वास्तविक संख्याएँ किससे मिलकर बनती हैं?
Real numbers are made up of which numbers?
#real numbers
#class 9
#number system
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A केवल प्राकृतिक संख्याएँ / Only natural numbers
B केवल पूर्णांक / Only integers
C परिमेय और अपरिमेय संख्याएँ / Rational and irrational numbers
D केवल ऋणात्मक संख्याएँ / Only negative numbers
Explanation opens after your attempt
Correct Answer
C. परिमेय और अपरिमेय संख्याएँ / Rational and irrational numbers
Step 1
Concept
Real numbers include both rational and irrational numbers. In exams remember the whole number system on the real number line.
Step 2
Why this answer is correct
The correct answer is C. परिमेय और अपरिमेय संख्याएँ / Rational and irrational numbers. Real numbers include both rational and irrational numbers. In exams remember the whole number system on the real number line.
Step 3
Exam Tip
वास्तविक संख्याओं में परिमेय और अपरिमेय दोनों संख्याएँ आती हैं। परीक्षा में वास्तविक संख्या रेखा की पूरी संख्या प्रणाली याद रखें।
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इनमें से कौन सी संख्या वास्तविक संख्या है?
Which of the following is a real number?
#real numbers
#class 9
#irrational
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A \( \sqrt{5} \)
B केवल कल्पित संख्या / Only imaginary number
C अपरिभाषित संख्या / Undefined number
D हर में शून्य वाला भिन्न / Fraction with zero denominator
Explanation opens after your attempt
Correct Answer
A. \( \sqrt{5} \)
Step 1
Concept
\( \sqrt{5} \) is irrational and every irrational number is real. It can be shown on the real number line.
Step 2
Why this answer is correct
The correct answer is A. \( \sqrt{5} \). \( \sqrt{5} \) is irrational and every irrational number is real. It can be shown on the real number line.
Step 3
Exam Tip
\( \sqrt{5} \) अपरिमेय है और हर अपरिमेय संख्या वास्तविक होती है। वास्तविक संख्या रेखा पर इसे दिखाया जा सकता है।
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कौन सा कथन सही है?
Which statement is correct?
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#subset
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A हर वास्तविक संख्या प्राकृतिक संख्या होती है / Every real number is a natural number
B हर प्राकृतिक संख्या वास्तविक संख्या होती है / Every natural number is a real number
C हर अपरिमेय संख्या पूर्णांक होती है / Every irrational number is an integer
D हर पूर्णांक अपरिमेय होता है / Every integer is irrational
Explanation opens after your attempt
Correct Answer
B. हर प्राकृतिक संख्या वास्तविक संख्या होती है / Every natural number is a real number
Step 1
Concept
Natural numbers are a part of real numbers. Smaller sets can be included in a larger number system.
Step 2
Why this answer is correct
The correct answer is B. हर प्राकृतिक संख्या वास्तविक संख्या होती है / Every natural number is a real number. Natural numbers are a part of real numbers. Smaller sets can be included in a larger number system.
Step 3
Exam Tip
प्राकृतिक संख्याएँ वास्तविक संख्याओं का भाग हैं। बड़ी संख्या प्रणाली में छोटे समूह शामिल हो सकते हैं।
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\( \sqrt{16} \) किस प्रकार की वास्तविक संख्या है?
What type of real number is \( \sqrt{16} \)?
#real numbers
#class 9
#square root
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A अपरिमेय संख्या / Irrational number
B परिमेय संख्या / Rational number
C न वास्तविक संख्या / Not a real number
D अपरिभाषित संख्या / Undefined number
Explanation opens after your attempt
Correct Answer
B. परिमेय संख्या / Rational number
Step 1
Concept
\( \sqrt{16}=4 \), and (4) is rational. The square root of a perfect square is rational.
Step 2
Why this answer is correct
The correct answer is B. परिमेय संख्या / Rational number. \( \sqrt{16}=4 \), and (4) is rational. The square root of a perfect square is rational.
Step 3
Exam Tip
\( \sqrt{16}=4 \) है और (4) परिमेय संख्या है। पूर्ण वर्ग का वर्गमूल परिमेय होता है।
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\( \sqrt{7} \) के बारे में सही विकल्प चुनिए।
Choose the correct option about \( \sqrt{7} \).
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#irrational square root
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A यह पूर्णांक है / It is an integer
B यह परिमेय संख्या है / It is a rational number
C यह वास्तविक नहीं है / It is not real
D यह अपरिमेय वास्तविक संख्या है / It is an irrational real number
Explanation opens after your attempt
Correct Answer
D. यह अपरिमेय वास्तविक संख्या है / It is an irrational real number
Step 1
Concept
(7) is not a perfect square, so \( \sqrt{7} \) is irrational. Still, it is a real number.
Step 2
Why this answer is correct
The correct answer is D. यह अपरिमेय वास्तविक संख्या है / It is an irrational real number. (7) is not a perfect square, so \( \sqrt{7} \) is irrational. Still, it is a real number.
Step 3
Exam Tip
(7) पूर्ण वर्ग नहीं है इसलिए \( \sqrt{7} \) अपरिमेय है। फिर भी यह वास्तविक संख्या है।
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कौन सी संख्या परिमेय वास्तविक संख्या है?
Which number is a rational real number?
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#rational real
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A \( \frac{-3}{8} \)
B \( \sqrt{11} \)
C \( \sqrt{13} \)
D असमाप्त अनावर्ती दशमलव / Non-terminating non-repeating decimal
Explanation opens after your attempt
Correct Answer
A. \( \frac{-3}{8} \)
Step 1
Concept
\( \frac{-3}{8} \) is a ratio of two integers with non-zero denominator. So it is both rational and real.
