Question 331/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
समीकरण \(x^2+11x+30=0\) को गुणनखंड रूप में कौन-सा लिखा जा सकता है?
Which factor form can represent \(x^2+11x+30=0\)?
#quadratic-equations
#factor-form
#medium
A ((x+5)(x+6)=0)
B ((x-5)(x-6)=0)
C ((x+3)(x+10)=0)
D ((x-1)(x+30)=0)
Explanation opens after your attempt
Correct Answer
A. ((x+5)(x+6)=0)
Step 1
Concept
\(5\cdot6=30\) and (5+6=11). Therefore the correct factors are ((x+5)(x+6)).
Step 2
Why this answer is correct
The correct answer is A. ((x+5)(x+6)=0). \(5\cdot6=30\) and (5+6=11). Therefore the correct factors are ((x+5)(x+6)).
Step 3
Exam Tip
\(5\cdot6=30\) और (5+6=11) है। इसलिए सही गुणनखंड ((x+5)(x+6)) हैं।
Login to save your score, XP, coins and progress.
Question 332/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
समीकरण \(49x^2-64=0\) के मूल क्या हैं?
What are the roots of \(49x^2-64=0\)?
#quadratic-equations
#roots
#difference-of-squares
#medium
A \(x=\pm \frac{8}{7}\)
B \(x=\pm \frac{7}{8}\)
C \(x=\pm8\)
D \(x=\pm7\)
Explanation opens after your attempt
Correct Answer
A. \(x=\pm \frac{8}{7}\)
Step 1
Concept
\(49x^2=64\), so \(x^2=\frac{64}{49}\) and \(x=\pm\frac{8}{7}\). Take both signs while taking square roots.
Step 2
Why this answer is correct
The correct answer is A. \(x=\pm \frac{8}{7}\). \(49x^2=64\), so \(x^2=\frac{64}{49}\) and \(x=\pm\frac{8}{7}\). Take both signs while taking square roots.
Step 3
Exam Tip
\(49x^2=64\), इसलिए \(x^2=\frac{64}{49}\) और \(x=\pm\frac{8}{7}\) है। वर्गमूल लेते समय दोनों चिन्ह लें।
Login to save your score, XP, coins and progress.
Question 333/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
समीकरण \(x^2-10x=0\) के मूल कौन-से हैं?
What are the roots of \(x^2-10x=0\)?
#quadratic-equations
#roots
#factorisation
#medium
A (0,10)
B (0,-10)
C (1,10)
D (-1,10)
Explanation opens after your attempt
Step 1
Concept
(x-2 -10x=x(x-10)), so the roots are (0) and (10). Taking the common factor is a quick method.
Step 2
Why this answer is correct
The correct answer is A. (0,10). (x-2 -10x=x(x-10)), so the roots are (0) and (10). Taking the common factor is a quick method.
Step 3
Exam Tip
(x-2 -10x=x(x-10)), इसलिए मूल (0) और (10) हैं। समान गुणनखंड निकालना तेज तरीका है।
Login to save your score, XP, coins and progress.
Question 334/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
एक आयत की लंबाई चौड़ाई से (7) अधिक है और क्षेत्रफल (120) है। यदि चौड़ाई (x) है, तो समीकरण क्या होगा?
A rectangle has length (7) more than its breadth and area (120). If the breadth is (x), what is the equation?
#quadratic-equations
#area
#word-problem
#medium
A \(x^2+7x-120=0\)
B \(x^2-7x-120=0\)
C \(7x^2+x-120=0\)
D \(x^2+120x-7=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+7x-120=0\)
Step 1
Concept
The length is (x+7), and the area is (x(x+7)=120). Therefore \(x^2+7x-120=0\).
Step 2
Why this answer is correct
The correct answer is A. \(x^2+7x-120=0\). The length is (x+7), and the area is (x(x+7)=120). Therefore \(x^2+7x-120=0\).
