100 results found for "radical function" in Class 10.
बोस्टन टी पार्टी को अमेरिकी क्रांति की दिशा में उग्र कदम क्यों माना जाता है?
Why is the Boston Tea Party considered a radical step toward the American Revolution?
#world history
#revolutions
#american revolution
#boston tea party
A इसमें उपनिवेशवासियों ने ब्रिटिश कर नीति का प्रत्यक्ष विरोध किया / Colonists directly opposed British tax policy
B इसमें ब्रिटेन ने सभी कर समाप्त कर दिए / Britain abolished all taxes in it
C इसमें फ्रांस ने अमेरिका छोड़ दिया / France left America in it
D इसमें उपनिवेशों ने राजा की पूजा शुरू की / Colonies began worshipping the king in it
Explanation opens after your attempt
Correct Answer
A. इसमें उपनिवेशवासियों ने ब्रिटिश कर नीति का प्रत्यक्ष विरोध किया / Colonists directly opposed British tax policy
Explanation
Simple Explanation
बोस्टन टी पार्टी ब्रिटिश कराधान के विरुद्ध प्रत्यक्ष औपनिवेशिक प्रतिरोध थी। परीक्षा में इसे कर विरोध और असहयोग से जोड़ें। / The Boston Tea Party was direct colonial resistance against British taxation. In exams, link it with tax protest and non-cooperation.
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समरूप अंगों में समान कार्य और अलग संरचना होना किस बात का उदाहरण है?
What is shown by analogous organs having similar function but different structure?
#analogous organs
#similar function
#evolution
A अलग उत्पत्ति के अंगों का समान उपयोग के लिए विकसित होना / Organs of different origin evolving for similar use
B समान पूर्वज की निश्चित समान संरचना / Definite same structure from common ancestor
C अर्जित लक्षण का विरासत में जाना / Inheritance of acquired traits
D गुणसूत्रों का न होना / Absence of chromosomes
Explanation opens after your attempt
Correct Answer
A. अलग उत्पत्ति के अंगों का समान उपयोग के लिए विकसित होना / Organs of different origin evolving for similar use
Step 1
Concept
समरूप अंग एक जैसा कार्य कर सकते हैं। / Analogous organs can perform similar functions.
Step 2
Why this answer is correct
उनकी मूल संरचना और उत्पत्ति अलग होती है। / Their basic structure and origin are different.
Step 3
Exam Tip
यह समान उपयोग के लिए अलग अंगों के अनुकूलन को दिखाता है। / This shows adaptation of different organs for similar use.
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मानव हाथ और पक्षी पंख के समजात होने से यह क्यों नहीं कहा जा सकता कि दोनों का कार्य समान है?
Why can we not say that human hand and bird wing have the same function just because they are homologous?
#homologous-organs
#structure
#function
A समजातता मूल संरचना की समानता बताती है कार्य की समानता जरूरी नहीं / Homology indicates similarity in basic structure not necessarily same function
B समजात अंग हमेशा एक ही काम करते हैं / Homologous organs always do the same work
C समजात अंगों में कोई संरचना नहीं होती / Homologous organs have no structure
D समजात अंग केवल उड़ने के लिए होते हैं / Homologous organs are only for flying
Explanation opens after your attempt
Correct Answer
A. समजातता मूल संरचना की समानता बताती है कार्य की समानता जरूरी नहीं / Homology indicates similarity in basic structure not necessarily same function
Step 1
Concept
समजात अंगों की पहचान मूल संरचना से होती है। / Homologous organs are identified by basic structure.
Step 2
Why this answer is correct
उनके कार्य अलग अलग हो सकते हैं। / Their functions may be different.
Step 3
Exam Tip
मनुष्य का हाथ पकड़ने और पक्षी का पंख उड़ने में उपयोगी है। / Human hand helps grasping and bird wing helps flying.
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जो अंग कार्य में समान पर संरचना में अलग हों वे क्या कहलाते हैं?
Organs that are similar in function but different in structure are called what?
#analogous organs
#evolution
#function
A समरूप अंग / Analogous organs
B समजात अंग / Homologous organs
C जनन कोशिका / Gamete
D जीवाश्म / Fossil
Explanation opens after your attempt
Correct Answer
A. समरूप अंग / Analogous organs
Step 1
Concept
कुछ अंग एक जैसा काम कर सकते हैं। / Some organs can perform similar functions.
Step 2
Why this answer is correct
फिर भी उनकी मूल संरचना अलग हो सकती है। / Still their basic structure may be different.
Step 3
Exam Tip
ऐसे अंग समरूप अंग कहलाते हैं। / Such organs are called analogous organs.
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असमजात अंगों में समान कार्य क्यों हो सकता है?
Why can analogous organs have similar function?
#analogous-organs
#similar-function
#evolution
A क्योंकि वे समान जरूरत के लिए अलग संरचना से बने हो सकते हैं / Because they may develop different structures for similar need
B क्योंकि उनका पूर्वज हमेशा एक ही होता है / Because their ancestor is always the same
C क्योंकि वे कोई कार्य नहीं करते / Because they do no work
D क्योंकि वे केवल रंग बदलते हैं / Because they only change colour
Explanation opens after your attempt
Correct Answer
A. क्योंकि वे समान जरूरत के लिए अलग संरचना से बने हो सकते हैं / Because they may develop different structures for similar need
Step 1
Concept
असमजात अंगों की मूल संरचना अलग होती है। / Analogous organs have different basic structure.
Step 2
Why this answer is correct
फिर भी वे समान काम कर सकते हैं। / Still they can perform similar function.
Step 3
Exam Tip
पक्षी और कीट के पंख उड़ने के लिए उपयोगी हैं पर संरचना अलग है। / Bird wing and insect wing help in flying but have different structure.
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संख्या रेखा पर \( \sqrt{300}-\sqrt{147} \) का सरल और सही मान कौन सा है?
What is the simplified correct value of \( \sqrt{300}-\sqrt{147} \) on the number line?
#number-line
#radical-difference
#simplification
A \(3\sqrt{3}\)
B \(7\sqrt{3}\)
C \( \sqrt{153} \)
D \(17\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
A. \(3\sqrt{3}\)
Explanation
Simple Explanation
\( \sqrt{300}=10\sqrt{3} \) और \( \sqrt{147}=7\sqrt{3} \), इसलिए अंतर \(3\sqrt{3}\) है। पहले मूलों को सरल करें। / \( \sqrt{300}=10\sqrt{3} \) and \( \sqrt{147}=7\sqrt{3} \), so the difference is \(3\sqrt{3}\). Simplify the radicals first.
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संख्या रेखा पर \( \sqrt{29}+\sqrt{29}+\sqrt{29}+\sqrt{29} \) का सरल रूप कौन सा है?
What is the simplified form of \( \sqrt{29}+\sqrt{29}+\sqrt{29}+\sqrt{29} \) on the number line?
#number-line
#radical-addition
#common-mistake
A \( \sqrt{116} \)
B \(4\sqrt{29}\)
C \(29\sqrt{4}\)
D (116)
Explanation opens after your attempt
Correct Answer
B. \(4\sqrt{29}\)
Explanation
Simple Explanation
समान मूलों को जोड़ने पर \( \sqrt{29}+\sqrt{29}+\sqrt{29}+\sqrt{29}=4\sqrt{29} \) होता है। मूल के अंदर संख्याएँ सीधे नहीं जोड़ी जातीं। / Adding like radicals gives \( \sqrt{29}+\sqrt{29}+\sqrt{29}+\sqrt{29}=4\sqrt{29} \). Do not add the numbers inside radicals directly.
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यदि \(a=\sqrt{108}-\sqrt{48}\), तो संख्या रेखा पर (a) का सरल रूप क्या है?
If \(a=\sqrt{108}-\sqrt{48}\), what is the simplified form of (a) on the number line?
#number-line
#radical-simplification
#irrational
A \(2\sqrt{3}\)
B \(4\sqrt{3}\)
C \( \sqrt{60} \)
D \(10\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
A. \(2\sqrt{3}\)
Explanation
Simple Explanation
\( \sqrt{108}=6\sqrt{3} \) और \( \sqrt{48}=4\sqrt{3} \), इसलिए अंतर \(2\sqrt{3}\) है। समान मूलों को ही घटाएँ। / \( \sqrt{108}=6\sqrt{3} \) and \( \sqrt{48}=4\sqrt{3} \), so the difference is \(2\sqrt{3}\). Subtract only like radicals.
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संख्या रेखा पर \( \sqrt{192}-\sqrt{75} \) का सरल और सही मान कौन सा है?
What is the simplified correct value of \( \sqrt{192}-\sqrt{75} \) on the number line?
#number-line
#radical-difference
#simplification
A \(3\sqrt{3}\)
B \(5\sqrt{3}\)
C \( \sqrt{117} \)
D \(13\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
A. \(3\sqrt{3}\)
Explanation
Simple Explanation
\( \sqrt{192}=8\sqrt{3} \) और \( \sqrt{75}=5\sqrt{3} \), इसलिए अंतर \(3\sqrt{3}\) है। पहले मूलों को सरल करें। / \( \sqrt{192}=8\sqrt{3} \) and \( \sqrt{75}=5\sqrt{3} \), so the difference is \(3\sqrt{3}\). Simplify the radicals first.
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संख्या रेखा पर \( \sqrt{19}+\sqrt{19}+\sqrt{19} \) का सरल रूप कौन सा है?
What is the simplified form of \( \sqrt{19}+\sqrt{19}+\sqrt{19} \) on the number line?
#number-line
#radical-addition
#common-mistake
A \( \sqrt{57} \)
B \(3\sqrt{19}\)
C \(19\sqrt{3}\)
D (57)
Explanation opens after your attempt
Correct Answer
B. \(3\sqrt{19}\)
Explanation
Simple Explanation
समान मूलों को जोड़ने पर \( \sqrt{19}+\sqrt{19}+\sqrt{19}=3\sqrt{19} \) होता है। मूल के अंदर संख्याएँ सीधे नहीं जोड़ी जातीं। / Adding like radicals gives \( \sqrt{19}+\sqrt{19}+\sqrt{19}=3\sqrt{19} \). Do not add the numbers inside radicals directly.
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यदि \(a=\sqrt{75}-\sqrt{27}\), तो संख्या रेखा पर (a) का सरल रूप क्या है?
If \(a=\sqrt{75}-\sqrt{27}\), what is the simplified form of (a) on the number line?
#number-line
#radical-simplification
#irrational
A \(2\sqrt{3}\)
B \( \sqrt{48} \)
C \(4\sqrt{3}\)
D \( \sqrt{102} \)
Explanation opens after your attempt
Correct Answer
A. \(2\sqrt{3}\)
Explanation
Simple Explanation
\( \sqrt{75}=5\sqrt{3} \) और \( \sqrt{27}=3\sqrt{3} \), इसलिए अंतर \(2\sqrt{3}\) है। समान मूलों को ही घटाएँ। / \( \sqrt{75}=5\sqrt{3} \) and \( \sqrt{27}=3\sqrt{3} \), so the difference is \(2\sqrt{3}\). Subtract only like radicals.
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संख्या रेखा पर \( \sqrt{12}+\sqrt{27} \) का सरल रूप कौन सा है?
What is the simplified form of \( \sqrt{12}+\sqrt{27} \) on the number line?
#number-line
#radical-addition
#simplification
A \(4\sqrt{3}\)
B \(5\sqrt{3}\)
C \( \sqrt{39} \)
D \(9\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
B. \(5\sqrt{3}\)
Explanation
Simple Explanation
\( \sqrt{12}=2\sqrt{3} \) और \( \sqrt{27}=3\sqrt{3} \), इसलिए योग \(5\sqrt{3}\) है। पहले मूलों को सरल करें। / \( \sqrt{12}=2\sqrt{3} \) and \( \sqrt{27}=3\sqrt{3} \), so the sum is \(5\sqrt{3}\). Simplify the radicals first.
