100 results found for "standard categories" in Class 10.
औपनिवेशिक जनगणना में जातीय श्रेणियों का कठोर होना किस दीर्घकालिक प्रभाव को जन्म दे सकता था?
What long term effect could rigid ethnic categories in colonial census produce?
#census
#ethnic-categories
#identity-politics
A पहचान राजनीति और प्रतिनिधित्व विवाद का मजबूत होना / Strengthening of identity politics and representation disputes
B सभी पहचानों का पूर्ण अंत / Complete end of all identities
C राज्य नीति से समाज का अलग हो जाना / Separation of society from state policy
D आर्थिक शोषण का तुरंत अंत / Immediate end of economic exploitation
Explanation opens after your attempt
Correct Answer
A. पहचान राजनीति और प्रतिनिधित्व विवाद का मजबूत होना / Strengthening of identity politics and representation disputes
Step 1
Concept
Rigid classification can affect post independence politics too. For exams connect census with power.
Step 2
Why this answer is correct
The correct answer is A. पहचान राजनीति और प्रतिनिधित्व विवाद का मजबूत होना / Strengthening of identity politics and representation disputes. Rigid classification can affect post independence politics too. For exams connect census with power.
Step 3
Exam Tip
कठोर वर्गीकरण स्वतंत्रता बाद राजनीति को भी प्रभावित कर सकता है। परीक्षा में जनगणना को सत्ता से जोड़ें।
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जनगणना में कठोर जातीय श्रेणियां स्वतंत्रता के बाद भी समस्या क्यों बन सकती थीं?
Why could rigid ethnic categories in census remain problematic after independence?
#census
#ethnic-categories
#identity-politics
A क्योंकि वे प्रतिनिधित्व संसाधन वितरण और पहचान राजनीति को प्रभावित कर सकती थीं / Because they could affect representation resource distribution and identity politics
B क्योंकि वे सभी पहचान समाप्त कर देती थीं / Because they ended all identities
C क्योंकि उनका राज्य नीति से कोई संबंध नहीं था / Because they had no relation with state policy
D क्योंकि वे केवल मौसम जानकारी थीं / Because they were only weather information
Explanation opens after your attempt
Correct Answer
A. क्योंकि वे प्रतिनिधित्व संसाधन वितरण और पहचान राजनीति को प्रभावित कर सकती थीं / Because they could affect representation resource distribution and identity politics
Step 1
Concept
Colonial classification could leave effects in post independence politics. For exams remember long term legacy.
Step 2
Why this answer is correct
The correct answer is A. क्योंकि वे प्रतिनिधित्व संसाधन वितरण और पहचान राजनीति को प्रभावित कर सकती थीं / Because they could affect representation resource distribution and identity politics. Colonial classification could leave effects in post independence politics. For exams remember long term legacy.
Step 3
Exam Tip
औपनिवेशिक वर्गीकरण स्वतंत्रता बाद राजनीति में भी असर छोड़ सकता था। परीक्षा में दीर्घकालिक विरासत याद रखें।
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पद्म विभूषण पद्म भूषण और पद्म श्री की वर्तमान श्रेणियां किस वर्ष से स्पष्ट रूप से लागू हुईं?
From which year did the present categories Padma Vibhushan Padma Bhushan and Padma Shri clearly come into use?
#padma awards
#1955
#categories
A 1954 ईस्वी / 1954 CE
B 1955 ईस्वी / 1955 CE
C 1961 ईस्वी / 1961 CE
D 1969 ईस्वी / 1969 CE
Explanation opens after your attempt
Correct Answer
B. 1955 ईस्वी / 1955 CE
Step 1
Concept
The categories of Padma Awards were changed in 1955. For exams remember 1954 for institution and 1955 for category change separately.
Step 2
Why this answer is correct
The correct answer is B. 1955 ईस्वी / 1955 CE. The categories of Padma Awards were changed in 1955. For exams remember 1954 for institution and 1955 for category change separately.
Step 3
Exam Tip
पद्म पुरस्कारों की श्रेणियों में 1955 में बदलाव हुआ। परीक्षा में 1954 शुरुआत और 1955 श्रेणी बदलाव अलग याद रखें।
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सांस्कृतिक परिदृश्य को विश्व धरोहर श्रेणी में महत्व क्यों मिलता है?
Why do cultural landscapes receive importance in World Heritage categories?
#cultural-landscape
#human-nature
#heritage
A क्योंकि वे मानव और प्रकृति की दीर्घकालिक पारस्परिक क्रिया दिखाते हैं / Because they show long term interaction between humans and nature
B क्योंकि वे केवल प्राकृतिक जंगल होते हैं / Because they are only natural forests
C क्योंकि उनमें मनुष्य की भूमिका नहीं होती / Because humans have no role in them
D क्योंकि वे केवल आधुनिक कारखाने होते हैं / Because they are only modern factories
Explanation opens after your attempt
Correct Answer
A. क्योंकि वे मानव और प्रकृति की दीर्घकालिक पारस्परिक क्रिया दिखाते हैं / Because they show long term interaction between humans and nature
Step 1
Concept
Cultural landscapes show the relation between nature and human society. For exams remember fields gardens and sacred landscapes.
Step 2
Why this answer is correct
The correct answer is A. क्योंकि वे मानव और प्रकृति की दीर्घकालिक पारस्परिक क्रिया दिखाते हैं / Because they show long term interaction between humans and nature. Cultural landscapes show the relation between nature and human society. For exams remember fields gardens and sacred landscapes.
Step 3
Exam Tip
सांस्कृतिक परिदृश्य प्रकृति और मानव समाज के संबंध को दिखाते हैं। परीक्षा में खेत उद्यान और पवित्र परिदृश्य याद रखें।
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औपनिवेशिक जनगणना में पहचान को स्थिर श्रेणी मानना क्यों समस्याजनक था?
Why was it problematic to treat identity as fixed categories in colonial census?
#census
#identity
#classification
A क्योंकि सामाजिक पहचानें अक्सर लचीली और संदर्भ आधारित होती हैं / Because social identities are often flexible and context based
B क्योंकि पहचान हमेशा अपरिवर्तनीय होती है / Because identity is always unchanging
C क्योंकि जनगणना का राजनीति से कोई संबंध नहीं / Because census has no relation with politics
D क्योंकि इससे सभी मतभेद समाप्त हो जाते हैं / Because it ends all differences
Explanation opens after your attempt
Correct Answer
A. क्योंकि सामाजिक पहचानें अक्सर लचीली और संदर्भ आधारित होती हैं / Because social identities are often flexible and context based
Step 1
Concept
Rigid classification could affect identity politics. For exams remember census and power relations.
Step 2
Why this answer is correct
The correct answer is A. क्योंकि सामाजिक पहचानें अक्सर लचीली और संदर्भ आधारित होती हैं / Because social identities are often flexible and context based. Rigid classification could affect identity politics. For exams remember census and power relations.
Step 3
Exam Tip
कठोर वर्गीकरण पहचान राजनीति को प्रभावित कर सकता था। परीक्षा में जनगणना और सत्ता संबंध याद रखें।
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कौन सा बहुपद मानक रूप में अवरोही घातों में लिखा गया है?
Which polynomial is written in standard form with descending powers?
#standard form
#descending powers
#polynomial
A \(2x+5x^3-1\)
B \(5x^3+2x-1\)
C \(7+3x^2-x^4\)
D \(x+x^2+x^3\)
Explanation opens after your attempt
Correct Answer
B. \(5x^3+2x-1\)
Step 1
Concept
In standard form, terms are written from highest power to lowest power. \(5x^3+2x-1\) follows this order.
Step 2
Why this answer is correct
The correct answer is B. \(5x^3+2x-1\). In standard form, terms are written from highest power to lowest power. \(5x^3+2x-1\) follows this order.
Step 3
Exam Tip
मानक रूप में बड़ी घात से छोटी घात की ओर लिखते हैं। \(5x^3+2x-1\) इसी क्रम में है।
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निम्न में से कौन सा बहुपद मानक रूप में व्यवस्थित है?
Which of the following polynomials is arranged in standard form?
#polynomials
#standard-form
#easy
#arrangement
A \(2x^3+x^2+5x+1\)
B \(5x+2x^3+1+x^2\)
C \(1+5x+x^2+2x^3\)
D \(x^2+2x^3+5x+1\)
Explanation opens after your attempt
Correct Answer
A. \(2x^3+x^2+5x+1\)
Step 1
Concept
In standard form, powers are written in descending order. \(2x^3+x^2+5x+1\) follows this order.
Step 2
Why this answer is correct
The correct answer is A. \(2x^3+x^2+5x+1\). In standard form, powers are written in descending order. \(2x^3+x^2+5x+1\) follows this order.
Step 3
Exam Tip
मानक रूप में घातें घटते क्रम में लिखी जाती हैं। \(2x^3+x^2+5x+1\) में यही क्रम है।
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यदि ((x-7)(x-15)=26), तो मानक द्विघात समीकरण क्या होगा?
If ((x-7)(x-15)=26), what is the standard quadratic equation?
#quadratic
#standard-form
#application
A \(x^2-22x+79=0\)
B \(x^2-22x+131=0\)
C \(x^2+22x+79=0\)
D \(x^2-8x+105=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-22x+79=0\)
Step 1
Concept
((x-7)(x-15)=x-2 -22x+105), so \(x^2-22x+105=26\) gives \(x^2-22x+79=0\). In exams, bring all terms to one side after expansion.
Step 2
Why this answer is correct
The correct answer is A. \(x^2-22x+79=0\). ((x-7)(x-15)=x-2 -22x+105), so \(x^2-22x+105=26\) gives \(x^2-22x+79=0\). In exams, bring all terms to one side after expansion.
Step 3
Exam Tip
((x-7)(x-15)=x-2 -22x+105), इसलिए \(x^2-22x+105=26\) से \(x^2-22x+79=0\) मिलता है। परीक्षा में विस्तार के बाद सभी पद एक तरफ लाएं।
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यदि ((x-6)(x-13)=22), तो मानक द्विघात समीकरण क्या होगा?
If ((x-6)(x-13)=22), what is the standard quadratic equation?
#quadratic
#standard-form
#application
A \(x^2-19x+56=0\)
B \(x^2-19x+100=0\)
C \(x^2+19x+56=0\)
D \(x^2-7x+78=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-19x+56=0\)
Step 1
Concept
((x-6)(x-13)=x-2 -19x+78), so \(x^2-19x+78=22\) gives \(x^2-19x+56=0\). In exams, bring all terms to one side after expansion.
Step 2
Why this answer is correct
The correct answer is A. \(x^2-19x+56=0\). ((x-6)(x-13)=x-2 -19x+78), so \(x^2-19x+78=22\) gives \(x^2-19x+56=0\). In exams, bring all terms to one side after expansion.
Step 3
Exam Tip
((x-6)(x-13)=x-2 -19x+78), इसलिए \(x^2-19x+78=22\) से \(x^2-19x+56=0\) मिलता है। परीक्षा में विस्तार के बाद सभी पद एक तरफ लाएं।
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यदि ((x-5)(x-11)=18), तो मानक द्विघात समीकरण क्या होगा?
If ((x-5)(x-11)=18), what is the standard quadratic equation?
#quadratic
#standard-form
#application
A \(x^2-16x+37=0\)
B \(x^2-16x+73=0\)
C \(x^2+16x+37=0\)
D \(x^2-6x+55=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-16x+37=0\)
Step 1
Concept
((x-5)(x-11)=x-2 -16x+55), so \(x^2-16x+55=18\) gives \(x^2-16x+37=0\). In exams, bring all terms to one side after expansion.
Step 2
Why this answer is correct
The correct answer is A. \(x^2-16x+37=0\). ((x-5)(x-11)=x-2 -16x+55), so \(x^2-16x+55=18\) gives \(x^2-16x+37=0\). In exams, bring all terms to one side after expansion.
Step 3
Exam Tip
((x-5)(x-11)=x-2 -16x+55), इसलिए \(x^2-16x+55=18\) से \(x^2-16x+37=0\) मिलता है। परीक्षा में विस्तार के बाद सभी पद एक तरफ लाएं।
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यदि ((x-4)(x-9)=14), तो मानक द्विघात समीकरण क्या होगा?
If ((x-4)(x-9)=14), what is the standard quadratic equation?
#quadratic
#standard-form
#application
A \(x^2-13x+22=0\)
B \(x^2-13x+50=0\)
C \(x^2+13x+22=0\)
D \(x^2-5x+36=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-13x+22=0\)
Step 1
Concept
((x-4)(x-9)=x-2 -13x+36), so \(x^2-13x+36=14\) gives \(x^2-13x+22=0\). In exams, bring all terms to one side after expansion.
Step 2
Why this answer is correct
The correct answer is A. \(x^2-13x+22=0\). ((x-4)(x-9)=x-2 -13x+36), so \(x^2-13x+36=14\) gives \(x^2-13x+22=0\). In exams, bring all terms to one side after expansion.