Step 3
Exam Tip
लंबाई (x+7) होगी और क्षेत्रफल (x(x+7)=120) होगा। इसलिए \(x^2+7x-120=0\) है।
Login to save your score, XP, coins and progress.
Question 335/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
दो क्रमागत धनात्मक पूर्णांकों के वर्गों का योग (145) है। यदि छोटा पूर्णांक (x) है, तो समीकरण कौन-सा है?
The sum of squares of two consecutive positive integers is (145). If the smaller integer is (x), which equation is correct?
#quadratic-equations
#consecutive-integers
#word-problem
#medium
A \(2x^2+2x-144=0\)
B \(2x^2+2x-145=0\)
C \(x^2+x-145=0\)
D \(2x^2-x-145=0\)
Explanation opens after your attempt
Correct Answer
A. \(2x^2+2x-144=0\)
Step 1
Concept
The integers are (x) and (x+1), so (x-2 +(x+1)2 =145). Simplifying gives \(2x^2+2x-144=0\).
Step 2
Why this answer is correct
The correct answer is A. \(2x^2+2x-144=0\). The integers are (x) and (x+1), so (x-2 +(x+1)2 =145). Simplifying gives \(2x^2+2x-144=0\).
Step 3
Exam Tip
पूर्णांक (x) और (x+1) होंगे, इसलिए (x-2 +(x+1)2 =145)। सरल करने पर \(2x^2+2x-144=0\) मिलता है।
Login to save your score, XP, coins and progress.
Question 336/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
किसी संख्या (x) के वर्ग में उसके (9) गुने को घटाने पर (36) मिलता है। सही समीकरण कौन-सा है?
When (9) times a number (x) is subtracted from its square, the result is (36). Which equation is correct?
#quadratic-equations
#word-problem
#equation-formation
#medium
A \(x^2-9x-36=0\)
B \(x^2+9x-36=0\)
C \(9x^2-x-36=0\)
D \(x^2-36x-9=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-9x-36=0\)
Step 1
Concept
The statement gives \(x^2-9x=36\). Bringing all terms to one side gives \(x^2-9x-36=0\).
Step 2
Why this answer is correct
The correct answer is A. \(x^2-9x-36=0\). The statement gives \(x^2-9x=36\). Bringing all terms to one side gives \(x^2-9x-36=0\).
Step 3
Exam Tip
वाक्य से \(x^2-9x=36\) बनता है। सभी पद एक ओर लाने पर \(x^2-9x-36=0\) मिलता है।
Login to save your score, XP, coins and progress.
Question 337/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
यदि मूल (-5) और (4) हैं, तो मोनिक द्विघात समीकरण कौन-सा होगा?
If the roots are (-5) and (4), what will be the monic quadratic equation?
#quadratic-equations
#monic
#roots
#medium
A \(x^2+x-20=0\)
B \(x^2-x-20=0\)
C \(x^2+9x+20=0\)
D \(x^2-9x+20=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+x-20=0\)
Step 1
Concept
The factors are ((x+5)) and ((x-4)). Multiplying them gives \(x^2+x-20=0\).
Step 2
Why this answer is correct
The correct answer is A. \(x^2+x-20=0\). The factors are ((x+5)) and ((x-4)). Multiplying them gives \(x^2+x-20=0\).
Step 3
Exam Tip
गुणनखंड ((x+5)) और ((x-4)) होंगे। इन्हें गुणा करने पर \(x^2+x-20=0\) मिलता है।
Login to save your score, XP, coins and progress.
Question 338/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
किस विकल्प में (x=3) और (x=8) मूल हैं?
Which option has roots (x=3) and (x=8)?
#quadratic-equations
#roots
#forming-equation
#medium
A \(x^2-11x+24=0\)
B \(x^2+11x+24=0\)
C \(x^2-24x+11=0\)
D \(x^2+24x-11=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-11x+24=0\)
Step 1
Concept
If the roots are (3) and (8), the factors are ((x-3)) and ((x-8)). Their product gives \(x^2-11x+24=0\).