Step 2
Why this answer is correct
The correct answer is A. \( \frac{-3}{8} \). \( \frac{-3}{8} \) is a ratio of two integers with non-zero denominator. So it is both rational and real.
Step 3
Exam Tip
\( \frac{-3}{8} \) दो पूर्णांकों का अनुपात है और हर शून्य नहीं है। इसलिए यह परिमेय और वास्तविक दोनों है।
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(0.625) किस प्रकार की वास्तविक संख्या है?
What type of real number is (0.625)?
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#class 9
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A अपरिमेय संख्या / Irrational number
B परिमेय संख्या / Rational number
C न वास्तविक संख्या / Not a real number
D केवल कल्पित संख्या / Only imaginary number
Explanation opens after your attempt
Correct Answer
B. परिमेय संख्या / Rational number
Step 1
Concept
(0.625) is a terminating decimal, so it can be converted into a fraction. Terminating decimals are rational.
Step 2
Why this answer is correct
The correct answer is B. परिमेय संख्या / Rational number. (0.625) is a terminating decimal, so it can be converted into a fraction. Terminating decimals are rational.
Step 3
Exam Tip
(0.625) समाप्त दशमलव है इसलिए इसे भिन्न में बदला जा सकता है। समाप्त दशमलव परिमेय होते हैं।
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\(0.\overline{6}\) किस प्रकार की संख्या है?
What type of number is \(0.\overline{6}\)?
#real numbers
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A अपरिमेय संख्या / Irrational number
B प्राकृतिक संख्या / Natural number
C परिमेय वास्तविक संख्या / Rational real number
D अपरिभाषित संख्या / Undefined number
Explanation opens after your attempt
Correct Answer
C. परिमेय वास्तविक संख्या / Rational real number
Step 1
Concept
\(0.\overline{6}\) 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 C. परिमेय वास्तविक संख्या / Rational real number. \(0.\overline{6}\) is a repeating decimal, so it is rational. Every rational number is also real.
Step 3
Exam Tip
\(0.\overline{6}\) आवर्ती दशमलव है इसलिए यह परिमेय है। हर परिमेय संख्या वास्तविक भी होती है।
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असमाप्त और अनावर्ती दशमलव किस प्रकार की संख्या होती है?
A non-terminating and non-repeating decimal is what type of number?
#real numbers
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#decimal type
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A परिमेय संख्या / Rational number
B अपरिमेय वास्तविक संख्या / Irrational real number
C पूर्ण संख्या / Whole number
D शून्य / Zero
Explanation opens after your attempt
Correct Answer
B. अपरिमेय वास्तविक संख्या / Irrational real number
Step 1
Concept
A non-terminating and non-repeating decimal is irrational. Still, it lies on the real number line.
Step 2
Why this answer is correct
The correct answer is B. अपरिमेय वास्तविक संख्या / Irrational real number. A non-terminating and non-repeating decimal is irrational. Still, it lies on the real number line.
Step 3
Exam Tip
असमाप्त और अनावर्ती दशमलव अपरिमेय होता है। फिर भी यह वास्तविक संख्या रेखा पर स्थित होता है।
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\( \frac{5}{0} \) वास्तविक संख्या क्यों नहीं है?
Why is \( \frac{5}{0} \) not a real number?
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#undefined
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A क्योंकि अंश धनात्मक है / Because the numerator is positive
B क्योंकि हर शून्य है / Because the denominator is zero
C क्योंकि यह भिन्न है / Because it is a fraction
D क्योंकि (5) अभाज्य है / Because (5) is prime
Explanation opens after your attempt
Correct Answer
B. क्योंकि हर शून्य है / Because the denominator is zero
Step 1
Concept
Division by zero is undefined. To be a real number, the number must be defined.
Step 2
Why this answer is correct
The correct answer is B. क्योंकि हर शून्य है / Because the denominator is zero. Division by zero is undefined. To be a real number, the number must be defined.
Step 3
Exam Tip
शून्य से भाग परिभाषित नहीं होता। वास्तविक संख्या बनने के लिए संख्या परिभाषित होनी चाहिए।
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कौन सी संख्या पूर्णांक होने के साथ वास्तविक भी है?
Which number is an integer and also real?
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#class 9
#integers
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A ( -12 )
B \( \sqrt{2} \)
C (0.37)
D \( \frac{4}{9} \)
Explanation opens after your attempt
Correct Answer
A. ( -12 )
Step 1
Concept
( -12 ) is an integer and every integer is a real number. An integer can be written as \( \frac{p}{1} \).
Step 2
Why this answer is correct
The correct answer is A. ( -12 ). ( -12 ) is an integer and every integer is a real number. An integer can be written as \( \frac{p}{1} \).
Step 3
Exam Tip
( -12 ) पूर्णांक है और हर पूर्णांक वास्तविक संख्या होता है। पूर्णांक को \( \frac{p}{1} \) के रूप में लिखा जा सकता है।
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सबसे छोटा प्राकृतिक संख्या समूह किस बड़े समूह में शामिल है?
The set of natural numbers is included in which larger set?
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#natural numbers
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A केवल अपरिमेय संख्याएँ / Only irrational numbers
B वास्तविक संख्याएँ / Real numbers
C अपरिभाषित संख्याएँ / Undefined numbers
D केवल ऋणात्मक संख्याएँ / Only negative numbers
Explanation opens after your attempt
Correct Answer
B. वास्तविक संख्याएँ / Real numbers
Step 1
Concept
Natural numbers are a subset of real numbers. Remember the number system as nested sets.
Step 2
Why this answer is correct
The correct answer is B. वास्तविक संख्याएँ / Real numbers. Natural numbers are a subset of real numbers. Remember the number system as nested sets.
