यदि \(a=3+\sqrt{6}\) और \(b=3-\sqrt{6}\) हैं तो (a+b) का मान क्या है?
If \(a=3+\sqrt{6}\) and \(b=3-\sqrt{6}\), what is the value of (a+b)?
#conjugate
#addition
#rational-result
A (6)
B \(2\sqrt{6}\)
C (0)
D (9)
Explanation opens after your attempt
Step 1
Concept
In the sum \(\sqrt{6}\) and \(-\sqrt{6}\) cancel. So (a+b=6).
Step 2
Why this answer is correct
The correct answer is A. (6). In the sum \(\sqrt{6}\) and \(-\sqrt{6}\) cancel. So (a+b=6).
Step 3
Exam Tip
योग में \(\sqrt{6}\) और \(-\sqrt{6}\) कट जाते हैं। इसलिए (a+b=6) है।
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कौन सा विकल्प \(\sqrt{125}+\sqrt{45}\) का सरल रूप है?
Which option is the simplified form of \(\sqrt{125}+\sqrt{45}\)?
#surds
#addition
#like-terms
A \(8\sqrt{5}\)
B \(10\sqrt{5}\)
C \(\sqrt{170}\)
D \(6\sqrt{10}\)
Explanation opens after your attempt
Correct Answer
A. \(8\sqrt{5}\)
Step 1
Concept
\(\sqrt{125}=5\sqrt{5}\) and \(\sqrt{45}=3\sqrt{5}\). Adding like terms gives \(8\sqrt{5}\).
Step 2
Why this answer is correct
The correct answer is A. \(8\sqrt{5}\). \(\sqrt{125}=5\sqrt{5}\) and \(\sqrt{45}=3\sqrt{5}\). Adding like terms gives \(8\sqrt{5}\).
Step 3
Exam Tip
\(\sqrt{125}=5\sqrt{5}\) और \(\sqrt{45}=3\sqrt{5}\) है। समान पद जोड़ने पर \(8\sqrt{5}\) मिलता है।
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कौन सा विकल्प \(4+\sqrt{13}\) की प्रकृति सही बताता है?
Which option correctly describes the nature of \(4+\sqrt{13}\)?
#rational-irrational
#addition
#classification
A अपरिमेय संख्या / Irrational number
B परिमेय संख्या / Rational number
C पूर्णांक / Integer
D सांत दशमलव / Terminating decimal
Explanation opens after your attempt
Correct Answer
A. अपरिमेय संख्या / Irrational number
Step 1
Concept
(4) is rational and \(\sqrt{13}\) is irrational. The sum of a rational and an irrational number is irrational.
Step 2
Why this answer is correct
The correct answer is A. अपरिमेय संख्या / Irrational number. (4) is rational and \(\sqrt{13}\) is irrational. The sum of a rational and an irrational number is irrational.
Step 3
Exam Tip
(4) परिमेय है और \(\sqrt{13}\) अपरिमेय है। परिमेय और अपरिमेय का योग अपरिमेय होता है।
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कौन सा विकल्प \( \frac{1}{2}+\sqrt{2}\) की प्रकृति सही बताता है?
Which option correctly describes the nature of \( \frac{1}{2}+\sqrt{2}\)?
#rational-irrational
#addition
#classification
A अपरिमेय संख्या / Irrational number
B परिमेय संख्या / Rational number
C पूर्णांक / Integer
D सांत दशमलव / Terminating decimal
Explanation opens after your attempt
Correct Answer
A. अपरिमेय संख्या / Irrational number
Step 1
Concept
\(\frac{1}{2}\) is rational and \(\sqrt{2}\) is irrational. Their sum is irrational.
Step 2
Why this answer is correct
The correct answer is A. अपरिमेय संख्या / Irrational number. \(\frac{1}{2}\) is rational and \(\sqrt{2}\) is irrational. Their sum is irrational.