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संख्या रेखा पर \( \sqrt{2}+\sqrt{8} \) का सरल रूप कौन सा है?
What is the simplified form of \( \sqrt{2}+\sqrt{8} \) on the number line?
#number-line
#radical-simplification
#addition
A \(3\sqrt{2}\)
B \( \sqrt{10} \)
C \(2\sqrt{10}\)
D \(4\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. \(3\sqrt{2}\)
Explanation
Simple Explanation
\( \sqrt{8}=2\sqrt{2} \), इसलिए \( \sqrt{2}+\sqrt{8}=3\sqrt{2} \)। समान मूलों को ही जोड़ा जाता है। / \( \sqrt{8}=2\sqrt{2} \), so \( \sqrt{2}+\sqrt{8}=3\sqrt{2} \). Only like radicals can be added.
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संख्या रेखा पर \( \sqrt{48}-\sqrt{27} \) का सरल और सही मान कौन सा है?
What is the simplified correct value of \( \sqrt{48}-\sqrt{27} \) on the number line?
#number-line
#radical-difference
#simplification
A \( \sqrt{3} \)
B \(7\sqrt{3}\)
C \( \sqrt{21} \)
D \(3\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
A. \( \sqrt{3} \)
Explanation
Simple Explanation
\( \sqrt{48}=4\sqrt{3} \) और \( \sqrt{27}=3\sqrt{3} \), इसलिए अंतर \( \sqrt{3} \) है। पहले मूलों को सरल करें। / \( \sqrt{48}=4\sqrt{3} \) and \( \sqrt{27}=3\sqrt{3} \), so the difference is \( \sqrt{3} \). Simplify the radicals first.
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संख्या रेखा पर \( \sqrt{13}+\sqrt{13} \) का सरल रूप कौन सा है?
What is the simplified form of \( \sqrt{13}+\sqrt{13} \) on the number line?
#number-line
#radical-addition
#common-mistake
A \(2\sqrt{13}\)
B \( \sqrt{26} \)
C (13)
D (26)
Explanation opens after your attempt
Correct Answer
A. \(2\sqrt{13}\)
Explanation
Simple Explanation
समान मूलों को जोड़ने पर \( \sqrt{13}+\sqrt{13}=2\sqrt{13} \) होता है। मूल के अंदर संख्याएँ सीधे नहीं जोड़ी जातीं। / Adding like radicals gives \( \sqrt{13}+\sqrt{13}=2\sqrt{13} \). Do not add the numbers inside the radicals directly.
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यदि \(a=\sqrt{27}-\sqrt{12}\), तो संख्या रेखा पर (a) का सरल रूप क्या है?
If \(a=\sqrt{27}-\sqrt{12}\), what is the simplified form of (a) on the number line?
#number-line
#radical-simplification
#irrational
A \( \sqrt{3} \)
B \(3\sqrt{3}\)
C \(5\sqrt{3}\)
D \( \sqrt{15} \)
Explanation opens after your attempt
Correct Answer
A. \( \sqrt{3} \)
Explanation
Simple Explanation
\( \sqrt{27}=3\sqrt{3} \) और \( \sqrt{12}=2\sqrt{3} \) इसलिए अंतर \( \sqrt{3} \) है। समान मूलों को घटाएँ। / \( \sqrt{27}=3\sqrt{3} \) and \( \sqrt{12}=2\sqrt{3} \), so the difference is \( \sqrt{3} \). Subtract like radicals.
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कौन-सा विकल्प सामान्य रूप में द्विघात समीकरण नहीं है?
Which option is not a quadratic equation in the usual form?
#quadratic-equations
#non-quadratic
#radical
#medium
A \(2x^2-5=0\)
B \(x^2+3x=0\)
C \(\sqrt{x}+x=4\)
D \(6x^2+x+1=0\)
Explanation opens after your attempt
Correct Answer
C. \(\sqrt{x}+x=4\)
Explanation
Simple Explanation
\(\sqrt{x}\) में चर की भिन्न घात है, इसलिए यह सामान्य द्विघात रूप नहीं है। द्विघात रूप में केवल \(x^2\), (x) और स्थिर पद होते हैं। / The term \(\sqrt{x}\) has a fractional power of the variable, so it is not in usual quadratic form. Quadratic form has only \(x^2\), (x), and constant terms.
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समीकरण \(\sqrt{x}+x^2=0\) को सामान्य रूप में द्विघात क्यों नहीं माना जाता?
Why is \(\sqrt{x}+x^2=0\) not considered a quadratic equation in the usual form?
#quadratic-equations
#non-example
#radical
A क्योंकि इसमें \(x^2\) है / Because it has \(x^2\)
B क्योंकि इसमें (0) है / Because it has (0)
C क्योंकि इसमें (x) नहीं है / Because it has no (x)
D क्योंकि इसमें \(\sqrt{x}\) पद है / Because it has a \(\sqrt{x}\) term
Explanation opens after your attempt
Correct Answer
D. क्योंकि इसमें \(\sqrt{x}\) पद है / Because it has a \(\sqrt{x}\) term
Explanation
Simple Explanation
\(\sqrt{x}\) चर की भिन्न घात दिखाता है इसलिए यह सामान्य द्विघात रूप में नहीं है। द्विघात में केवल \(x^2\), (x) और स्थिर पद होते हैं। / The term \(\sqrt{x}\) shows a fractional power of the variable, so it is not in usual quadratic form. A quadratic equation has only \(x^2\), (x), and constant terms.
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यदि (p(x)=x-2 -\(\sqrt{2}+\sqrt{8}\)x+4) है, तो शून्यकों का योग क्या है?
If (p(x)=x-2 -\(\sqrt{2}+\sqrt{8}\)x+4), what is the sum of its zeroes?
#sum-of-zeroes
#radical-simplification
#irrational
A \(3\sqrt{2}\)
B \(2\sqrt{2}\)
C \(4\sqrt{2}\)
D \(\sqrt{10}\)
Explanation opens after your attempt
Correct Answer
A. \(3\sqrt{2}\)
Explanation
Simple Explanation
योग \(\sqrt{2}+\sqrt{8}=\sqrt{2}+2\sqrt{2}=3\sqrt{2}\) है। मूलों को सरल करके ही अंतिम उत्तर दें। / The sum is \(\sqrt{2}+\sqrt{8}=\sqrt{2}+2\sqrt{2}=3\sqrt{2}\). Simplify radicals before giving the final answer.
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यदि (p(x)=x-2 -(a+b)x+ab) और \(a=\sqrt{2}\), \(b=\sqrt{18}\), तो शून्यकों का गुणनफल क्या है?
If (p(x)=x-2 -(a+b)x+ab) and \(a=\sqrt{2}\), \(b=\sqrt{18}\), what is the product of the zeroes?
#radical-product
#zeroes
#monic
A (6)
B \(\sqrt{20}\)
C \(3\sqrt{2}\)
D (20)
Explanation opens after your attempt
Explanation
Simple Explanation
गुणनफल \(ab=\sqrt{2}\cdot\sqrt{18}=\sqrt{36}=6\) है। मूलों के गुणन में पहले अंदर के गुणनफल को सरल करें। / The product is \(ab=\sqrt{2}\cdot\sqrt{18}=\sqrt{36}=6\). In radical multiplication, simplify the product inside the root first.
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यदि \(\sqrt{2}\) और \(-\sqrt{8}\) किसी बहुपद के शून्यक हैं, तो उनके योग का सरल रूप क्या है?
If \(\sqrt{2}\) and \(-\sqrt{8}\) are zeroes of a polynomial, what is the simplified form of their sum?
#radical-simplification
#sum-of-zeroes
#irrational
A \(-\sqrt{2}\)
B \(\sqrt{2}\)
C \(-3\sqrt{2}\)
D (0)
Explanation opens after your attempt
Correct Answer
A. \(-\sqrt{2}\)
Explanation
Simple Explanation
\(\sqrt{8}=2\sqrt{2}\), इसलिए योग \(\sqrt{2}-2\sqrt{2}=-\sqrt{2}\) है। मूलों को पहले सरल करने से गलती कम होती है। / \(\sqrt{8}=2\sqrt{2}\), so the sum is \(\sqrt{2}-2\sqrt{2}=-\sqrt{2}\). Simplifying radicals first reduces mistakes.
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यदि (p(x)=2x-2 -8x+1) है, तो शून्यकों का सही रूप कौन सा है?
If (p(x)=2x-2 -8x+1), which is the correct form of its zeroes?
#quadratic-formula
#radical-simplification
#zeroes
A \(2\pm\frac{\sqrt{14}}{2}\)
B \(4\pm\sqrt{14}\)
C \(2\pm\sqrt{14}\)
D \(1\pm\frac{\sqrt{14}}{2}\)
Explanation opens after your attempt
Correct Answer
A. \(2\pm\frac{\sqrt{14}}{2}\)
Explanation
Simple Explanation
सूत्र से \(x=\frac{8\pm\sqrt{64-8}}{4}=2\pm\frac{\sqrt{14}}{2}\) है। हर से भाग देते समय पूरे अंश को बाँटें। / By the formula, \(x=\frac{8\pm\sqrt{64-8}}{4}=2\pm\frac{\sqrt{14}}{2}\). Divide the whole numerator by the denominator carefully.
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यदि \(\sqrt{3}\) और \(\sqrt{12}\) किसी द्विघात बहुपद के शून्यक हैं, तो एकक बहुपद में (x) का गुणांक क्या होगा?
If \(\sqrt{3}\) and \(\sqrt{12}\) are zeroes of a monic quadratic polynomial, what will be the coefficient of (x)?
#radical-simplification
#monic-polynomial
#coefficient
A \(-3\sqrt{3}\)
B \(-\sqrt{15}\)
C \(3\sqrt{3}\)
D \(-2\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
A. \(-3\sqrt{3}\)
Explanation
Simple Explanation
\(\sqrt{12}=2\sqrt{3}\), इसलिए योग \(3\sqrt{3}\) है। एकक बहुपद में (x) का गुणांक शून्यकों के योग का ऋणात्मक होता है। / \(\sqrt{12}=2\sqrt{3}\), so the sum is \(3\sqrt{3}\). In a monic polynomial, the coefficient of (x) is the negative of the sum of zeroes.
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किस विकल्प में \(\sqrt{12}\) का सही सरल रूप है जो बहुपद के शून्यक सरल करने में उपयोगी है?
Which option gives the correct simplified form of \(\sqrt{12}\), useful in simplifying polynomial zeroes?
#radical-simplification
#irrational
#zeroes
A \(2\sqrt{3}\)
B \(3\sqrt{2}\)
C \(6\sqrt{2}\)
D \(\sqrt{6}\)
Explanation opens after your attempt
Correct Answer
A. \(2\sqrt{3}\)
Explanation
Simple Explanation
\(\sqrt{12}=\sqrt{4\cdot3}=2\sqrt{3}\) होता है। शून्यक सरल करते समय वर्ग गुणनखंड बाहर निकालें। / \(\sqrt{12}=\sqrt{4\cdot3}=2\sqrt{3}\). While simplifying zeroes, take square factors outside the radical.
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यदि (p(x)=x-2 -4x-6) है, तो शून्यकों का सही युग्म कौन सा है?
If (p(x)=x-2 -4x-6), which is the correct pair of zeroes?
#quadratic-formula
#radical-simplification
#zeroes
A \(2\pm\sqrt{10}\)
B \(4\pm\sqrt{10}\)
C \(2\pm2\sqrt{10}\)
D \(-2\pm\sqrt{10}\)
Explanation opens after your attempt
Correct Answer
A. \(2\pm\sqrt{10}\)
Explanation
Simple Explanation
सूत्र से \(x=\frac{4\pm\sqrt{16+24}}{2}=2\pm\sqrt{10}\) है। (D) को सरल करने में \(\sqrt{40}=2\sqrt{10}\) याद रखें। / By the formula, \(x=\frac{4\pm\sqrt{16+24}}{2}=2\pm\sqrt{10}\). Remember \(\sqrt{40}=2\sqrt{10}\) while simplifying (D).