Step 3
Exam Tip
प्राकृतिक संख्याएँ वास्तविक संख्याओं का उपसमूह हैं। संख्या प्रणाली को उपसमूह के रूप में याद करें।
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\( \sqrt{25} \) का वास्तविक मान क्या है?
What is the real value of \( \sqrt{25} \)?
#real numbers
#class 9
#perfect square
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A (5)
B (10)
C \( \frac{25}{2} \)
D \( \sqrt{50} \)
Explanation opens after your attempt
Step 1
Concept
\( \sqrt{25}=5 \) because \(5^2=25\). Identify square roots of perfect squares quickly.
Step 2
Why this answer is correct
The correct answer is A. (5). \( \sqrt{25}=5 \) because \(5^2=25\). Identify square roots of perfect squares quickly.
Step 3
Exam Tip
\( \sqrt{25}=5 \) क्योंकि \(5^2=25\)। पूर्ण वर्गों के वर्गमूल जल्दी पहचानें।
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कौन सी संख्या वास्तविक संख्या रेखा पर (0) और (1) के बीच आती है?
Which number lies between (0) and (1) on the real number line?
#real numbers
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#number line
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A \( \frac{7}{5} \)
B \( -\frac{1}{2} \)
C \( \frac{3}{4} \)
D (2)
Explanation opens after your attempt
Correct Answer
C. \( \frac{3}{4} \)
Step 1
Concept
\( \frac{3}{4}=0.75 \), which lies between (0) and (1). Decimal form can help in comparison.
Step 2
Why this answer is correct
The correct answer is C. \( \frac{3}{4} \). \( \frac{3}{4}=0.75 \), which lies between (0) and (1). Decimal form can help in comparison.
Step 3
Exam Tip
\( \frac{3}{4}=0.75 \) है जो (0) और (1) के बीच है। तुलना के लिए दशमलव रूप उपयोगी हो सकता है।
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( -2.5 ) संख्या रेखा पर कहाँ स्थित है?
Where is ( -2.5 ) located on the number line?
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A (2) और (3) के बीच / Between (2) and (3)
B ( -3 ) और ( -2 ) के बीच / Between ( -3 ) and ( -2 )
C (0) और (1) के बीच / Between (0) and (1)
D ( -1 ) और (0) के बीच / Between ( -1 ) and (0)
Explanation opens after your attempt
Correct Answer
B. ( -3 ) और ( -2 ) के बीच / Between ( -3 ) and ( -2 )
Step 1
Concept
( -2.5 ) is negative and lies between ( -3 ) and ( -2 ). Be careful with the left direction for negative numbers.
Step 2
Why this answer is correct
The correct answer is B. ( -3 ) और ( -2 ) के बीच / Between ( -3 ) and ( -2 ). ( -2.5 ) is negative and lies between ( -3 ) and ( -2 ). Be careful with the left direction for negative numbers.
Step 3
Exam Tip
( -2.5 ) ऋणात्मक है और ( -3 ) तथा ( -2 ) के बीच आता है। ऋणात्मक संख्याओं में बाईं दिशा ध्यान रखें।
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\( \sqrt{2} \) का अनुमानित स्थान किसके बीच है?
The approximate position of \( \sqrt{2} \) is between which numbers?
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A (0) और (1) / (0) and (1)
B (1) और (2) / (1) and (2)
C (2) और (3) / (2) and (3)
D (3) और (4) / (3) and (4)
Explanation opens after your attempt
Correct Answer
B. (1) और (2) / (1) and (2)
Step 1
Concept
Since \(1^2<2<2^2\), \( \sqrt{2} \) lies between (1) and (2). Compare squares to locate square roots.
Step 2
Why this answer is correct
The correct answer is B. (1) और (2) / (1) and (2). Since \(1^2<2<2^2\), \( \sqrt{2} \) lies between (1) and (2). Compare squares to locate square roots.
Step 3
Exam Tip
\(1^2<2<2^2\) इसलिए \( \sqrt{2} \) (1) और (2) के बीच है। वर्गों की तुलना से वर्गमूल का स्थान मिलता है।
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\( \sqrt{10} \) किस दो पूर्णांकों के बीच है?
Between which two integers does \( \sqrt{10} \) lie?
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#estimation
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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 \( \sqrt{10} \) lies between (3) and (4). First check nearby 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 \( \sqrt{10} \) lies between (3) and (4). First check nearby perfect squares.
Step 3
Exam Tip
\(3^2=9\) और \(4^2=16\) है इसलिए \( \sqrt{10} \) (3) और (4) के बीच है। पहले निकट पूर्ण वर्ग देखें।
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दो वास्तविक संख्याओं का योग हमेशा किस प्रकार की संख्या होता है?
The sum of two real numbers is always what type of number?
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#class 9
#closure addition
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A वास्तविक संख्या / Real number
B केवल प्राकृतिक संख्या / Only natural number
C केवल अपरिमेय संख्या / Only irrational number
D अपरिभाषित संख्या / Undefined number
Explanation opens after your attempt
Correct Answer
A. वास्तविक संख्या / Real number
Step 1
Concept
Real numbers are closed under addition. The sum of two real numbers is always a real number.
Step 2
Why this answer is correct
The correct answer is A. वास्तविक संख्या / Real number. Real numbers are closed under addition. The sum of two real numbers is always a real number.
Step 3
Exam Tip
वास्तविक संख्याएँ योग के लिए संवृत होती हैं। दो वास्तविक संख्याओं का योग वास्तविक संख्या ही होता है।
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दो वास्तविक संख्याओं का गुणनफल हमेशा क्या होता है?
The product of two real numbers is always what?
#real numbers
#class 9
#closure multiplication
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A केवल पूर्णांक / Only integer
B वास्तविक संख्या / Real number
C केवल परिमेय संख्या / Only rational number
D केवल शून्य / Only zero
Explanation opens after your attempt
Correct Answer
B. वास्तविक संख्या / Real number
Step 1
Concept
Real numbers are closed under multiplication. Hence their product is a real number.