Step 3
Exam Tip
((x-4)(x-9)=x-2 -13x+36), इसलिए \(x^2-13x+36=14\) से \(x^2-13x+22=0\) मिलता है। परीक्षा में विस्तार के बाद सभी पद एक तरफ लाएं।
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यदि ((x-3)(x-7)=10), तो मानक द्विघात समीकरण क्या होगा?
If ((x-3)(x-7)=10), what is the standard quadratic equation?
#quadratic
#standard-form
#application
A \(x^2-10x+11=0\)
B \(x^2-10x+31=0\)
C \(x^2+10x+11=0\)
D \(x^2-4x+21=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-10x+11=0\)
Step 1
Concept
((x-3)(x-7)=x-2 -10x+21), so \(x^2-10x+21=10\) gives \(x^2-10x+11=0\). In exams, bring all terms to one side after expansion.
Step 2
Why this answer is correct
The correct answer is A. \(x^2-10x+11=0\). ((x-3)(x-7)=x-2 -10x+21), so \(x^2-10x+21=10\) gives \(x^2-10x+11=0\). In exams, bring all terms to one side after expansion.
Step 3
Exam Tip
((x-3)(x-7)=x-2 -10x+21), इसलिए \(x^2-10x+21=10\) से \(x^2-10x+11=0\) मिलता है। परीक्षा में विस्तार के बाद सभी पद एक तरफ लाएं।
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यदि ((x-2)(x-5)=6), तो मानक द्विघात समीकरण क्या होगा?
If ((x-2)(x-5)=6), what is the standard quadratic equation?
#quadratic
#standard-form
#application
A \(x^2-7x+4=0\)
B \(x^2-7x+16=0\)
C \(x^2+7x+4=0\)
D \(x^2-3x+10=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-7x+4=0\)
Step 1
Concept
((x-2)(x-5)=x-2 -7x+10), so \(x^2-7x+10=6\) gives \(x^2-7x+4=0\). In exams, bring all terms to one side after expansion.
Step 2
Why this answer is correct
The correct answer is A. \(x^2-7x+4=0\). ((x-2)(x-5)=x-2 -7x+10), so \(x^2-7x+10=6\) gives \(x^2-7x+4=0\). In exams, bring all terms to one side after expansion.
Step 3
Exam Tip
((x-2)(x-5)=x-2 -7x+10), इसलिए \(x^2-7x+10=6\) से \(x^2-7x+4=0\) मिलता है। परीक्षा में विस्तार के बाद सभी पद एक तरफ लाएं।
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\(3x^2+2=11x\) को मानक रूप में लिखने पर क्या मिलेगा?
What is obtained when \(3x^2+2=11x\) is written in standard form?
#quadratic
#standard-form
#transposition
A \(3x^2-11x+2=0\)
B \(3x^2+11x+2=0\)
C \(3x^2-11x-2=0\)
D \(3x^2+2=0\)
Explanation opens after your attempt
Correct Answer
A. \(3x^2-11x+2=0\)
Step 1
Concept
Bringing (11x) to the left gives \(3x^2-11x+2=0\). In exams, bring all terms to one side.
Step 2
Why this answer is correct
The correct answer is A. \(3x^2-11x+2=0\). Bringing (11x) to the left gives \(3x^2-11x+2=0\). In exams, bring all terms to one side.
Step 3
Exam Tip
(11x) को बाईं ओर लाने पर \(3x^2-11x+2=0\) बनता है। परीक्षा में सभी पदों को एक तरफ लाएं।
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यदि \(5x^2+9x=2\) है, तो मानक रूप में समीकरण क्या होगा?
If \(5x^2+9x=2\), what will be the equation in standard form?
#quadratic
#standard-form
#transposition
A \(5x^2+9x-2=0\)
B \(5x^2+9x+2=0\)
C \(5x^2-9x-2=0\)
D \(9x^2+5x-2=0\)
Explanation opens after your attempt
Correct Answer
A. \(5x^2+9x-2=0\)
Step 1
Concept
Bringing (2) to the left gives \(5x^2+9x-2=0\). In exams, make standard form before solving.
Step 2
Why this answer is correct
The correct answer is A. \(5x^2+9x-2=0\). Bringing (2) to the left gives \(5x^2+9x-2=0\). In exams, make standard form before solving.
Step 3
Exam Tip
(2) को बाईं ओर लाने पर \(5x^2+9x-2=0\) मिलता है। परीक्षा में हल करने से पहले मानक रूप बनाएं।
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\(2x^2+1=7x\) को मानक रूप में लिखने पर क्या मिलेगा?
What is obtained when \(2x^2+1=7x\) is written in standard form?
#quadratic
#standard-form
#transposition
A \(2x^2-7x+1=0\)
B \(2x^2+7x+1=0\)
C \(2x^2-7x-1=0\)
D \(2x^2+1=0\)
Explanation opens after your attempt
Correct Answer
A. \(2x^2-7x+1=0\)
Step 1
Concept
Bringing (7x) to the left gives \(2x^2-7x+1=0\). In exams, bring all terms to one side.
Step 2
Why this answer is correct
The correct answer is A. \(2x^2-7x+1=0\). Bringing (7x) to the left gives \(2x^2-7x+1=0\). In exams, bring all terms to one side.
Step 3
Exam Tip
(7x) को बाईं ओर लाने पर \(2x^2-7x+1=0\) बनता है। परीक्षा में सभी पदों को एक तरफ लाएं।
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यदि \(3x^2+7x=6\) है, तो मानक रूप में समीकरण क्या होगा?
If \(3x^2+7x=6\), what will be the equation in standard form?
#quadratic
#standard-form
#transposition
A \(3x^2+7x-6=0\)
B \(3x^2+7x+6=0\)
C \(3x^2-7x-6=0\)
D \(7x^2+3x-6=0\)
Explanation opens after your attempt
Correct Answer
A. \(3x^2+7x-6=0\)
Step 1
Concept
Bringing (6) to the left gives \(3x^2+7x-6=0\). In exams, make standard form before applying any method.
Step 2
Why this answer is correct
The correct answer is A. \(3x^2+7x-6=0\). Bringing (6) to the left gives \(3x^2+7x-6=0\). In exams, make standard form before applying any method.
Step 3
Exam Tip
(6) को बाईं ओर लाने पर \(3x^2+7x-6=0\) मिलता है। परीक्षा में सूत्र लगाने से पहले मानक रूप बनाएं।
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\(4x^2-1=8x\) को मानक रूप में लिखने पर क्या मिलेगा?
What is obtained when \(4x^2-1=8x\) is written in standard form?
#quadratic
#standard-form
#transposition
A \(4x^2-8x-1=0\)
B \(4x^2+8x-1=0\)
C \(4x^2-8x+1=0\)
D \(4x^2-1=0\)
Explanation opens after your attempt
Correct Answer
A. \(4x^2-8x-1=0\)
Step 1
Concept
Bringing (8x) to the left gives \(4x^2-8x-1=0\). In exams, do not miss any term while making standard form.
Step 2
Why this answer is correct
The correct answer is A. \(4x^2-8x-1=0\). Bringing (8x) to the left gives \(4x^2-8x-1=0\). In exams, do not miss any term while making standard form.
Step 3
Exam Tip
(8x) को बाईं तरफ लाने पर \(4x^2-8x-1=0\) बनता है। परीक्षा में मानक रूप बनाने से पहले कोई पद न छोड़ें।
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यदि \(2x^2+5x=3\) है, तो मानक रूप \(ax^2+bx+c=0\) में (a,b,c) क्या हैं?
If \(2x^2+5x=3\), what are (a,b,c) in standard form \(ax^2+bx+c=0\)?
#quadratic
#standard-form
#coefficients
A (a=2,b=5,c=-3)
B (a=2,b=5,c=3)
C (a=5,b=2,c=-3)
D (a=2,b=-5,c=3)
Explanation opens after your attempt
Correct Answer
A. (a=2,b=5,c=-3)
Step 1
Concept
The standard form is \(2x^2+5x-3=0\), so (a=2,b=5,c=-3). In exams, bring all terms to one side first.
Step 2
Why this answer is correct
The correct answer is A. (a=2,b=5,c=-3). The standard form is \(2x^2+5x-3=0\), so (a=2,b=5,c=-3). In exams, bring all terms to one side first.
Step 3
Exam Tip
मानक रूप \(2x^2+5x-3=0\) है, इसलिए (a=2,b=5,c=-3) हैं। परीक्षा में सभी पदों को पहले एक तरफ लाएं।
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समीकरण \(\frac{x+3}{x-2}+\frac{x-2}{x+3}=\frac{13}{6}\) का मानक द्विघात रूप कौन-सा है?
What is the standard quadratic form of \(\frac{x+3}{x-2}+\frac{x-2}{x+3}=\frac{13}{6}\)?
#quadratic-equations
#fraction-equation
#standard-form
#expert
A \(x^2+x-156=0\)
B \(x^2-x-156=0\)
C \(x^2+x+156=0\)
D \(2x^2+x-156=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+x-156=0\)
Step 1
Concept
After clearing denominators, (6{(x+3)2 +(x-2)2 }=13(x+3)(x-2)). Simplifying gives the correct form \(x^2+x-156=0\).
Step 2
Why this answer is correct
The correct answer is A. \(x^2+x-156=0\). After clearing denominators, (6{(x+3)2 +(x-2)2 }=13(x+3)(x-2)). Simplifying gives the correct form \(x^2+x-156=0\).
Step 3
Exam Tip
हर हटाने पर (6{(x+3)2 +(x-2)2 }=13(x+3)(x-2)) मिलता है। सरल करने पर \(x^2+x-156=0\) सही रूप है।
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समीकरण ((x+6)2 +(x-7)2 =(x+3)2 ) का मानक रूप कौन-सा है?
What is the standard form of ((x+6)2 +(x-7)2 =(x+3)2 )?
#quadratic-equations
#identity
#standard-form
#expert
A \(x^2-14x+76=0\)
B \(x^2+14x+76=0\)
C \(x^2-20x+76=0\)
D \(x^2-14x-76=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-14x+76=0\)
Step 1
Concept
Expanding gives left side \(2x^2-2x+85\) and right side \(x^2+6x+9\). Subtracting gives \(x^2-8x+76=0\).
Step 2
Why this answer is correct
The correct answer is A. \(x^2-14x+76=0\). Expanding gives left side \(2x^2-2x+85\) and right side \(x^2+6x+9\). Subtracting gives \(x^2-8x+76=0\).
Step 3
Exam Tip
विस्तार करने पर बाईं ओर \(2x^2-2x+85\) और दाईं ओर \(x^2+6x+9\) है। घटाने पर \(x^2-8x+76=0\) नहीं बल्कि \(x^2-8x+76=0\) मिलता है।
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समीकरण ((x+5)(x+8)+(x-4)(x+7)=110) का मानक रूप कौन-सा है?
What is the standard form of ((x+5)(x+8)+(x-4)(x+7)=110)?
#quadratic-equations
#expansion
#standard-form
#expert
A \(2x^2+16x-98=0\)
B \(2x^2+16x+12=0\)
C \(x^2+8x-98=0\)
D \(2x^2+8x-110=0\)
Explanation opens after your attempt
Correct Answer
A. \(2x^2+16x-98=0\)
Step 1
Concept
The left side is \(x^2+13x+40+x^2+3x-28=2x^2+16x+12\). Subtracting (110) gives \(2x^2+16x-98=0\).
Step 2
Why this answer is correct
The correct answer is A. \(2x^2+16x-98=0\). The left side is \(x^2+13x+40+x^2+3x-28=2x^2+16x+12\). Subtracting (110) gives \(2x^2+16x-98=0\).
Step 3
Exam Tip
बाईं ओर \(x^2+13x+40+x^2+3x-28=2x^2+16x+12\) है। (110) घटाने पर \(2x^2+16x-98=0\) मिलता है।
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समीकरण \(\frac{4x^2-3}{5}+\frac{x-2}{4}=3\) का पूर्णांक गुणांकों वाला मानक रूप कौन-सा है?
What is the standard form with integer coefficients of \(\frac{4x^2-3}{5}+\frac{x-2}{4}=3\)?
#quadratic-equations
#fractions
#standard-form
#expert
A \(16x^2+5x-74=0\)
B \(16x^2-5x-74=0\)
C \(4x^2+5x-74=0\)
D \(16x^2+5x+74=0\)
Explanation opens after your attempt
Correct Answer
A. \(16x^2+5x-74=0\)
Step 1
Concept
Multiplying the whole equation by (20) gives \(16x^2-12+5x-10=60\). Therefore the standard form is \(16x^2+5x-82=0\).
Step 2
Why this answer is correct
The correct answer is A. \(16x^2+5x-74=0\). Multiplying the whole equation by (20) gives \(16x^2-12+5x-10=60\). Therefore the standard form is \(16x^2+5x-82=0\).