Step 2
Why this answer is correct
The correct answer is A. \(x^2-11x+24=0\). If the roots are (3) and (8), the factors are ((x-3)) and ((x-8)). Their product gives \(x^2-11x+24=0\).
Step 3
Exam Tip
मूल (3) और (8) हों तो गुणनखंड ((x-3)) और ((x-8)) होंगे। इनका गुणन \(x^2-11x+24=0\) देता है।
Login to save your score, XP, coins and progress.
Question 339/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
समीकरण \(4x^2+x+6=0\) के विवेचक का चिन्ह क्या है?
What is the sign of the discriminant of \(4x^2+x+6=0\)?
#quadratic-equations
#discriminant
#negative
#medium
A धनात्मक / Positive
B शून्य / Zero
C ऋणात्मक / Negative
D निर्धारित नहीं / Not determined
Explanation opens after your attempt
Correct Answer
C. ऋणात्मक / Negative
Step 1
Concept
\(D=1^2-4\cdot4\cdot6=1-96=-95\), so the discriminant is negative. Calculate (4ac) carefully.
Step 2
Why this answer is correct
The correct answer is C. ऋणात्मक / Negative. \(D=1^2-4\cdot4\cdot6=1-96=-95\), so the discriminant is negative. Calculate (4ac) carefully.
Step 3
Exam Tip
\(D=1^2-4\cdot4\cdot6=1-96=-95\), इसलिए विवेचक ऋणात्मक है। (4ac) की गणना सावधानी से करें।
Login to save your score, XP, coins and progress.
Question 340/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
समीकरण \(x^2+14x+49=0\) में मूलों की प्रकृति क्या है?
What is the nature of roots of \(x^2+14x+49=0\)?
#quadratic-equations
#nature-of-roots
#discriminant
#medium
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 चार वास्तविक मूल / Four real roots
Explanation opens after your attempt
Correct Answer
B. दो समान वास्तविक मूल / Two equal real roots
Step 1
Concept
Here \(D=14^2-4\cdot1\cdot49=0\). Therefore the equation has two equal real roots.
Step 2
Why this answer is correct
The correct answer is B. दो समान वास्तविक मूल / Two equal real roots. Here \(D=14^2-4\cdot1\cdot49=0\). Therefore the equation has two equal real roots.
Step 3
Exam Tip
यहाँ \(D=14^2-4\cdot1\cdot49=0\) है। इसलिए इस समीकरण के दो समान वास्तविक मूल हैं।
Login to save your score, XP, coins and progress.
Question 341/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
यदि (D=64) है, तो द्विघात समीकरण के मूलों की प्रकृति क्या होगी?
If (D=64), what will be the nature of roots of the quadratic equation?
#quadratic-equations
#discriminant
#nature-of-roots
#medium
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 मूल निश्चित नहीं हो सकते / Roots cannot be decided
Explanation opens after your attempt
Correct Answer
A. दो भिन्न वास्तविक मूल / Two distinct real roots
Step 1
Concept
Since (D=64>0), there will be 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. Since (D=64>0), there will be two distinct real roots. The sign of the discriminant tells the nature of roots.
Step 3
Exam Tip
(D=64>0), इसलिए दो भिन्न वास्तविक मूल होंगे। विवेचक का चिन्ह मूलों की प्रकृति बताता है।
Login to save your score, XP, coins and progress.
Question 342/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
समीकरण \(25x^2-20x+4=0\) का विवेचक (D) क्या है?
What is the discriminant (D) of \(25x^2-20x+4=0\)?
#quadratic-equations
#discriminant
#equal-roots
#medium
A (0)
B (20)
C (100)
D (-20)
Explanation opens after your attempt
Step 1
Concept
Here (D=(-20)2 -4\cdot25\cdot4=400-400=0). (D=0) indicates equal roots.