Step 2
Why this answer is correct
The correct answer is B. वास्तविक संख्या / Real number. Real numbers are closed under multiplication. Hence their product is a real number.
Step 3
Exam Tip
वास्तविक संख्याएँ गुणन के लिए संवृत होती हैं। इसलिए गुणनफल वास्तविक संख्या होता है।
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\( \sqrt{3}+\sqrt{3} \) का मान क्या है?
What is the value of \( \sqrt{3}+\sqrt{3} \)?
#real numbers
#class 9
#surd addition
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A \( \sqrt{6} \)
B \(2\sqrt{3}\)
C \(3\sqrt{2}\)
D (6)
Explanation opens after your attempt
Correct Answer
B. \(2\sqrt{3}\)
Step 1
Concept
Like terms are added, so \( \sqrt{3}+\sqrt{3}=2\sqrt{3} \). Do not add numbers inside square roots directly.
Step 2
Why this answer is correct
The correct answer is B. \(2\sqrt{3}\). Like terms are added, so \( \sqrt{3}+\sqrt{3}=2\sqrt{3} \). Do not add numbers inside square roots directly.
Step 3
Exam Tip
समान पदों को जोड़ा जाता है इसलिए \( \sqrt{3}+\sqrt{3}=2\sqrt{3} \)। वर्गमूल को सीधे अंदर जोड़ना गलत है।
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\( \sqrt{9}+\sqrt{4} \) का मान क्या है?
What is the value of \( \sqrt{9}+\sqrt{4} \)?
#real numbers
#class 9
#square roots
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A (5)
B \( \sqrt{13} \)
C (7)
D (1)
Explanation opens after your attempt
Step 1
Concept
\( \sqrt{9}=3 \) and \( \sqrt{4}=2 \), so the sum is (5). First find square roots of perfect squares.
Step 2
Why this answer is correct
The correct answer is A. (5). \( \sqrt{9}=3 \) and \( \sqrt{4}=2 \), so the sum is (5). First find square roots of perfect squares.
Step 3
Exam Tip
\( \sqrt{9}=3 \) और \( \sqrt{4}=2 \) इसलिए योग (5) है। पहले पूर्ण वर्गों के वर्गमूल निकालें।
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\( \sqrt{18} \) को सरल करने पर क्या मिलेगा?
What is obtained by simplifying \( \sqrt{18} \)?
#real numbers
#class 9
#surd simplification
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A \(3\sqrt{2}\)
B \(2\sqrt{3}\)
C \(9\sqrt{2}\)
D \( \sqrt{9} \)
Explanation opens after your attempt
Correct Answer
A. \(3\sqrt{2}\)
Step 1
Concept
Since \(18=9\times2\), \( \sqrt{18}=3\sqrt{2} \). Separate perfect-square factors inside square roots.
Step 2
Why this answer is correct
The correct answer is A. \(3\sqrt{2}\). Since \(18=9\times2\), \( \sqrt{18}=3\sqrt{2} \). Separate perfect-square factors inside square roots.
Step 3
Exam Tip
\(18=9\times2\) इसलिए \( \sqrt{18}=3\sqrt{2} \)। वर्गमूल में पूर्ण वर्ग गुणनखंड अलग करें।
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\( \sqrt{50} \) का सरल रूप क्या है?
What is the simplified form of \( \sqrt{50} \)?
#real numbers
#class 9
#surd simplification
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A \(10\sqrt{5}\)
B \(5\sqrt{2}\)
C \(2\sqrt{5}\)
D \(25\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
B. \(5\sqrt{2}\)
Step 1
Concept
Since \(50=25\times2\), \( \sqrt{50}=5\sqrt{2} \). Choose the largest perfect-square factor.
Step 2
Why this answer is correct
The correct answer is B. \(5\sqrt{2}\). Since \(50=25\times2\), \( \sqrt{50}=5\sqrt{2} \). Choose the largest perfect-square factor.
Step 3
Exam Tip
\(50=25\times2\) इसलिए \( \sqrt{50}=5\sqrt{2} \)। सबसे बड़ा पूर्ण वर्ग गुणनखंड चुनें।
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\( \sqrt{8} \) को सरल करने पर सही उत्तर क्या है?
What is the correct simplified form of \( \sqrt{8} \)?
#real numbers
#class 9
#surd simplification
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A \(4\sqrt{2}\)
B \(2\sqrt{2}\)
C \(8\sqrt{2}\)
D \( \sqrt{4} \)
Explanation opens after your attempt
Correct Answer
B. \(2\sqrt{2}\)
Step 1
Concept
Since \(8=4\times2\), \( \sqrt{8}=2\sqrt{2} \). Take the perfect square (4) outside.
Step 2
Why this answer is correct
The correct answer is B. \(2\sqrt{2}\). Since \(8=4\times2\), \( \sqrt{8}=2\sqrt{2} \). Take the perfect square (4) outside.
Step 3
Exam Tip
\(8=4\times2\) इसलिए \( \sqrt{8}=2\sqrt{2} \)। पूर्ण वर्ग (4) को बाहर निकालें।
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\( \sqrt{2}\times\sqrt{8} \) का मान क्या है?
What is the value of \( \sqrt{2}\times\sqrt{8} \)?
#real numbers
#class 9
#surd multiplication
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A \( \sqrt{10} \)
B \(2\sqrt{8}\)
C (4)
D (8)
Explanation opens after your attempt
Step 1
Concept
\( \sqrt{2}\times\sqrt{8}=\sqrt{16}=4 \). In multiplication, numbers inside square roots can be multiplied.