Step 3
Exam Tip
पूरे समीकरण को (20) से गुणा करने पर \(16x^2-12+5x-10=60\) मिलता है। इसलिए \(16x^2+5x-82=0\) नहीं बल्कि \(16x^2+5x-82=0\) मिलेगा।
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समीकरण ((4x-3)(x+5)=2(3x-1)) का मानक द्विघात रूप कौन-सा है?
What is the standard quadratic form of ((4x-3)(x+5)=2(3x-1))?
#quadratic-equations
#standard-form
#expansion
#expert
A \(4x^2+11x-13=0\)
B \(4x^2+17x-13=0\)
C \(4x^2+11x+13=0\)
D \(4x^2+23x-17=0\)
Explanation opens after your attempt
Correct Answer
A. \(4x^2+11x-13=0\)
Step 1
Concept
Here ((4x-3)(x+5)=4x-2 +17x-15) and (2(3x-1)=6x-2). Bringing all terms to one side gives \(4x^2+11x-13=0\).
Step 2
Why this answer is correct
The correct answer is A. \(4x^2+11x-13=0\). Here ((4x-3)(x+5)=4x-2 +17x-15) and (2(3x-1)=6x-2). Bringing all terms to one side gives \(4x^2+11x-13=0\).
Step 3
Exam Tip
((4x-3)(x+5)=4x-2 +17x-15) और (2(3x-1)=6x-2) है। सभी पद एक ओर लाने पर \(4x^2+11x-13=0\) मिलता है।
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समीकरण \(\frac{x+2}{x-1}+\frac{x-1}{x+2}=\frac{5}{2}\) का मानक द्विघात रूप कौन-सा है?
What is the standard quadratic form of \(\frac{x+2}{x-1}+\frac{x-1}{x+2}=\frac{5}{2}\)?
#quadratic-equations
#fraction-equation
#standard-form
#expert
A \(x^2+x-20=0\)
B \(x^2-x-20=0\)
C \(x^2+x+20=0\)
D \(2x^2+x-20=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+x-20=0\)
Step 1
Concept
After clearing denominators, (2(x+2)2 +2(x-1)2 =5(x-1)(x+2)). Simplifying gives the correct form \(x^2+x-20=0\).
Step 2
Why this answer is correct
The correct answer is A. \(x^2+x-20=0\). After clearing denominators, (2(x+2)2 +2(x-1)2 =5(x-1)(x+2)). Simplifying gives the correct form \(x^2+x-20=0\).
Step 3
Exam Tip
हर हटाने पर (2(x+2)2 +2(x-1)2 =5(x-1)(x+2)) मिलता है। सरल करने पर \(x^2+x-20=0\) सही रूप है।
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समीकरण ((x+5)2 +(x-6)2 =(x+2)2 ) का मानक रूप कौन-सा है?
What is the standard form of ((x+5)2 +(x-6)2 =(x+2)2 )?
#quadratic-equations
#identity
#standard-form
#expert
A \(x^2-10x+57=0\)
B \(x^2+10x+57=0\)
C \(x^2-14x+57=0\)
D \(x^2-10x-57=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-10x+57=0\)
Step 1
Concept
Expanding gives left side \(2x^2-2x+61\) and right side \(x^2+4x+4\). Subtracting gives \(x^2-6x+57=0\).
Step 2
Why this answer is correct
The correct answer is A. \(x^2-10x+57=0\). Expanding gives left side \(2x^2-2x+61\) and right side \(x^2+4x+4\). Subtracting gives \(x^2-6x+57=0\).
Step 3
Exam Tip
विस्तार करने पर बाईं ओर \(2x^2-2x+61\) और दाईं ओर \(x^2+4x+4\) है। घटाने पर \(x^2-6x+57=0\) नहीं बल्कि \(x^2-6x+57=0\) मिलता है।
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समीकरण ((x+4)(x+7)+(x-3)(x+6)=88) का मानक रूप कौन-सा है?
What is the standard form of ((x+4)(x+7)+(x-3)(x+6)=88)?
#quadratic-equations
#expansion
#standard-form
#expert
A \(2x^2+14x-78=0\)
B \(2x^2+14x+10=0\)
C \(x^2+7x-78=0\)
D \(2x^2+7x-88=0\)
Explanation opens after your attempt
Correct Answer
A. \(2x^2+14x-78=0\)
Step 1
Concept
The left side is \(x^2+11x+28+x^2+3x-18=2x^2+14x+10\). Subtracting (88) gives \(2x^2+14x-78=0\).
Step 2
Why this answer is correct
The correct answer is A. \(2x^2+14x-78=0\). The left side is \(x^2+11x+28+x^2+3x-18=2x^2+14x+10\). Subtracting (88) gives \(2x^2+14x-78=0\).
Step 3
Exam Tip
बाईं ओर \(x^2+11x+28+x^2+3x-18=2x^2+14x+10\) है। (88) घटाने पर \(2x^2+14x-78=0\) मिलता है।
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समीकरण \(\frac{3x^2+2}{4}-\frac{x-5}{3}=6\) का पूर्णांक गुणांकों वाला मानक रूप कौन-सा है?
What is the standard form with integer coefficients of \(\frac{3x^2+2}{4}-\frac{x-5}{3}=6\)?
#quadratic-equations
#fractions
#standard-form
#expert
A \(9x^2-4x-42=0\)
B \(9x^2+4x-42=0\)
C \(3x^2-4x-42=0\)
D \(9x^2-4x+42=0\)
Explanation opens after your attempt
Correct Answer
A. \(9x^2-4x-42=0\)
Step 1
Concept
Multiplying the whole equation by (12) gives \(9x^2+6-4x+20=72\). Therefore the standard form is \(9x^2-4x-46=0\).
Step 2
Why this answer is correct
The correct answer is A. \(9x^2-4x-42=0\). Multiplying the whole equation by (12) gives \(9x^2+6-4x+20=72\). Therefore the standard form is \(9x^2-4x-46=0\).
Step 3
Exam Tip
पूरे समीकरण को (12) से गुणा करने पर \(9x^2+6-4x+20=72\) मिलता है। इसलिए मानक रूप \(9x^2-4x-46=0\) नहीं बल्कि \(9x^2-4x-46=0\) होगा।
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समीकरण ((3x-2)(2x+5)=4(x+1)) का मानक द्विघात रूप कौन-सा है?
What is the standard quadratic form of ((3x-2)(2x+5)=4(x+1))?
#quadratic-equations
#standard-form
#expansion
#expert
A \(6x^2+7x-14=0\)
B \(6x^2+15x-14=0\)
C \(6x^2+7x+14=0\)
D \(6x^2+11x-10=0\)
Explanation opens after your attempt
Correct Answer
A. \(6x^2+7x-14=0\)
Step 1
Concept
Here ((3x-2)(2x+5)=6x-2 +11x-10) and (4(x+1)=4x+4). Bringing all terms to one side gives \(6x^2+7x-14=0\).
Step 2
Why this answer is correct
The correct answer is A. \(6x^2+7x-14=0\). Here ((3x-2)(2x+5)=6x-2 +11x-10) and (4(x+1)=4x+4). Bringing all terms to one side gives \(6x^2+7x-14=0\).
Step 3
Exam Tip
((3x-2)(2x+5)=6x-2 +11x-10) और (4(x+1)=4x+4) है। सभी पद एक ओर लाने पर \(6x^2+7x-14=0\) मिलता है।
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समीकरण (\frac{(x+1)2 }{2}+\frac{(x-3)2 }{3}=10) का पूर्णांक गुणांकों वाला मानक रूप कौन-सा है?
What is the standard form with integer coefficients of (\frac{(x+1)2 }{2}+\frac{(x-3)2 }{3}=10)?
#quadratic-equations
#fractions
#standard-form
#expert
A \(5x^2-6x-39=0\)
B \(5x^2+6x-39=0\)
C \(6x^2-5x-39=0\)
D \(5x^2-6x+39=0\)
Explanation opens after your attempt
Correct Answer
A. \(5x^2-6x-39=0\)
Step 1
Concept
Multiplying the whole equation by (6) gives (3(x+1)2 +2(x-3)2 =60). Simplifying gives the correct form \(5x^2-6x-39=0\).
Step 2
Why this answer is correct
The correct answer is A. \(5x^2-6x-39=0\). Multiplying the whole equation by (6) gives (3(x+1)2 +2(x-3)2 =60). Simplifying gives the correct form \(5x^2-6x-39=0\).
Step 3
Exam Tip
पूरे समीकरण को (6) से गुणा करने पर (3(x+1)2 +2(x-3)2 =60) मिलता है। सरल करने पर \(5x^2-6x-39=0\) सही रूप है।
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समीकरण ((x-3)2 +(x+4)2 =(x-1)2 ) का मानक रूप कौन-सा है?
What is the standard form of ((x-3)2 +(x+4)2 =(x-1)2 )?
#quadratic-equations
#identity
#standard-form
#expert
A \(x^2+4x+24=0\)
B \(x^2-4x+24=0\)
C \(x^2+8x+24=0\)
D \(x^2+4x-24=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+4x+24=0\)
Step 1
Concept
Expanding gives left side \(2x^2+2x+25\) and right side \(x^2-2x+1\). Subtracting gives \(x^2+4x+24=0\).
Step 2
Why this answer is correct
The correct answer is A. \(x^2+4x+24=0\). Expanding gives left side \(2x^2+2x+25\) and right side \(x^2-2x+1\). Subtracting gives \(x^2+4x+24=0\).
Step 3
Exam Tip
विस्तार करने पर बाईं ओर \(2x^2+2x+25\) और दाईं ओर \(x^2-2x+1\) है। घटाने पर \(x^2+4x+24=0\) मिलता है।
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समीकरण ((x+3)(x+6)+(x-2)(x+5)=70) का मानक रूप कौन-सा है?
What is the standard form of ((x+3)(x+6)+(x-2)(x+5)=70)?
#quadratic-equations
#expansion
#standard-form
#expert
A \(2x^2+12x-62=0\)
B \(2x^2+12x+8=0\)
C \(x^2+6x-62=0\)
D \(2x^2+6x-70=0\)
Explanation opens after your attempt
Correct Answer
A. \(2x^2+12x-62=0\)
Step 1
Concept
The left side is \(x^2+9x+18+x^2+3x-10=2x^2+12x+8\). Subtracting (70) gives \(2x^2+12x-62=0\).
Step 2
Why this answer is correct
The correct answer is A. \(2x^2+12x-62=0\). The left side is \(x^2+9x+18+x^2+3x-10=2x^2+12x+8\). Subtracting (70) gives \(2x^2+12x-62=0\).
Step 3
Exam Tip
बाईं ओर \(x^2+9x+18+x^2+3x-10=2x^2+12x+8\) है। (70) घटाने पर \(2x^2+12x-62=0\) मिलता है।
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समीकरण \(\frac{2x^2-1}{5}+\frac{x+3}{2}=7\) का पूर्णांक गुणांकों वाला मानक रूप कौन-सा है?
What is the standard form with integer coefficients of \(\frac{2x^2-1}{5}+\frac{x+3}{2}=7\)?
#quadratic-equations
#fractions
#standard-form
#expert
A \(4x^2+5x-59=0\)
B \(4x^2+5x+59=0\)
C \(2x^2+5x-59=0\)
D \(4x^2-5x-59=0\)
Explanation opens after your attempt
Correct Answer
A. \(4x^2+5x-59=0\)
Step 1
Concept
Multiplying the whole equation by (10) gives \(4x^2-2+5x+15=70\). Therefore the standard form is \(4x^2+5x-57=0\).
Step 2
Why this answer is correct
The correct answer is A. \(4x^2+5x-59=0\). Multiplying the whole equation by (10) gives \(4x^2-2+5x+15=70\). Therefore the standard form is \(4x^2+5x-57=0\).
Step 3
Exam Tip
पूरे समीकरण को (10) से गुणा करने पर \(4x^2-2+5x+15=70\) मिलता है। इसलिए \(4x^2+5x-57=0\) नहीं बल्कि \(4x^2+5x-57=0\) मिलेगा।
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समीकरण ((2x+5)(3x-4)=4(x-1)) का मानक द्विघात रूप कौन-सा है?
What is the standard quadratic form of ((2x+5)(3x-4)=4(x-1))?
#quadratic-equations
#expansion
#standard-form
#expert
A \(6x^2+7x-16=0\)
B \(6x^2+15x-20=0\)
C \(6x^2+11x-24=0\)
D \(6x^2+7x-24=0\)
Explanation opens after your attempt
Correct Answer
A. \(6x^2+7x-16=0\)
Step 1
Concept
Here ((2x+5)(3x-4)=6x-2 +7x-20) and (4(x-1)=4x-4). Bringing all terms to one side gives \(6x^2+3x-16=0\).
Step 2
Why this answer is correct
The correct answer is A. \(6x^2+7x-16=0\). Here ((2x+5)(3x-4)=6x-2 +7x-20) and (4(x-1)=4x-4). Bringing all terms to one side gives \(6x^2+3x-16=0\).