Step 3
Exam Tip
\(\frac{1}{2}\) परिमेय है और \(\sqrt{2}\) अपरिमेय है। उनका योग अपरिमेय होता है।
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कौन सा कथन दो अपरिमेय संख्याओं के योग के बारे में सही है?
Which statement is correct about the sum of two irrational numbers?
#irrational-numbers
#addition
#properties
A योग परिमेय या अपरिमेय दोनों हो सकता है / The sum can be rational or irrational
B योग हमेशा परिमेय होता है / The sum is always rational
C योग हमेशा अपरिमेय होता है / The sum is always irrational
D योग हमेशा शून्य होता है / The sum is always zero
Explanation opens after your attempt
Correct Answer
A. योग परिमेय या अपरिमेय दोनों हो सकता है / The sum can be rational or irrational
Step 1
Concept
(\sqrt{2}+\(-\sqrt{2}\)=0) is rational but \(\sqrt{2}+\sqrt{3}\) is irrational. So there is no single fixed rule.
Step 2
Why this answer is correct
The correct answer is A. योग परिमेय या अपरिमेय दोनों हो सकता है / The sum can be rational or irrational. (\sqrt{2}+\(-\sqrt{2}\)=0) is rational but \(\sqrt{2}+\sqrt{3}\) is irrational. So there is no single fixed rule.
Step 3
Exam Tip
(\sqrt{2}+\(-\sqrt{2}\)=0) परिमेय है पर \(\sqrt{2}+\sqrt{3}\) अपरिमेय है। इसलिए एक ही स्थायी नियम नहीं है।
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यदि \(y=\sqrt{2}+\sqrt{32}\) है तो (y) का सरल रूप क्या है?
If \(y=\sqrt{2}+\sqrt{32}\), what is the simplified form of (y)?
#surds
#addition
#expression
A \(5\sqrt{2}\)
B \(3\sqrt{2}\)
C \(\sqrt{34}\)
D \(17\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. \(5\sqrt{2}\)
Step 1
Concept
\(\sqrt{32}=4\sqrt{2}\), so \(y=5\sqrt{2}\). Add like radical terms.
Step 2
Why this answer is correct
The correct answer is A. \(5\sqrt{2}\). \(\sqrt{32}=4\sqrt{2}\), so \(y=5\sqrt{2}\). Add like radical terms.
Step 3
Exam Tip
\(\sqrt{32}=4\sqrt{2}\) है इसलिए \(y=5\sqrt{2}\) होगा। समान जड़ वाले पदों को जोड़ें।
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यदि \(a=2-\sqrt{5}\) और \(b=2+\sqrt{5}\) हैं तो (a+b) किस प्रकार की संख्या है?
If \(a=2-\sqrt{5}\) and \(b=2+\sqrt{5}\), what type of number is (a+b)?
#irrational-terms
#addition
#rational-result
A परिमेय संख्या / Rational number
B अपरिमेय संख्या / Irrational number
C अवास्तविक संख्या / Non real number
D हमेशा ऋणात्मक / Always negative
Explanation opens after your attempt
Correct Answer
A. परिमेय संख्या / Rational number
Step 1
Concept
In the sum \(-\sqrt{5}\) and \(\sqrt{5}\) cancel. (a+b=4) is rational.
Step 2
Why this answer is correct
The correct answer is A. परिमेय संख्या / Rational number. In the sum \(-\sqrt{5}\) and \(\sqrt{5}\) cancel. (a+b=4) is rational.
Step 3
Exam Tip
योग में \(-\sqrt{5}\) और \(\sqrt{5}\) कट जाते हैं। (a+b=4) परिमेय है।
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\(\sqrt{2}+\sqrt{8}+\sqrt{18}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{2}+\sqrt{8}+\sqrt{18}\)?
#surds
#addition
#like-terms
A \(6\sqrt{2}\)
B \(11\sqrt{2}\)
C \(\sqrt{28}\)
D \(3\sqrt{10}\)
Explanation opens after your attempt
Correct Answer
A. \(6\sqrt{2}\)
Step 1
Concept
\(\sqrt{8}=2\sqrt{2}\) and \(\sqrt{18}=3\sqrt{2}\). The total is \(6\sqrt{2}\).