Step 2
Why this answer is correct
The correct answer is C. (4). \( \sqrt{2}\times\sqrt{8}=\sqrt{16}=4 \). In multiplication, numbers inside square roots can be multiplied.
Step 3
Exam Tip
\( \sqrt{2}\times\sqrt{8}=\sqrt{16}=4 \)। गुणन में वर्गमूल के अंदर की संख्याएँ गुणा की जा सकती हैं।
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\( \sqrt{27}\div\sqrt{3} \) का मान क्या है?
What is the value of \( \sqrt{27}\div\sqrt{3} \)?
#real numbers
#class 9
#surd division
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A (3)
B (9)
C \( \sqrt{30} \)
D \( \sqrt{24} \)
Explanation opens after your attempt
Step 1
Concept
\( \frac{\sqrt{27}}{\sqrt{3}}=\sqrt{9}=3 \). The same square-root rule also works in division.
Step 2
Why this answer is correct
The correct answer is A. (3). \( \frac{\sqrt{27}}{\sqrt{3}}=\sqrt{9}=3 \). The same square-root rule also works in division.
Step 3
Exam Tip
\( \frac{\sqrt{27}}{\sqrt{3}}=\sqrt{9}=3 \)। समान वर्गमूल नियम भाग में भी लागू होता है।
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कौन सी संख्या (2) से बड़ी और (3) से छोटी है?
Which number is greater than (2) and less than (3)?
#real numbers
#class 9
#comparison
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A \( \sqrt{3} \)
B \( \sqrt{6} \)
C \( \sqrt{10} \)
D \( \sqrt{16} \)
Explanation opens after your attempt
Correct Answer
B. \( \sqrt{6} \)
Step 1
Concept
Since \(2^2<6<3^2\), \( \sqrt{6} \) lies between (2) and (3). Compare squares for estimation.
Step 2
Why this answer is correct
The correct answer is B. \( \sqrt{6} \). Since \(2^2<6<3^2\), \( \sqrt{6} \) lies between (2) and (3). Compare squares for estimation.
Step 3
Exam Tip
\(2^2<6<3^2\) इसलिए \( \sqrt{6} \) (2) और (3) के बीच है। अनुमान के लिए वर्गों की तुलना करें।
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\( \sqrt{49} \) कौन सी संख्या है?
What type of number is \( \sqrt{49} \)?
#real numbers
#class 9
#perfect square
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A अपरिमेय वास्तविक संख्या / Irrational real number
B परिमेय वास्तविक संख्या / Rational real number
C अपरिभाषित संख्या / Undefined number
D नकारात्मक संख्या / Negative number
Explanation opens after your attempt
Correct Answer
B. परिमेय वास्तविक संख्या / Rational real number
Step 1
Concept
\( \sqrt{49}=7 \), and (7) is a rational real number. The square root of a perfect square can be an integer.
Step 2
Why this answer is correct
The correct answer is B. परिमेय वास्तविक संख्या / Rational real number. \( \sqrt{49}=7 \), and (7) is a rational real number. The square root of a perfect square can be an integer.
Step 3
Exam Tip
\( \sqrt{49}=7 \) है और (7) परिमेय वास्तविक संख्या है। पूर्ण वर्ग का वर्गमूल पूर्णांक हो सकता है।
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\( \pi \) को सामान्यतः किस प्रकार की संख्या माना जाता है?
What type of number is \( \pi \) generally considered?
#real numbers
#class 9
#pi
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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
\( \pi \) is an irrational number and lies on the real number line. Do not treat it as exactly equal to \( \frac{22}{7} \).
Step 2
Why this answer is correct
The correct answer is B. अपरिमेय वास्तविक संख्या / Irrational real number. \( \pi \) is an irrational number and lies on the real number line. Do not treat it as exactly equal to \( \frac{22}{7} \).
Step 3
Exam Tip
\( \pi \) अपरिमेय संख्या है और वास्तविक संख्या रेखा पर स्थित है। इसे \( \frac{22}{7} \) के बिल्कुल बराबर न मानें।
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\( \frac{22}{7} \) किस प्रकार की वास्तविक संख्या है?
What type of real number is \( \frac{22}{7} \)?
#real numbers
#class 9
#rational
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A परिमेय वास्तविक संख्या / Rational real number
B अपरिमेय वास्तविक संख्या / Irrational real number
C अपरिभाषित संख्या / Undefined number
D केवल प्राकृतिक संख्या / Only natural number
Explanation opens after your attempt
Correct Answer
A. परिमेय वास्तविक संख्या / Rational real number
Step 1
Concept
\( \frac{22}{7} \) 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 A. परिमेय वास्तविक संख्या / Rational real number. \( \frac{22}{7} \) is a ratio of two integers with non-zero denominator. So it is a rational real number.
Step 3
Exam Tip
\( \frac{22}{7} \) दो पूर्णांकों का अनुपात है और हर शून्य नहीं है। इसलिए यह परिमेय वास्तविक संख्या है।
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किस विकल्प में केवल वास्तविक संख्याएँ दी गई हैं?
Which option contains only real numbers?
#real numbers
#class 9
#classification
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A \( \frac{1}{2} \), \( \sqrt{3} \), ( -5 )
B \( \frac{2}{0} \), (3), (4)
C अपरिभाषित, (1), (2) / Undefined, (1), (2)
D केवल हर में शून्य वाले भिन्न / Only fractions with zero denominator
Explanation opens after your attempt
Correct Answer
A. \( \frac{1}{2} \), \( \sqrt{3} \), ( -5 )
Step 1
Concept
\( \frac{1}{2} \), \( \sqrt{3} \), and ( -5 ) are all real numbers. A fraction with zero denominator is not real.