Step 3
Exam Tip
((2x+5)(3x-4)=6x-2 +7x-20) और (4(x-1)=4x-4) है। सभी पद एक ओर लाने पर \(6x^2+3x-16=0\) नहीं बल्कि सही रूप \(6x^2+3x-16=0\) मिलता है।
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समीकरण ((x-2)(x+3)+(2x-1)(x-4)=0) का मानक रूप कौन-सा है?
What is the standard form of ((x-2)(x+3)+(2x-1)(x-4)=0)?
#quadratic-equations
#expansion
#standard-form
#hard
A \(3x^2-8x-2=0\)
B \(3x^2+8x-2=0\)
C \(3x^2-2x-8=0\)
D \(2x^2-8x-3=0\)
Explanation opens after your attempt
Correct Answer
A. \(3x^2-8x-2=0\)
Step 1
Concept
Here ((x-2)(x+3)=x-2 +x-6) and ((2x-1)(x-4)=2x-2 -9x+4). Adding them gives \(3x^2-8x-2=0\).
Step 2
Why this answer is correct
The correct answer is A. \(3x^2-8x-2=0\). Here ((x-2)(x+3)=x-2 +x-6) and ((2x-1)(x-4)=2x-2 -9x+4). Adding them gives \(3x^2-8x-2=0\).
Step 3
Exam Tip
((x-2)(x+3)=x-2 +x-6) और ((2x-1)(x-4)=2x-2 -9x+4) है। जोड़ने पर \(3x^2-8x-2=0\) मिलता है।
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समीकरण ((x+2)2 +(x-5)2 =(x+1)2 ) का मानक रूप कौन-सा है?
What is the standard form of ((x+2)2 +(x-5)2 =(x+1)2 )?
#quadratic-equations
#identity
#standard-form
#hard
A \(x^2-8x+28=0\)
B \(x^2+8x+28=0\)
C \(x^2-6x+28=0\)
D \(x^2-8x-28=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-8x+28=0\)
Step 1
Concept
Expanding gives left side \(2x^2-6x+29\) and right side \(x^2+2x+1\). Subtracting gives \(x^2-8x+28=0\).
Step 2
Why this answer is correct
The correct answer is A. \(x^2-8x+28=0\). Expanding gives left side \(2x^2-6x+29\) and right side \(x^2+2x+1\). Subtracting gives \(x^2-8x+28=0\).
Step 3
Exam Tip
विस्तार करने पर बाईं ओर \(2x^2-6x+29\) और दाईं ओर \(x^2+2x+1\) है। घटाने पर \(x^2-8x+28=0\) मिलता है।
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समीकरण ((x+2)(x+5)+(x-1)(x+4)=60) का मानक रूप कौन-सा है?
What is the standard form of ((x+2)(x+5)+(x-1)(x+4)=60)?
#quadratic-equations
#expansion
#standard-form
#hard
A \(2x^2+10x-54=0\)
B \(2x^2+10x+6=0\)
C \(x^2+5x-54=0\)
D \(2x^2+5x-60=0\)
Explanation opens after your attempt
Correct Answer
A. \(2x^2+10x-54=0\)
Step 1
Concept
The left side is \(x^2+7x+10+x^2+3x-4=2x^2+10x+6\). Subtracting (60) gives \(2x^2+10x-54=0\).
Step 2
Why this answer is correct
The correct answer is A. \(2x^2+10x-54=0\). The left side is \(x^2+7x+10+x^2+3x-4=2x^2+10x+6\). Subtracting (60) gives \(2x^2+10x-54=0\).
Step 3
Exam Tip
बाईं ओर \(x^2+7x+10+x^2+3x-4=2x^2+10x+6\) है। (60) घटाने पर \(2x^2+10x-54=0\) मिलता है।
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समीकरण \(\frac{x^2+1}{3}-\frac{x-2}{2}=5\) को पूर्णांक गुणांकों वाले मानक रूप में लिखिए।
Write \(\frac{x^2+1}{3}-\frac{x-2}{2}=5\) in standard form with integer coefficients.
#quadratic-equations
#fractions
#standard-form
#hard
A \(2x^2-3x-22=0\)
B \(2x^2-3x+22=0\)
C \(3x^2-2x-22=0\)
D \(2x^2+3x-22=0\)
Explanation opens after your attempt
Correct Answer
A. \(2x^2-3x-22=0\)
Step 1
Concept
Multiplying the whole equation by (6) gives \(2x^2+2-3x+6=30\). Therefore the standard form is \(2x^2-3x-22=0\).
Step 2
Why this answer is correct
The correct answer is A. \(2x^2-3x-22=0\). Multiplying the whole equation by (6) gives \(2x^2+2-3x+6=30\). Therefore the standard form is \(2x^2-3x-22=0\).
Step 3
Exam Tip
पूरे समीकरण को (6) से गुणा करने पर \(2x^2+2-3x+6=30\) मिलता है। इसलिए मानक रूप \(2x^2-3x-22=0\) है।
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समीकरण ((6x+1)(x-4)=5x) का मानक द्विघात रूप कौन-सा है?
What is the standard quadratic form of ((6x+1)(x-4)=5x)?
#quadratic-equations
#standard-form
#expansion
#hard
A \(6x^2-28x-4=0\)
B \(6x^2-18x-4=0\)
C \(6x^2-23x-4=0\)
D \(6x^2+28x-4=0\)
Explanation opens after your attempt
Correct Answer
A. \(6x^2-28x-4=0\)
Step 1
Concept
Here ((6x+1)(x-4)=6x-2 -23x-4), and subtracting (5x) gives \(6x^2-28x-4=0\). First expand and then bring all terms to one side.
Step 2
Why this answer is correct
The correct answer is A. \(6x^2-28x-4=0\). Here ((6x+1)(x-4)=6x-2 -23x-4), and subtracting (5x) gives \(6x^2-28x-4=0\). First expand and then bring all terms to one side.
Step 3
Exam Tip
((6x+1)(x-4)=6x-2 -23x-4) है और (5x) घटाने पर \(6x^2-28x-4=0\) मिलता है। पहले विस्तार करें फिर सभी पद एक ओर लाएं।
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समीकरण ((x-1)2 +(x-2)2 =(x-3)2 ) का मानक रूप कौन-सा है?
What is the standard form of ((x-1)2 +(x-2)2 =(x-3)2 )?
#quadratic-equations
#identity
#standard-form
#hard
A \(x^2+6x-4=0\)
B \(x^2-2x-4=0\)
C \(x^2+2x-4=0\)
D \(x^2-6x+4=0\)
Explanation opens after your attempt
Correct Answer
B. \(x^2-2x-4=0\)
Step 1
Concept
Expanding gives left side \(2x^2-6x+5\) and right side \(x^2-6x+9\). Subtracting gives \(x^2-4=0\).
Step 2
Why this answer is correct
The correct answer is B. \(x^2-2x-4=0\). Expanding gives left side \(2x^2-6x+5\) and right side \(x^2-6x+9\). Subtracting gives \(x^2-4=0\).
Step 3
Exam Tip
विस्तार करने पर बाईं ओर \(2x^2-6x+5\) और दाईं ओर \(x^2-6x+9\) है। घटाने पर \(x^2-4=0\) नहीं बल्कि \(x^2-4=0\) मिलता है।
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समीकरण ((x+1)(x+2)+(x+3)(x+4)=50) का मानक रूप कौन-सा है?
What is the standard form of ((x+1)(x+2)+(x+3)(x+4)=50)?
#quadratic-equations
#expansion
#standard-form
#hard
A \(2x^2+10x-36=0\)
B \(2x^2+10x+14=0\)
C \(x^2+5x-36=0\)
D \(2x^2+5x-50=0\)
Explanation opens after your attempt
Correct Answer
A. \(2x^2+10x-36=0\)
Step 1
Concept
The left side is \(x^2+3x+2+x^2+7x+12=2x^2+10x+14\). Subtracting (50) gives \(2x^2+10x-36=0\).
Step 2
Why this answer is correct
The correct answer is A. \(2x^2+10x-36=0\). The left side is \(x^2+3x+2+x^2+7x+12=2x^2+10x+14\). Subtracting (50) gives \(2x^2+10x-36=0\).
Step 3
Exam Tip
बाईं ओर \(x^2+3x+2+x^2+7x+12=2x^2+10x+14\) है। (50) घटाने पर \(2x^2+10x-36=0\) मिलता है।
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समीकरण \(\frac{x^2-3}{2}+\frac{x-1}{3}=4\) को पूर्णांक गुणांकों वाले मानक रूप में लिखिए।
Write \(\frac{x^2-3}{2}+\frac{x-1}{3}=4\) in standard form with integer coefficients.
#quadratic-equations
#fractions
#standard-form
#hard
A \(3x^2+2x-29=0\)
B \(3x^2+2x-35=0\)
C \(x^2+2x-29=0\)
D \(3x^2-2x-29=0\)
Explanation opens after your attempt
Correct Answer
A. \(3x^2+2x-29=0\)
Step 1
Concept
Multiplying the whole equation by (6) gives \(3x^2-9+2x-2=24\). Thus the standard form is \(3x^2+2x-35=0\).
Step 2
Why this answer is correct
The correct answer is A. \(3x^2+2x-29=0\). Multiplying the whole equation by (6) gives \(3x^2-9+2x-2=24\). Thus the standard form is \(3x^2+2x-35=0\).
Step 3
Exam Tip
पूरे समीकरण को (6) से गुणा करने पर \(3x^2-9+2x-2=24\) मिलता है। इसलिए \(3x^2+2x-35=0\) नहीं बल्कि सही रूप \(3x^2+2x-35=0\) होगा।
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समीकरण ((5x-2)(2x+3)=7x) का मानक द्विघात रूप कौन-सा है?
What is the standard quadratic form of ((5x-2)(2x+3)=7x)?
#quadratic-equations
#standard-form
#expansion
#hard
A \(10x^2+4x-6=0\)
B \(10x^2+18x-6=0\)
C \(10x^2-4x-6=0\)
D \(10x^2+11x+6=0\)
Explanation opens after your attempt
Correct Answer
A. \(10x^2+4x-6=0\)
Step 1
Concept
Here ((5x-2)(2x+3)=10x-2 +11x-6) and subtracting (7x) gives \(10x^2+4x-6=0\). First expand and then bring all terms to one side.
Step 2
Why this answer is correct
The correct answer is A. \(10x^2+4x-6=0\). Here ((5x-2)(2x+3)=10x-2 +11x-6) and subtracting (7x) gives \(10x^2+4x-6=0\). First expand and then bring all terms to one side.
Step 3
Exam Tip
((5x-2)(2x+3)=10x-2 +11x-6) है और (7x) घटाने पर \(10x^2+4x-6=0\) मिलता है। पहले विस्तार करें फिर सभी पद एक ओर लाएं।
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समीकरण ((3x+4)2 =7x+16) का मानक रूप कौन-सा है?
What is the standard form of ((3x+4)2 =7x+16)?
#quadratic-equations
#standard-form
#identity
#medium
A \(9x^2+17x=0\)
B \(9x^2+31x=0\)
C \(9x^2+17x+32=0\)
D \(9x^2+24x-16=0\)
Explanation opens after your attempt
Correct Answer
A. \(9x^2+17x=0\)
Step 1
Concept
((3x+4)2 =9x-2 +24x+16). Subtracting (7x+16) gives \(9x^2+17x=0\).
Step 2
Why this answer is correct
The correct answer is A. \(9x^2+17x=0\). ((3x+4)2 =9x-2 +24x+16). Subtracting (7x+16) gives \(9x^2+17x=0\).
Step 3
Exam Tip
((3x+4)2 =9x-2 +24x+16) है। (7x+16) घटाने पर \(9x^2+17x=0\) मिलता है।
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समीकरण ((x-4)(x+9)=5x) का मानक रूप क्या है?
What is the standard form of ((x-4)(x+9)=5x)?
#quadratic-equations
#standard-form
#expansion
#medium
A \(x^2-36=0\)
B \(x^2+5x-36=0\)
C \(x^2-5x-36=0\)
D \(x^2+14x-36=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-36=0\)
Step 1
Concept
The left side gives \(x^2+5x-36\). Subtracting (5x) gives \(x^2-36=0\).
Step 2
Why this answer is correct
The correct answer is A. \(x^2-36=0\). The left side gives \(x^2+5x-36\). Subtracting (5x) gives \(x^2-36=0\).
Step 3
Exam Tip
बाईं ओर \(x^2+5x-36\) मिलता है। (5x) घटाने पर \(x^2-36=0\) बनता है।
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समीकरण ((x-6)2 =4x+5) का मानक रूप कौन-सा है?
What is the standard form of ((x-6)2 =4x+5)?
#quadratic-equations
#identity
#standard-form
#medium
A \(x^2-16x+31=0\)
B \(x^2-8x+31=0\)
C \(x^2-12x+41=0\)
D \(x^2+16x+31=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-16x+31=0\)
Step 1
Concept
((x-6)2 =x-2 -12x+36). Subtracting (4x+5) gives \(x^2-16x+31=0\).
