100 results found for "standard form" in Class 10.
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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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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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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\(3x^2+2=11x\) 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 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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(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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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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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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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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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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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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(305) को (24) से भाग देने का सही यूक्लिडीय रूप कौन-सा है?
Which is the correct Euclidean form when (305) is divided by (24)?
#real-numbers
#euclidean-form
#standard-form
A \(305=24 \times 12+17\)
B \(305=24 \times 13-7\)
C \(305=24 \times 11+41\)
D \(305=24 \times 10+65\)
Explanation opens after your attempt
Correct Answer
A. \(305=24 \times 12+17\)
Step 1
Concept
\(24 \times 12=288\) and \(24 \times 13=312\).
Step 2
Why this answer is correct
Since (312) is greater, \(305=24 \times 12+17\) is correct.
Step 3
Exam Tip
A form with a negative remainder is not the standard Euclidean form. चरण 1: \(24 \times 12=288\) और \(24 \times 13=312\) है। चरण 2: (312) बड़ा है, इसलिए \(305=24 \times 12+17\) सही है। चरण 3: ऋणात्मक शेषफल वाला रूप मानक यूक्लिडीय रूप नहीं होता।
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(400) को (31) से भाग देने पर सही यूक्लिडीय रूप कौन-सा है?
Which is the correct Euclidean form when (400) is divided by (31)?
#real-numbers
#euclidean-form
#standard-form
A \(400=31 \times 12+28\)
B \(400=31 \times 13-3\)
C \(400=31 \times 11+59\)
D \(400=31 \times 10+90\)
Explanation opens after your attempt
Correct Answer
A. \(400=31 \times 12+28\)
Step 1
Concept
\(31 \times 12=372\) and \(31 \times 13=403\).
Step 2
Why this answer is correct
Since (403) is greater, \(400=31 \times 12+28\).
Step 3
Exam Tip
A form with a negative remainder is not the standard Euclidean form. चरण 1: \(31 \times 12=372\) और \(31 \times 13=403\)। चरण 2: (403) बड़ा है, इसलिए \(400=31 \times 12+28\)। चरण 3: ऋणात्मक शेषफल वाला रूप मानक यूक्लिडीय रूप नहीं 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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\(\frac{x+6}{x}=\frac{49}{x+6}\), \(x\neq0,-6\), का सही द्विघात रूप कौनसा है?
What is the correct quadratic form of \(\frac{x+6}{x}=\frac{49}{x+6}\), \(x\neq0,-6\)?
#quadratic
#rational-equation
#standard-form
A \(x^2-37x+36=0\)
B \(x^2+12x-13=0\)
C \(x^2-49x+36=0\)
D \(x^2+37x+36=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-37x+36=0\)
Step 1
Concept
Cross multiplication gives ((x+6)2 =49x), so \(x^2+12x+36-49x=0\), and \(x^2-37x+36=0\). In exams, cross multiply carefully.
Step 2
Why this answer is correct
The correct answer is A. \(x^2-37x+36=0\). Cross multiplication gives ((x+6)2 =49x), so \(x^2+12x+36-49x=0\), and \(x^2-37x+36=0\). In exams, cross multiply carefully.
Step 3
Exam Tip
क्रॉस गुणा करने पर ((x+6)2 =49x), इसलिए \(x^2+12x+36-49x=0\) और \(x^2-37x+36=0\) है। परीक्षा में क्रॉस गुणा सावधानी से करें।
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\(\frac{1}{x}+x=\frac{50}{7}\), \(x\neq0\), को द्विघात रूप में बदलने पर क्या मिलेगा?
For \(\frac{1}{x}+x=\frac{50}{7}\), \(x\neq0\), what quadratic form is obtained?
#quadratic
#reciprocal-equation
#standard-form
A \(7x^2-50x+7=0\)
B \(7x^2+50x+7=0\)
C \(x^2-50x+7=0\)
D \(7x^2-50=0\)
Explanation opens after your attempt
Correct Answer
A. \(7x^2-50x+7=0\)
Step 1
Concept
Multiplying both sides by (7x) gives \(7+7x^2=50x\), that is \(7x^2-50x+7=0\). In exams, remember the condition \(x\neq0\).
Step 2
Why this answer is correct
The correct answer is A. \(7x^2-50x+7=0\). Multiplying both sides by (7x) gives \(7+7x^2=50x\), that is \(7x^2-50x+7=0\). In exams, remember the condition \(x\neq0\).
Step 3
Exam Tip
दोनों पक्षों को (7x) से गुणा करने पर \(7+7x^2=50x\), यानी \(7x^2-50x+7=0\) मिलता है। परीक्षा में \(x\neq0\) शर्त याद रखें।
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\(\frac{x+5}{x}=\frac{36}{x+5}\), \(x\neq0,-5\), का सही द्विघात रूप कौनसा है?
What is the correct quadratic form of \(\frac{x+5}{x}=\frac{36}{x+5}\), \(x\neq0,-5\)?
#quadratic
#rational-equation
#standard-form
A \(x^2-26x+25=0\)
B \(x^2+10x-11=0\)
C \(x^2-36x+25=0\)
D \(x^2+26x+25=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-26x+25=0\)
Step 1
Concept
Cross multiplication gives ((x+5)2 =36x), so \(x^2+10x+25-36x=0\), and \(x^2-26x+25=0\). In exams, cross multiply carefully.