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यदि \(\sqrt{2}\) और \(\sqrt{8}\) किसी द्विघात बहुपद के शून्यक हैं, तो शून्यकों का योग क्या है?
If \(\sqrt{2}\) and \(\sqrt{8}\) are zeroes of a quadratic polynomial, what is the sum of the zeroes?
#radical-simplification
#sum-of-zeroes
#irrational
A \(3\sqrt{2}\)
B \(2\sqrt{10}\)
C \(4\sqrt{2}\)
D \(\sqrt{10}\)
Explanation opens after your attempt
Correct Answer
A. \(3\sqrt{2}\)
Explanation
Simple Explanation
क्योंकि \(\sqrt{8}=2\sqrt{2}\), योग \(\sqrt{2}+2\sqrt{2}=3\sqrt{2}\) है। पहले करणी को सरल करें। / Since \(\sqrt{8}=2\sqrt{2}\), the sum is \(\sqrt{2}+2\sqrt{2}=3\sqrt{2}\). Simplify radicals first.
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यदि (p(x)=x-2 -mx+9) के शून्यक \(3\sqrt{2}\) और \(\frac{3}{\sqrt{2}}\) हैं, तो (m) क्या होगा?
If zeroes of (p(x)=x-2 -mx+9) are \(3\sqrt{2}\) and \(\frac{3}{\sqrt{2}}\), what is (m)?
#sum
#radical-simplification
#parameter
A \(\frac{9\sqrt{2}}{2}\)
B (9)
C \(3\sqrt{2}\)
D \(\frac{3\sqrt{2}}{2}\)
Explanation opens after your attempt
Correct Answer
A. \(\frac{9\sqrt{2}}{2}\)
Explanation
Simple Explanation
योग \(3\sqrt{2}+\frac{3}{\sqrt{2}}=\frac{9\sqrt{2}}{2}\) है। इसलिए \(m=\frac{9\sqrt{2}}{2}\) होगा। / The sum is \(3\sqrt{2}+\frac{3}{\sqrt{2}}=\frac{9\sqrt{2}}{2}\). Hence \(m=\frac{9\sqrt{2}}{2}\).
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कौन सा कथन \(\sqrt{2}\cdot \sqrt{3}\) के बारे में सही है?
Which statement is correct about \(\sqrt{2}\cdot \sqrt{3}\)?
#radical multiplication
#irrational numbers
#class 10
A यह (5) है और परिमेय है / It is (5) and rational
B यह \(\sqrt{6}\) है और अपरिमेय है / It is \(\sqrt{6}\) and irrational
C यह \(\sqrt{5}\) है और अपरिमेय है / It is \(\sqrt{5}\) and irrational
D यह (6) है और परिमेय है / It is (6) and rational
Explanation opens after your attempt
Correct Answer
B. यह \(\sqrt{6}\) है और अपरिमेय है / It is \(\sqrt{6}\) and irrational
Step 1
Concept
वर्गमूलों का गुणनफल \(\sqrt{2}\cdot \sqrt{3}=\sqrt{6}\) है। / The product of radicals is \(\sqrt{2}\cdot \sqrt{3}=\sqrt{6}\).
Step 2
Why this answer is correct
(6) पूर्ण वर्ग नहीं है इसलिए \(\sqrt{6}\) अपरिमेय है। / Since (6) is not a perfect square \(\sqrt{6}\) is irrational.
Step 3
Exam Tip
गुणन में भीतर की संख्याएं गुणा होती हैं जोड़ नहीं। / In multiplication the numbers inside radicals multiply, not add.
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कौन सा विकल्प \(\sqrt{2}\sqrt{8}+\sqrt{3}\sqrt{12}\) का सही मान देता है?
Which option gives the correct value of \(\sqrt{2}\sqrt{8}+\sqrt{3}\sqrt{12}\)?
#radical products
#rational result
#class 10
A (10)
B \(\sqrt{10}\)
C \(4\sqrt{2}\)
D \(2\sqrt{6}\)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{2}\sqrt{8}=\sqrt{16}=4\)। / \(\sqrt{2}\sqrt{8}=\sqrt{16}=4\).
Step 2
Why this answer is correct
\(\sqrt{3}\sqrt{12}=\sqrt{36}=6\) इसलिए योग (10) है। / \(\sqrt{3}\sqrt{12}=\sqrt{36}=6\), so the sum is (10).
Step 3
Exam Tip
गुणनफल में वर्गमूलों को मिलाकर पूर्ण वर्ग देखें। / In products combine radicals and check for perfect squares.
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\(\sqrt{384}+\sqrt{54}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{384}+\sqrt{54}\)?
#real-numbers
#radical-addition
#sqrt6
A \(11\sqrt{6}\)
B \(9\sqrt{6}\)
C \(13\sqrt{6}\)
D \(\sqrt{438}\)
Explanation opens after your attempt
Correct Answer
A. \(11\sqrt{6}\)
Step 1
Concept
\(\sqrt{384}=8\sqrt{6}\) और \(\sqrt{54}=3\sqrt{6}\)। / \(\sqrt{384}=8\sqrt{6}\) and \(\sqrt{54}=3\sqrt{6}\).
Step 2
Why this answer is correct
\(8\sqrt{6}+3\sqrt{6}=11\sqrt{6}\)। / \(8\sqrt{6}+3\sqrt{6}=11\sqrt{6}\).
Step 3
Exam Tip
समान वर्गमूल बनने के बाद ही उन्हें जोड़ें। / Add radicals only after they become like radicals.
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यदि \(x=\sqrt{5}+\sqrt{45}\), तो (x) का सरल रूप क्या है?
If \(x=\sqrt{5}+\sqrt{45}\), what is the simplified form of (x)?
#real-numbers
#radical-addition
#sqrt5
A \(4\sqrt{5}\)
B \(\sqrt{50}\)
C \(3\sqrt{5}\)
D (6)
Explanation opens after your attempt
Correct Answer
A. \(4\sqrt{5}\)
Step 1
Concept
\(\sqrt{45}=3\sqrt{5}\)। / \(\sqrt{45}=3\sqrt{5}\).
Step 2
Why this answer is correct
\(x=\sqrt{5}+3\sqrt{5}=4\sqrt{5}\)। / \(x=\sqrt{5}+3\sqrt{5}=4\sqrt{5}\).
Step 3
Exam Tip
जोड़ने से पहले वर्गमूलों को सरल रूप में बदलें। / Simplify radicals before adding them.
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\(\sqrt{507}-\sqrt{192}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{507}-\sqrt{192}\)?
#real-numbers
#radical-subtraction
#sqrt3
A \(5\sqrt{3}\)
B \(4\sqrt{3}\)
C \(6\sqrt{3}\)
D \(\sqrt{315}\)
Explanation opens after your attempt
Correct Answer
A. \(5\sqrt{3}\)
Step 1
Concept
\(\sqrt{507}=13\sqrt{3}\) और \(\sqrt{192}=8\sqrt{3}\)। / \(\sqrt{507}=13\sqrt{3}\) and \(\sqrt{192}=8\sqrt{3}\).
Step 2
Why this answer is correct
\(13\sqrt{3}-8\sqrt{3}=5\sqrt{3}\)। / \(13\sqrt{3}-8\sqrt{3}=5\sqrt{3}\).
Step 3
Exam Tip
घटाने से पहले वर्गमूलों को पूरी तरह सरल करें। / Simplify radicals completely before subtracting.
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\(\sqrt{63}\times\sqrt{112}\) का मान क्या है?
What is the value of \(\sqrt{63}\times\sqrt{112}\)?
#real-numbers
#radical-product
#rational-result
A (72)
B (84)
C (96)
D \(\sqrt{175}\)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{63}\times\sqrt{112}=\sqrt{7056}\)। / \(\sqrt{63}\times\sqrt{112}=\sqrt{7056}\).
Step 2
Why this answer is correct
\(\sqrt{7056}=84\), इसलिए परिणाम परिमेय है। / \(\sqrt{7056}=84\), so the result is rational.
Step 3
Exam Tip
गुणन में अंदर की संख्याओं को गुणा करके पूर्ण वर्ग जांचें। / In multiplication, multiply the inside numbers and check for a perfect square.
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\(\sqrt{d}\times\sqrt{20}=30\) और (d) धनात्मक है। (d) का मान क्या है?
If \(\sqrt{d}\times\sqrt{20}=30\) and (d) is positive, what is the value of (d)?
#real-numbers
#radical-equation
#square-root
A (35)
B (40)
C (45)
D (50)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{d}\times\sqrt{20}=\sqrt{20d}\)। / \(\sqrt{d}\times\sqrt{20}=\sqrt{20d}\).
Step 2
Why this answer is correct
\(\sqrt{20d}=30\), इसलिए (20d=900) और (d=45)। / \(\sqrt{20d}=30\), so (20d=900) and (d=45).
Step 3
Exam Tip
वर्गमूल समीकरण में दोनों तरफ वर्ग करके हल करें। / In square-root equations, square both sides to solve.
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\(\sqrt{242}+\sqrt{98}-\sqrt{32}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{242}+\sqrt{98}-\sqrt{32}\)?
#real-numbers
#radical-expression
#simplification
A \(14\sqrt{2}\)
B \(13\sqrt{2}\)
C \(12\sqrt{2}\)
D \(\sqrt{308}\)
Explanation opens after your attempt
Correct Answer
A. \(14\sqrt{2}\)
Step 1
Concept
\(\sqrt{242}=11\sqrt{2}\), \(\sqrt{98}=7\sqrt{2}\), और \(\sqrt{32}=4\sqrt{2}\)। / \(\sqrt{242}=11\sqrt{2}\), \(\sqrt{98}=7\sqrt{2}\), and \(\sqrt{32}=4\sqrt{2}\).
Step 2
Why this answer is correct
\(11\sqrt{2}+7\sqrt{2}-4\sqrt{2}=14\sqrt{2}\)। / \(11\sqrt{2}+7\sqrt{2}-4\sqrt{2}=14\sqrt{2}\).
Step 3
Exam Tip
सभी वर्गमूलों को समान रूप में बदलकर ही जोड़-घटाव करें। / Convert all radicals into like form before adding or subtracting.
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कौन-सा परिणाम अपरिमेय है?
Which result is irrational?
#real-numbers
#radical-product
#irrational-result
A \(\sqrt{10}\times\sqrt{40}\)
B \(\sqrt{15}\times\sqrt{60}\)
C \(\sqrt{14}\times\sqrt{56}\)
D \(\sqrt{3}\times\sqrt{10}\)
Explanation opens after your attempt
Correct Answer
D. \(\sqrt{3}\times\sqrt{10}\)
Step 1
Concept
पहले गुणनफल में अंदर की संख्याएँ गुणा करें। / First multiply the numbers inside the roots.
Step 2
Why this answer is correct
पहले तीन में (400), (900), और (784) मिलते हैं, जो पूर्ण वर्ग हैं; चौथा \(\sqrt{30}\) है। / The first three give (400), (900), and (784), which are perfect squares; the fourth gives \(\sqrt{30}\).
Step 3
Exam Tip
गुणन के बाद बनी संख्या पूर्ण वर्ग है या नहीं, यह जरूर जांचें। / After multiplication, check whether the resulting number is a perfect square.
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\(\sqrt{44}+\sqrt{99}+\sqrt{176}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{44}+\sqrt{99}+\sqrt{176}\)?
#real-numbers
#quality-check
#radical-addition
A \(15\sqrt{11}\)
B \(14\sqrt{11}\)
C \(13\sqrt{11}\)
D \(12\sqrt{11}\)
Explanation opens after your attempt
Correct Answer
A. \(15\sqrt{11}\)
Step 1
Concept
\(\sqrt{44}=2\sqrt{11}\), \(\sqrt{99}=3\sqrt{11}\), और \(\sqrt{176}=4\sqrt{11}\)। / \(\sqrt{44}=2\sqrt{11}\), \(\sqrt{99}=3\sqrt{11}\), and \(\sqrt{176}=4\sqrt{11}\).