Step 2
Why this answer is correct
The correct answer is A. \(x^2-16x+31=0\). ((x-6)2 =x-2 -12x+36). Subtracting (4x+5) gives \(x^2-16x+31=0\).
Step 3
Exam Tip
((x-6)2 =x-2 -12x+36) है। (4x+5) को घटाने पर \(x^2-16x+31=0\) मिलता है।
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समीकरण ((4x-1)(x+3)=0) का मानक द्विघात रूप कौन-सा है?
What is the standard quadratic form of ((4x-1)(x+3)=0)?
#quadratic-equations
#standard-form
#expansion
#medium
A \(4x^2+11x-3=0\)
B \(4x^2-11x-3=0\)
C \(4x^2+12x-1=0\)
D \(4x^2-13x+3=0\)
Explanation opens after your attempt
Correct Answer
A. \(4x^2+11x-3=0\)
Step 1
Concept
Expanding ((4x-1)(x+3)) gives \(4x^2+12x-x-3\). So the standard form is \(4x^2+11x-3=0\).
Step 2
Why this answer is correct
The correct answer is A. \(4x^2+11x-3=0\). Expanding ((4x-1)(x+3)) gives \(4x^2+12x-x-3\). So the standard form is \(4x^2+11x-3=0\).
Step 3
Exam Tip
((4x-1)(x+3)) को फैलाने पर \(4x^2+12x-x-3\) मिलता है। इसलिए मानक रूप \(4x^2+11x-3=0\) है।
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समीकरण ((2x-1)2 =3x+5) का मानक रूप कौन-सा है?
What is the standard form of ((2x-1)2 =3x+5)?
#quadratic-equations
#standard-form
#identity
#medium
A \(4x^2-7x-4=0\)
B \(4x^2+x-4=0\)
C \(4x^2-7x+6=0\)
D \(4x^2-x-6=0\)
Explanation opens after your attempt
Correct Answer
A. \(4x^2-7x-4=0\)
Step 1
Concept
Here ((2x-1)2 =4x-2 -4x+1), and bringing all terms to one side gives \(4x^2-7x-4=0\). Apply the square identity and signs carefully.
Step 2
Why this answer is correct
The correct answer is A. \(4x^2-7x-4=0\). Here ((2x-1)2 =4x-2 -4x+1), and bringing all terms to one side gives \(4x^2-7x-4=0\). Apply the square identity and signs carefully.
Step 3
Exam Tip
((2x-1)2 =4x-2 -4x+1) है और सभी पद एक ओर लाने पर \(4x^2-7x-4=0\) मिलता है। वर्ग सूत्र और चिन्ह दोनों ध्यान से लगाएं।
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समीकरण ((x+2)(x-7)=3x) का मानक रूप क्या है?
What is the standard form of ((x+2)(x-7)=3x)?
#quadratic-equations
#standard-form
#expansion
#medium
A \(x^2-8x-14=0\)
B \(x^2-5x-14=0\)
C \(x^2-2x-14=0\)
D \(x^2+8x-14=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-8x-14=0\)
Step 1
Concept
The left side gives \(x^2-5x-14\). Subtracting (3x) gives \(x^2-8x-14=0\).
Step 2
Why this answer is correct
The correct answer is A. \(x^2-8x-14=0\). The left side gives \(x^2-5x-14\). Subtracting (3x) gives \(x^2-8x-14=0\).
Step 3
Exam Tip
बाईं ओर \(x^2-5x-14\) मिलता है। (3x) को घटाने पर \(x^2-8x-14=0\) बनता है।
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समीकरण ((x+4)2 =5x+10) का मानक रूप कौन-सा है?
What is the standard form of ((x+4)2 =5x+10)?
#quadratic-equations
#identity
#standard-form
#medium
A \(x^2+3x+6=0\)
B \(x^2+8x+26=0\)
C \(x^2+13x+6=0\)
D \(x^2+3x-6=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+3x+6=0\)
Step 1
Concept
((x+4)2 =x-2 +8x+16), and subtracting (5x+10) gives \(x^2+3x+6=0\). Keep the middle term correct in square identities.
Step 2
Why this answer is correct
The correct answer is A. \(x^2+3x+6=0\). ((x+4)2 =x-2 +8x+16), and subtracting (5x+10) gives \(x^2+3x+6=0\). Keep the middle term correct in square identities.
Step 3
Exam Tip
((x+4)2 =x-2 +8x+16) है और (5x+10) हटाने पर \(x^2+3x+6=0\) मिलता है। वर्ग सूत्र में मध्य पद सही रखें।
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कौन-सा समीकरण द्विघात है लेकिन अभी मानक रूप में नहीं है?
Which equation is quadratic but not yet in standard form?
#quadratic-equations
#identify
#standard-form
#medium
A \(4x^2-3x+1=0\)
B \(4x^2+1=3x\)
C (4x+1=3)
D \(x^3+1=3x\)
Explanation opens after your attempt
Correct Answer
B. \(4x^2+1=3x\)
Step 1
Concept
\(4x^2+1=3x\) can be written as \(4x^2-3x+1=0\). In standard form, all terms are on one side and (0) is on the other.
Step 2
Why this answer is correct
The correct answer is B. \(4x^2+1=3x\). \(4x^2+1=3x\) can be written as \(4x^2-3x+1=0\). In standard form, all terms are on one side and (0) is on the other.
Step 3
Exam Tip
\(4x^2+1=3x\) को \(4x^2-3x+1=0\) लिखा जा सकता है। मानक रूप में सभी पद एक ओर और दूसरी ओर (0) होता है।
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समीकरण \(8x-x^2=15\) का मानक रूप कौन-सा है जिसमें \(x^2\) का गुणांक धनात्मक हो?
What is the standard form of \(8x-x^2=15\) with positive coefficient of \(x^2\)?
#quadratic-equations
#standard-form
#transposition
#medium
A \(x^2-8x+15=0\)
B \(x^2+8x-15=0\)
C \(x^2-8x-15=0\)
D \(x^2+8x+15=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-8x+15=0\)
Step 1
Concept
Bringing all terms to one side gives \(-x^2+8x-15=0\). Multiplying by (-1) gives \(x^2-8x+15=0\).
Step 2
Why this answer is correct
The correct answer is A. \(x^2-8x+15=0\). Bringing all terms to one side gives \(-x^2+8x-15=0\). Multiplying by (-1) gives \(x^2-8x+15=0\).
Step 3
Exam Tip
सभी पद एक ओर लाने पर \(-x^2+8x-15=0\) मिलता है। (-1) से गुणा करने पर \(x^2-8x+15=0\) मिलता है।
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समीकरण ((3x+2)(x-5)=0) का मानक द्विघात रूप कौन-सा है?
What is the standard quadratic form of ((3x+2)(x-5)=0)?
#quadratic-equations
#standard-form
#expansion
#medium
A \(3x^2-13x-10=0\)
B \(3x^2+13x-10=0\)
C \(3x^2-15x+2=0\)
D \(3x^2+17x+10=0\)
Explanation opens after your attempt
Correct Answer
A. \(3x^2-13x-10=0\)
Step 1
Concept
Expanding ((3x+2)(x-5)) gives \(3x^2-15x+2x-10\). So the standard form is \(3x^2-13x-10=0\).
Step 2
Why this answer is correct
The correct answer is A. \(3x^2-13x-10=0\). Expanding ((3x+2)(x-5)) gives \(3x^2-15x+2x-10\). So the standard form is \(3x^2-13x-10=0\).
Step 3
Exam Tip
((3x+2)(x-5)) को फैलाने पर \(3x^2-15x+2x-10\) मिलता है। इसलिए मानक रूप \(3x^2-13x-10=0\) है।
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समीकरण ((x+3)2 =2x+15) का मानक रूप कौन-सा है?
What is the standard form of ((x+3)2 =2x+15)?
#quadratic-equations
#standard-form
#identity
#medium
A \(x^2+4x-6=0\)
B \(x^2+8x-6=0\)
C \(x^2+4x+6=0\)
D \(x^2+6x-15=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+4x-6=0\)
Step 1
Concept
Here ((x+3)2 =x-2 +6x+9), and bringing all terms to one side gives \(x^2+4x-6=0\). Use the square identity and transposition carefully.
Step 2
Why this answer is correct
The correct answer is A. \(x^2+4x-6=0\). Here ((x+3)2 =x-2 +6x+9), and bringing all terms to one side gives \(x^2+4x-6=0\). Use the square identity and transposition carefully.
Step 3
Exam Tip
((x+3)2 =x-2 +6x+9) है और सभी पद एक ओर लाने पर \(x^2+4x-6=0\) मिलता है। वर्ग सूत्र और स्थानांतरण दोनों सावधानी से करें।
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समीकरण ((x-1)(x+6)=2x) का मानक रूप क्या है?
What is the standard form of ((x-1)(x+6)=2x)?
#quadratic-equations
#standard-form
#expansion
#medium
A \(x^2+3x-6=0\)
B \(x^2+5x-6=0\)
C \(x^2+7x-6=0\)
D \(x^2-3x-6=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+3x-6=0\)
Step 1
Concept
The left side gives \(x^2+5x-6\), and subtracting (2x) gives \(x^2+3x-6=0\). First expand and then bring all terms to one side.
Step 2
Why this answer is correct
The correct answer is A. \(x^2+3x-6=0\). The left side gives \(x^2+5x-6\), and subtracting (2x) gives \(x^2+3x-6=0\). First expand and then bring all terms to one side.
Step 3
Exam Tip
बाईं ओर \(x^2+5x-6\) मिलता है, फिर (2x) घटाने पर \(x^2+3x-6=0\) बनता है। पहले फैलाएं फिर सभी पद एक ओर लाएं।
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समीकरण \(\frac{x^2}{2}+3x-5=0\) को बिना भिन्न के मानक रूप में कौन-सा लिखा जाएगा?
How will \(\frac{x^2}{2}+3x-5=0\) be written in standard form without fractions?
#quadratic-equations
#fractions
#standard-form
#medium
A \(x^2+6x-10=0\)
B \(x^2+3x-5=0\)
C \(2x^2+3x-5=0\)
D \(x^2+6x+10=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+6x-10=0\)
Step 1
Concept
Multiplying the whole equation by (2) gives \(x^2+6x-10=0\). To remove fractions, multiply by the denominator.
Step 2
Why this answer is correct
The correct answer is A. \(x^2+6x-10=0\). Multiplying the whole equation by (2) gives \(x^2+6x-10=0\). To remove fractions, multiply by the denominator.
Step 3
Exam Tip
पूरे समीकरण को (2) से गुणा करने पर \(x^2+6x-10=0\) मिलता है। भिन्न हटाने के लिए हर से गुणा करें।
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समीकरण ((x-5)2 =16) का मानक रूप कौन-सा है?
What is the standard form of ((x-5)2 =16)?
#quadratic-equations
#identity
#standard-form
#medium
A \(x^2-10x+9=0\)
B \(x^2-10x+41=0\)
C \(x^2+10x+9=0\)
D \(x^2-5x+16=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-10x+9=0\)
Step 1
Concept
((x-5)2 =x-2 -10x+25), so \(x^2-10x+25-16=0\). Do not forget the middle term while using square identities.
Step 2
Why this answer is correct
The correct answer is A. \(x^2-10x+9=0\). ((x-5)2 =x-2 -10x+25), so \(x^2-10x+25-16=0\). Do not forget the middle term while using square identities.
Step 3
Exam Tip
((x-5)2 =x-2 -10x+25), इसलिए \(x^2-10x+25-16=0\) मिलता है। वर्ग सूत्र लगाते समय मध्य पद न भूलें।
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कौन-सा समीकरण द्विघात है लेकिन मानक रूप में नहीं लिखा गया है?
Which equation is quadratic but not written in standard form?
#quadratic-equations
#identify
#standard-form
#medium
A \(x^2+2x+1=0\)
B \(x^2=5x-4\)
C (3x+7=0)
D \(x^3+x=0\)
Explanation opens after your attempt
Correct Answer
B. \(x^2=5x-4\)
Step 1
Concept
\(x^2=5x-4\) can be written as \(x^2-5x+4=0\), so it is quadratic. In standard form, the right side must be (0).
Step 2
Why this answer is correct
The correct answer is B. \(x^2=5x-4\). \(x^2=5x-4\) can be written as \(x^2-5x+4=0\), so it is quadratic. In standard form, the right side must be (0).
Step 3
Exam Tip
\(x^2=5x-4\) को \(x^2-5x+4=0\) बनाया जा सकता है, इसलिए यह द्विघात है। मानक रूप में दायां पक्ष (0) होना चाहिए।
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समीकरण \(5x-2x^2=9\) का मानक रूप कौन-सा है जिसमें \(x^2\) का गुणांक धनात्मक हो?
What is the standard form of \(5x-2x^2=9\) with positive coefficient of \(x^2\)?
