Question 481/600
Easy Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
यदि किसी द्विघात समीकरण का विवेचक (D>0) है तो मूल कैसे होंगे?
If the discriminant (D>0) for a quadratic equation, how will the roots be?
#quadratic-equations
#discriminant
#roots
A दो भिन्न वास्तविक मूल / Two distinct real roots
B दो समान वास्तविक मूल / Two equal real roots
C कोई वास्तविक मूल नहीं / No real roots
D केवल एक मूल / Only one root
Explanation opens after your attempt
Correct Answer
A. दो भिन्न वास्तविक मूल / Two distinct real roots
Step 1
Concept
When (D>0), the equation has two distinct real roots. The sign of the discriminant tells the nature of roots.
Step 2
Why this answer is correct
The correct answer is A. दो भिन्न वास्तविक मूल / Two distinct real roots. When (D>0), the equation has two distinct real roots. The sign of the discriminant tells the nature of roots.
Step 3
Exam Tip
(D>0) होने पर दो भिन्न वास्तविक मूल मिलते हैं। विवेचक का चिन्ह मूलों की प्रकृति बताता है।
Login to save your score, XP, coins and progress.
Question 482/600
Easy Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
द्विघात समीकरण \(ax^2+bx+c=0\) का विवेचक क्या होता है?
What is the discriminant of \(ax^2+bx+c=0\)?
#quadratic-equations
#discriminant
#introduction
A \(a^2-4bc\)
B \(b^2+4ac\)
C \(b^2-4ac\)
D \(c^2-4ab\)
Explanation opens after your attempt
Correct Answer
C. \(b^2-4ac\)
Step 1
Concept
The discriminant is \(D=b^2-4ac\). Remembering it helps in understanding the nature of roots.
Step 2
Why this answer is correct
The correct answer is C. \(b^2-4ac\). The discriminant is \(D=b^2-4ac\). Remembering it helps in understanding the nature of roots.
Step 3
Exam Tip
विवेचक \(D=b^2-4ac\) होता है। इसे याद रखने से मूलों की प्रकृति समझना आसान होता है।
Login to save your score, XP, coins and progress.
Question 483/600
Easy Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
समीकरण ((m-2 )x-2 +3x+1=0) द्विघात कब होगा?
When will ((m-2 )x-2 +3x+1=0) be quadratic?
#quadratic-equations
#parameter
#condition
A (m=2)
B \(m\neq 2\)
C (m=0)
D (m=1)
Explanation opens after your attempt
Correct Answer
B. \(m\neq 2\)
Step 1
Concept
For the equation to be quadratic, the coefficient of \(x^2\) must not be (0). Thus \(m-2\neq 0\), so \(m\neq 2\).
Step 2
Why this answer is correct
The correct answer is B. \(m\neq 2\). For the equation to be quadratic, the coefficient of \(x^2\) must not be (0). Thus \(m-2\neq 0\), so \(m\neq 2\).
Step 3
Exam Tip
द्विघात होने के लिए \(x^2\) का गुणांक (0) नहीं होना चाहिए। इसलिए \(m-2\neq 0\) यानी \(m\neq 2\)।
Login to save your score, XP, coins and progress.
Question 484/600
Easy Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
क्या (x=0) समीकरण \(x^2+5x=0\) का मूल है?
Is (x=0) a root of \(x^2+5x=0\)?
#quadratic-equations
#root-verification
#easy
A हाँ / Yes
B नहीं / No
C केवल (x=5) मूल है / Only (x=5) is a root
D केवल (x=-5) मूल है / Only (x=-5) is a root
Explanation opens after your attempt
Correct Answer
A. हाँ / Yes
Step 1
Concept
Putting (x=0) gives \(0^2+5\cdot0=0\). Substitution is the easiest way to check a root.
Step 2
Why this answer is correct
The correct answer is A. हाँ / Yes. Putting (x=0) gives \(0^2+5\cdot0=0\). Substitution is the easiest way to check a root.
Step 3
Exam Tip
(x=0) रखने पर \(0^2+5\cdot0=0\) मिलता है। मूल जांचने में प्रतिस्थापन सबसे आसान तरीका है।
Login to save your score, XP, coins and progress.
Question 485/600
Easy Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
निम्न में से मोनिक द्विघात समीकरण कौन-सा है?
Which of the following is a monic quadratic equation?