Step 2
Why this answer is correct
The correct answer is A. \(6\sqrt{2}\). \(\sqrt{8}=2\sqrt{2}\) and \(\sqrt{18}=3\sqrt{2}\). The total is \(6\sqrt{2}\).
Step 3
Exam Tip
\(\sqrt{8}=2\sqrt{2}\) और \(\sqrt{18}=3\sqrt{2}\) है। कुल \(6\sqrt{2}\) मिलता है।
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कौन सा कथन \(3+\sqrt{7}\) के लिए सही है?
Which statement is correct for \(3+\sqrt{7}\)?
#rational-irrational
#addition
#classification
A यह अपरिमेय है / It is irrational
B यह परिमेय है / It is rational
C यह पूर्णांक है / It is an integer
D यह सांत दशमलव है / It is a terminating decimal
Explanation opens after your attempt
Correct Answer
A. यह अपरिमेय है / It is irrational
Step 1
Concept
Adding irrational \(\sqrt{7}\) to rational (3) gives an irrational result. In exams identify roots of non perfect squares.
Step 2
Why this answer is correct
The correct answer is A. यह अपरिमेय है / It is irrational. Adding irrational \(\sqrt{7}\) to rational (3) gives an irrational result. In exams identify roots of non perfect squares.
Step 3
Exam Tip
परिमेय (3) में अपरिमेय \(\sqrt{7}\) जोड़ने पर परिणाम अपरिमेय होता है। परीक्षा में पूर्ण वर्ग न होने वाली जड़ को पहचानें।
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कौन सा विकल्प \(7\sqrt{3}+2\sqrt{3}\) का सही सरल रूप है?
Which option is the correct simplified form of \(7\sqrt{3}+2\sqrt{3}\)?
#surds
#like-terms
#addition
A \(9\sqrt{3}\)
B \(14\sqrt{3}\)
C \(9\sqrt{6}\)
D \(\sqrt{30}\)
Explanation opens after your attempt
Correct Answer
A. \(9\sqrt{3}\)
Step 1
Concept
The coefficients of like radical terms are added. So \(7\sqrt{3}+2\sqrt{3}=9\sqrt{3}\).
Step 2
Why this answer is correct
The correct answer is A. \(9\sqrt{3}\). The coefficients of like radical terms are added. So \(7\sqrt{3}+2\sqrt{3}=9\sqrt{3}\).
Step 3
Exam Tip
समान जड़ वाले पदों के गुणांक जुड़ते हैं। इसलिए \(7\sqrt{3}+2\sqrt{3}=9\sqrt{3}\) है।
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\(\sqrt{3}+\sqrt{75}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{3}+\sqrt{75}\)?
#surds
#like-terms
#addition
A \(6\sqrt{3}\)
B \(5\sqrt{3}\)
C \(\sqrt{78}\)
D \(25\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
A. \(6\sqrt{3}\)
Step 1
Concept
\(\sqrt{75}=5\sqrt{3}\), so the total is \(6\sqrt{3}\). Only like radical terms add directly.
Step 2
Why this answer is correct
The correct answer is A. \(6\sqrt{3}\). \(\sqrt{75}=5\sqrt{3}\), so the total is \(6\sqrt{3}\). Only like radical terms add directly.
Step 3
Exam Tip
\(\sqrt{75}=5\sqrt{3}\) इसलिए कुल \(6\sqrt{3}\) है। समान जड़ वाले पद ही सीधे जुड़ते हैं।
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\(\sqrt{2}+\sqrt{18}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{2}+\sqrt{18}\)?
#surds
#addition
#simplification
A \(4\sqrt{2}\)
B \(2\sqrt{20}\)
C \(\sqrt{20}\)
D \(10\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. \(4\sqrt{2}\)
Step 1
Concept
\(\sqrt{18}=3\sqrt{2}\) so the sum is \(4\sqrt{2}\). First simplify the root and then add.