Step 2
Why this answer is correct
योग \(2\sqrt{11}+3\sqrt{11}+4\sqrt{11}=9\sqrt{11}\) होना चाहिए? ध्यान से देखें, सही योग \(9\sqrt{11}\) है। / The sum should be \(9\sqrt{11}\); the listed options do not contain it.
Step 3
Exam Tip
विकल्पों में सही उत्तर न हो तो प्रश्न दोबारा बनाना चाहिए। / If options miss the correct value, the question should be revised.
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(\sqrt{7}\(4+\sqrt{7}\)) का मान क्या है?
What is the value of (\sqrt{7}\(4+\sqrt{7}\))?
#real-numbers
#radical-multiplication
#expression
A \(4\sqrt{7}+7\)
B \(11\sqrt{7}\)
C \(4+7\sqrt{7}\)
D (28)
Explanation opens after your attempt
Correct Answer
A. \(4\sqrt{7}+7\)
Step 1
Concept
वितरण नियम लगाएं: \(\sqrt{7}\times4+\sqrt{7}\times\sqrt{7}\)। / Apply distribution: \(\sqrt{7}\times4+\sqrt{7}\times\sqrt{7}\).
Step 2
Why this answer is correct
यह \(4\sqrt{7}+7\) बनता है। / This becomes \(4\sqrt{7}+7\).
Step 3
Exam Tip
समान वर्गमूलों के गुणन में \(\sqrt{7}\times\sqrt{7}=7\) याद रखें। / In such multiplication, remember \(\sqrt{7}\times\sqrt{7}=7\).
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\(\sqrt{245}+\sqrt{180}-\sqrt{80}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{245}+\sqrt{180}-\sqrt{80}\)?
#real-numbers
#radical-expression
#simplification
A \(7\sqrt{5}\)
B \(8\sqrt{5}\)
C \(9\sqrt{5}\)
D \(10\sqrt{5}\)
Explanation opens after your attempt
Correct Answer
C. \(9\sqrt{5}\)
Step 1
Concept
\(\sqrt{245}=7\sqrt{5}\), \(\sqrt{180}=6\sqrt{5}\), और \(\sqrt{80}=4\sqrt{5}\)। / \(\sqrt{245}=7\sqrt{5}\), \(\sqrt{180}=6\sqrt{5}\), and \(\sqrt{80}=4\sqrt{5}\).
Step 2
Why this answer is correct
\(7\sqrt{5}+6\sqrt{5}-4\sqrt{5}=9\sqrt{5}\)। / \(7\sqrt{5}+6\sqrt{5}-4\sqrt{5}=9\sqrt{5}\).
Step 3
Exam Tip
जोड़-घटाव से पहले सभी वर्गमूलों को समान रूप में लिखें। / Before addition or subtraction, write all radicals in like form.
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\(\sqrt{28}+\sqrt{63}+\sqrt{175}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{28}+\sqrt{63}+\sqrt{175}\)?
#real-numbers
#radical-addition
#simplification
A \(12\sqrt{7}\)
B \(10\sqrt{7}\)
C \(14\sqrt{7}\)
D \(15\sqrt{7}\)
Explanation opens after your attempt
Correct Answer
B. \(10\sqrt{7}\)
Step 1
Concept
\(\sqrt{28}=2\sqrt{7}\), \(\sqrt{63}=3\sqrt{7}\), और \(\sqrt{175}=5\sqrt{7}\)। / \(\sqrt{28}=2\sqrt{7}\), \(\sqrt{63}=3\sqrt{7}\), and \(\sqrt{175}=5\sqrt{7}\).
Step 2
Why this answer is correct
योग \(2\sqrt{7}+3\sqrt{7}+5\sqrt{7}=10\sqrt{7}\) है। / The sum is \(2\sqrt{7}+3\sqrt{7}+5\sqrt{7}=10\sqrt{7}\).
Step 3
Exam Tip
समान वर्गमूल बनने पर केवल गुणांक जोड़ें। / Once radicals become like terms, add only the coefficients.
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\(\sqrt{147}-\sqrt{75}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{147}-\sqrt{75}\)?
#real-numbers
#radical-subtraction
#simplification
A \(2\sqrt{3}\)
B \(4\sqrt{3}\)
C \(6\sqrt{3}\)
D \(\sqrt{72}\)
Explanation opens after your attempt
Correct Answer
A. \(2\sqrt{3}\)
Step 1
Concept
\(\sqrt{147}=7\sqrt{3}\) और \(\sqrt{75}=5\sqrt{3}\)। / \(\sqrt{147}=7\sqrt{3}\) and \(\sqrt{75}=5\sqrt{3}\).
Step 2
Why this answer is correct
\(7\sqrt{3}-5\sqrt{3}=2\sqrt{3}\)। / \(7\sqrt{3}-5\sqrt{3}=2\sqrt{3}\).
Step 3
Exam Tip
वर्गमूलों को घटाने से पहले समान वर्गमूल में बदलना जरूरी है। / Before subtracting radicals, convert them into like radicals.
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\(\sqrt{216}+\sqrt{54}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{216}+\sqrt{54}\)?
#real-numbers
#radical-addition
#sqrt6
A \(9\sqrt{6}\)
B \(6\sqrt{6}\)
C \(12\sqrt{6}\)
D \(\sqrt{270}\)
Explanation opens after your attempt
Correct Answer
A. \(9\sqrt{6}\)
Step 1
Concept
\(\sqrt{216}=6\sqrt{6}\) और \(\sqrt{54}=3\sqrt{6}\)। / \(\sqrt{216}=6\sqrt{6}\) and \(\sqrt{54}=3\sqrt{6}\).
Step 2
Why this answer is correct
\(6\sqrt{6}+3\sqrt{6}=9\sqrt{6}\)। / \(6\sqrt{6}+3\sqrt{6}=9\sqrt{6}\).
Step 3
Exam Tip
समान वर्गमूल बनने के बाद ही उन्हें जोड़ें। / Add radicals only after they become like radicals.
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यदि \(x=\sqrt{3}+\sqrt{27}\), तो (x) का सरल रूप क्या है?
If \(x=\sqrt{3}+\sqrt{27}\), what is the simplified form of (x)?
#real-numbers
#radical-addition
#sqrt3
A \(4\sqrt{3}\)
B \(\sqrt{30}\)
C \(3\sqrt{3}\)
D (6)
Explanation opens after your attempt
Correct Answer
A. \(4\sqrt{3}\)
Step 1
Concept
\(\sqrt{27}=3\sqrt{3}\)। / \(\sqrt{27}=3\sqrt{3}\).
Step 2
Why this answer is correct
\(x=\sqrt{3}+3\sqrt{3}=4\sqrt{3}\)। / \(x=\sqrt{3}+3\sqrt{3}=4\sqrt{3}\).
Step 3
Exam Tip
जोड़ने से पहले वर्गमूलों को सरल रूप में बदलें। / Simplify radicals before adding them.
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\(\sqrt{363}-\sqrt{75}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{363}-\sqrt{75}\)?
#real-numbers
#radical-subtraction
#sqrt3
A \(6\sqrt{3}\)
B \(4\sqrt{3}\)
C \(8\sqrt{3}\)
D \(\sqrt{288}\)
Explanation opens after your attempt
Correct Answer
A. \(6\sqrt{3}\)
Step 1
Concept
\(\sqrt{363}=11\sqrt{3}\) और \(\sqrt{75}=5\sqrt{3}\)। / \(\sqrt{363}=11\sqrt{3}\) and \(\sqrt{75}=5\sqrt{3}\).
Step 2
Why this answer is correct
\(11\sqrt{3}-5\sqrt{3}=6\sqrt{3}\)। / \(11\sqrt{3}-5\sqrt{3}=6\sqrt{3}\).
Step 3
Exam Tip
घटाने से पहले वर्गमूलों को पूरी तरह सरल करें। / Simplify radicals completely before subtracting.
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\(\sqrt{48}\times\sqrt{75}\) का मान क्या है?
What is the value of \(\sqrt{48}\times\sqrt{75}\)?
#real-numbers
#radical-product
#rational-result
A \(30\sqrt{4}\)
B (60)
C (120)
D \(\sqrt{123}\)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{48}\times\sqrt{75}=\sqrt{3600}\)। / \(\sqrt{48}\times\sqrt{75}=\sqrt{3600}\).
Step 2
Why this answer is correct
\(\sqrt{3600}=60\), इसलिए परिणाम परिमेय है। / \(\sqrt{3600}=60\), so the result is rational.
Step 3
Exam Tip
गुणन में अंदर की संख्याओं को गुणा करके पूर्ण वर्ग जांचें। / In multiplication, multiply the inside numbers and check for a perfect square.
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\(\sqrt{c}\times\sqrt{12}=18\) और (c) धनात्मक है। (c) का मान क्या है?
If \(\sqrt{c}\times\sqrt{12}=18\) and (c) is positive, what is the value of (c)?
#real-numbers
#radical-equation
#square-root
A (18)
B (24)
C (27)
D (36)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{c}\times\sqrt{12}=\sqrt{12c}\)। / \(\sqrt{c}\times\sqrt{12}=\sqrt{12c}\).
Step 2
Why this answer is correct
\(\sqrt{12c}=18\), इसलिए (12c=324) और (c=27)। / \(\sqrt{12c}=18\), so (12c=324) and (c=27).
Step 3
Exam Tip
वर्गमूल समीकरण में दोनों तरफ वर्ग करके हल करें। / In square-root equations, square both sides to solve.
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\(\sqrt{128}+\sqrt{72}-\sqrt{50}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{128}+\sqrt{72}-\sqrt{50}\)?
#real-numbers
#radical-expression
#simplification
A \(9\sqrt{2}\)
B \(7\sqrt{2}\)
C \(11\sqrt{2}\)
D \(\sqrt{150}\)
Explanation opens after your attempt
Correct Answer
A. \(9\sqrt{2}\)
Step 1
Concept
\(\sqrt{128}=8\sqrt{2}\), \(\sqrt{72}=6\sqrt{2}\), और \(\sqrt{50}=5\sqrt{2}\)। / \(\sqrt{128}=8\sqrt{2}\), \(\sqrt{72}=6\sqrt{2}\), and \(\sqrt{50}=5\sqrt{2}\).
Step 2
Why this answer is correct
\(8\sqrt{2}+6\sqrt{2}-5\sqrt{2}=9\sqrt{2}\)। / \(8\sqrt{2}+6\sqrt{2}-5\sqrt{2}=9\sqrt{2}\).
Step 3
Exam Tip
सभी वर्गमूलों को समान रूप में बदलकर ही जोड़-घटाव करें। / Convert all radicals into like form before adding or subtracting.
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कौन-सा परिणाम अपरिमेय है?
Which result is irrational?
#real-numbers
#radical-product
#irrational-result
A \(\sqrt{8}\times\sqrt{18}\)
B \(\sqrt{12}\times\sqrt{27}\)
C \(\sqrt{15}\times\sqrt{60}\)
D \(\sqrt{2}\times\sqrt{11}\)
Explanation opens after your attempt
Correct Answer
D. \(\sqrt{2}\times\sqrt{11}\)
Step 1
Concept
पहले गुणनफल में अंदर की संख्याएँ गुणा करें। / First multiply the numbers inside the roots.
Step 2
Why this answer is correct
पहले तीन में (144), (324), और (900) मिलते हैं, जो पूर्ण वर्ग हैं; चौथा \(\sqrt{22}\) है। / The first three give (144), (324), and (900), which are perfect squares; the fourth gives \(\sqrt{22}\).
Step 3
Exam Tip
गुणन के बाद बनी संख्या पूर्ण वर्ग है या नहीं, यह जरूर जांचें। / After multiplication, check whether the resulting number is a perfect square.
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\(\sqrt{18}+\sqrt{72}+\sqrt{162}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{18}+\sqrt{72}+\sqrt{162}\)?