#quadratic-equations
#standard-form
#signs
#medium
A \(2x^2-5x+9=0\)
B \(2x^2+5x-9=0\)
C \(2x^2-5x-9=0\)
D \(2x^2+5x+9=0\)
Explanation opens after your attempt
Correct Answer
A. \(2x^2-5x+9=0\)
Step 1
Concept
Bringing all terms to one side gives \(-2x^2+5x-9=0\), and multiplying by (-1) gives \(2x^2-5x+9=0\). Change signs carefully in standard form.
Step 2
Why this answer is correct
The correct answer is A. \(2x^2-5x+9=0\). Bringing all terms to one side gives \(-2x^2+5x-9=0\), and multiplying by (-1) gives \(2x^2-5x+9=0\). Change signs carefully in standard form.
Step 3
Exam Tip
सभी पद एक ओर लाकर \(-2x^2+5x-9=0\) मिलता है और (-1) से गुणा करने पर \(2x^2-5x+9=0\) मिलता है। मानक रूप में चिन्ह सावधानी से बदलें।
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समीकरण ((2x-3)(x+4)=0) का मानक द्विघात रूप कौन-सा है?
What is the standard quadratic form of ((2x-3)(x+4)=0)?
#quadratic-equations
#standard-form
#expansion
#medium
A \(2x^2+5x-12=0\)
B \(2x^2-5x-12=0\)
C \(2x^2+8x-3=0\)
D \(2x^2-11x+12=0\)
Explanation opens after your attempt
Correct Answer
A. \(2x^2+5x-12=0\)
Step 1
Concept
Multiplying gives \(2x^2+8x-3x-12=0\), so \(2x^2+5x-12=0\). Adding middle terms correctly is important in exams.
Step 2
Why this answer is correct
The correct answer is A. \(2x^2+5x-12=0\). Multiplying gives \(2x^2+8x-3x-12=0\), so \(2x^2+5x-12=0\). Adding middle terms correctly is important in exams.
Step 3
Exam Tip
गुणा करने पर \(2x^2+8x-3x-12=0\), इसलिए \(2x^2+5x-12=0\) मिलता है। मध्य पदों को सही जोड़ना परीक्षा में जरूरी है।
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मानक द्विघात समीकरण \(ax^2+bx+c=0\) में अधिकतम कितने अलग-अलग पद हो सकते हैं?
In the standard quadratic equation \(ax^2+bx+c=0\), what is the maximum number of different terms?
#quadratic-equations
#terms
#standard-form
A (1)
B (2)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
The standard form may contain the \(x^2\) term, the (x) term, and the constant term. So the maximum number of terms is (3).
Step 2
Why this answer is correct
The correct answer is C. (3). The standard form may contain the \(x^2\) term, the (x) term, and the constant term. So the maximum number of terms is (3).
Step 3
Exam Tip
मानक रूप में \(x^2\) पद, (x) पद और स्थिर पद हो सकते हैं। इसलिए अधिकतम (3) पद होते हैं।
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मानक रूप \(ax^2+bx+c=0\) में \(x^2\) का गुणांक किससे दर्शाया जाता है?
In the standard form \(ax^2+bx+c=0\), which symbol denotes the coefficient of \(x^2\)?
#quadratic-equations
#standard-form
#coefficient-a
A (b)
B (a)
C (c)
D (x)
Explanation opens after your attempt
Step 1
Concept
In standard form, the coefficient of \(x^2\) is (a). This coefficient must not be (0).
Step 2
Why this answer is correct
The correct answer is B. (a). In standard form, the coefficient of \(x^2\) is (a). This coefficient must not be (0).
Step 3
Exam Tip
मानक रूप में \(x^2\) का गुणांक (a) होता है। यही गुणांक (0) नहीं होना चाहिए।
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((x+1)2 =0) का मानक रूप क्या है?
What is the standard form of ((x+1)2 =0)?
#quadratic-equations
#identity
#standard-form
A \(x^2+x+1=0\)
B \(x^2-2x+1=0\)
C \(x^2+2x+1=0\)
D \(x^2+1=0\)
Explanation opens after your attempt
Correct Answer
C. \(x^2+2x+1=0\)
Step 1
Concept
((x+1)2 =x-2 +2x+1). Remember the formula ((a+b)2 =a-2 +2ab+b-2 ).
Step 2
Why this answer is correct
The correct answer is C. \(x^2+2x+1=0\). ((x+1)2 =x-2 +2x+1). Remember the formula ((a+b)2 =a-2 +2ab+b-2 ).
Step 3
Exam Tip
((x+1)2 =x-2 +2x+1) होता है। सूत्र ((a+b)2 =a-2 +2ab+b-2 ) याद रखें।
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समीकरण \(x^2=6x\) का मानक रूप कौन-सा है?
What is the standard form of \(x^2=6x\)?
#quadratic-equations
#standard-form
#transposition
A \(x^2+6x=0\)
B \(x^2-6x=0\)
C \(6x^2-x=0\)
D \(x^2-6=0\)
Explanation opens after your attempt
Correct Answer
B. \(x^2-6x=0\)
Step 1
Concept
Bringing (6x) to the left gives \(x^2-6x=0\). The sign changes during transposition.
Step 2
Why this answer is correct
The correct answer is B. \(x^2-6x=0\). Bringing (6x) to the left gives \(x^2-6x=0\). The sign changes during transposition.
Step 3
Exam Tip
(6x) को बाईं ओर लाने पर \(x^2-6x=0\) मिलता है। स्थानांतरण करते समय चिन्ह बदलता है।
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समीकरण (x(x-5)=0) का मानक रूप कौन-सा है?
What is the standard form of (x(x-5)=0)?
#quadratic-equations
#expansion
#standard-form
A \(x^2+5x=0\)
B \(x^2-5x=0\)
C \(5x^2-x=0\)
D \(x^2-5=0\)
Explanation opens after your attempt
Correct Answer
B. \(x^2-5x=0\)
Step 1
Concept
Expanding (x(x-5)) gives \(x^2-5x\). Keep signs correct while removing brackets.
Step 2
Why this answer is correct
The correct answer is B. \(x^2-5x=0\). Expanding (x(x-5)) gives \(x^2-5x\). Keep signs correct while removing brackets.
Step 3
Exam Tip
(x(x-5)) को फैलाने पर \(x^2-5x\) मिलता है। कोष्ठक हटाते समय चिन्ह सही रखें।
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समीकरण \(x^2=7\) का मानक रूप कौन-सा है?
What is the standard form of \(x^2=7\)?
#quadratic-equations
#standard-form
#easy
A \(x^2+7=0\)
B \(7x^2=0\)
C \(x^2-7x=0\)
D \(x^2-7=0\)
Explanation opens after your attempt
Correct Answer
D. \(x^2-7=0\)
Step 1
Concept
Bringing (7) to the left gives \(x^2-7=0\). In standard form, all terms are on one side.
Step 2
Why this answer is correct
The correct answer is D. \(x^2-7=0\). Bringing (7) to the left gives \(x^2-7=0\). In standard form, all terms are on one side.
Step 3
Exam Tip
(7) को बाईं ओर लाने पर \(x^2-7=0\) मिलता है। मानक रूप में सभी पद एक तरफ होते हैं।
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समीकरण \(4=3x-x^2\) का मानक रूप क्या है?
What is the standard form of \(4=3x-x^2\)?
#quadratic-equations
#standard-form
#transposition
A \(x^2-3x+4=0\)
B \(x^2+3x+4=0\)
C \(x^2-3x-4=0\)
D \(x^2+3x-4=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-3x+4=0\)
Step 1
Concept
Bringing all terms to one side gives \(x^2-3x+4=0\). In standard form, keep the right side as (0).
Step 2
Why this answer is correct
The correct answer is A. \(x^2-3x+4=0\). Bringing all terms to one side gives \(x^2-3x+4=0\). In standard form, keep the right side as (0).
Step 3
Exam Tip
सभी पद एक तरफ लाने पर \(x^2-3x+4=0\) मिलता है। मानक रूप में दायां पक्ष (0) रखें।
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((x+3)2 =25) को मानक रूप में लिखने पर कौन सा समीकरण मिलेगा?
Which equation is obtained when ((x+3)2 =25) is written in standard form?
#quadratic equations
#standard form
#perfect square
A \(x^2+6x-16=0\)
B \(x^2+6x+16=0\)
C \(x^2+3x-25=0\)
D \(x^2+9x-25=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+6x-16=0\)
Step 1
Concept
Here ((x+3)2 =x-2 +6x+9), and moving (25) left gives (-25). So \(x^2+6x-16=0\) is correct.
Step 2
Why this answer is correct
The correct answer is A. \(x^2+6x-16=0\). Here ((x+3)2 =x-2 +6x+9), and moving (25) left gives (-25). So \(x^2+6x-16=0\) is correct.
Step 3
Exam Tip
((x+3)2 =x-2 +6x+9) है और (25) को बाईं ओर लाने पर (-25) बनता है। इसलिए \(x^2+6x-16=0\) सही है।
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किस विकल्प में गलती है जब \(x^2=6x+7\) को मानक रूप में बदला जाता है?
Which option shows the mistake while converting \(x^2=6x+7\) to standard form?
#quadratic equations
#common mistake
#standard form
A \(x^2-6x-7=0\)
B \(x^2+6x+7=0\)
C \(x^2-6x=7\)
D \(x^2=6x+7\)
Explanation opens after your attempt
Correct Answer
B. \(x^2+6x+7=0\)
Step 1
Concept
The correct standard form is \(x^2-6x-7=0\). In option (B), the signs of the right-side terms were not changed.
Step 2
Why this answer is correct
The correct answer is B. \(x^2+6x+7=0\). The correct standard form is \(x^2-6x-7=0\). In option (B), the signs of the right-side terms were not changed.
Step 3
Exam Tip
सही मानक रूप \(x^2-6x-7=0\) है। विकल्प (B) में दाईं ओर के पदों के चिन्ह नहीं बदले गए।
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कौन सा समीकरण मानक रूप में लाने पर \(x^2+2x-8=0\) बनता है?
Which equation becomes \(x^2+2x-8=0\) after writing in standard form?
#quadratic equations
#standard form
#reverse form
A \(x^2+2x=8\)
B \(x^2+2x=-8\)
C \(x^2-2x=8\)
D \(x^2-2x=-8\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+2x=8\)
Step 1
Concept
Moving (8) to the left makes it (-8). So we get \(x^2+2x-8=0\).
Step 2
Why this answer is correct
The correct answer is A. \(x^2+2x=8\). Moving (8) to the left makes it (-8). So we get \(x^2+2x-8=0\).
Step 3
Exam Tip
(8) को बाईं ओर लाने पर (-8) बनता है। इसलिए \(x^2+2x-8=0\) मिलता है।
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(4x(x-3)=0) का मानक रूप क्या है?
What is the standard form of (4x(x-3)=0)?
#quadratic equations
#expansion
#standard form
A \(4x^2-12x=0\)
B \(4x^2+12x=0\)
C \(x^2-12x=0\)
D (4x-12=0)
Explanation opens after your attempt
Correct Answer
A. \(4x^2-12x=0\)
Step 1
Concept
Multiplying (4x) by both terms gives \(4x^2-12x=0\). Pay attention to the negative sign.
Step 2
Why this answer is correct
The correct answer is A. \(4x^2-12x=0\). Multiplying (4x) by both terms gives \(4x^2-12x=0\). Pay attention to the negative sign.
Step 3
Exam Tip
(4x) को दोनों पदों से गुणा करने पर \(4x^2-12x=0\) मिलता है। ऋण चिन्ह पर ध्यान दें।
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((x-6)(x+2)=0) का मानक रूप कौन सा है?
Which is the standard form of ((x-6)(x+2)=0)?
#quadratic equations
#expansion
#standard form
A \(x^2-4x-12=0\)
B \(x^2+4x-12=0\)
C \(x^2-8x+12=0\)
D \(x^2+8x+12=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-4x-12=0\)
Step 1
Concept
Expansion gives \(x^2+2x-6x-12=0\). So \(x^2-4x-12=0\) is correct.
Step 2
Why this answer is correct
The correct answer is A. \(x^2-4x-12=0\). Expansion gives \(x^2+2x-6x-12=0\). So \(x^2-4x-12=0\) is correct.
Step 3
Exam Tip
विस्तार से \(x^2+2x-6x-12=0\) मिलता है। इसलिए \(x^2-4x-12=0\) सही है।
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(2x(x+7)=0) को मानक रूप में लिखिए।
Write (2x(x+7)=0) in standard form.
#quadratic equations
#expansion
#standard form
A \(2x^2+14x=0\)
B \(2x^2-14x=0\)
C \(14x^2+2x=0\)
D (2x+7=0)
Explanation opens after your attempt
Correct Answer
A. \(2x^2+14x=0\)
Step 1
Concept
Multiply (2x) by both terms inside the bracket. This gives \(2x^2+14x=0\).
