100 results found for "standard-condition" 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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किस शर्त पर \(ax^2+bx+c=0\) द्विघात समीकरण कहलाता है?
Under which condition is \(ax^2+bx+c=0\) called a quadratic equation?
#quadratic equations
#condition
#standard form
A (a=0)
B \(a\neq0\)
C (b=0)
D (c=0)
Explanation opens after your attempt
Correct Answer
B. \(a\neq0\)
Step 1
Concept
The quadratic term must remain, so \(a\neq0\). If (a=0), it may become linear.
Step 2
Why this answer is correct
The correct answer is B. \(a\neq0\). The quadratic term must remain, so \(a\neq0\). If (a=0), it may become linear.
Step 3
Exam Tip
द्विघात पद बना रहे इसलिए \(a\neq0\) होना चाहिए। परीक्षा में (a=0) होने पर यह रैखिक बन सकता 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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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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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 (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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कौन-सा रूप (a=31q+r) के लिए सही शेषफल की शर्त पूरी करता है?
Which form satisfies the correct remainder condition for (a=31q+r)?
#real-numbers
#valid-remainder
#standard-form
A (a=31q+31)
B (a=31q+37)
C (a=31q+30)
D (a=31q-1)
Explanation opens after your attempt
Correct Answer
C. (a=31q+30)
Step 1
Concept
On division by (31), the remainder must be from (0) to (30).
Step 2
Why this answer is correct
In (31q+30), the remainder is (30), which is less than (31).
Step 3
Exam Tip
A remainder (31), (37), or negative is not in standard form. चरण 1: (31) से भाग देने पर शेषफल (0) से (30) तक होना चाहिए। चरण 2: (31q+30) में शेषफल (30) है, जो (31) से छोटा है। चरण 3: शेषफल (31), (37) या ऋणात्मक हो तो वह मानक रूप नहीं होगा।
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विश्व धरोहर स्थल के लिए अखंडता की शर्त किस बात से संबंधित है?
The condition of integrity for a World Heritage Site is related to what?
#integrity
#heritage-condition
#site-management
A स्थल की पूर्णता और उसके मूल्य को बनाए रखने वाली स्थिति / Wholeness of the site and condition supporting its value
B केवल टिकट खिड़की की संख्या / Only number of ticket counters
C केवल स्थानीय भोजन सूची / Only local food list
D स्थल के नाम की लंबाई / Length of the site's name
Explanation opens after your attempt
Correct Answer
A. स्थल की पूर्णता और उसके मूल्य को बनाए रखने वाली स्थिति / Wholeness of the site and condition supporting its value
Step 1
Concept
Integrity shows whether the site's value is sufficiently represented and protected. For exams keep integrity and authenticity separate.
Step 2
Why this answer is correct
The correct answer is A. स्थल की पूर्णता और उसके मूल्य को बनाए रखने वाली स्थिति / Wholeness of the site and condition supporting its value. Integrity shows whether the site's value is sufficiently represented and protected. For exams keep integrity and authenticity separate.
Step 3
Exam Tip
अखंडता बताती है कि स्थल का मूल्य सुरक्षित और पर्याप्त रूप से प्रतिनिधित है या नहीं। परीक्षा में अखंडता और प्रामाणिकता अलग रखें।
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यदि (5x+8y=37) और (15x+24y=m) असंगत युग्म हों, तो (m) के लिए सही शर्त क्या है?
If (5x+8y=37) and (15x+24y=m) form an inconsistent pair, what is the correct condition for (m)?
#linear equations
#expert
#inconsistent
#condition
A (m=111)
B \(m\ne111\)
C (m=37)
D (m=74)
Explanation opens after your attempt
Correct Answer
B. \(m\ne111\)
Step 1
Concept
The first two ratios are equal. For inconsistency, the constant ratio must be different.
Step 2
Why this answer is correct
The correct answer is B. \(m\ne111\). The first two ratios are equal. For inconsistency, the constant ratio must be different.