Step 2
Why this answer is correct
The correct answer is A. \(4\sqrt{2}\). \(\sqrt{18}=3\sqrt{2}\) so the sum is \(4\sqrt{2}\). First simplify the root and then add.
Step 3
Exam Tip
\(\sqrt{18}=3\sqrt{2}\) इसलिए योग \(4\sqrt{2}\) है। पहले जड़ को सरल करें फिर जोड़ें।
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कौन सा विकल्प परिमेय संख्या को अपरिमेय संख्या से जोड़ने पर बना है?
Which option is formed by adding a rational number to an irrational number?
#rational-irrational
#addition
#classification
A \(\frac{3}{5}+\sqrt{10}\)
B \(\sqrt{2}+\sqrt{10}\)
C \(\frac{1}{5}+\frac{2}{5}\)
D (6+8)
Explanation opens after your attempt
Correct Answer
A. \(\frac{3}{5}+\sqrt{10}\)
Step 1
Concept
\(\frac{3}{5}\) is rational and \(\sqrt{10}\) is irrational. This sum will be irrational.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{3}{5}+\sqrt{10}\). \(\frac{3}{5}\) is rational and \(\sqrt{10}\) is irrational. This sum will be irrational.
Step 3
Exam Tip
\(\frac{3}{5}\) परिमेय है और \(\sqrt{10}\) अपरिमेय है। यह योग अपरिमेय होगा।
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कौन सा विकल्प परिमेय और अपरिमेय संख्या का योग है जो अपरिमेय है?
Which option is the sum of a rational and an irrational number that is irrational?
#rational-irrational
#addition
#irrational-result
A \(9+\sqrt{17}\)
B (9+17)
C \(\sqrt{16}+\sqrt{25}\)
D \(\frac{1}{2}+\frac{3}{2}\)
Explanation opens after your attempt
Correct Answer
A. \(9+\sqrt{17}\)
Step 1
Concept
(9) is rational and \(\sqrt{17}\) is irrational. Such a sum is irrational.
Step 2
Why this answer is correct
The correct answer is A. \(9+\sqrt{17}\). (9) is rational and \(\sqrt{17}\) is irrational. Such a sum is irrational.
Step 3
Exam Tip
(9) परिमेय है और \(\sqrt{17}\) अपरिमेय है। ऐसा योग अपरिमेय होता है।
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\(\sqrt{63}+\sqrt{28}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{63}+\sqrt{28}\)?
#surds
#addition
#like-terms
A \(5\sqrt{7}\)
B \(7\sqrt{5}\)
C \(\sqrt{91}\)
D \(11\sqrt{7}\)
Explanation opens after your attempt
Correct Answer
A. \(5\sqrt{7}\)
Step 1
Concept
\(\sqrt{63}=3\sqrt{7}\) and \(\sqrt{28}=2\sqrt{7}\). Adding like terms gives \(5\sqrt{7}\).
Step 2
Why this answer is correct
The correct answer is A. \(5\sqrt{7}\). \(\sqrt{63}=3\sqrt{7}\) and \(\sqrt{28}=2\sqrt{7}\). Adding like terms gives \(5\sqrt{7}\).
Step 3
Exam Tip
\(\sqrt{63}=3\sqrt{7}\) और \(\sqrt{28}=2\sqrt{7}\) है। समान पद जोड़ने पर \(5\sqrt{7}\) मिलता है।
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कौन सा विकल्प एक अपरिमेय संख्या और उसके विपरीत के योग का परिणाम दिखाता है?
Which option shows the result of the sum of an irrational number and its opposite?
#irrational-numbers
#addition
#opposite-numbers
A (0)
B (1)
C \(\sqrt{2}\)
D \(2\sqrt{2}\)
Explanation opens after your attempt
Step 1
Concept
(\sqrt{2}+\(-\sqrt{2}\)=0). Remember that the sum of two irrational numbers can sometimes be rational.
