why this answer is correct
The correct answer is A. अपरिमेय वास्तविक संख्या / Irrational real number. Subtracting an irrational number from a rational number gives an irrational result. Thus \(5-\sqrt{2}\) is an irrational real number.
Step 3
Exam Tip
परिमेय संख्या में अपरिमेय संख्या घटाने पर परिणाम अपरिमेय होता है। इसलिए \(5-\sqrt{2}\) अपरिमेय वास्तविक संख्या है।
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\( \sqrt{7}\times\sqrt{7} \) का मान क्या है?
What is the value of \( \sqrt{7}\times\sqrt{7} \)?
#real numbers
#surd multiplication
#square root
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A \( \sqrt{14} \)
B (14)
C (7)
D (49)
Explanation opens after your attempt
Step 1
Concept
Multiplying the same square root by itself gives the number inside. Therefore \( \sqrt{7}\times\sqrt{7}=7 \).
Step 2
Why this answer is correct
The correct answer is C. (7). Multiplying the same square root by itself gives the number inside. Therefore \( \sqrt{7}\times\sqrt{7}=7 \).
Step 3
Exam Tip
एक ही वर्गमूल को स्वयं से गुणा करने पर अंदर की संख्या मिलती है। इसलिए \( \sqrt{7}\times\sqrt{7}=7 \)।
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\( \sqrt{40} \) को किस सरल करणी रूप में लिखा जाएगा?
In which simplified surd form will \( \sqrt{40} \) be written?
#real numbers
#surd form
#simplification
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A \(2\sqrt{10}\)
B \(4\sqrt{10}\)
C \(10\sqrt{4}\)
D \(20\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. \(2\sqrt{10}\)
Step 1
Concept
Since \(40=4\times10\), \( \sqrt{40}=2\sqrt{10} \). Take the perfect square (4) outside.
Step 2
Why this answer is correct
The correct answer is A. \(2\sqrt{10}\). Since \(40=4\times10\), \( \sqrt{40}=2\sqrt{10} \). Take the perfect square (4) outside.
Step 3
Exam Tip
\(40=4\times10\) इसलिए \( \sqrt{40}=2\sqrt{10} \)। पूर्ण वर्ग (4) को बाहर निकालें।
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