Step 2
Why this answer is correct
The correct answer is A. \( \frac{1}{2} \), \( \sqrt{3} \), ( -5 ). \( \frac{1}{2} \), \( \sqrt{3} \), and ( -5 ) are all real numbers. A fraction with zero denominator is not real.
Step 3
Exam Tip
\( \frac{1}{2} \), \( \sqrt{3} \) और ( -5 ) सभी वास्तविक संख्याएँ हैं। हर में शून्य वाला भिन्न वास्तविक नहीं होता।
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\( -\sqrt{4} \) का मान क्या है?
What is the value of \( -\sqrt{4} \)?
#real numbers
#class 9
#negative square root
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A (2)
B ( -2 )
C (4)
D ( -4 )
Explanation opens after your attempt
Step 1
Concept
\( \sqrt{4}=2 \), so \( -\sqrt{4}=-2 \). Apply the outside negative sign after finding the square root.
Step 2
Why this answer is correct
The correct answer is B. ( -2 ). \( \sqrt{4}=2 \), so \( -\sqrt{4}=-2 \). Apply the outside negative sign after finding the square root.
Step 3
Exam Tip
\( \sqrt{4}=2 \) इसलिए \( -\sqrt{4}=-2 \)। वर्गमूल निकालने के बाद बाहर का ऋण चिह्न लगाएँ।
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( | -7 | ) का वास्तविक मान क्या है?
What is the real value of ( | -7 | )?
#real numbers
#class 9
#absolute value
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A ( -7 )
B (0)
C (7)
D (14)
Explanation opens after your attempt
Step 1
Concept
Absolute value represents distance, so it is not negative. ( | -7 |=7 ).
Step 2
Why this answer is correct
The correct answer is C. (7). Absolute value represents distance, so it is not negative. ( | -7 |=7 ).
Step 3
Exam Tip
निरपेक्ष मान दूरी बताता है इसलिए यह ऋणात्मक नहीं होता। ( | -7 |=7 )।
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वास्तविक संख्या रेखा पर ( -4 ) और (3) के बीच कितनी वास्तविक संख्याएँ होती हैं?
How many real numbers are there between ( -4 ) and (3) on the real number line?
#real numbers
#class 9
#density
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A केवल (7) / Only (7)
B केवल (10) / Only (10)
C कोई नहीं / None
D अनंत / Infinitely many
Explanation opens after your attempt
Correct Answer
D. अनंत / Infinitely many
Step 1
Concept
There are infinitely many real numbers between any two distinct real numbers. This is an important property of the number line.
Step 2
Why this answer is correct
The correct answer is D. अनंत / Infinitely many. There are infinitely many real numbers between any two distinct real numbers. This is an important property of the number line.
Step 3
Exam Tip
किसी भी दो अलग-अलग वास्तविक संख्याओं के बीच अनंत वास्तविक संख्याएँ होती हैं। यह संख्या रेखा का महत्वपूर्ण गुण है।
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(1.414213...) यदि असमाप्त और अनावर्ती है तो यह किस प्रकार की संख्या है?
If (1.414213...) is non-terminating and non-repeating, what type of number is it?
#real numbers
#class 9
#irrational decimal
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A परिमेय संख्या / Rational number
B अपरिमेय वास्तविक संख्या / Irrational real number
C पूर्णांक / Integer
D पूर्ण संख्या / Whole number
Explanation opens after your attempt
Correct Answer
B. अपरिमेय वास्तविक संख्या / Irrational real number
Step 1
Concept
A non-terminating and non-repeating decimal is irrational. It can still be a real number.
Step 2
Why this answer is correct
The correct answer is B. अपरिमेय वास्तविक संख्या / Irrational real number. A non-terminating and non-repeating decimal is irrational. It can still be a real number.
Step 3
Exam Tip
असमाप्त और अनावर्ती दशमलव अपरिमेय होता है। यह वास्तविक संख्या हो सकता है।
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(2.333...) में (3) बार-बार आता है तो यह किस प्रकार की संख्या है?
If (3) repeats in (2.333...), what type of number is it?
#real numbers
#class 9
#repeating decimal
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A परिमेय वास्तविक संख्या / Rational real number
B अपरिमेय संख्या / Irrational number
C अपरिभाषित संख्या / Undefined number
D केवल पूर्णांक / Only integer
Explanation opens after your attempt
Correct Answer
A. परिमेय वास्तविक संख्या / Rational real number
Step 1
Concept
A repeating decimal is a rational number. Therefore (2.333...) is a rational real number.
Step 2
Why this answer is correct
The correct answer is A. परिमेय वास्तविक संख्या / Rational real number. A repeating decimal is a rational number. Therefore (2.333...) is a rational real number.
Step 3
Exam Tip
आवर्ती दशमलव परिमेय संख्या होता है। इसलिए (2.333...) वास्तविक परिमेय संख्या है।
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\( \sqrt{36} \) और \( \sqrt{64} \) के बीच कौन सा सही संबंध है?
Which relation is correct between \( \sqrt{36} \) and \( \sqrt{64} \)?
#real numbers
#class 9
#comparison
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A \( \sqrt{36}>\sqrt{64} \)
B \( \sqrt{36}=\sqrt{64} \)
C \( \sqrt{36}<\sqrt{64} \)
D दोनों वास्तविक नहीं हैं / Both are not real
Explanation opens after your attempt
Correct Answer
C. \( \sqrt{36}<\sqrt{64} \)
Step 1
Concept
\( \sqrt{36}=6 \) and \( \sqrt{64}=8 \), so (6<8). Find square roots before comparing.
Step 2
Why this answer is correct
The correct answer is C. \( \sqrt{36}<\sqrt{64} \). \( \sqrt{36}=6 \) and \( \sqrt{64}=8 \), so (6<8). Find square roots before comparing.