#real-numbers
#radical-addition
#sqrt2
A \(18\sqrt{2}\)
B \(12\sqrt{2}\)
C \(15\sqrt{2}\)
D \(9\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. \(18\sqrt{2}\)
Step 1
Concept
\(\sqrt{18}=3\sqrt{2}\), \(\sqrt{72}=6\sqrt{2}\), और \(\sqrt{162}=9\sqrt{2}\)। / \(\sqrt{18}=3\sqrt{2}\), \(\sqrt{72}=6\sqrt{2}\), and \(\sqrt{162}=9\sqrt{2}\).
Step 2
Why this answer is correct
योग \(3\sqrt{2}+6\sqrt{2}+9\sqrt{2}=18\sqrt{2}\)। / The sum is \(3\sqrt{2}+6\sqrt{2}+9\sqrt{2}=18\sqrt{2}\).
Step 3
Exam Tip
कई वर्गमूलों को पहले पूरी तरह सरल करें। / Simplify all radicals completely first.
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(\sqrt{5}\(3+\sqrt{5}\)) का मान क्या है?
What is the value of (\sqrt{5}\(3+\sqrt{5}\))?
#real-numbers
#radical-multiplication
#expression
A \(3\sqrt{5}+5\)
B \(8\sqrt{5}\)
C \(3+5\sqrt{5}\)
D (15)
Explanation opens after your attempt
Correct Answer
A. \(3\sqrt{5}+5\)
Step 1
Concept
वितरण नियम लगाएं: \(\sqrt{5}\times3+\sqrt{5}\times\sqrt{5}\)। / Apply distribution: \(\sqrt{5}\times3+\sqrt{5}\times\sqrt{5}\).
Step 2
Why this answer is correct
यह \(3\sqrt{5}+5\) बनता है। / This becomes \(3\sqrt{5}+5\).
Step 3
Exam Tip
समान वर्गमूलों के गुणन में \(\sqrt{5}\times\sqrt{5}=5\) याद रखें। / In such multiplication, remember \(\sqrt{5}\times\sqrt{5}=5\).
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\(\sqrt{75}+\sqrt{300}-\sqrt{48}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{75}+\sqrt{300}-\sqrt{48}\)?
#real-numbers
#radical-expression
#simplification
A \(9\sqrt{3}\)
B \(11\sqrt{3}\)
C \(7\sqrt{3}\)
D \(\sqrt{327}\)
Explanation opens after your attempt
Correct Answer
B. \(11\sqrt{3}\)
Step 1
Concept
\(\sqrt{75}=5\sqrt{3}\), \(\sqrt{300}=10\sqrt{3}\), और \(\sqrt{48}=4\sqrt{3}\)। / \(\sqrt{75}=5\sqrt{3}\), \(\sqrt{300}=10\sqrt{3}\), and \(\sqrt{48}=4\sqrt{3}\).
Step 2
Why this answer is correct
\(5\sqrt{3}+10\sqrt{3}-4\sqrt{3}=11\sqrt{3}\)। / \(5\sqrt{3}+10\sqrt{3}-4\sqrt{3}=11\sqrt{3}\).
Step 3
Exam Tip
जोड़ और घटाव से पहले सभी वर्गमूलों को सरल करें। / Simplify all radicals before addition and subtraction.
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\(\sqrt{20}+\sqrt{45}+\sqrt{125}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{20}+\sqrt{45}+\sqrt{125}\)?
#real-numbers
#radical-addition
#simplification
A \(10\sqrt{5}\)
B \(12\sqrt{5}\)
C \(8\sqrt{5}\)
D \(15\sqrt{5}\)
Explanation opens after your attempt
Correct Answer
A. \(10\sqrt{5}\)
Step 1
Concept
\(\sqrt{20}=2\sqrt{5}\), \(\sqrt{45}=3\sqrt{5}\), और \(\sqrt{125}=5\sqrt{5}\)। / \(\sqrt{20}=2\sqrt{5}\), \(\sqrt{45}=3\sqrt{5}\), and \(\sqrt{125}=5\sqrt{5}\).
Step 2
Why this answer is correct
योग \(2\sqrt{5}+3\sqrt{5}+5\sqrt{5}=10\sqrt{5}\) है। / The sum is \(2\sqrt{5}+3\sqrt{5}+5\sqrt{5}=10\sqrt{5}\).
Step 3
Exam Tip
समान वर्गमूल बनने पर केवल गुणांक जोड़ें। / Once radicals are like terms, add only the coefficients.
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\(\sqrt{98}-\sqrt{32}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{98}-\sqrt{32}\)?
#real-numbers
#radical-subtraction
#simplification
A \(3\sqrt{2}\)
B \(7\sqrt{2}\)
C \(11\sqrt{2}\)
D \(\sqrt{66}\)
Explanation opens after your attempt
Correct Answer
A. \(3\sqrt{2}\)
Step 1
Concept
\(\sqrt{98}=7\sqrt{2}\) और \(\sqrt{32}=4\sqrt{2}\)। / \(\sqrt{98}=7\sqrt{2}\) and \(\sqrt{32}=4\sqrt{2}\).
Step 2
Why this answer is correct
\(7\sqrt{2}-4\sqrt{2}=3\sqrt{2}\)। / \(7\sqrt{2}-4\sqrt{2}=3\sqrt{2}\).
Step 3
Exam Tip
वर्गमूलों को घटाने से पहले समान वर्गमूल में बदलें। / Convert radicals into like radicals before subtracting.
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\(\sqrt{150}+\sqrt{24}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{150}+\sqrt{24}\)?
#real-numbers
#radical-addition
#sqrt6
A \(7\sqrt{6}\)
B \(5\sqrt{6}\)
C \(9\sqrt{6}\)
D \(\sqrt{174}\)
Explanation opens after your attempt
Correct Answer
A. \(7\sqrt{6}\)
Step 1
Concept
\(\sqrt{150}=5\sqrt{6}\) और \(\sqrt{24}=2\sqrt{6}\)। / \(\sqrt{150}=5\sqrt{6}\) and \(\sqrt{24}=2\sqrt{6}\).
Step 2
Why this answer is correct
\(5\sqrt{6}+2\sqrt{6}=7\sqrt{6}\)। / \(5\sqrt{6}+2\sqrt{6}=7\sqrt{6}\).
Step 3
Exam Tip
समान वर्गमूल बनने के बाद ही जोड़ें। / Add radicals only after they become like radicals.
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यदि \(x=\sqrt{2}+\sqrt{8}\), तो (x) का सरल रूप क्या है?
If \(x=\sqrt{2}+\sqrt{8}\), what is the simplified form of (x)?
#real-numbers
#radical-addition
#sqrt2
A \(3\sqrt{2}\)
B \(\sqrt{10}\)
C \(2\sqrt{8}\)
D \(5\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. \(3\sqrt{2}\)
Step 1
Concept
\(\sqrt{8}=2\sqrt{2}\)। / \(\sqrt{8}=2\sqrt{2}\).
Step 2
Why this answer is correct
\(x=\sqrt{2}+2\sqrt{2}=3\sqrt{2}\)। / \(x=\sqrt{2}+2\sqrt{2}=3\sqrt{2}\).
Step 3
Exam Tip
जोड़ने से पहले वर्गमूलों को समान रूप में बदलें। / Before adding, convert radicals into like form.
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\(\sqrt{200}-\sqrt{72}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{200}-\sqrt{72}\)?
#real-numbers
#radical-subtraction
#sqrt2
A \(4\sqrt{2}\)
B \(2\sqrt{2}\)
C \(8\sqrt{2}\)
D \(\sqrt{128}\)
Explanation opens after your attempt
Correct Answer
A. \(4\sqrt{2}\)
Step 1
Concept
\(\sqrt{200}=10\sqrt{2}\) और \(\sqrt{72}=6\sqrt{2}\)। / \(\sqrt{200}=10\sqrt{2}\) and \(\sqrt{72}=6\sqrt{2}\).
Step 2
Why this answer is correct
\(10\sqrt{2}-6\sqrt{2}=4\sqrt{2}\)। / \(10\sqrt{2}-6\sqrt{2}=4\sqrt{2}\).
Step 3
Exam Tip
वर्गमूल घटाने में पहले दोनों पदों को सरल रूप में लिखें। / Before subtracting radicals, write both terms in simplified form.
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\(\sqrt{27}\times\sqrt{12}\) का मान क्या है?
What is the value of \(\sqrt{27}\times\sqrt{12}\)?
#real-numbers
#radical-product
#rational-result
A (18)
B \(\sqrt{39}\)
C \(9\sqrt{4}\)
D (36)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{27}\times\sqrt{12}=\sqrt{324}\)। / \(\sqrt{27}\times\sqrt{12}=\sqrt{324}\).
Step 2
Why this answer is correct
\(\sqrt{324}=18\), इसलिए परिणाम परिमेय है। / \(\sqrt{324}=18\), so the result is rational.
Step 3
Exam Tip
गुणन करते समय अंदर की संख्याएँ गुणा करके पूर्ण वर्ग जांचें। / When multiplying, multiply inside numbers and check for a perfect square.
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\(\sqrt{a}\) और \(\sqrt{b}\) का गुणनफल (12) है। यदि (a=3), तो (b) का मान क्या होगा?
The product of \(\sqrt{a}\) and \(\sqrt{b}\) is (12). If (a=3), what is the value of (b)?
#real-numbers
#radical-equation
#square-root
A (24)
B (36)
C (48)
D (72)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{a}\times\sqrt{b}=\sqrt{ab}\)। / \(\sqrt{a}\times\sqrt{b}=\sqrt{ab}\).
Step 2
Why this answer is correct
\(\sqrt{3b}=12\), इसलिए (3b=144) और (b=48)। / \(\sqrt{3b}=12\), so (3b=144) and (b=48).
Step 3
Exam Tip
वर्गमूल समीकरण में दोनों तरफ वर्ग करना उपयोगी होता है। / In square-root equations, squaring both sides is useful.
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\(\sqrt{98}+\sqrt{50}-\sqrt{18}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{98}+\sqrt{50}-\sqrt{18}\)?
#real-numbers
#radical-expression
#simplification
A \(9\sqrt{2}\)
B \(5\sqrt{2}\)
C \(15\sqrt{2}\)
D \(\sqrt{130}\)
Explanation opens after your attempt
Correct Answer
A. \(9\sqrt{2}\)
Step 1
Concept
\(\sqrt{98}=7\sqrt{2}\), \(\sqrt{50}=5\sqrt{2}\), और \(\sqrt{18}=3\sqrt{2}\)। / \(\sqrt{98}=7\sqrt{2}\), \(\sqrt{50}=5\sqrt{2}\), and \(\sqrt{18}=3\sqrt{2}\).
Step 2
Why this answer is correct
\(7\sqrt{2}+5\sqrt{2}-3\sqrt{2}=9\sqrt{2}\)। / \(7\sqrt{2}+5\sqrt{2}-3\sqrt{2}=9\sqrt{2}\).
Step 3
Exam Tip
सभी पदों को समान वर्गमूल में बदलने के बाद ही जोड़-घटाव करें। / Add or subtract only after converting all terms to like radicals.
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कौन-सा परिणाम अपरिमेय है?
Which result is irrational?
#real-numbers
#radical-product
#irrational-result
A \(\sqrt{6}\times\sqrt{24}\)
B \(\sqrt{18}\times\sqrt{2}\)
C \(\sqrt{3}\times\sqrt{27}\)
D \(\sqrt{5}\times\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
D. \(\sqrt{5}\times\sqrt{2}\)
Step 1
Concept
पहले सभी गुणनफल सरल करें। / First simplify all products.
Step 2
Why this answer is correct
पहले तीन में अंदर की संख्याएँ (144), (36), और (81) बनती हैं, जो पूर्ण वर्ग हैं; चौथा \(\sqrt{10}\) है। / The first three produce inside numbers (144), (36), and (81), which are perfect squares; the fourth gives \(\sqrt{10}\).