#quadratic-equations
#monic-quadratic
#easy
A \(x^2+5x+6=0\)
B \(2x^2+x+1=0\)
C \(-3x^2+x=0\)
D \(4x^2-1=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+5x+6=0\)
Step 1
Concept
In a monic quadratic equation, the coefficient of \(x^2\) is (1). So \(x^2+5x+6=0\) is correct.
Step 2
Why this answer is correct
The correct answer is A. \(x^2+5x+6=0\). In a monic quadratic equation, the coefficient of \(x^2\) is (1). So \(x^2+5x+6=0\) is correct.
Step 3
Exam Tip
मोनिक द्विघात में \(x^2\) का गुणांक (1) होता है। इसलिए \(x^2+5x+6=0\) सही है।
Login to save your score, XP, coins and progress.
Question 486/600
Easy Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
निम्न में से शुद्ध द्विघात समीकरण कौन-सा है?
Which of the following is a pure quadratic equation?
#quadratic-equations
#pure-quadratic
#easy
A \(x^2+2x+1=0\)
B (3x+9=0)
C \(4x^2-9=0\)
D \(x^3-1=0\)
Explanation opens after your attempt
Correct Answer
C. \(4x^2-9=0\)
Step 1
Concept
A pure quadratic equation has no (x) term. In \(4x^2-9=0\), the linear term is absent.
Step 2
Why this answer is correct
The correct answer is C. \(4x^2-9=0\). A pure quadratic equation has no (x) term. In \(4x^2-9=0\), the linear term is absent.
Step 3
Exam Tip
शुद्ध द्विघात में (x) वाला पद नहीं होता है। \(4x^2-9=0\) में रैखिक पद अनुपस्थित है।
Login to save your score, XP, coins and progress.
Question 487/600
Easy Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
समीकरण \(6x^2-x+5=0\) में द्विघात पद कौन-सा है?
Which is the quadratic term in \(6x^2-x+5=0\)?
#quadratic-equations
#quadratic-term
#easy
A (-x)
B \(6x^2\)
C (5)
D (x)
Explanation opens after your attempt
Correct Answer
B. \(6x^2\)
Step 1
Concept
The term containing \(x^2\) is the quadratic term. Here the quadratic term is \(6x^2\).
Step 2
Why this answer is correct
The correct answer is B. \(6x^2\). The term containing \(x^2\) is the quadratic term. Here the quadratic term is \(6x^2\).
Step 3
Exam Tip
जिस पद में \(x^2\) होता है वह द्विघात पद है। यहाँ द्विघात पद \(6x^2\) है।
Login to save your score, XP, coins and progress.
Question 488/600
Easy Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
समीकरण \(2x^2+3x-8=0\) में स्थिर पद कौन-सा है?
What is the constant term in \(2x^2+3x-8=0\)?
#quadratic-equations
#constant-term
#easy
A (2)
B (3)
C (8)
D (-8)
Explanation opens after your attempt
Step 1
Concept
The term without (x) is the constant term. Here the constant term is (-8).
Step 2
Why this answer is correct
The correct answer is D. (-8). The term without (x) is the constant term. Here the constant term is (-8).
Step 3
Exam Tip
जिस पद में (x) नहीं होता वह स्थिर पद होता है। यहाँ स्थिर पद (-8) है।
Login to save your score, XP, coins and progress.
Question 489/600
Easy Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
समीकरण \(x^2-7=0\) में रैखिक पद कौन-सा है?
What is the linear term in \(x^2-7=0\)?
#quadratic-equations
#linear-term
#missing-term
A \(x^2\)
B (-7)
C (0x)
D (7x)
Explanation opens after your attempt
Step 1
Concept
There is no (x) term, so the linear term is considered (0x). A missing term has coefficient (0).
Step 2
Why this answer is correct
The correct answer is C. (0x). There is no (x) term, so the linear term is considered (0x). A missing term has coefficient (0).
Step 3
Exam Tip
इसमें (x) वाला पद नहीं है इसलिए रैखिक पद (0x) माना जाता है। अनुपस्थित पद का गुणांक (0) होता है।
Login to save your score, XP, coins and progress.
Question 490/600
Easy Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
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।
Login to save your score, XP, coins and progress.
Question 491/600
Easy Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
समीकरण \(5x^2-2x+1=0\) में \(x^2\) का गुणांक क्या है?
What is the coefficient of \(x^2\) in \(5x^2-2x+1=0\)?
#quadratic-equations
#coefficient-a
#easy
A (5)
B (2)
C (1)
D (-2)
Explanation opens after your attempt
Step 1
Concept
The coefficient attached to \(x^2\) is (5). While writing a coefficient, take the numerical part attached to the term.