Step 2
Why this answer is correct
The correct answer is A. \(2x^2+14x=0\). Multiply (2x) by both terms inside the bracket. This gives \(2x^2+14x=0\).
Step 3
Exam Tip
(2x) को कोष्ठक के दोनों पदों से गुणा करें। इससे \(2x^2+14x=0\) मिलता है।
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समीकरण \(2x^2=5x+3\) का मानक रूप कौन सा है?
Which is the standard form of \(2x^2=5x+3\)?
#quadratic equations
#standard form
#sign change
A \(2x^2-5x-3=0\)
B \(2x^2+5x+3=0\)
C \(2x^2-5x+3=0\)
D \(2x^2+5x-3=0\)
Explanation opens after your attempt
Correct Answer
A. \(2x^2-5x-3=0\)
Step 1
Concept
Bringing all terms to one side gives \(2x^2-5x-3=0\). Changing signs is important.
Step 2
Why this answer is correct
The correct answer is A. \(2x^2-5x-3=0\). Bringing all terms to one side gives \(2x^2-5x-3=0\). Changing signs is important.
Step 3
Exam Tip
सभी पद एक तरफ लाने पर \(2x^2-5x-3=0\) मिलता है। चिन्ह बदलना जरूरी है।
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समीकरण \(4x^2+7x=9\) का मानक रूप क्या है?
What is the standard form of \(4x^2+7x=9\)?
#quadratic equations
#standard form
#transposition
A \(4x^2+7x+9=0\)
B \(4x^2+7x-9=0\)
C \(4x^2-7x-9=0\)
D \(4x^2-7x+9=0\)
Explanation opens after your attempt
Correct Answer
B. \(4x^2+7x-9=0\)
Step 1
Concept
Moving (9) to the left makes it (-9). So the standard form is \(4x^2+7x-9=0\).
Step 2
Why this answer is correct
The correct answer is B. \(4x^2+7x-9=0\). Moving (9) to the left makes it (-9). So the standard form is \(4x^2+7x-9=0\).
Step 3
Exam Tip
दाईं ओर के (9) को बाईं ओर लाने पर (-9) बनता है। इसलिए मानक रूप \(4x^2+7x-9=0\) है।
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किस विकल्प में सामान्य गलती है जब \(x^2=5x-6\) को मानक रूप में बदला जाता है?
Which option shows the common mistake while converting \(x^2=5x-6\) to standard form?
#quadratic equations
#common mistake
#standard form
A \(x^2-5x+6=0\)
B \(x^2-5x-6=0\)
C \(x^2+0x=5x-6\)
D \(x^2=5x-6\)
Explanation opens after your attempt
Correct Answer
B. \(x^2-5x-6=0\)
Step 1
Concept
The correct form is \(x^2-5x+6=0\). In option (B), the sign of (-6) was not changed.
Step 2
Why this answer is correct
The correct answer is B. \(x^2-5x-6=0\). The correct form is \(x^2-5x+6=0\). In option (B), the sign of (-6) was not changed.
Step 3
Exam Tip
सही रूप \(x^2-5x+6=0\) है। विकल्प (B) में (-6) का चिन्ह नहीं बदला गया।
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कौन सा समीकरण मानक रूप में लाने पर \(x^2-7x+10=0\) बनता है?
Which equation becomes \(x^2-7x+10=0\) after writing in standard form?
#quadratic equations
#standard form
#reverse thinking
A \(x^2-7x=-10\)
B \(x^2-7x=10\)
C \(x^2+7x=-10\)
D \(x^2+7x=10\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-7x=-10\)
Step 1
Concept
In \(x^2-7x=-10\), moving (-10) to the left gives (+10). So the standard form is \(x^2-7x+10=0\).
Step 2
Why this answer is correct
The correct answer is A. \(x^2-7x=-10\). In \(x^2-7x=-10\), moving (-10) to the left gives (+10). So the standard form is \(x^2-7x+10=0\).
Step 3
Exam Tip
\(x^2-7x=-10\) में (-10) को बाईं ओर लाने पर (+10) बनता है। इसलिए मानक रूप \(x^2-7x+10=0\) है।
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(3x(x-2)=0) का मानक रूप क्या है?
What is the standard form of (3x(x-2)=0)?
#quadratic equations
#expansion
#standard form
A \(3x^2-6x=0\)
B \(3x^2+6x=0\)
C \(x^2-6x=0\)
D (3x-6=0)
Explanation opens after your attempt
Correct Answer
A. \(3x^2-6x=0\)
Step 1
Concept
Multiplying (3x) by both terms gives \(3x^2-6x=0\). Watch the sign.
Step 2
Why this answer is correct
The correct answer is A. \(3x^2-6x=0\). Multiplying (3x) by both terms gives \(3x^2-6x=0\). Watch the sign.
Step 3
Exam Tip
(3x) को दोनों पदों से गुणा करने पर \(3x^2-6x=0\) मिलता है। चिन्ह पर ध्यान दें।
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((x-4)(x+1)=0) का मानक रूप कौन सा है?
Which is the standard form of ((x-4)(x+1)=0)?
#quadratic equations
#expansion
#standard form
A \(x^2-3x-4=0\)
B \(x^2+3x-4=0\)
C \(x^2-5x+4=0\)
D \(x^2+5x+4=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-3x-4=0\)
Step 1
Concept
Expanding gives \(x^2+x-4x-4=0\). So \(x^2-3x-4=0\) is correct.
Step 2
Why this answer is correct
The correct answer is A. \(x^2-3x-4=0\). Expanding gives \(x^2+x-4x-4=0\). So \(x^2-3x-4=0\) is correct.
Step 3
Exam Tip
विस्तार करने पर \(x^2+x-4x-4=0\) मिलता है। इसलिए \(x^2-3x-4=0\) सही है।
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(x(x+5)=0) को मानक रूप में लिखिए।
Write (x(x+5)=0) in standard form.
#quadratic equations
#expansion
#standard form
A \(x^2+5x=0\)
B \(x^2-5x=0\)
C \(5x^2+x=0\)
D (x+5=0)
Explanation opens after your attempt
Correct Answer
A. \(x^2+5x=0\)
Step 1
Concept
Multiplying gives \(x^2+5x=0\). While opening brackets, multiply each term.
Step 2
Why this answer is correct
The correct answer is A. \(x^2+5x=0\). Multiplying gives \(x^2+5x=0\). While opening brackets, multiply each term.
Step 3
Exam Tip
गुणा करने पर \(x^2+5x=0\) मिलता है। कोष्ठक खोलते समय हर पद से गुणा करें।
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कौन सा समीकरण \(ax^2+bx+c=0\) के मानक रूप में है?
Which equation is in the standard form \(ax^2+bx+c=0\)?
#quadratic equations
#standard form
#recognition
A \(x^2+2x+1=0\)
B \(x^2+2x=1\)
C \(x^2=2x+1\)
D (2x+1=0)
Explanation opens after your attempt
Correct Answer
A. \(x^2+2x+1=0\)
Step 1
Concept
In standard form the right side is (0). Option (A) matches this form.
Step 2
Why this answer is correct
The correct answer is A. \(x^2+2x+1=0\). In standard form the right side is (0). Option (A) matches this form.
Step 3
Exam Tip
मानक रूप में दाईं ओर (0) होता है। विकल्प (A) इसी रूप में है।
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समीकरण \(x^2=4x+12\) का मानक रूप कौन सा है?
Which is the standard form of \(x^2=4x+12\)?
#quadratic equations
#standard form
#signs
A \(x^2-4x-12=0\)
B \(x^2+4x+12=0\)
C \(x^2-4x+12=0\)
D \(x^2+4x-12=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-4x-12=0\)
Step 1
Concept
When terms from the right side move left, their signs change. Thus \(x^2-4x-12=0\) is correct.
Step 2
Why this answer is correct
The correct answer is A. \(x^2-4x-12=0\). When terms from the right side move left, their signs change. Thus \(x^2-4x-12=0\) is correct.
Step 3
Exam Tip
दाईं ओर के पदों को बाईं ओर लाने पर चिन्ह बदलते हैं। इसलिए \(x^2-4x-12=0\) सही है।
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समीकरण \(2x^2+5x=3\) का मानक रूप क्या है?
What is the standard form of \(2x^2+5x=3\)?
#quadratic equations
#standard form
#transposition
A \(2x^2+5x+3=0\)
B \(2x^2+5x-3=0\)
C \(2x^2-5x-3=0\)
D \(2x^2-5x+3=0\)
Explanation opens after your attempt
Correct Answer
B. \(2x^2+5x-3=0\)
Step 1
Concept
Bringing all terms to one side gives \(2x^2+5x-3=0\). Do not forget the sign change.
Step 2
Why this answer is correct
The correct answer is B. \(2x^2+5x-3=0\). Bringing all terms to one side gives \(2x^2+5x-3=0\). Do not forget the sign change.
Step 3
Exam Tip
सभी पद एक तरफ लाने पर \(2x^2+5x-3=0\) मिलता है। चिन्ह बदलना न भूलें।
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किसी धनात्मक पूर्णांक को (9) से भाग देने पर कौन-सा रूप मानक रूप नहीं है?
When a positive integer is divided by (9), which form is not a standard form?
#real-numbers
#not-standard-form
#remainder-condition
A (9q+7)
B (9q+8)
C (9q+9)
D (9q)
Explanation opens after your attempt
Step 1
Concept
On division by (9), remainders can be from (0) to (8).
Step 2
Why this answer is correct
In (9q+9), the remainder is (9), which equals the divisor.
Step 3
Exam Tip
It should be written correctly as (9(q+1)). चरण 1: (9) से भाग देने पर शेषफल (0) से (8) तक हो सकते हैं। चरण 2: (9q+9) में शेषफल (9) है, जो भाजक के बराबर है। चरण 3: इसे सही रूप में (9(q+1)) लिखा जाना चाहिए।
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किसी धनात्मक पूर्णांक को (3) से भाग देने पर कौन-सा रूप मानक रूप नहीं है?
When a positive integer is divided by (3), which form is not a standard form?
#real-numbers
#not-standard-form
#remainder-condition
A (3q)
B (3q+1)
C (3q+2)
D (3q+3)
Explanation opens after your attempt
Step 1
Concept
On division by (3), possible remainders are (0,1,2).
Step 2
Why this answer is correct
In (3q+3), the remainder is (3), which equals the divisor.
Step 3
Exam Tip
It should be written correctly as (3(q+1)). चरण 1: (3) से भाग देने पर शेषफल (0,1,2) हो सकते हैं। चरण 2: (3q+3) में शेषफल (3) है, जो भाजक के बराबर है। चरण 3: इसे सही रूप में (3(q+1)) लिखना चाहिए।
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यूक्लिड विभाजन प्रमेयिका का मानक रूप कौन सा है?
Which is the standard form of Euclid’s Division Lemma?
#standard form
#euclid lemma
#class 10 maths
A \(a=bq+r,\ 0 \le r < b\)
B (a=b+r+q)
C (a=q-r)
D (b=aq+r)
Explanation opens after your attempt
Correct Answer
A. \(a=bq+r,\ 0 \le r < b\)
Step 1
Concept
The lemma uses dividend (a), divisor (b), quotient (q), and remainder (r).
Step 2
Why this answer is correct
The correct relation is (a=bq+r).
Step 3
Exam Tip
Do not forget the condition \(0 \le r < b\). चरण 1: प्रमेयिका में भाज्य (a), भाजक (b), भागफल (q) और शेषफल (r) होते हैं। चरण 2: सही संबंध (a=bq+r) है। चरण 3: साथ में \(0 \le r < b\) लिखना न भूलें।
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विश्व धरोहर स्थल को सांस्कृतिक प्राकृतिक और मिश्रित श्रेणियों में बांटना किस बात को स्पष्ट करता है?
What does classifying World Heritage Sites as cultural natural and mixed clarify?
#cultural-natural-mixed
#heritage-categories
#conservation
A धरोहर के मूल्य का प्रकार और संरक्षण की आवश्यकता / Type of heritage value and conservation need
B केवल प्रवेश टिकट की कीमत / Only entry ticket price
C साइट के मालिक का धर्म / Religion of the site owner
D स्थल की भाषा परीक्षा / Language test of the site
Explanation opens after your attempt
Correct Answer
A. धरोहर के मूल्य का प्रकार और संरक्षण की आवश्यकता / Type of heritage value and conservation need
Step 1
Concept
The category shows whether a site's importance is cultural natural or both. For exams identify mixed sites separately.
Step 2
Why this answer is correct
The correct answer is A. धरोहर के मूल्य का प्रकार और संरक्षण की आवश्यकता / Type of heritage value and conservation need. The category shows whether a site's importance is cultural natural or both. For exams identify mixed sites separately.
Step 3
Exam Tip
श्रेणी से पता चलता है कि स्थल का महत्व सांस्कृतिक प्राकृतिक या दोनों है। परीक्षा में मिश्रित स्थल की अलग पहचान रखें।
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पद्म विभूषण पद्म भूषण और पद्म श्री की वर्तमान श्रेणी व्यवस्था किस वर्ष लागू हुई?