Step 3
Exam Tip
पहले दो अनुपात बराबर हैं। असंगत होने के लिए स्थिर पद का अनुपात अलग होना चाहिए।
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यदि (7x+3y=25) और (14x+6y=m) असंगत युग्म हों, तो (m) के लिए सही शर्त क्या है?
If (7x+3y=25) and (14x+6y=m) form an inconsistent pair, what is the correct condition for (m)?
#linear equations
#hard
#inconsistent
#condition
A (m=50)
B \(m \ne 50\)
C (m=25)
D (m=75)
Explanation opens after your attempt
Correct Answer
B. \(m \ne 50\)
Step 1
Concept
The first two ratios are equal. For inconsistency, the constant ratio must be different so \(m \ne 50\).
Step 2
Why this answer is correct
The correct answer is B. \(m \ne 50\). The first two ratios are equal. For inconsistency, the constant ratio must be different so \(m \ne 50\).
Step 3
Exam Tip
पहले दो अनुपात बराबर हैं। असंगत होने के लिए स्थिर पद का अनुपात अलग होना चाहिए इसलिए \(m \ne 50\)।
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यदि (3x+8y=25) और (9x+24y=m) असंगत युग्म हों, तो (m) के लिए सही शर्त क्या है?
If (3x+8y=25) and (9x+24y=m) form an inconsistent pair, what is the correct condition for (m)?
#linear equations
#hard
#inconsistent
#condition
A (m=75)
B \(m \ne 75\)
C (m=25)
D (m=50)
Explanation opens after your attempt
Correct Answer
B. \(m \ne 75\)
Step 1
Concept
The first two ratios are equal, so the constant ratio must be different for inconsistency. Hence, \(m \ne 75\) is correct.
Step 2
Why this answer is correct
The correct answer is B. \(m \ne 75\). The first two ratios are equal, so the constant ratio must be different for inconsistency. Hence, \(m \ne 75\) is correct.
Step 3
Exam Tip
पहले दो अनुपात बराबर हैं, इसलिए असंगत होने के लिए स्थिर पद का अनुपात अलग होना चाहिए। अतः \(m \ne 75\) सही है।
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यदि (2x+5y=17) और (4x+10y=m) असंगत युग्म हों, तो (m) के लिए सही शर्त क्या है?
If (2x+5y=17) and (4x+10y=m) form an inconsistent pair, what is the correct condition for (m)?
#linear equations
#hard
#inconsistent
#condition
A (m=34)
B \(m \ne 34\)
C (m=17)
D (m=68)
Explanation opens after your attempt
Correct Answer
B. \(m \ne 34\)
Step 1
Concept
The first two ratios are equal, so the constant ratio must be different for inconsistency. Hence, \(m \ne 34\).
Step 2
Why this answer is correct
The correct answer is B. \(m \ne 34\). The first two ratios are equal, so the constant ratio must be different for inconsistency. Hence, \(m \ne 34\).
Step 3
Exam Tip
पहले दो अनुपात बराबर हैं, इसलिए असंगत होने के लिए स्थिर पद का अनुपात अलग होना चाहिए। अतः \(m \ne 34\) होगा।
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यदि (5x+2y=13) और (10x+4y=m) असंगत युग्म हैं तो (m) के लिए सही शर्त क्या है?
If (5x+2y=13) and (10x+4y=m) form an inconsistent pair then what is the correct condition for (m)?
#linear equations
#inconsistent
#condition
A (m=26)
B (m=13)
C \(m \ne 26\)
D (m=39)
Explanation opens after your attempt
Correct Answer
C. \(m \ne 26\)
Step 1
Concept
The first two ratios are equal so the constant ratio must differ for inconsistency. Hence \(m \ne 26\).
Step 2
Why this answer is correct
The correct answer is C. \(m \ne 26\). The first two ratios are equal so the constant ratio must differ for inconsistency. Hence \(m \ne 26\).