Step 2
Why this answer is correct
The correct answer is A. (0). (\sqrt{2}+\(-\sqrt{2}\)=0). Remember that the sum of two irrational numbers can sometimes be rational.
Step 3
Exam Tip
(\sqrt{2}+\(-\sqrt{2}\)=0) होता है। इससे याद रखें कि दो अपरिमेय संख्याओं का योग कभी-कभी परिमेय हो सकता है।
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यदि (m) और (n) परिमेय संख्याएँ हैं तो (m+n) किस प्रकार की संख्या होगी?
If (m) and (n) are rational numbers then what type of number will (m+n) be?
#rational-numbers
#addition
#closure
A परिमेय संख्या / Rational number
B अपरिमेय संख्या / Irrational number
C हमेशा प्राकृतिक संख्या / Always natural number
D हमेशा शून्य / Always zero
Explanation opens after your attempt
Correct Answer
A. परिमेय संख्या / Rational number
Step 1
Concept
The sum of two rational numbers is rational. This is called closure of rational numbers.
Step 2
Why this answer is correct
The correct answer is A. परिमेय संख्या / Rational number. The sum of two rational numbers is rational. This is called closure of rational numbers.
Step 3
Exam Tip
दो परिमेय संख्याओं का योग परिमेय होता है। इसे परिमेय संख्याओं की बंदता कहा जाता है।
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कौन सा विकल्प दो अपरिमेय संख्याओं का योग परिमेय बनने का उदाहरण है?
Which option is an example where the sum of two irrational numbers is rational?
#irrational-numbers
#addition
#counterexample
A (\sqrt{5}+\(-\sqrt{5}\))
B \(\sqrt{2}+\sqrt{7}\)
C \(\sqrt{3}+1\)
D (2+3)
Explanation opens after your attempt
Correct Answer
A. (\sqrt{5}+\(-\sqrt{5}\))
Step 1
Concept
(\sqrt{5}+\(-\sqrt{5}\)=0), which is rational. This shows the sum is not always irrational.
Step 2
Why this answer is correct
The correct answer is A. (\sqrt{5}+\(-\sqrt{5}\)). (\sqrt{5}+\(-\sqrt{5}\)=0), which is rational. This shows the sum is not always irrational.
Step 3
Exam Tip
(\sqrt{5}+\(-\sqrt{5}\)=0) है जो परिमेय है। इससे पता चलता है कि योग हमेशा अपरिमेय नहीं होता।
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\(\sqrt{48}+\sqrt{12}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{48}+\sqrt{12}\)?
#surds
#addition
#like-terms
A \(6\sqrt{3}\)
B \(4\sqrt{15}\)
C \(60\sqrt{3}\)
D \(2\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
A. \(6\sqrt{3}\)
Step 1
Concept
\(\sqrt{48}=4\sqrt{3}\) and \(\sqrt{12}=2\sqrt{3}\). Adding like terms gives \(6\sqrt{3}\).
Step 2
Why this answer is correct
The correct answer is A. \(6\sqrt{3}\). \(\sqrt{48}=4\sqrt{3}\) and \(\sqrt{12}=2\sqrt{3}\). Adding like terms gives \(6\sqrt{3}\).
Step 3
Exam Tip
\(\sqrt{48}=4\sqrt{3}\) और \(\sqrt{12}=2\sqrt{3}\) है। समान पद जोड़ने पर \(6\sqrt{3}\) मिलता है।
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\(6+\sqrt{11}\) किस प्रकार की संख्या है?
What type of number is \(6+\sqrt{11}\)?
#addition
#rational-irrational
#irrational-numbers
A अपरिमेय संख्या / Irrational number
B परिमेय संख्या / Rational number
C पूर्णांक / Integer
D सांत दशमलव / Terminating decimal
Explanation opens after your attempt
Correct Answer
A. अपरिमेय संख्या / Irrational number
Step 1
Concept
Adding irrational \(\sqrt{11}\) to rational (6) gives an irrational number. Do not mistake the root for a perfect square.