Step 2
Why this answer is correct
The correct answer is A. (5). The coefficient attached to \(x^2\) is (5). While writing a coefficient, take the numerical part attached to the term.
Step 3
Exam Tip
\(x^2\) के साथ लगा गुणांक (5) है। गुणांक लिखते समय केवल पद के साथ लगा संख्यात्मक भाग लें।
Login to save your score, XP, coins and progress.
Question 492/600
Easy Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
एक द्विघात समीकरण के अधिकतम कितने मूल हो सकते हैं?
What is the maximum number of roots of a quadratic equation?
#quadratic-equations
#roots
#max-roots
#easy
A (1)
B (2)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
A quadratic equation has degree (2), so it can have at most (2) roots. Remember degree and maximum number of roots together.
Step 2
Why this answer is correct
The correct answer is B. (2). A quadratic equation has degree (2), so it can have at most (2) roots. Remember degree and maximum number of roots together.
Step 3
Exam Tip
द्विघात समीकरण की घात (2) होती है इसलिए अधिकतम (2) मूल हो सकते हैं। घात और अधिकतम मूल की संख्या को जोड़कर याद रखें।
Login to save your score, XP, coins and progress.
Question 493/600
Easy Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
समीकरण (3x+2=0) द्विघात क्यों नहीं है?
Why is (3x+2=0) not a quadratic equation?
#quadratic-equations
#non-example
#linear-equation
A क्योंकि इसमें \(x^2\) पद है / Because it has an \(x^2\) term
B क्योंकि इसमें स्थिर पद है / Because it has a constant term
C क्योंकि इसमें (x) नहीं है / Because it has no (x)
D क्योंकि सबसे बड़ी घात (1) है / Because the highest power is (1)
Explanation opens after your attempt
Correct Answer
D. क्योंकि सबसे बड़ी घात (1) है / Because the highest power is (1)
Step 1
Concept
In (3x+2=0), the highest power of (x) is (1). A quadratic equation must have highest power (2).
Step 2
Why this answer is correct
The correct answer is D. क्योंकि सबसे बड़ी घात (1) है / Because the highest power is (1). In (3x+2=0), the highest power of (x) is (1). A quadratic equation must have highest power (2).
Step 3
Exam Tip
(3x+2=0) में (x) की सबसे बड़ी घात (1) है। द्विघात के लिए सबसे बड़ी घात (2) होनी चाहिए।
Login to save your score, XP, coins and progress.
Question 494/600
Easy Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
किसी संख्या (x) के वर्ग में उसके (3) गुने को जोड़ने पर (10) मिलता है। सही समीकरण कौन-सा है?
The square of a number (x) plus (3) times the number is (10). Which equation is correct?
#quadratic-equations
#word-problem
#formation
A \(x+3x^2=10\)
B \(x^2+3x=10\)
C (2x+3=10)
D \(x^2-3x=10\)
Explanation opens after your attempt
Correct Answer
B. \(x^2+3x=10\)
Step 1
Concept
Square means \(x^2\) and (3) times means (3x). In word problems, convert the sentence slowly into an equation.
Step 2
Why this answer is correct
The correct answer is B. \(x^2+3x=10\). Square means \(x^2\) and (3) times means (3x). In word problems, convert the sentence slowly into an equation.
Step 3
Exam Tip
वर्ग का अर्थ \(x^2\) और (3) गुना का अर्थ (3x) है। शब्द प्रश्न में वाक्य को धीरे-धीरे समीकरण में बदलें।
Login to save your score, XP, coins and progress.
Question 495/600
Easy Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
क्या (x=2) समीकरण \(x^2-4=0\) का मूल है?
Is (x=2) a root of \(x^2-4=0\)?
#quadratic-equations
#root-checking
#easy
A हाँ / Yes
B नहीं / No
C केवल (x=-2) मूल है / Only (x=-2) is a root
D निर्धारित नहीं हो सकता / Cannot be determined
Explanation opens after your attempt
Correct Answer
A. हाँ / Yes
Step 1
Concept
Putting (x=2) gives \(2^2-4=0\). To check a root, substitute the value and see if the result is (0).
Step 2
Why this answer is correct
The correct answer is A. हाँ / Yes. Putting (x=2) gives \(2^2-4=0\). To check a root, substitute the value and see if the result is (0).