Step 3
Exam Tip
पहले दो अनुपात बराबर हैं इसलिए असंगत होने के लिए स्थिर पद का अनुपात अलग होना चाहिए। अतः \(m \ne 26\)।
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यदि (4x+5y=16) और (8x+10y=m) असंगत युग्म हैं, तो (m) के लिए सही शर्त क्या है?
If (4x+5y=16) and (8x+10y=m) form an inconsistent pair, what is the correct condition for (m)?
#linear equations
#inconsistent
#condition
A (m=32)
B \(m \ne 32\)
C (m=16)
D (m=24)
Explanation opens after your attempt
Correct Answer
B. \(m \ne 32\)
Step 1
Concept
The first two ratios are equal, so for inconsistency the constant ratio must differ. Hence, \(m \ne 32\).
Step 2
Why this answer is correct
The correct answer is B. \(m \ne 32\). The first two ratios are equal, so for inconsistency the constant ratio must differ. Hence, \(m \ne 32\).
Step 3
Exam Tip
पहले दो अनुपात बराबर हैं, इसलिए असंगत होने के लिए स्थिर पद का अनुपात अलग होना चाहिए। अतः \(m \ne 32\)।
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यदि (2x+3y=7) और (4x+6y=m) असंगत युग्म हैं, तो (m) के लिए सही शर्त क्या है?
If (2x+3y=7) and (4x+6y=m) form an inconsistent pair, what is the correct condition for (m)?
#linear equations
#inconsistent pair
#condition
A (m=14)
B \(m \ne 14\)
C (m=7)
D (m=21)
Explanation opens after your attempt
Correct Answer
B. \(m \ne 14\)
Step 1
Concept
The first two ratios are equal, so for inconsistency the constant ratio must differ. Hence \(m \ne 14\).
Step 2
Why this answer is correct
The correct answer is B. \(m \ne 14\). The first two ratios are equal, so for inconsistency the constant ratio must differ. Hence \(m \ne 14\).
Step 3
Exam Tip
पहले दो अनुपात बराबर हैं, इसलिए असंगत होने के लिए स्थिर पद का अनुपात अलग होना चाहिए। अतः \(m \ne 14\)।
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किस स्थिति में दो रैखिक समीकरणों का युग्म संगत और आश्रित कहलाता है?
In which condition is a pair of two linear equations called consistent and dependent?
#linear equations
#consistent dependent
#condition
A जब (a_1 / a_2=b_1 / b_2=c_1 / c_2) हो / When \(a_1 / c_2\)
B जब (a_1 / a_2 \ne b_1 / b_2) हो / When \(a_1 / b_2\)
C जब (a_1 / a_2=b_1 / b_2 \ne c_1 / c_2) हो / When \(a_1 / c_2\)
D जब रेखाएं कटती हों / When lines intersect
Explanation opens after your attempt
Correct Answer
A. जब (a_1 / a_2=b_1 / b_2=c_1 / c_2) हो / When \(a_1 / c_2\)
Step 1
Concept
If all three ratios are equal both equations represent the same line. This is a consistent and dependent pair.
Step 2
Why this answer is correct
The correct answer is A. जब \(a_1 / a_2=b_1 / b_2=c_1 / c_2\) हो / When \(a_1 / c_2\). If all three ratios are equal both equations represent the same line. This is a consistent and dependent pair.
Step 3
Exam Tip
तीनों अनुपात बराबर हों तो दोनों समीकरण समान रेखा दर्शाते हैं। यही संगत और आश्रित युग्म है।
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किस स्थिति में दो रैखिक समीकरणों का युग्म संगत और स्वतंत्र कहलाता है?
In which condition is a pair of two linear equations called consistent and independent?
#linear equations
#consistent independent
#condition
A जब (a_1 / a_2=b_1 / b_2=c_1 / c_2) हो / When \(a_1 / c_2\)
B जब (a_1 / a_2=b_1 / b_2 \ne c_1 / c_2) हो / When \(a_1 / c_2\)
C जब (a_1 / a_2 \ne b_1 / b_2) हो / When \(a_1 / b_2\)
D जब कोई हल न हो / When there is no solution
Explanation opens after your attempt
Correct Answer
C. जब (a_1 / a_2 \ne b_1 / b_2) हो / When \(a_1 / b_2\)
Step 1
Concept
A consistent and independent pair has one unique solution. For this the ratios of (a) and (b) must be different.