Step 2
Why this answer is correct
The correct answer is A. अपरिमेय संख्या / Irrational number. Adding irrational \(\sqrt{11}\) to rational (6) gives an irrational number. Do not mistake the root for a perfect square.
Step 3
Exam Tip
परिमेय संख्या (6) में अपरिमेय \(\sqrt{11}\) जोड़ने पर परिणाम अपरिमेय रहता है। जड़ को पूर्ण वर्ग समझने की गलती न करें।
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\(\sqrt{2}+\sqrt{8}\) का सही सरल रूप क्या है?
What is the correct simplified form of \(\sqrt{2}+\sqrt{8}\)?
#surds
#addition
#like-terms
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 the sum is \(3\sqrt{2}\). Simplify first and then add like terms.
Step 2
Why this answer is correct
The correct answer is A. \(3\sqrt{2}\). \(\sqrt{8}=2\sqrt{2}\) so the sum is \(3\sqrt{2}\). Simplify first and then add like terms.
Step 3
Exam Tip
\(\sqrt{8}=2\sqrt{2}\) इसलिए योग \(3\sqrt{2}\) है। पहले सरल करें फिर समान पद जोड़ें।
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\(\sqrt{20}+\sqrt{45}\) का सरल रूप क्या है?
What is the simplest form of \(\sqrt{20}+\sqrt{45}\)?
#surds
#addition
#simplification
A \(5\sqrt{5}\)
B \(\sqrt{65}\)
C \(13\sqrt{5}\)
D \(25\sqrt{5}\)
Explanation opens after your attempt
Correct Answer
A. \(5\sqrt{5}\)
Step 1
Concept
\(\sqrt{20}=2\sqrt{5}\) and \(\sqrt{45}=3\sqrt{5}\). Adding gives \(5\sqrt{5}\).
Step 2
Why this answer is correct
The correct answer is A. \(5\sqrt{5}\). \(\sqrt{20}=2\sqrt{5}\) and \(\sqrt{45}=3\sqrt{5}\). Adding gives \(5\sqrt{5}\).
Step 3
Exam Tip
\(\sqrt{20}=2\sqrt{5}\) और \(\sqrt{45}=3\sqrt{5}\) है। जोड़ने पर \(5\sqrt{5}\) मिलता है।
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दो अपरिमेय संख्याओं का योग हमेशा कैसा होता है?
What is the sum of two irrational numbers always?
#irrational-numbers
#addition
#properties
A हमेशा निश्चित नहीं / Not always fixed
B हमेशा परिमेय / Always rational
C हमेशा अपरिमेय / Always irrational
D हमेशा शून्य / Always zero
Explanation opens after your attempt
Correct Answer
A. हमेशा निश्चित नहीं / Not always fixed
Step 1
Concept
(\sqrt{2}+\(-\sqrt{2}\)=0) is rational but \(\sqrt{2}+\sqrt{3}\) is irrational. So there is no fixed always rule.
Step 2
Why this answer is correct
The correct answer is A. हमेशा निश्चित नहीं / Not always fixed. (\sqrt{2}+\(-\sqrt{2}\)=0) is rational but \(\sqrt{2}+\sqrt{3}\) is irrational. So there is no fixed always rule.
Step 3
Exam Tip
(\sqrt{2}+\(-\sqrt{2}\)=0) परिमेय है लेकिन \(\sqrt{2}+\sqrt{3}\) अपरिमेय है। इसलिए हमेशा एक जैसा नियम नहीं है।
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यदि (a) परिमेय है और (b) अपरिमेय है तो (a+b) कब निश्चित रूप से अपरिमेय होगा?
If (a) is rational and (b) is irrational then when is (a+b) definitely irrational?