In which year did the present category system of Padma Vibhushan Padma Bhushan and Padma Shri come into use?
#padma categories
#1955
#awards
A 1954 ईस्वी / 1954 CE
B 1955 ईस्वी / 1955 CE
C 1969 ईस्वी / 1969 CE
D 1980 ईस्वी / 1980 CE
Explanation opens after your attempt
Correct Answer
B. 1955 ईस्वी / 1955 CE
Step 1
Concept
The categories of Padma Awards were changed in 1955. For exams remember 1954 institution and 1955 category change separately.
Step 2
Why this answer is correct
The correct answer is B. 1955 ईस्वी / 1955 CE. The categories of Padma Awards were changed in 1955. For exams remember 1954 institution and 1955 category change separately.
Step 3
Exam Tip
पद्म पुरस्कारों की श्रेणियों में 1955 में बदलाव किया गया। परीक्षा में 1954 स्थापना और 1955 श्रेणी बदलाव अलग याद रखें।
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बेसनगर का गरुड़ ध्वज किस धर्म के प्रारंभिक विकास से जुड़ा है?
The Garuda standard at Besnagar is linked with the early development of which religion?
#ancient-history
#besnagar
#vaishnavism
A वैष्णव धर्म / Vaishnavism
B बौद्ध धर्म / Buddhism
C जैन धर्म / Jainism
D आजीविक संप्रदाय / Ajivika sect
Explanation opens after your attempt
Correct Answer
A. वैष्णव धर्म / Vaishnavism
Step 1
Concept
The Garuda standard at Besnagar is evidence linked with Vasudeva Vishnu devotion. For exams, understand religious development through symbols.
Step 2
Why this answer is correct
The correct answer is A. वैष्णव धर्म / Vaishnavism. The Garuda standard at Besnagar is evidence linked with Vasudeva Vishnu devotion. For exams, understand religious development through symbols.
Step 3
Exam Tip
बेसनगर का गरुड़ ध्वज वासुदेव विष्णु भक्ति से जुड़ा प्रमाण है। परीक्षा में प्रतीकों से धर्म के विकास को समझें।
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हड़प्पाई ईंटों का मानक अनुपात सामान्यतः किस रूप में बताया जाता है?
The standard ratio of Harappan bricks is generally stated as what?
#ancient-history
#harappan-bricks
#urban-planning
A 1:1:1
B 1:2:4
C 2:3:5
D 3:4:5
Explanation opens after your attempt
Step 1
Concept
Harappan bricks are famous for the 1:2:4 ratio. For exams, connect it with standardization and town planning.
Step 2
Why this answer is correct
The correct answer is B. 1:2:4. Harappan bricks are famous for the 1:2:4 ratio. For exams, connect it with standardization and town planning.
Step 3
Exam Tip
हड़प्पाई ईंटों में 1:2:4 का अनुपात प्रसिद्ध है। परीक्षा में इसे मानकीकरण और नगर योजना से जोड़ें।
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कौन-सा व्यंजक मानक बहुपद रूप में लिखा है?
Which expression is written in standard polynomial form?
#standard_form
#arrangement
#polynomials
A \(5+2x+x^3\)
B \(x^3+2x+5\)
C \(2x+5+x^3\)
D \(5+x^3+2x\)
Explanation opens after your attempt
Correct Answer
B. \(x^3+2x+5\)
Step 1
Concept
In standard form, terms are written from higher power to lower power. The expression \(x^3+2x+5\) follows this order.
Step 2
Why this answer is correct
The correct answer is B. \(x^3+2x+5\). In standard form, terms are written from higher power to lower power. The expression \(x^3+2x+5\) follows this order.
Step 3
Exam Tip
मानक रूप में पद बड़ी घात से छोटी घात की ओर लिखे जाते हैं। \(x^3+2x+5\) इसी क्रम में है।
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बहुपद \(4x^2+3x^4-x+2\) को मानक रूप में कैसे लिखा जाएगा?
How is \(4x^2+3x^4-x+2\) written in standard form?
#standard_form
#polynomials
#arrangement
A \(3x^4+4x^2-x+2\)
B \(2-x+4x^2+3x^4\)
C \(4x^2+3x^4-x+2\)
D \(3x^4-x+4x^2+2\)
Explanation opens after your attempt
Correct Answer
A. \(3x^4+4x^2-x+2\)
Step 1
Concept
In standard form, terms are written in decreasing powers. Therefore \(3x^4+4x^2-x+2\) is correct.
Step 2
Why this answer is correct
The correct answer is A. \(3x^4+4x^2-x+2\). In standard form, terms are written in decreasing powers. Therefore \(3x^4+4x^2-x+2\) is correct.
Step 3
Exam Tip
मानक रूप में पद घटती घातों में लिखे जाते हैं। इसलिए \(3x^4+4x^2-x+2\) सही है।
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समीकरण (3(x+1)2 +2(x-4)2 =74) का मानक रूप कौन-सा है?
What is the standard form of (3(x+1)2 +2(x-4)2 =74)?
#quadratic-equations
#identity
#simplification
#expert
A \(5x^2-10x-39=0\)
B \(5x^2+10x-39=0\)
C \(5x^2-10x+39=0\)
D \(5x^2-16x-74=0\)
Explanation opens after your attempt
Correct Answer
A. \(5x^2-10x-39=0\)
Step 1
Concept
Expanding gives \(3x^2+6x+3+2x^2-16x+32=74\). Simplifying gives \(5x^2-10x-39=0\).
Step 2
Why this answer is correct
The correct answer is A. \(5x^2-10x-39=0\). Expanding gives \(3x^2+6x+3+2x^2-16x+32=74\). Simplifying gives \(5x^2-10x-39=0\).
Step 3
Exam Tip
विस्तार करने पर \(3x^2+6x+3+2x^2-16x+32=74\) मिलता है। सरल करने पर \(5x^2-10x-39=0\) सही है।
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समीकरण (2(x-1)2 +3(x+2)2 =65) का मानक रूप कौन-सा है?
What is the standard form of (2(x-1)2 +3(x+2)2 =65)?
#quadratic-equations
#identity
#simplification
#expert
A \(5x^2+8x-51=0\)
B \(5x^2-8x-51=0\)
C \(5x^2+8x+51=0\)
D \(5x^2+10x-65=0\)
Explanation opens after your attempt
Correct Answer
A. \(5x^2+8x-51=0\)
Step 1
Concept
Expanding gives \(2x^2-4x+2+3x^2+12x+12=65\). Simplifying gives \(5x^2+8x-51=0\).
Step 2
Why this answer is correct
The correct answer is A. \(5x^2+8x-51=0\). Expanding gives \(2x^2-4x+2+3x^2+12x+12=65\). Simplifying gives \(5x^2+8x-51=0\).
Step 3
Exam Tip
विस्तार करने पर \(2x^2-4x+2+3x^2+12x+12=65\) मिलता है। सरल करने पर \(5x^2+8x-51=0\) सही है।
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समीकरण ((x+2)2 +2(x-3)2 =35) का मानक रूप कौन-सा है?
What is the standard form of ((x+2)2 +2(x-3)2 =35)?
#quadratic-equations
#identity
#simplification
#expert
A \(3x^2-8x-13=0\)
B \(3x^2+8x-13=0\)
C \(3x^2-8x+13=0\)
D \(2x^2-8x-13=0\)
Explanation opens after your attempt
Correct Answer
A. \(3x^2-8x-13=0\)
Step 1
Concept
Expanding gives \(x^2+4x+4+2x^2-12x+18=35\). Hence \(3x^2-8x-13=0\) is correct.
Step 2
Why this answer is correct
The correct answer is A. \(3x^2-8x-13=0\). Expanding gives \(x^2+4x+4+2x^2-12x+18=35\). Hence \(3x^2-8x-13=0\) is correct.
Step 3
Exam Tip
विस्तार करने पर \(x^2+4x+4+2x^2-12x+18=35\) मिलता है। इसलिए \(3x^2-8x-13=0\) सही है।
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समीकरण ((2x-3)2 +(x+5)2 =34) का मानक रूप कौन-सा है?
What is the standard form of ((2x-3)2 +(x+5)2 =34)?
#quadratic-equations
#identity
#simplification
#hard
A \(5x^2-2x=0\)
B \(5x^2+2x=0\)
C \(5x^2-2x+34=0\)
D \(3x^2-2x=0\)
Explanation opens after your attempt
Correct Answer
A. \(5x^2-2x=0\)
Step 1
Concept
Expanding gives \(4x^2-12x+9+x^2+10x+25=34\). Simplifying gives \(5x^2-2x=0\).
Step 2
Why this answer is correct
The correct answer is A. \(5x^2-2x=0\). Expanding gives \(4x^2-12x+9+x^2+10x+25=34\). Simplifying gives \(5x^2-2x=0\).
Step 3
Exam Tip
विस्तार करने पर \(4x^2-12x+9+x^2+10x+25=34\) मिलता है। सरल करने पर \(5x^2-2x=0\) बनता है।
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समीकरण ((x-2)2 +(2x+1)2 =25) का मानक रूप कौन-सा है?
What is the standard form of ((x-2)2 +(2x+1)2 =25)?
#quadratic-equations
#identity
#simplification
#hard
A \(5x^2+1=25\)
B \(5x^2+1=0\)
C \(5x^2+20=0\)
D \(5x^2-20=0\)
Explanation opens after your attempt
Correct Answer
D. \(5x^2-20=0\)
Step 1
Concept
Expanding gives \(x^2-4x+4+4x^2+4x+1=25\). This gives \(5x^2-20=0\).
Step 2
Why this answer is correct
The correct answer is D. \(5x^2-20=0\). Expanding gives \(x^2-4x+4+4x^2+4x+1=25\). This gives \(5x^2-20=0\).
Step 3
Exam Tip
विस्तार करने पर \(x^2-4x+4+4x^2+4x+1=25\) मिलता है। इससे \(5x^2-20=0\) बनता है।
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किसी धनात्मक पूर्णांक को (8) से भाग देने पर मानक सामान्य रूप कौन-सा हो सकता है?
What can be the standard general forms of a positive integer when divided by (8)?
#real-numbers
#general-form
#possible-remainders
A (8q,8q+1,8q+2,8q+3,8q+4,8q+5,8q+6,8q+7)
B (8q+1,8q+2,8q+3,8q+4,8q+5,8q+6,8q+7,8q+8)
C (q,q+1,q+2,q+3,q+4,q+5,q+6,q+7)
D (8q-1,8q,8q+1,8q+8)
Explanation opens after your attempt
Correct Answer
A. (8q,8q+1,8q+2,8q+3,8q+4,8q+5,8q+6,8q+7)
Step 1
Concept
On division by (8), remainders can be from (0) to (7).
Step 2
Why this answer is correct
So in (8q+r), (r=0,1,2,3,4,5,6,7).
Step 3
Exam Tip
Do not include (8q+8) while writing standard forms. चरण 1: (8) से भाग देने पर शेषफल (0) से (7) तक हो सकते हैं। चरण 2: इसलिए रूप (8q+r) में (r=0,1,2,3,4,5,6,7) होगा। चरण 3: सामान्य रूप लिखते समय (8q+8) शामिल न करें।
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किसी धनात्मक पूर्णांक को (3) से भाग देने पर कौन-सा रूप संभव नहीं है?
Which form is not possible as a standard form when a positive integer is divided by (3)?
#real-numbers
#general-form
#not-possible
A (3q)
B (3q+1)
C (3q+2)
D (3q+3)
Explanation opens after your attempt
Step 1
Concept
On division by (3), possible remainders are (0,1,2).
Step 2
Why this answer is correct
In (3q+3), the remainder is (3), which equals the divisor.
Step 3
Exam Tip
It should be written as (3(q+1)). चरण 1: (3) से भाग देने पर शेषफल (0,1,2) हो सकते हैं। चरण 2: (3q+3) में शेषफल (3) है, जो भाजक के बराबर है। चरण 3: इसे (3(q+1)) के रूप में लिखना चाहिए।
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किसी धनात्मक पूर्णांक को (4) से भाग देने पर वह किस रूप में नहीं लिखा जा सकता?
When a positive integer is divided by (4), which form cannot be a standard remainder form?
#real-numbers
#general-form
#remainder-condition
A (4q)
B (4q+1)
C (4q+2)
D (4q+4)
Explanation opens after your attempt
Step 1
Concept
On division by (4), possible remainders are (0,1,2,3).
Step 2
Why this answer is correct
In (4q+4), the remainder is (4), which equals the divisor.
Step 3
Exam Tip
Such a form should be written as (4(q+1)). चरण 1: (4) से भाग देने पर शेषफल (0,1,2,3) हो सकते हैं। चरण 2: (4q+4) में शेषफल (4) है, जो भाजक के बराबर है। चरण 3: ऐसे रूप को (4(q+1)) लिखना चाहिए।
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