Step 2
Why this answer is correct
The correct answer is C. जब \(a_1 / a_2 \ne b_1 / b_2\) हो / When \(a_1 / b_2\). A consistent and independent pair has one unique solution. For this the ratios of (a) and (b) must be different.
Step 3
Exam Tip
संगत और स्वतंत्र युग्म में एक अद्वितीय हल होता है। इसके लिए (a) और (b) के अनुपात अलग होने चाहिए।
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यदि \(a_1x+b_1y+c_1=0\) और \(a_2x+b_2y+c_2=0\) के ग्राफ प्रतिच्छेदी हैं, तो कौन सी शर्त सही है?
If the graphs of \(a_1x+b_1y+c_1=0\) and \(a_2x+b_2y+c_2=0\) are intersecting, which condition is correct?
#linear equations
#graphical method
#intersecting lines
#ratio condition
A \(\frac{a_1}{a_2}=\frac{b_1}{b_2}\)
B \(\frac{a_1}{a_2}\neq\frac{b_1}{b_2}\)
C \(\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}\)
D \(\frac{c_1}{c_2}=0\)
Explanation opens after your attempt
Correct Answer
B. \(\frac{a_1}{a_2}\neq\frac{b_1}{b_2}\)
Step 1
Concept
For intersecting lines, the coefficient ratios of (x) and (y) are not equal. This is the condition for a unique solution.
Step 2
Why this answer is correct
The correct answer is B. \(\frac{a_1}{a_2}\neq\frac{b_1}{b_2}\). For intersecting lines, the coefficient ratios of (x) and (y) are not equal. This is the condition for a unique solution.
Step 3
Exam Tip
प्रतिच्छेदी रेखाओं के लिए (x) और (y) के गुणांक अनुपात बराबर नहीं होते। यही अद्वितीय समाधान की शर्त है।
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किस स्थिति में दो रेखाओं का ग्राफ अनंत समाधान दिखाता है?
In which condition does the graph of two lines show infinitely many solutions?
#linear equations
#graphical method
#ratio condition
#infinite solutions
A \(\frac{a_1}{a_2}\neq\frac{b_1}{b_2}\)
B \(\frac{a_1}{a_2}=\frac{b_1}{b_2}\neq\frac{c_1}{c_2}\)
C \(\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}\)
D \(\frac{a_1}{a_2}=0\)
Explanation opens after your attempt
Correct Answer
C. \(\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}\)
Step 1
Concept
Infinite solutions occur when both lines are the same line. For this, all three ratios are equal.
Step 2
Why this answer is correct
The correct answer is C. \(\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}\). Infinite solutions occur when both lines are the same line. For this, all three ratios are equal.
Step 3
Exam Tip
अनंत समाधान तब होते हैं जब दोनों रेखाएं एक ही रेखा हों। इसके लिए तीनों अनुपात बराबर होते हैं।
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समीकरण (x-2 +2(k+1)x+k-2 +6k+9=0) के वास्तविक मूल न होने के लिए (k) पर क्या शर्त है?
What condition on (k) is needed for (x-2 +2(k+1)x+k-2 +6k+9=0) to have no real roots?
#quadratic equations
#no real roots
#parameter condition
A (k>-2)
B (k<-2)
C (k=-2)
D सभी वास्तविक (k) / All real (k)
Explanation opens after your attempt
Step 1
Concept
For no real roots, (D<0) is needed. Here (D=-16(k+2)), so (k>-2).
Step 2
Why this answer is correct
The correct answer is A. (k>-2). For no real roots, (D<0) is needed. Here (D=-16(k+2)), so (k>-2).