Step 2
Why this answer is correct
The correct answer is A. \(x^2-26x+25=0\). Cross multiplication gives ((x+5)2 =36x), so \(x^2+10x+25-36x=0\), and \(x^2-26x+25=0\). In exams, cross multiply carefully.
Step 3
Exam Tip
क्रॉस गुणा करने पर ((x+5)2 =36x), इसलिए \(x^2+10x+25-36x=0\) और \(x^2-26x+25=0\) है। परीक्षा में क्रॉस गुणा सावधानी से करें।
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\(\frac{1}{x}+x=\frac{37}{6}\), \(x\neq0\), को द्विघात रूप में बदलने पर क्या मिलेगा?
For \(\frac{1}{x}+x=\frac{37}{6}\), \(x\neq0\), what quadratic form is obtained?
#quadratic
#reciprocal-equation
#standard-form
A \(6x^2-37x+6=0\)
B \(6x^2+37x+6=0\)
C \(x^2-37x+6=0\)
D \(6x^2-37=0\)
Explanation opens after your attempt
Correct Answer
A. \(6x^2-37x+6=0\)
Step 1
Concept
Multiplying both sides by (6x) gives \(6+6x^2=37x\), that is \(6x^2-37x+6=0\). In exams, remember the condition \(x\neq0\).
Step 2
Why this answer is correct
The correct answer is A. \(6x^2-37x+6=0\). Multiplying both sides by (6x) gives \(6+6x^2=37x\), that is \(6x^2-37x+6=0\). In exams, remember the condition \(x\neq0\).
Step 3
Exam Tip
दोनों पक्षों को (6x) से गुणा करने पर \(6+6x^2=37x\), यानी \(6x^2-37x+6=0\) मिलता है। परीक्षा में \(x\neq0\) शर्त याद रखें।
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\(\frac{x+4}{x}=\frac{25}{x+4}\), \(x\neq0,-4\), का सही द्विघात रूप कौनसा है?
What is the correct quadratic form of \(\frac{x+4}{x}=\frac{25}{x+4}\), \(x\neq0,-4\)?
#quadratic
#rational-equation
#standard-form
A \(x^2-17x+16=0\)
B \(x^2+8x-9=0\)
C \(x^2-25x+16=0\)
D \(x^2+17x+16=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-17x+16=0\)
Step 1
Concept
Cross multiplication gives ((x+4)2 =25x), so \(x^2+8x+16-25x=0\), and \(x^2-17x+16=0\). In exams, cross multiply carefully.
Step 2
Why this answer is correct
The correct answer is A. \(x^2-17x+16=0\). Cross multiplication gives ((x+4)2 =25x), so \(x^2+8x+16-25x=0\), and \(x^2-17x+16=0\). In exams, cross multiply carefully.
Step 3
Exam Tip
क्रॉस गुणा करने पर ((x+4)2 =25x), इसलिए \(x^2+8x+16-25x=0\) और \(x^2-17x+16=0\) है। परीक्षा में क्रॉस गुणा सावधानी से करें।
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\(\frac{1}{x}+x=\frac{26}{5}\), \(x\neq0\), को द्विघात रूप में बदलने पर क्या मिलेगा?
For \(\frac{1}{x}+x=\frac{26}{5}\), \(x\neq0\), what quadratic form is obtained?
#quadratic
#reciprocal-equation
#standard-form
A \(5x^2-26x+5=0\)
B \(5x^2+26x+5=0\)
C \(x^2-26x+5=0\)
D \(5x^2-26=0\)
Explanation opens after your attempt
Correct Answer
A. \(5x^2-26x+5=0\)
Step 1
Concept
Multiplying both sides by (5x) gives \(5+5x^2=26x\), that is \(5x^2-26x+5=0\). In exams, remember the condition \(x\neq0\).
Step 2
Why this answer is correct
The correct answer is A. \(5x^2-26x+5=0\). Multiplying both sides by (5x) gives \(5+5x^2=26x\), that is \(5x^2-26x+5=0\). In exams, remember the condition \(x\neq0\).
Step 3
Exam Tip
दोनों पक्षों को (5x) से गुणा करने पर \(5+5x^2=26x\), यानी \(5x^2-26x+5=0\) मिलता है। परीक्षा में \(x\neq0\) शर्त याद रखें।
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\(\frac{x+3}{x}=\frac{16}{x+3}\), \(x\neq0,-3\), का सही द्विघात रूप कौनसा है?
What is the correct quadratic form of \(\frac{x+3}{x}=\frac{16}{x+3}\), \(x\neq0,-3\)?
#quadratic
#rational-equation
#standard-form
A \(x^2-10x+9=0\)
B \(x^2+6x-7=0\)
C \(x^2-16x+9=0\)
D \(x^2+10x+9=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-10x+9=0\)
Step 1
Concept
Cross multiplication gives ((x+3)2 =16x), so \(x^2+6x+9-16x=0\), and \(x^2-10x+9=0\). In exams, cross multiply carefully.
Step 2
Why this answer is correct
The correct answer is A. \(x^2-10x+9=0\). Cross multiplication gives ((x+3)2 =16x), so \(x^2+6x+9-16x=0\), and \(x^2-10x+9=0\). In exams, cross multiply carefully.
Step 3
Exam Tip
क्रॉस गुणा करने पर ((x+3)2 =16x), इसलिए \(x^2+6x+9-16x=0\) और \(x^2-10x+9=0\) है। परीक्षा में क्रॉस गुणा सावधानी से करें।
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