Step 3
Exam Tip
(x=2) रखने पर \(2^2-4=0\) मिलता है। मूल जांचने के लिए मान रखकर परिणाम (0) देखें।
Login to save your score, XP, coins and progress.
Question 496/600
Easy Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
द्विघात समीकरण \(ax^2+bx+c=0\) में (a) के लिए आवश्यक शर्त क्या है?
What is the required condition for (a) in \(ax^2+bx+c=0\)?
#quadratic-equations
#condition-on-a
#easy
A (a=0)
B (a<0)
C \(a\neq 0\)
D (a=1)
Explanation opens after your attempt
Correct Answer
C. \(a\neq 0\)
Step 1
Concept
If (a=0), the \(x^2\) term disappears. So \(a\neq 0\) is necessary for a quadratic equation.
Step 2
Why this answer is correct
The correct answer is C. \(a\neq 0\). If (a=0), the \(x^2\) term disappears. So \(a\neq 0\) is necessary for a quadratic equation.
Step 3
Exam Tip
यदि (a=0) हो जाए तो \(x^2\) पद नहीं बचेगा। इसलिए द्विघात होने के लिए \(a\neq 0\) जरूरी है।
Login to save your score, XP, coins and progress.
Question 497/600
Easy Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
समीकरण \(x^2-5x+6=0\) में (a,b,c) के मान क्या हैं?
What are the values of (a,b,c) in \(x^2-5x+6=0\)?
#quadratic-equations
#coefficients
#standard-form
A (a=1,\ b=-5,\ c=6)
B (a=1,\ b=5,\ c=6)
C (a=-1,\ b=-5,\ c=6)
D (a=6,\ b=-5,\ c=1)
Explanation opens after your attempt
Correct Answer
A. (a=1,\ b=-5,\ c=6)
Step 1
Concept
Comparing with standard form gives (a=1,\ b=-5,\ c=6). Pay special attention to signs.
Step 2
Why this answer is correct
The correct answer is A. (a=1,\ b=-5,\ c=6). Comparing with standard form gives (a=1,\ b=-5,\ c=6). Pay special attention to signs.
Step 3
Exam Tip
मानक रूप से मिलाने पर (a=1,\ b=-5,\ c=6) मिलता है। चिन्हों पर विशेष ध्यान रखें।
Login to save your score, XP, coins and progress.
Question 498/600
Easy Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
समीकरण \(7x^2-4x+9=0\) की घात क्या है?
What is the degree of the equation \(7x^2-4x+9=0\)?
#quadratic-equations
#degree
#easy
A (1)
B (2)
C (3)
D (0)
Explanation opens after your attempt
Step 1
Concept
The highest power of (x) in this equation is (2). Degree is decided by the greatest power of the variable.
Step 2
Why this answer is correct
The correct answer is B. (2). The highest power of (x) in this equation is (2). Degree is decided by the greatest power of the variable.
Step 3
Exam Tip
इस समीकरण में (x) की सबसे बड़ी घात (2) है। घात हमेशा चर की सबसे बड़ी शक्ति से तय होती है।
Login to save your score, XP, coins and progress.
Question 499/600
Easy Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
निम्न में से कौन-सा द्विघात समीकरण है?
Which of the following is a quadratic equation?
#quadratic-equations
#identify-equation
#class-10
#easy
A \(x^2+3x+2=0\)
B (2x+5=0)
C \(x^3-x=0\)
D \(\frac{1}{x}+2=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+3x+2=0\)
Step 1
Concept
In \(x^2+3x+2=0\), the highest power is (2). Check the power first while choosing an option.
Step 2
Why this answer is correct
The correct answer is A. \(x^2+3x+2=0\). In \(x^2+3x+2=0\), the highest power is (2). Check the power first while choosing an option.
Step 3
Exam Tip
\(x^2+3x+2=0\) में सबसे बड़ी घात (2) है। विकल्प चुनते समय घात को सबसे पहले देखें।
Login to save your score, XP, coins and progress.
Question 500/600
Easy Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
द्विघात समीकरण का सामान्य रूप कौन-सा है?
What is the general form of a quadratic equation?
#quadratic-equations
#introduction
#standard-form
#easy
A \(ax^2+bx+c=0,\ a\neq 0\)
B (ax+b=0)
C \(ax^3+bx+c=0\)
D \(\frac{a}{x}+b=0\)
Explanation opens after your attempt
Correct Answer
A. \(ax^2+bx+c=0,\ a\neq 0\)
Step 1
Concept
A quadratic equation has highest power (2) of (x) and \(a\neq 0\). In exams identify the standard form first.