Step 3
Exam Tip
वास्तविक मूल न होने के लिए (D<0) चाहिए। यहाँ (D=-16(k+2)), इसलिए (k>-2)।
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यदि \(x^2+2gx+g^2-6g+11=0\) के वास्तविक मूल हैं, तो (g) पर क्या शर्त है?
If \(x^2+2gx+g^2-6g+11=0\) has real roots, what condition on (g) is required?
#quadratic equations
#real roots
#fraction condition
A \(g\ge\frac{11}{6}\)
B \(g<\frac{11}{6}\)
C (g=0)
D सभी वास्तविक (g) / All real (g)
Explanation opens after your attempt
Correct Answer
A. \(g\ge\frac{11}{6}\)
Step 1
Concept
Here (D=4g-2 -4\(g^2-6g+11\)=24g-44). From \(D\ge0\), \(g\ge\frac{11}{6}\).
Step 2
Why this answer is correct
The correct answer is A. \(g\ge\frac{11}{6}\). Here (D=4g-2 -4\(g^2-6g+11\)=24g-44). From \(D\ge0\), \(g\ge\frac{11}{6}\).
Step 3
Exam Tip
यहाँ (D=4g-2 -4\(g^2-6g+11\)=24g-44) है। \(D\ge0\) से \(g\ge\frac{11}{6}\) मिलता है।
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यदि \(x^2+2px+2p+9=0\) के मूल वास्तविक हैं, तो (p) पर सही शर्त कौन सी है?
If \(x^2+2px+2p+9=0\) has real roots, which condition on (p) is correct?
#quadratic equations
#real roots
#interval condition
A \(p\le -2\) या \(p\ge \frac{9}{2}\) / \(p\le -2\) or \(p\ge \frac{9}{2}\)
B \(-2<p<\frac{9}{2}\)
C (p=-2) केवल / (p=-2) only
D \(p=\frac{9}{2}\) केवल / \(p=\frac{9}{2}\) only
Explanation opens after your attempt
Correct Answer
A. \(p\le -2\) या \(p\ge \frac{9}{2}\) / \(p\le -2\) or \(p\ge \frac{9}{2}\)
Step 1
Concept
For real roots, \(D\ge0\) is required. Here (D=4(p+2)(2p-9)), so \(p\le -2\) or \(p\ge \frac{9}{2}\).
Step 2
Why this answer is correct
The correct answer is A. \(p\le -2\) या \(p\ge \frac{9}{2}\) / \(p\le -2\) or \(p\ge \frac{9}{2}\). For real roots, \(D\ge0\) is required. Here (D=4(p+2)(2p-9)), so \(p\le -2\) or \(p\ge \frac{9}{2}\).
Step 3
Exam Tip
वास्तविक मूलों के लिए \(D\ge0\) चाहिए। यहाँ (D=4(p+2)(2p-9)), इसलिए \(p\le -2\) या \(p\ge \frac{9}{2}\)।
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यदि \(x^2+2kx+k^2-4k+8=0\) के वास्तविक मूल हैं, तो (k) पर क्या शर्त है?
If \(x^2+2kx+k^2-4k+8=0\) has real roots, what is the condition on (k)?
#quadratic equations
#real roots
#parameter condition
A \(k\ge2\)
B \(k\le2\)
C (k>4)
D (k<0)
Explanation opens after your attempt
Correct Answer
A. \(k\ge2\)
Step 1
Concept
Here (D=4k-2 -4\(k^2-4k+8\)=16(k-2)). For real roots \(D\ge0\), so \(k\ge2\).
Step 2
Why this answer is correct
The correct answer is A. \(k\ge2\). Here (D=4k-2 -4\(k^2-4k+8\)=16(k-2)). For real roots \(D\ge0\), so \(k\ge2\).
Step 3
Exam Tip
यहाँ (D=4k-2 -4\(k^2-4k+8\)=16(k-2)) है। वास्तविक मूलों के लिए \(D\ge0\), इसलिए \(k\ge2\)।
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