Step 3
Exam Tip
\( \sqrt{36}=6 \) और \( \sqrt{64}=8 \) इसलिए (6<8)। तुलना से पहले वर्गमूल निकालें।
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\( \frac{3}{2} \) और \( \sqrt{2} \) में कौन बड़ी है?
Which is greater between \( \frac{3}{2} \) and \( \sqrt{2} \)?
#real numbers
#class 9
#ordering
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A \( \sqrt{2} \)
B \( \frac{3}{2} \)
C दोनों बराबर / Both are equal
D निर्धारित नहीं / Cannot be determined
Explanation opens after your attempt
Correct Answer
B. \( \frac{3}{2} \)
Step 1
Concept
\( \frac{3}{2}=1.5 \) and \( \sqrt{2}\approx1.414 \). Therefore \( \frac{3}{2} \) is greater.
Step 2
Why this answer is correct
The correct answer is B. \( \frac{3}{2} \). \( \frac{3}{2}=1.5 \) and \( \sqrt{2}\approx1.414 \). Therefore \( \frac{3}{2} \) is greater.
Step 3
Exam Tip
\( \frac{3}{2}=1.5 \) और \( \sqrt{2}\approx1.414 \) है। इसलिए \( \frac{3}{2} \) बड़ी है।
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वास्तविक संख्याओं में योग का तत्समक अवयव कौन सा है?
What is the additive identity in real numbers?
#real numbers
#class 9
#additive identity
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A (1)
B ( -1 )
C (0)
D (2)
Explanation opens after your attempt
Step 1
Concept
Adding (0) to any real number gives the same number. Hence (0) is the additive identity.
Step 2
Why this answer is correct
The correct answer is C. (0). Adding (0) to any real number gives the same number. Hence (0) is the additive identity.
Step 3
Exam Tip
किसी भी वास्तविक संख्या में (0) जोड़ने पर वही संख्या मिलती है। इसलिए (0) योग का तत्समक अवयव है।
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वास्तविक संख्याओं में गुणन का तत्समक अवयव कौन सा है?
What is the multiplicative identity in real numbers?
#real numbers
#class 9
#multiplicative identity
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A (0)
B (1)
C ( -1 )
D (10)
Explanation opens after your attempt
Step 1
Concept
Multiplying any real number by (1) gives the same number. Hence (1) is the multiplicative identity.
Step 2
Why this answer is correct
The correct answer is B. (1). Multiplying any real number by (1) gives the same number. Hence (1) is the multiplicative identity.
Step 3
Exam Tip
किसी भी वास्तविक संख्या को (1) से गुणा करने पर वही संख्या मिलती है। इसलिए (1) गुणन का तत्समक अवयव है।
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( -9 ) का योज्य प्रतिलोम क्या है?
What is the additive inverse of ( -9 )?
#real numbers
#class 9
#additive inverse
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A ( -9 )
B (0)
C \( \frac{1}{9} \)
D (9)
Explanation opens after your attempt
Step 1
Concept
The additive inverse gives (0) when added. Since ( -9+9=0 ), the answer is (9).
Step 2
Why this answer is correct
The correct answer is D. (9). The additive inverse gives (0) when added. Since ( -9+9=0 ), the answer is (9).
Step 3
Exam Tip
योज्य प्रतिलोम जोड़ने पर (0) देता है। ( -9+9=0 ) इसलिए उत्तर (9) है।
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\( \frac{4}{7} \) का गुणात्मक प्रतिलोम क्या है?
What is the multiplicative inverse of \( \frac{4}{7} \)?
#real numbers
#class 9
#multiplicative inverse
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A \( \frac{7}{4} \)
B \( \frac{-4}{7} \)
C \( \frac{4}{-7} \)
D \( \frac{11}{7} \)
Explanation opens after your attempt
Correct Answer
A. \( \frac{7}{4} \)
Step 1
Concept
In the multiplicative inverse, numerator and denominator are interchanged. \( \frac{4}{7}\times\frac{7}{4}=1 \).
Step 2
Why this answer is correct
The correct answer is A. \( \frac{7}{4} \). In the multiplicative inverse, numerator and denominator are interchanged. \( \frac{4}{7}\times\frac{7}{4}=1 \).
Step 3
Exam Tip
गुणात्मक प्रतिलोम में अंश और हर बदल जाते हैं। \( \frac{4}{7}\times\frac{7}{4}=1 \)।
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कौन सी वास्तविक संख्या न धनात्मक है न ऋणात्मक?
Which real number is neither positive nor negative?
#real numbers
#class 9
#zero
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A (0)
B (1)
C ( -1 )
D \( \frac{1}{2} \)
Explanation opens after your attempt
Step 1
Concept
(0) is neither positive nor negative. Keep (0) separate in number classification.
Step 2
Why this answer is correct
The correct answer is A. (0). (0) is neither positive nor negative. Keep (0) separate in number classification.
Step 3
Exam Tip
(0) न धनात्मक होता है न ऋणात्मक। संख्या वर्गीकरण में (0) को अलग रखें।
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कौन सा विकल्प सही क्रम दिखाता है?
Which option shows the correct order?
#real numbers
#class 9
#ordering
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A ( -3<-1<2 )
B (2<-1<-3)
C ( -1<-3<2 )
D (2<-3<-1)
Explanation opens after your attempt
Correct Answer
A. ( -3<-1<2 )
Step 1
Concept
On the number line, the left number is smaller and the right number is greater. Therefore ( -3<-1<2 ) is correct.
Step 2
Why this answer is correct
The correct answer is A. ( -3<-1<2 ). On the number line, the left number is smaller and the right number is greater. Therefore ( -3<-1<2 ) is correct.
Step 3
Exam Tip
संख्या रेखा पर बाईं संख्या छोटी और दाईं संख्या बड़ी होती है। इसलिए ( -3<-1<2 ) सही है।
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\( \sqrt{121} \) का मान क्या है?