Step 2
Why this answer is correct
The correct answer is A. \(ax^2+bx+c=0,\ a\neq 0\). A quadratic equation has highest power (2) of (x) and \(a\neq 0\). In exams identify the standard form first.
Step 3
Exam Tip
द्विघात समीकरण में (x) की सबसे बड़ी घात (2) होती है और \(a\neq 0\) होता है। परीक्षा में पहले मानक रूप पहचानें।
Login to save your score, XP, coins and progress.
Question 501/600
Easy Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
किसी संख्या का वर्ग उस संख्या के (5) गुने से (6) अधिक है। यदि संख्या (x) है तो समीकरण क्या होगा?
The square of a number is (6) more than (5) times the number. If the number is (x), what is the equation?
#quadratic equations
#word problem
#forming equation
A \(x^2=5x+6\)
B \(x^2+5x=6\)
C \(5x^2=x+6\)
D \(x^2=6x+5\)
Explanation opens after your attempt
Correct Answer
A. \(x^2=5x+6\)
Step 1
Concept
The square is \(x^2\), and (6) more than (5) times the number is (5x+6). So the equation is \(x^2=5x+6\).
Step 2
Why this answer is correct
The correct answer is A. \(x^2=5x+6\). The square is \(x^2\), and (6) more than (5) times the number is (5x+6). So the equation is \(x^2=5x+6\).
Step 3
Exam Tip
संख्या का वर्ग \(x^2\) और (5) गुने से (6) अधिक (5x+6) है। इसलिए समीकरण \(x^2=5x+6\) बनेगा।
Login to save your score, XP, coins and progress.
Question 502/600
Easy Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
यदि (x=-1) समीकरण \(x^2+mx-6=0\) का हल है तो (m) का मान क्या होगा?
If (x=-1) is a solution of \(x^2+mx-6=0\), what is the value of (m)?
#quadratic equations
#solution
#parameter
A (5)
B (-5)
C (7)
D (-7)
Explanation opens after your attempt
Step 1
Concept
Putting (x=-1) gives (1-m-6 =0). So (-m-5 =0) and (m=-5).
Step 2
Why this answer is correct
The correct answer is B. (-5). Putting (x=-1) gives (1-m-6 =0). So (-m-5 =0) and (m=-5).
Step 3
Exam Tip
(x=-1) रखने पर (1-m-6 =0) मिलता है। इसलिए (-m-5 =0) और (m=-5) है।
Login to save your score, XP, coins and progress.
Question 503/600
Easy Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
((2x+1)(x-4)=0) का विस्तृत रूप क्या है?
What is the expanded form of ((2x+1)(x-4)=0)?
#quadratic equations
#expansion
#binomial product
A \(2x^2-7x-4=0\)
B \(2x^2+7x-4=0\)
C \(2x^2-8x+1=0\)
D \(2x^2-7x+4=0\)
Explanation opens after your attempt
Correct Answer
A. \(2x^2-7x-4=0\)
Step 1
Concept
Expanding gives \(2x^2-8x+x-4=0\). Combining like terms gives \(2x^2-7x-4=0\).
Step 2
Why this answer is correct
The correct answer is A. \(2x^2-7x-4=0\). Expanding gives \(2x^2-8x+x-4=0\). Combining like terms gives \(2x^2-7x-4=0\).
Step 3
Exam Tip
विस्तार करने पर \(2x^2-8x+x-4=0\) मिलता है। समान पद जोड़कर \(2x^2-7x-4=0\) बनता है।
Login to save your score, XP, coins and progress.
Question 504/600
Easy Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
द्विघात समीकरण के बारे में कौन सा कथन गलत है?
Which statement about a quadratic equation is false?
#quadratic equations
#true false
#concept clarity
A इसकी घात (2) होती है / Its degree is (2)
B मानक रूप \(ax^2+bx+c=0\) है / Its standard form is \(ax^2+bx+c=0\)
C इसमें \(a\neq0\) होना चाहिए / It must have \(a\neq0\)
D इसमें हमेशा \(c\neq0\) होना चाहिए / It must always have \(c\neq0\)
Explanation opens after your attempt
Correct Answer
D. इसमें हमेशा \(c\neq0\) होना चाहिए / It must always have \(c\neq0\)
Step 1
Concept
In a quadratic equation, (c) can also be (0). The necessary condition is only \(a\neq0\).