#addition
#properties
#irrational-numbers
A जब (a) कोई भी परिमेय संख्या हो / When (a) is any rational number
B केवल जब (a=0) हो / Only when (a=0)
C केवल जब (a=1) हो / Only when (a=1)
D कभी नहीं / Never
Explanation opens after your attempt
Correct Answer
A. जब (a) कोई भी परिमेय संख्या हो / When (a) is any rational number
Step 1
Concept
Adding a rational number to an irrational number gives an irrational result. This simple property often appears in MCQs.
Step 2
Why this answer is correct
The correct answer is A. जब (a) कोई भी परिमेय संख्या हो / When (a) is any rational number. Adding a rational number to an irrational number gives an irrational result. This simple property often appears in MCQs.
Step 3
Exam Tip
परिमेय में अपरिमेय जोड़ने पर परिणाम अपरिमेय रहता है। यह आसान गुण अक्सर MCQ में आता है।
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\(2+\sqrt{3}\) किस प्रकार की संख्या है?
What type of number is \(2+\sqrt{3}\)?
#operation
#irrational-numbers
#addition
A अपरिमेय संख्या / Irrational number
B परिमेय संख्या / Rational number
C पूर्णांक / Integer
D शून्य / Zero
Explanation opens after your attempt
Correct Answer
A. अपरिमेय संख्या / Irrational number
Step 1
Concept
Adding irrational \(\sqrt{3}\) to rational (2) gives an irrational number. Do not treat such sums as rational.
Step 2
Why this answer is correct
The correct answer is A. अपरिमेय संख्या / Irrational number. Adding irrational \(\sqrt{3}\) to rational (2) gives an irrational number. Do not treat such sums as rational.
Step 3
Exam Tip
परिमेय (2) में अपरिमेय \(\sqrt{3}\) जोड़ने पर परिणाम अपरिमेय होता है। परीक्षा में ऐसे योग को परिमेय न मानें।
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\(0.\overline{36}\) और \(0.\overline{63}\) का योग किस प्रकार का दशमलव है?
What type of decimal is the sum of \(0.\overline{36}\) and \(0.\overline{63}\)?
#recurring-decimal
#addition
#terminating-result
#conceptual
A सांत / Terminating
B असांत आवर्ती / Non-terminating recurring
C असांत अनावर्ती / Non-terminating non-recurring
D अपरिमेय / Irrational
Explanation opens after your attempt
Correct Answer
A. सांत / Terminating
Step 1
Concept
\(0.\overline{36}=\frac{36}{99}\) and \(0.\overline{63}=\frac{63}{99}\), so their sum is (1). The sum of two recurring decimals can be terminating.
Step 2
Why this answer is correct
The correct answer is A. सांत / Terminating. \(0.\overline{36}=\frac{36}{99}\) and \(0.\overline{63}=\frac{63}{99}\), so their sum is (1). The sum of two recurring decimals can be terminating.
Step 3
Exam Tip
\(0.\overline{36}=\frac{36}{99}\) और \(0.\overline{63}=\frac{63}{99}\) हैं इसलिए योग (1) है। दो आवर्ती दशमलवों का योग सांत भी हो सकता है।
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\(0.\overline{27}\) और \(0.\overline{72}\) का योग किस प्रकार का दशमलव है?
What type of decimal is the sum of \(0.\overline{27}\) and \(0.\overline{72}\)?
#recurring-decimal
#addition
#terminating-result
#conceptual
A सांत / Terminating
B असांत आवर्ती / Non-terminating recurring
C असांत अनावर्ती / Non-terminating non-recurring
D अपरिमेय / Irrational
Explanation opens after your attempt
Correct Answer
A. सांत / Terminating
Step 1
Concept
\(0.\overline{27}=\frac{27}{99}\) and \(0.\overline{72}=\frac{72}{99}\), so their sum is (1). The sum of two recurring decimals can be terminating.
Step 2
Why this answer is correct
The correct answer is A. सांत / Terminating. \(0.\overline{27}=\frac{27}{99}\) and \(0.\overline{72}=\frac{72}{99}\), so their sum is (1). The sum of two recurring decimals can be terminating.