What is the value of \( \sqrt{121} \)?
#real numbers
#class 9
#square root
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A (10)
B (11)
C (12)
D (121)
Explanation opens after your attempt
Step 1
Concept
Since \(11^2=121\), \( \sqrt{121}=11 \). Remembering perfect squares is useful.
Step 2
Why this answer is correct
The correct answer is B. (11). Since \(11^2=121\), \( \sqrt{121}=11 \). Remembering perfect squares is useful.
Step 3
Exam Tip
\(11^2=121\) इसलिए \( \sqrt{121}=11 \)। पूर्ण वर्गों की सूची याद रखना उपयोगी है।
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\( \sqrt{12} \) का सरल रूप क्या है?
What is the simplified form of \( \sqrt{12} \)?
#real numbers
#class 9
#surd simplification
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A \(6\sqrt{2}\)
B \(2\sqrt{3}\)
C \(3\sqrt{2}\)
D \(4\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
B. \(2\sqrt{3}\)
Step 1
Concept
Since \(12=4\times3\), \( \sqrt{12}=2\sqrt{3} \). Take the perfect-square factor outside the square root.
Step 2
Why this answer is correct
The correct answer is B. \(2\sqrt{3}\). Since \(12=4\times3\), \( \sqrt{12}=2\sqrt{3} \). Take the perfect-square factor outside the square root.
Step 3
Exam Tip
\(12=4\times3\) इसलिए \( \sqrt{12}=2\sqrt{3} \)। पूर्ण वर्ग गुणनखंड को वर्गमूल से बाहर निकालें।
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किस विकल्प में एक परिमेय और एक अपरिमेय वास्तविक संख्या है?
Which option has one rational and one irrational real number?
#real numbers
#class 9
#rational irrational
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A (5) और \( \sqrt{2} \) / (5) and \( \sqrt{2} \)
B (3) और (4) / (3) and (4)
C \( \sqrt{5} \) और \( \sqrt{7} \) / \( \sqrt{5} \) and \( \sqrt{7} \)
D \( \frac{1}{2} \) और (0.25) / \( \frac{1}{2} \) and (0.25)
Explanation opens after your attempt
Correct Answer
A. (5) और \( \sqrt{2} \) / (5) and \( \sqrt{2} \)
Step 1
Concept
(5) is rational and \( \sqrt{2} \) is irrational. Both lie on the real number line.
Step 2
Why this answer is correct
The correct answer is A. (5) और \( \sqrt{2} \) / (5) and \( \sqrt{2} \). (5) is rational and \( \sqrt{2} \) is irrational. Both lie on the real number line.
Step 3
Exam Tip
(5) परिमेय है और \( \sqrt{2} \) अपरिमेय है। दोनों वास्तविक संख्या रेखा पर स्थित हैं।
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\( \sqrt{5} \) और \( \sqrt{6} \) में कौन बड़ी है?
Which is greater between \( \sqrt{5} \) and \( \sqrt{6} \)?
#real numbers
#class 9
#square root comparison
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A \( \sqrt{5} \)
B \( \sqrt{6} \)
C दोनों बराबर / Both are equal
D दोनों वास्तविक नहीं / Both are not real
Explanation opens after your attempt
Correct Answer
B. \( \sqrt{6} \)
Step 1
Concept
For positive numbers, the square root of the greater number is also greater. Since (6>5), \( \sqrt{6}>\sqrt{5} \).
Step 2
Why this answer is correct
The correct answer is B. \( \sqrt{6} \). For positive numbers, the square root of the greater number is also greater. Since (6>5), \( \sqrt{6}>\sqrt{5} \).
Step 3
Exam Tip
धनात्मक संख्याओं में बड़ी संख्या का वर्गमूल भी बड़ा होता है। (6>5) इसलिए \( \sqrt{6}>\sqrt{5} \)।
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\(3+\sqrt{2}\) किस प्रकार की संख्या है?
What type of number is \(3+\sqrt{2}\)?
#real numbers
#class 9
#irrational sum
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A परिमेय संख्या / Rational number
B अपरिमेय वास्तविक संख्या / Irrational real number
C पूर्णांक / Integer
D पूर्ण संख्या / Whole number
Explanation opens after your attempt
Correct Answer
B. अपरिमेय वास्तविक संख्या / Irrational real number
Step 1
Concept
Adding the irrational \( \sqrt{2} \) to the rational number (3) generally gives an irrational number. It is also real.
Step 2
Why this answer is correct
The correct answer is B. अपरिमेय वास्तविक संख्या / Irrational real number. Adding the irrational \( \sqrt{2} \) to the rational number (3) generally gives an irrational number. It is also real.
Step 3
Exam Tip
परिमेय संख्या (3) में अपरिमेय \( \sqrt{2} \) जोड़ने पर सामान्यतः अपरिमेय संख्या मिलती है। यह वास्तविक संख्या भी है।
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वास्तविक संख्या रेखा पर \( \sqrt{0} \) कहाँ स्थित है?
Where is \( \sqrt{0} \) located on the real number line?
#real numbers
#class 9
#zero square root
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A (0) पर / At (0)
B (1) पर / At (1)
C ( -1 ) पर / At ( -1 )
D (2) पर / At (2)
Explanation opens after your attempt
Correct Answer
A. (0) पर / At (0)
Step 1
Concept
\( \sqrt{0}=0 \). Therefore it is located at the origin on the number line.
Step 2
Why this answer is correct
The correct answer is A. (0) पर / At (0). \( \sqrt{0}=0 \). Therefore it is located at the origin on the number line.
Step 3
Exam Tip
\( \sqrt{0}=0 \) होता है। इसलिए यह संख्या रेखा पर मूल बिंदु पर स्थित है।
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