Step 2
Why this answer is correct
The correct answer is D. इसमें हमेशा \(c\neq0\) होना चाहिए / It must always have \(c\neq0\). In a quadratic equation, (c) can also be (0). The necessary condition is only \(a\neq0\).
Step 3
Exam Tip
द्विघात समीकरण में (c) (0) भी हो सकता है। जरूरी शर्त केवल \(a\neq0\) है।
Login to save your score, XP, coins and progress.
Question 505/600
Easy Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
समीकरण ((k-1)x-2 +3x+2=0) द्विघात रहे इसके लिए कौन सी शर्त सही है?
Which condition is correct for ((k-1)x-2 +3x+2=0) to remain quadratic?
#quadratic equations
#parameter
#leading coefficient
A (k=1)
B \(k\neq1\)
C (k=0)
D (k=-1)
Explanation opens after your attempt
Correct Answer
B. \(k\neq1\)
Step 1
Concept
The coefficient of the quadratic term is ((k-1)), which must not be (0). Hence \(k\neq1\) is necessary.
Step 2
Why this answer is correct
The correct answer is B. \(k\neq1\). The coefficient of the quadratic term is ((k-1)), which must not be (0). Hence \(k\neq1\) is necessary.
Step 3
Exam Tip
द्विघात पद का गुणांक ((k-1)) है जो (0) नहीं होना चाहिए। इसलिए \(k\neq1\) होना जरूरी है।
Login to save your score, XP, coins and progress.
Question 506/600
Easy Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
((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।
Login to save your score, XP, coins and progress.
Question 507/600
Easy Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
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।
Login to save your score, XP, coins and progress.
Question 508/600
Easy Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
दो लगातार धन सम संख्याओं का गुणनफल (48) है। यदि छोटी संख्या (x) है तो समीकरण क्या होगा?
The product of two consecutive positive even numbers is (48). If the smaller number is (x), what is the equation?
#quadratic equations
#word problem
#consecutive even numbers
A (x(x+2)=48)
B (x(x+1)=48)
C (x+x+2=48)
D (2x=48)
Explanation opens after your attempt
Correct Answer
A. (x(x+2)=48)
Step 1
Concept
The next consecutive even number is (x+2). So the product equation is (x(x+2)=48).
Step 2
Why this answer is correct
The correct answer is A. (x(x+2)=48). The next consecutive even number is (x+2). So the product equation is (x(x+2)=48).
Step 3
Exam Tip
लगातार सम संख्या (x+2) होगी। इसलिए गुणनफल का समीकरण (x(x+2)=48) है।
Login to save your score, XP, coins and progress.
Question 509/600
Easy Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
यदि एक वर्ग की भुजा (x+2) है और क्षेत्रफल (49) है तो समीकरण क्या बनेगा?
If the side of a square is (x+2) and the area is (49), what equation is formed?
#quadratic equations
#word problem
#area
A ((x+2)2 =49)
B (x+2=49)
C (2x+2=49)
D \(x^2+2=49\)
Explanation opens after your attempt
Correct Answer
A. ((x+2)2 =49)
Step 1
Concept
The area of a square is the square of its side. So the equation is ((x+2)2 =49).
Step 2
Why this answer is correct
The correct answer is A. ((x+2)2 =49). The area of a square is the square of its side. So the equation is ((x+2)2 =49).
Step 3
Exam Tip
वर्ग का क्षेत्रफल भुजा का वर्ग होता है। इसलिए समीकरण ((x+2)2 =49) बनेगा।
Login to save your score, XP, coins and progress.
Question 510/600
Easy Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
कौन सा विकल्प \(x^2+x-12=0\) का गुणनखंड रूप है?
Which option is the factor form of \(x^2+x-12=0\)?
#quadratic equations
#factor form
#verification
A ((x+4)(x-3)=0)
B ((x-4)(x+3)=0)
C ((x+4)(x+3)=0)
D ((x-4)(x-3)=0)
Explanation opens after your attempt
Correct Answer
A. ((x+4)(x-3)=0)
Step 1
Concept
Expanding ((x+4)(x-3)) gives \(x^2+x-12\). To check factors, expand them.
Step 2
Why this answer is correct
The correct answer is A. ((x+4)(x-3)=0). Expanding ((x+4)(x-3)) gives \(x^2+x-12\). To check factors, expand them.
Step 3
Exam Tip
((x+4)(x-3)) फैलाने पर \(x^2+x-12\) मिलता है। गुणनखंड जांचने के लिए विस्तार करें।
Login to save your score, XP, coins and progress.