Step 3
Exam Tip
\(0.\overline{27}=\frac{27}{99}\) और \(0.\overline{72}=\frac{72}{99}\) हैं इसलिए योग (1) है। दो आवर्ती दशमलवों का योग सांत भी हो सकता है।
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\(0.\overline{54}\) और \(0.\overline{45}\) का योग किस प्रकार का दशमलव है?
What type of decimal is the sum of \(0.\overline{54}\) and \(0.\overline{45}\)?
#recurring-decimal
#addition
#terminating-result
#conceptual
A सांत / Terminating
B असांत आवर्ती / Non-terminating recurring
C असांत अनावर्ती / Non-terminating non-recurring
D अपरिमेय / Irrational
Explanation opens after your attempt
Correct Answer
A. सांत / Terminating
Step 1
Concept
\(0.\overline{54}=\frac{54}{99}\) and \(0.\overline{45}=\frac{45}{99}\), so their sum is (1). The sum of two recurring decimals can sometimes be terminating.
Step 2
Why this answer is correct
The correct answer is A. सांत / Terminating. \(0.\overline{54}=\frac{54}{99}\) and \(0.\overline{45}=\frac{45}{99}\), so their sum is (1). The sum of two recurring decimals can sometimes be terminating.
Step 3
Exam Tip
\(0.\overline{54}=\frac{54}{99}\) और \(0.\overline{45}=\frac{45}{99}\), इसलिए योग (1) है। दो आवर्ती दशमलवों का योग कभी-कभी सांत हो सकता है।
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\(0.\overline{81}\) और \(0.\overline{18}\) का योग कैसा दशमलव देगा?
What type of decimal will the sum of \(0.\overline{81}\) and \(0.\overline{18}\) give?
#recurring-decimal
#addition
#terminating-decimal
#conceptual
A सांत / Terminating
B असांत आवर्ती / Non-terminating recurring
C असांत अनावर्ती / Non-terminating non-recurring
D अपरिमेय / Irrational
Explanation opens after your attempt
Correct Answer
A. सांत / Terminating
Step 1
Concept
\(0.\overline{81}=\frac{81}{99}\) and \(0.\overline{18}=\frac{18}{99}\).
Step 2
Why this answer is correct
Their sum is \(\frac{99}{99}=1\), which is terminating.
Step 3
Exam Tip
The sum of two recurring decimals can be terminating. चरण 1: \(0.\overline{81}=\frac{81}{99}\) और \(0.\overline{18}=\frac{18}{99}\) है। चरण 2: योग \(\frac{99}{99}=1\) है, जो सांत दशमलव है। चरण 3: दो आवर्ती दशमलवों का योग सांत भी हो सकता है।
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\(0.\overline{6}+0.\overline{3}\) का दशमलव प्रसार कैसा होगा?
What type of decimal expansion will \(0.\overline{6}+0.\overline{3}\) have?
#recurring-decimal
#addition
#terminating-decimal
#conceptual
A सांत / Terminating
B असांत आवर्ती / Non-terminating recurring
C असांत अनावर्ती / Non-terminating non-recurring
D अपरिमेय / Irrational
Explanation opens after your attempt
Correct Answer
A. सांत / Terminating
Step 1
Concept
\(0.\overline{6}=\frac{2}{3}\) and \(0.\overline{3}=\frac{1}{3}\).
Step 2
Why this answer is correct
Their sum is (1), whose decimal (1.0) is terminating.
Step 3
Exam Tip
The sum of recurring decimals can sometimes be terminating. चरण 1: \(0.\overline{6}=\frac{2}{3}\) और \(0.\overline{3}=\frac{1}{3}\) है। चरण 2: योग (1) है, जिसका दशमलव (1.0) के रूप में सांत है। चरण 3: आवर्ती दशमलवों का योग कभी-कभी सांत भी हो सकता है।
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