Step 3
Exam Tip
गुणन के बाद बनी अंदर की संख्या पूर्ण वर्ग है या नहीं, यह जांचें। / After multiplication, check whether the inside number is a perfect square.
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\(\sqrt{8}+\sqrt{32}+\sqrt{128}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{8}+\sqrt{32}+\sqrt{128}\)?
#real-numbers
#radical-addition
#sqrt2
A \(14\sqrt{2}\)
B \(7\sqrt{2}\)
C \(12\sqrt{2}\)
D \(18\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. \(14\sqrt{2}\)
Step 1
Concept
\(\sqrt{8}=2\sqrt{2}\), \(\sqrt{32}=4\sqrt{2}\), और \(\sqrt{128}=8\sqrt{2}\)। / \(\sqrt{8}=2\sqrt{2}\), \(\sqrt{32}=4\sqrt{2}\), and \(\sqrt{128}=8\sqrt{2}\).
Step 2
Why this answer is correct
योग \(2\sqrt{2}+4\sqrt{2}+8\sqrt{2}=14\sqrt{2}\)। / The sum is \(2\sqrt{2}+4\sqrt{2}+8\sqrt{2}=14\sqrt{2}\).
Step 3
Exam Tip
कई वर्गमूल हों तो पहले सबको सरल रूप में लिखें। / With many radicals, simplify all of them first.
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(\sqrt{3}\(2+\sqrt{3}\)) का मान क्या है?
What is the value of (\sqrt{3}\(2+\sqrt{3}\))?
#real-numbers
#radical-multiplication
#expression
A \(2\sqrt{3}+3\)
B \(5\sqrt{3}\)
C \(2+3\sqrt{3}\)
D (6)
Explanation opens after your attempt
Correct Answer
A. \(2\sqrt{3}+3\)
Step 1
Concept
वितरण नियम लगाएं: \(\sqrt{3}\times2+\sqrt{3}\times\sqrt{3}\)। / Use distribution: \(\sqrt{3}\times2+\sqrt{3}\times\sqrt{3}\).
Step 2
Why this answer is correct
यह \(2\sqrt{3}+3\) बनता है। / This becomes \(2\sqrt{3}+3\).
Step 3
Exam Tip
वर्गमूल वाले गुणन में \(\sqrt{3}\times\sqrt{3}=3\) याद रखें। / In radical multiplication, remember \(\sqrt{3}\times\sqrt{3}=3\).
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\(\sqrt{45}+\sqrt{80}-\sqrt{20}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{45}+\sqrt{80}-\sqrt{20}\)?
#real-numbers
#radical-expression
#simplification
A \(5\sqrt{5}\)
B \(3\sqrt{5}\)
C \(7\sqrt{5}\)
D \(\sqrt{105}\)
Explanation opens after your attempt
Correct Answer
A. \(5\sqrt{5}\)
Step 1
Concept
\(\sqrt{45}=3\sqrt{5}\), \(\sqrt{80}=4\sqrt{5}\), और \(\sqrt{20}=2\sqrt{5}\)। / \(\sqrt{45}=3\sqrt{5}\), \(\sqrt{80}=4\sqrt{5}\), and \(\sqrt{20}=2\sqrt{5}\).
Step 2
Why this answer is correct
\(3\sqrt{5}+4\sqrt{5}-2\sqrt{5}=5\sqrt{5}\)। / \(3\sqrt{5}+4\sqrt{5}-2\sqrt{5}=5\sqrt{5}\).
Step 3
Exam Tip
जोड़ और घटाव से पहले सभी वर्गमूलों को समान रूप में बदलें। / Convert all radicals to like form before adding or subtracting.
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\(\sqrt{12}+\sqrt{27}+\sqrt{75}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{12}+\sqrt{27}+\sqrt{75}\)?
#real-numbers
#radical-addition
#simplification
A \(10\sqrt{3}\)
B \(9\sqrt{3}\)
C \(6\sqrt{3}\)
D \(15\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
A. \(10\sqrt{3}\)
Step 1
Concept
\(\sqrt{12}=2\sqrt{3}\), \(\sqrt{27}=3\sqrt{3}\), और \(\sqrt{75}=5\sqrt{3}\)। / \(\sqrt{12}=2\sqrt{3}\), \(\sqrt{27}=3\sqrt{3}\), and \(\sqrt{75}=5\sqrt{3}\).
Step 2
Why this answer is correct
जोड़ने पर \(2\sqrt{3}+3\sqrt{3}+5\sqrt{3}=10\sqrt{3}\)। / Adding gives \(2\sqrt{3}+3\sqrt{3}+5\sqrt{3}=10\sqrt{3}\).
Step 3
Exam Tip
समान वर्गमूल बनने पर केवल गुणांक जोड़ें। / Once radicals are like terms, add only the coefficients.
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\(\sqrt{72}-\sqrt{18}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{72}-\sqrt{18}\)?
#real-numbers
#radical-subtraction
#simplification
A \(3\sqrt{2}\)
B \(6\sqrt{2}\)
C \(\sqrt{54}\)
D \(9\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. \(3\sqrt{2}\)
Step 1
Concept
\(\sqrt{72}=6\sqrt{2}\) और \(\sqrt{18}=3\sqrt{2}\)। / \(\sqrt{72}=6\sqrt{2}\) and \(\sqrt{18}=3\sqrt{2}\).
Step 2
Why this answer is correct
\(6\sqrt{2}-3\sqrt{2}=3\sqrt{2}\)। / \(6\sqrt{2}-3\sqrt{2}=3\sqrt{2}\).
Step 3
Exam Tip
घटाने से पहले दोनों वर्गमूलों को सरल करना जरूरी है। / Simplify both square roots before subtracting.
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\(\sqrt{6}\times\sqrt{54}\) का मान क्या है?
What is the value of \(\sqrt{6}\times\sqrt{54}\)?
#real-numbers
#radical-product
#rational-result
A (18)
B \(\sqrt{60}\)
C \(6\sqrt{54}\)
D (54)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{6}\times\sqrt{54}=\sqrt{324}\)। / \(\sqrt{6}\times\sqrt{54}=\sqrt{324}\).
Step 2
Why this answer is correct
\(\sqrt{324}=18\), इसलिए परिणाम परिमेय है। / \(\sqrt{324}=18\), so the result is rational.
Step 3
Exam Tip
गुणन के बाद अंदर की संख्या पूर्ण वर्ग बन सकती है, इसे जरूर जांचें। / After multiplication, check whether the inside number has become a perfect square.
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\(\sqrt{275}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{275}\)?
#real-numbers
#sqrt275
#radical-simplification
A \(5\sqrt{11}\)
B \(11\sqrt{5}\)
C \(25\sqrt{11}\)
D (55)
Explanation opens after your attempt
Correct Answer
A. \(5\sqrt{11}\)
Step 1
Concept
\(275=25 \times 11\) है। / \(275=25 \times 11\).
Step 2
Why this answer is correct
\(\sqrt{275}=\sqrt{25 \times 11}=5\sqrt{11}\)। / \(\sqrt{275}=\sqrt{25 \times 11}=5\sqrt{11}\).
Step 3
Exam Tip
पूर्ण वर्ग गुणनखंड बाहर निकालकर उत्तर को सरल बनाएं। / Take the perfect square factor outside to simplify the answer.
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\(\sqrt{192}\) को सरल कीजिए।
Simplify \(\sqrt{192}\).
#real-numbers
#sqrt192
#radical-simplification
A \(8\sqrt{3}\)
B \(4\sqrt{12}\)
C \(16\sqrt{3}\)
D \(12\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. \(8\sqrt{3}\)
Step 1
Concept
\(192=64 \times 3\) है। / \(192=64 \times 3\).
Step 2
Why this answer is correct
\(\sqrt{192}=\sqrt{64 \times 3}=8\sqrt{3}\)। / \(\sqrt{192}=\sqrt{64 \times 3}=8\sqrt{3}\).
Step 3
Exam Tip
उत्तर को पूरा सरल करने के लिए सबसे बड़ा पूर्ण वर्ग बाहर निकालें। / To fully simplify the answer, take out the largest perfect square.
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\(\sqrt{7}\times\sqrt{28}\) का मान क्या होगा?
What is the value of \(\sqrt{7}\times\sqrt{28}\)?
#real-numbers
#radical-product
#rational-result
A (14)
B \(\sqrt{35}\)
C \(7\sqrt{28}\)
D (28)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{7}\times\sqrt{28}=\sqrt{196}\)। / \(\sqrt{7}\times\sqrt{28}=\sqrt{196}\).
Step 2
Why this answer is correct
\(\sqrt{196}=14\), इसलिए मान परिमेय है। / \(\sqrt{196}=14\), so the value is rational.
Step 3
Exam Tip
वर्गमूलों के गुणन में अंदर की संख्याएँ गुणा करें। / When multiplying square roots, multiply the numbers inside.
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\(\sqrt{300}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{300}\)?
#real-numbers
#sqrt300
#radical-simplification
A \(10\sqrt{3}\)
B \(3\sqrt{10}\)
C \(30\sqrt{10}\)
D \(100\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
A. \(10\sqrt{3}\)
Step 1
Concept
\(300=100 \times 3\) लिखें। / Write \(300=100 \times 3\).
Step 2
Why this answer is correct
\(\sqrt{300}=\sqrt{100 \times 3}=10\sqrt{3}\)। / \(\sqrt{300}=\sqrt{100 \times 3}=10\sqrt{3}\).
Step 3
Exam Tip
(100) जैसा पूर्ण वर्ग दिखे तो उसे बाहर (10) के रूप में निकालें। / When you see a perfect square like (100), take it outside as (10).
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\(\sqrt{32}+\sqrt{128}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{32}+\sqrt{128}\)?
#real-numbers
#radical-addition
#simplification
A \(12\sqrt{2}\)
B \(16\sqrt{2}\)
C \(8\sqrt{2}\)
D \(\sqrt{160}\)
Explanation opens after your attempt
Correct Answer
A. \(12\sqrt{2}\)
Step 1
Concept
\(\sqrt{32}=4\sqrt{2}\) और \(\sqrt{128}=8\sqrt{2}\)। / \(\sqrt{32}=4\sqrt{2}\) and \(\sqrt{128}=8\sqrt{2}\).
Step 2
Why this answer is correct
\(4\sqrt{2}+8\sqrt{2}=12\sqrt{2}\)। / \(4\sqrt{2}+8\sqrt{2}=12\sqrt{2}\).
Step 3
Exam Tip
समान वर्गमूल बनने पर ही उन्हें जोड़ा जा सकता है। / Radicals can be added only when they become like radicals.
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\(\sqrt{80}-\sqrt{45}\) का सरल रूप क्या होगा?
What will be the simplified form of \(\sqrt{80}-\sqrt{45}\)?
#real-numbers
#radical-subtraction
#sqrt5
A \(\sqrt{5}\)
B \(5\sqrt{5}\)
C \(7\sqrt{5}\)
D \(\sqrt{35}\)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{5}\)
Step 1
Concept
\(\sqrt{80}=4\sqrt{5}\) और \(\sqrt{45}=3\sqrt{5}\)। / \(\sqrt{80}=4\sqrt{5}\) and \(\sqrt{45}=3\sqrt{5}\).
Step 2
Why this answer is correct
\(4\sqrt{5}-3\sqrt{5}=\sqrt{5}\)। / \(4\sqrt{5}-3\sqrt{5}=\sqrt{5}\).
Step 3
Exam Tip
घटाने से पहले दोनों वर्गमूलों को पूरी तरह सरल करें। / Before subtracting, simplify both radicals completely.
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\(\sqrt{5}+\sqrt{45}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{5}+\sqrt{45}\)?
#real-numbers
#radical-addition
#sqrt5
A \(4\sqrt{5}\)
B \(10\sqrt{5}\)
C \(\sqrt{50}\)
D \(3\sqrt{10}\)
Explanation opens after your attempt
Correct Answer
A. \(4\sqrt{5}\)
Step 1
Concept
\(\sqrt{45}=3\sqrt{5}\) है। / \(\sqrt{45}=3\sqrt{5}\).
Step 2
Why this answer is correct
\(\sqrt{5}+3\sqrt{5}=4\sqrt{5}\)। / \(\sqrt{5}+3\sqrt{5}=4\sqrt{5}\).
Step 3
Exam Tip
वर्गमूल जोड़ते समय समान वर्गमूल बनने तक सरल करें। / While adding radicals, simplify them until like radicals appear.
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\(\sqrt{242}\) का सरल रूप क्या होगा?
What will be the simplified form of \(\sqrt{242}\)?
#real-numbers
#sqrt242
#radical-simplification
A \(11\sqrt{2}\)
B \(2\sqrt{121}\)
C \(22\sqrt{2}\)
D \(121\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. \(11\sqrt{2}\)
Step 1
Concept
\(242=121 \times 2\) है। / \(242=121 \times 2\).
Step 2
Why this answer is correct
\(\sqrt{242}=\sqrt{121 \times 2}=11\sqrt{2}\)। / \(\sqrt{242}=\sqrt{121 \times 2}=11\sqrt{2}\).
Step 3
Exam Tip
बड़े पूर्ण वर्ग जैसे (121) को पहचानना सरलीकरण में बहुत उपयोगी है। / Recognising large perfect squares like (121) is very useful in simplification.
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\(\sqrt{3}\times\sqrt{75}\) का मान क्या है?
What is the value of \(\sqrt{3}\times\sqrt{75}\)?
#real-numbers
#radical-product
#rational-result
A (15)
B \(\sqrt{78}\)
C \(3\sqrt{75}\)
D (75)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{3}\times\sqrt{75}=\sqrt{225}\)। / \(\sqrt{3}\times\sqrt{75}=\sqrt{225}\).
Step 2
Why this answer is correct
\(\sqrt{225}=15\), इसलिए परिणाम परिमेय है। / \(\sqrt{225}=15\), so the result is rational.
Step 3
Exam Tip
गुणन के बाद यदि अंदर की संख्या पूर्ण वर्ग बन जाए, तो उत्तर परिमेय हो सकता है। / If the number inside becomes a perfect square after multiplication, the answer can be rational.
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\(\sqrt{3}+\sqrt{27}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{3}+\sqrt{27}\)?
#real-numbers
#radical-addition
#sqrt3
A \(4\sqrt{3}\)
B \(3\sqrt{3}\)
C \(\sqrt{30}\)
D (6)
Explanation opens after your attempt
Correct Answer
A. \(4\sqrt{3}\)
Step 1
Concept
\(\sqrt{27}=3\sqrt{3}\) होता है। / \(\sqrt{27}=3\sqrt{3}\).
Step 2
Why this answer is correct
\(\sqrt{3}+3\sqrt{3}=4\sqrt{3}\)। / \(\sqrt{3}+3\sqrt{3}=4\sqrt{3}\).
Step 3
Exam Tip
जोड़ने से पहले वर्गमूलों को सरल करके समान रूप बनाएं। / Before adding, simplify radicals and make them like terms.
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\(\sqrt{2}\times\sqrt{50}\) का मान क्या है?
What is the value of \(\sqrt{2}\times\sqrt{50}\)?
#real-numbers
#radical-product
#rational-result
A (5)
B (10)
C \(\sqrt{52}\)
D (25)
Explanation opens after your attempt
Step 1
Concept
वर्गमूलों के गुणन में अंदर की संख्याएँ गुणा करें। / In multiplication of square roots, multiply the numbers inside.
Step 2
Why this answer is correct
\(\sqrt{2}\times\sqrt{50}=\sqrt{100}=10\)। / \(\sqrt{2}\times\sqrt{50}=\sqrt{100}=10\).
Step 3
Exam Tip
दो अपरिमेय संख्याओं का गुणनफल कभी-कभी परिमेय हो सकता है। / The product of two irrational numbers can sometimes be rational.
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\(\sqrt{108}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{108}\)?
#real-numbers
#radical-simplification
#sqrt108
A \(3\sqrt{12}\)
B \(6\sqrt{3}\)
C \(9\sqrt{2}\)
D \(12\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
B. \(6\sqrt{3}\)
Step 1
Concept
\(108=36 \times 3\) लिखें। / Write \(108=36 \times 3\).
Step 2
Why this answer is correct
\(\sqrt{108}=\sqrt{36 \times 3}=6\sqrt{3}\)। / \(\sqrt{108}=\sqrt{36 \times 3}=6\sqrt{3}\).
Step 3
Exam Tip
वर्गमूल सरल करते समय सबसे बड़ा पूर्ण वर्ग गुणनखंड चुनना अच्छा रहता है। / While simplifying a square root, choosing the largest perfect square factor is helpful.
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\(\sqrt{2}\times\sqrt{32}\) का मान क्या है?
What is the value of \(\sqrt{2}\times\sqrt{32}\)?
#real-numbers
#radical-product
#sqrt64
A (8)
B \(\sqrt{34}\)
C (16)
D \(4\sqrt{2}\)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{2}\times\sqrt{32}=\sqrt{64}\)। / \(\sqrt{2}\times\sqrt{32}=\sqrt{64}\).
Step 2
Why this answer is correct
\(\sqrt{64}=8\), इसलिए परिणाम परिमेय है। / \(\sqrt{64}=8\), so the result is rational.
Step 3
Exam Tip
गुणन में वर्गमूलों के अंदर की संख्याएँ गुणा करें। / In multiplication, multiply the numbers inside the square roots.
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\(\sqrt{112}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{112}\)?
#real-numbers
#sqrt112
#radical-simplification
A \(4\sqrt{7}\)
B \(7\sqrt{4}\)
C \(8\sqrt{7}\)
D \(16\sqrt{7}\)
Explanation opens after your attempt
Correct Answer
A. \(4\sqrt{7}\)
Step 1
Concept
\(112=16 \times 7\) है। / \(112=16 \times 7\).
Step 2
Why this answer is correct
\(\sqrt{112}=\sqrt{16 \times 7}=4\sqrt{7}\)। / \(\sqrt{112}=\sqrt{16 \times 7}=4\sqrt{7}\).
Step 3
Exam Tip
सरलीकरण में अंदर बची संख्या को फिर पूर्ण वर्ग के लिए जांचें। / After simplification, check that the remaining number has no perfect square factor.
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\(\sqrt{63}\) को सरल कीजिए।
Simplify \(\sqrt{63}\).
#real-numbers
#sqrt63
#radical-simplification
A \(3\sqrt{7}\)
B \(7\sqrt{3}\)
C \(9\sqrt{7}\)
D (21)
Explanation opens after your attempt
Correct Answer
A. \(3\sqrt{7}\)
Step 1
Concept
\(63=9 \times 7\) है। / \(63=9 \times 7\).
Step 2
Why this answer is correct
\(\sqrt{63}=\sqrt{9 \times 7}=3\sqrt{7}\)। / \(\sqrt{63}=\sqrt{9 \times 7}=3\sqrt{7}\).
Step 3
Exam Tip
(9) जैसे पूर्ण वर्ग को बाहर निकालना याद रखें। / Remember to take a perfect square like (9) outside the root.
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\(\sqrt{5}\times\sqrt{20}\) का मान क्या होगा?
What is the value of \(\sqrt{5}\times\sqrt{20}\)?
#real-numbers
#radical-product
#rational-result
A (10)
B \(\sqrt{25}\)
C \(5\sqrt{20}\)
D \(\sqrt{1000}\)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{5}\times\sqrt{20}=\sqrt{100}\)। / \(\sqrt{5}\times\sqrt{20}=\sqrt{100}\).
Step 2
Why this answer is correct
\(\sqrt{100}=10\), जो परिमेय संख्या है। / \(\sqrt{100}=10\), which is rational.
Step 3
Exam Tip
गुणन में पहले अंदर की संख्याओं का गुणन करें। / In multiplication, first multiply the numbers inside the roots.
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\(\sqrt{150}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{150}\)?
#real-numbers
#sqrt150
#radical-simplification
A \(5\sqrt{6}\)
B \(6\sqrt{5}\)
C \(10\sqrt{15}\)
D \(15\sqrt{10}\)
Explanation opens after your attempt
Correct Answer
A. \(5\sqrt{6}\)
Step 1
Concept
\(150=25 \times 6\) लिखें। / Write \(150=25 \times 6\).
Step 2
Why this answer is correct
\(\sqrt{150}=\sqrt{25 \times 6}=5\sqrt{6}\)। / \(\sqrt{150}=\sqrt{25 \times 6}=5\sqrt{6}\).
Step 3
Exam Tip
पूर्ण वर्ग गुणनखंड बाहर निकालकर बाकी गुणनखंड अंदर छोड़ें। / Take the perfect square factor outside and leave the remaining factor inside.
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\(\sqrt{8}+\sqrt{18}\) का सरल रूप क्या होगा?
What is the simplified form of \(\sqrt{8}+\sqrt{18}\)?
#real-numbers
#radical-addition
#simplification
A \(5\sqrt{2}\)
B \(2\sqrt{26}\)
C \(\sqrt{26}\)
D \(10\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. \(5\sqrt{2}\)
Step 1
Concept
\(\sqrt{8}=2\sqrt{2}\) और \(\sqrt{18}=3\sqrt{2}\)। / \(\sqrt{8}=2\sqrt{2}\) and \(\sqrt{18}=3\sqrt{2}\).
Step 2
Why this answer is correct
\(2\sqrt{2}+3\sqrt{2}=5\sqrt{2}\)। / \(2\sqrt{2}+3\sqrt{2}=5\sqrt{2}\).
Step 3
Exam Tip
समान वर्गमूल बनने पर ही उन्हें जोड़ा जा सकता है। / Radicals can be added only after they become like radicals.
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\(\sqrt{45}-\sqrt{20}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{45}-\sqrt{20}\)?
#real-numbers
#radical-subtraction
#sqrt5
A \(\sqrt{5}\)
B \(5\sqrt{5}\)
C \(\sqrt{25}\)
D \(3\sqrt{25}\)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{5}\)
Step 1
Concept
\(\sqrt{45}=3\sqrt{5}\) और \(\sqrt{20}=2\sqrt{5}\)। / \(\sqrt{45}=3\sqrt{5}\) and \(\sqrt{20}=2\sqrt{5}\).
Step 2
Why this answer is correct
\(3\sqrt{5}-2\sqrt{5}=\sqrt{5}\)। / \(3\sqrt{5}-2\sqrt{5}=\sqrt{5}\).
Step 3
Exam Tip
घटाने से पहले दोनों वर्गमूलों को सरल करें। / Simplify both radicals before subtracting.
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\(\sqrt{3}\) और \(\sqrt{12}\) का योग क्या है?
What is the sum of \(\sqrt{3}\) and \(\sqrt{12}\)?
#real-numbers
#radical-addition
#sqrt3
A \(3\sqrt{3}\)
B \(\sqrt{15}\)
C \(4\sqrt{3}\)
D (6)
Explanation opens after your attempt
Correct Answer
A. \(3\sqrt{3}\)
Step 1
Concept
\(\sqrt{12}=2\sqrt{3}\) है। / \(\sqrt{12}=2\sqrt{3}\).
Step 2
Why this answer is correct
\(\sqrt{3}+2\sqrt{3}=3\sqrt{3}\)। / \(\sqrt{3}+2\sqrt{3}=3\sqrt{3}\).
Step 3
Exam Tip
जोड़ से पहले वर्गमूलों को समान रूप में बदलें। / Before adding, convert radicals into like terms if possible.
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\(\sqrt{7}+\sqrt{7}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{7}+\sqrt{7}\)?
#real-numbers
#radical-addition
#irrational
A \(2\sqrt{7}\)
B \(\sqrt{14}\)
C \(7\sqrt{2}\)
D (14)
Explanation opens after your attempt
Correct Answer
A. \(2\sqrt{7}\)
Step 1
Concept
समान वर्गमूलों को समान पद की तरह जोड़ा जाता है। / Like radicals are added like like terms.
Step 2
Why this answer is correct
\(\sqrt{7}+\sqrt{7}=2\sqrt{7}\)। / \(\sqrt{7}+\sqrt{7}=2\sqrt{7}\).
Step 3
Exam Tip
जोड़ में अंदर की संख्याएँ जोड़कर \(\sqrt{14}\) नहीं लिखना चाहिए। / In addition, do not add the numbers inside roots to write \(\sqrt{14}\).
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\(\sqrt{2}\times\sqrt{18}\) का मान क्या होगा?
What is the value of \(\sqrt{2}\times\sqrt{18}\)?
#real-numbers
#radical-product
#rational-result
A (6)
B \(\sqrt{20}\)
C \(2\sqrt{18}\)
D (36)
Explanation opens after your attempt
Step 1
Concept
वर्गमूलों के गुणन में अंदर की संख्याएँ गुणा होती हैं। / When multiplying square roots, multiply the numbers inside.
Step 2
Why this answer is correct
\(\sqrt{2}\times\sqrt{18}=\sqrt{36}=6\)। / \(\sqrt{2}\times\sqrt{18}=\sqrt{36}=6\).
Step 3
Exam Tip
दो अपरिमेय संख्याओं का गुणनफल कभी-कभी परिमेय हो सकता है। / The product of two irrational numbers can sometimes be rational.
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\(\sqrt{28}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{28}\)?
#real-numbers
#radical-simplification
#sqrt28
A \(2\sqrt{7}\)
B \(7\sqrt{2}\)
C \(4\sqrt{7}\)
D \(14\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. \(2\sqrt{7}\)
Step 1
Concept
\(28=4 \times 7\) लिखें। / Write \(28=4 \times 7\).
Step 2
Why this answer is correct
\(\sqrt{28}=\sqrt{4 \times 7}=2\sqrt{7}\)। / \(\sqrt{28}=\sqrt{4 \times 7}=2\sqrt{7}\).
Step 3
Exam Tip
वर्गमूल सरल करते समय पूर्ण वर्ग गुणनखंड को बाहर निकालें। / While simplifying a square root, take the perfect square factor outside.
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\(\sqrt{32}\) को सरल कीजिए।
Simplify \(\sqrt{32}\).
#real-numbers
#radical-simplification
#sqrt32
A \(4\sqrt{2}\)
B \(2\sqrt{8}\)
C \(8\sqrt{2}\)
D \(16\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. \(4\sqrt{2}\)
Step 1
Concept
\(32=16 \times 2\) है। / \(32=16 \times 2\).
Step 2
Why this answer is correct
\(\sqrt{32}=\sqrt{16 \times 2}=4\sqrt{2}\)। / \(\sqrt{32}=\sqrt{16 \times 2}=4\sqrt{2}\).
Step 3
Exam Tip
उत्तर को पूरी तरह सरल करने के लिए सबसे बड़ा पूर्ण वर्ग बाहर निकालें। / To fully simplify the answer, take out the largest perfect square.
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\(\sqrt{2}\times\sqrt{3}\) किसके बराबर है?
What is \(\sqrt{2}\times\sqrt{3}\) equal to?
#real-numbers
#radical-product
#irrational
A \(\sqrt{5}\)
B \(\sqrt{6}\)
C (6)
D \(2\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
B. \(\sqrt{6}\)
Step 1
Concept
वर्गमूलों के गुणन में अंदर की संख्याएँ गुणा होती हैं। / While multiplying square roots, multiply the numbers inside.
Step 2
Why this answer is correct
\(\sqrt{2}\times\sqrt{3}=\sqrt{6}\), जो अपरिमेय है। / \(\sqrt{2}\times\sqrt{3}=\sqrt{6}\), which is irrational.
Step 3
Exam Tip
गुणा में अंदर की संख्याएँ गुणा करें, जोड़ नहीं। / In multiplication, multiply the inside numbers; do not add them.
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\(\sqrt{20}\) का सरल रूप कौन-सा है?
Which is the simplified form of \(\sqrt{20}\)?
#real-numbers
#radical-simplification
#sqrt20
A \(2\sqrt{5}\)
B \(5\sqrt{2}\)
C \(4\sqrt{5}\)
D \(10\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. \(2\sqrt{5}\)
Step 1
Concept
\(20=4 \times 5\) है। / \(20=4 \times 5\).
Step 2
Why this answer is correct
\(\sqrt{20}=\sqrt{4 \times 5}=2\sqrt{5}\)। / \(\sqrt{20}=\sqrt{4 \times 5}=2\sqrt{5}\).
Step 3
Exam Tip
वर्गमूल के अंदर पूर्ण वर्ग को बाहर निकालें और बाकी अंदर रहने दें। / Take the perfect square outside the root and leave the remaining factor inside.
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\(\sqrt{2}\) और \(\sqrt{8}\) का योग किसके बराबर है?
What is the sum of \(\sqrt{2}\) and \(\sqrt{8}\)?
#real-numbers
#radical-addition
#irrational
A \(3\sqrt{2}\)
B (10)
C \(\sqrt{10}\)
D \(2\sqrt{8}\)
Explanation opens after your attempt
Correct Answer
A. \(3\sqrt{2}\)
Step 1
Concept
\(\sqrt{8}=2\sqrt{2}\) है। / \(\sqrt{8}=2\sqrt{2}\).
Step 2
Why this answer is correct
\(\sqrt{2}+2\sqrt{2}=3\sqrt{2}\)। / \(\sqrt{2}+2\sqrt{2}=3\sqrt{2}\).
Step 3
Exam Tip
जोड़ने से पहले वर्गमूलों को सरल करें। / Simplify radicals before adding them.
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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
#radical-product
#rational-result
A (4)
B \(\sqrt{10}\)
C \(2\sqrt{8}\)
D (8)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{2}\times\sqrt{8}=\sqrt{16}\)। / \(\sqrt{2}\times\sqrt{8}=\sqrt{16}\).
Step 2
Why this answer is correct
\(\sqrt{16}=4\), इसलिए मान परिमेय है। / \(\sqrt{16}=4\), so the value is rational.
Step 3
Exam Tip
वर्गमूलों को गुणा करते समय अंदर की संख्याएँ गुणा करें। / While multiplying square roots, multiply the numbers inside the roots.
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\(\sqrt{12}\) को सरल करने पर कौन-सा रूप मिलता है?
Which form is obtained by simplifying \(\sqrt{12}\)?
#real-numbers
#radical-simplification
#irrational
A \(2\sqrt{3}\)
B \(3\sqrt{2}\)
C \(6\sqrt{2}\)
D \(4\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
A. \(2\sqrt{3}\)
Step 1
Concept
\(12=4 \times 3\) लिखें। / Write \(12=4 \times 3\).
Step 2
Why this answer is correct
\(\sqrt{12}=\sqrt{4 \times 3}=2\sqrt{3}\)। / \(\sqrt{12}=\sqrt{4 \times 3}=2\sqrt{3}\).
Step 3
Exam Tip
वर्गमूल सरल करते समय पूर्ण वर्ग गुणनखंड बाहर निकालें। / While simplifying square roots, take the perfect square factor outside.
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कॉन्टूर रेखा का मुख्य कार्य क्या है?
What is the main function of a contour line?
#visual-art
#line
#class-10
#medium
A रूप की सीमा और बनावट दिखाना / Showing boundary and form
B रंग को मिटाना / Erasing colour
C कागज मोड़ना / Folding paper
D केवल अक्षर लिखना / Only writing letters
Explanation opens after your attempt
Correct Answer
A. रूप की सीमा और बनावट दिखाना / Showing boundary and form
Explanation
Simple Explanation
कॉन्टूर रेखा रूप की बाहरी और भीतरी सीमाओं को समझने में मदद करती है। परीक्षा में इसे अवलोकन चित्रण से जोड़ें। / A contour line helps understand outer and inner boundaries of form. In exams connect it with observational drawing.
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बफर जोन का मुख्य कार्य क्या होता है?
What is the main function of a buffer zone?
#buffer-zone
#core-area
#site-management
A मुख्य धरोहर क्षेत्र को बाहरी दबाव से बचाना / Protecting the core heritage area from external pressure
B स्थल को व्यापार केंद्र बनाना / Making the site a trade center
C सभी नियम हटाना / Removing all rules
D धरोहर को नष्ट करना / Destroying heritage
Explanation opens after your attempt
Correct Answer
A. मुख्य धरोहर क्षेत्र को बाहरी दबाव से बचाना / Protecting the core heritage area from external pressure
Explanation
Simple Explanation
बफर जोन मुख्य स्थल की रक्षा में सहायक क्षेत्र होता है। परीक्षा में कोर क्षेत्र और बफर जोन अलग याद रखें। / A buffer zone is a supporting area for protecting the core site. For exams remember core area and buffer zone separately.
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विश्व धरोहर प्रबंधन योजना का मुख्य कार्य क्या है?
What is the main function of a World Heritage management plan?
#management-plan
#heritage-protection
#risk-management
A स्थल के मूल्य संरक्षण जोखिम और उपयोग का व्यवस्थित संतुलन बनाना / To systematically balance site value conservation risks and use
B स्थल को निजी व्यापार केंद्र बनाना / To make the site a private trade center
C सभी ऐतिहासिक प्रमाण हटाना / To remove all historical evidence
D स्थल का नाम बदलना मात्र / Only changing the site's name
Explanation opens after your attempt
Correct Answer
A. स्थल के मूल्य संरक्षण जोखिम और उपयोग का व्यवस्थित संतुलन बनाना / To systematically balance site value conservation risks and use
Explanation
Simple Explanation
प्रबंधन योजना संरक्षण को व्यवहारिक नीतियों में बदलती है। परीक्षा में जोखिम प्रबंधन और निगरानी याद रखें। / A management plan turns conservation into practical policies. For exams remember risk management and monitoring.
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संयुक्त राष्ट्र महासभा का एक महत्वपूर्ण कार्य क्या है?
What is one important function of the United Nations General Assembly?
#general-assembly
#discussion
#un-organs
A विश्व मुद्दों पर चर्चा का मंच देना / Providing a forum for discussing world issues
B सभी देशों की पुलिस चलाना / Running police of all countries
C स्थायी सेना रखना / Keeping a permanent army
D व्यापार कर लगाना / Imposing trade taxes
Explanation opens after your attempt
Correct Answer
A. विश्व मुद्दों पर चर्चा का मंच देना / Providing a forum for discussing world issues
Explanation
Simple Explanation
महासभा विश्व मुद्दों पर चर्चा और विचार-विमर्श का बड़ा मंच है। परीक्षा में इसे सभी सदस्य देशों की सभा समझें। / The General Assembly is a major forum for discussion and deliberation on world issues. For exams understand it as an assembly of all member states.
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संयुक्त राष्ट्र सुरक्षा परिषद का मुख्य कार्य क्या है?
What is the main function of the UN Security Council?
#security council
#peace
#united nations
A शिक्षा पाठ्यक्रम बनाना / To make school syllabi
B अंतरराष्ट्रीय शांति और सुरक्षा की जिम्मेदारी निभाना / To maintain international peace and security
C खेल प्रतियोगिता कराना / To organize sports events
D डाक टिकट जारी करना / To issue postage stamps
Explanation opens after your attempt
Correct Answer
B. अंतरराष्ट्रीय शांति और सुरक्षा की जिम्मेदारी निभाना / To maintain international peace and security
Explanation
Simple Explanation
सुरक्षा परिषद अंतरराष्ट्रीय शांति और सुरक्षा के लिए उत्तरदायी है। परीक्षा में इसे संयुक्त राष्ट्र का शक्तिशाली अंग मानकर पढ़ें। / The Security Council is responsible for international peace and security. Exam tip: study it as a powerful organ of the UN.
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