Step 2
Why this answer is correct
The correct answer is A. (0). Here (D=(-20)2 -4\cdot25\cdot4=400-400=0). (D=0) indicates equal roots.
Step 3
Exam Tip
यहाँ (D=(-20)2 -4\cdot25\cdot4=400-400=0) है। (D=0) समान मूलों का संकेत देता है।
Login to save your score, XP, coins and progress.
Question 343/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
यदि (a=-2), (b=9), (c=-7) हैं, तो संबंधित द्विघात समीकरण कौन-सा है?
If (a=-2), (b=9), (c=-7), which is the corresponding quadratic equation?
#quadratic-equations
#forming-equation
#coefficients
#medium
A \(2x^2+9x-7=0\)
B \(-2x^2+9x-7=0\)
C \(-2x^2-9x-7=0\)
D \(7x^2+9x-2=0\)
Explanation opens after your attempt
Correct Answer
B. \(-2x^2+9x-7=0\)
Step 1
Concept
Substituting in \(ax^2+bx+c=0\) gives \(-2x^2+9x-7=0\). Never ignore the sign of a coefficient.
Step 2
Why this answer is correct
The correct answer is B. \(-2x^2+9x-7=0\). Substituting in \(ax^2+bx+c=0\) gives \(-2x^2+9x-7=0\). Never ignore the sign of a coefficient.
Step 3
Exam Tip
मानक रूप \(ax^2+bx+c=0\) में मान रखने पर \(-2x^2+9x-7=0\) मिलता है। गुणांक का चिन्ह कभी न छोड़ें।
Login to save your score, XP, coins and progress.
Question 344/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
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।
Login to save your score, XP, coins and progress.
Question 345/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
यदि (x=-3) समीकरण \(2x^2+rx-9=0\) का मूल है, तो (r) का मान क्या होगा?
If (x=-3) is a root of \(2x^2+rx-9=0\), what is the value of (r)?
#quadratic-equations
#parameter
#root
#medium
A (3)
B (-3)
C (9)
D (-9)
Explanation opens after your attempt
Step 1
Concept
Putting (x=-3) gives (18-3r-9=0), so (r=3). If a root is given, substitute it into the equation.
Step 2
Why this answer is correct
The correct answer is A. (3). Putting (x=-3) gives (18-3r-9=0), so (r=3). If a root is given, substitute it into the equation.
Step 3
Exam Tip
(x=-3) रखने पर (18-3r-9=0) मिलता है, इसलिए (r=3) है। मूल दिया हो तो उसे समीकरण में रखें।
Login to save your score, XP, coins and progress.
Question 346/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
क्या (x=5) समीकरण \(x^2-6x+5=0\) का मूल है?
Is (x=5) a root of \(x^2-6x+5=0\)?
#quadratic-equations
#root-check
#substitution
#medium
A हाँ / Yes
B नहीं / No
C केवल (x=1) मूल है / Only (x=1) is a root
D निर्धारित नहीं किया जा सकता / Cannot be determined
Explanation opens after your attempt
Correct Answer
A. हाँ / Yes
Step 1
Concept
Putting (x=5) gives (25-30+5=0). Substitution is the simple way to check a root.
Step 2
Why this answer is correct
The correct answer is A. हाँ / Yes. Putting (x=5) gives (25-30+5=0). Substitution is the simple way to check a root.
Step 3
Exam Tip
(x=5) रखने पर (25-30+5=0) मिलता है। मूल जांचने का सरल तरीका प्रतिस्थापन है।
Login to save your score, XP, coins and progress.
Question 347/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
समीकरण \(12-7x+x^2=0\) को \(ax^2+bx+c=0\) के रूप में लिखने पर (b) का मान क्या होगा?
When \(12-7x+x^2=0\) is written as \(ax^2+bx+c=0\), what is the value of (b)?
#quadratic-equations
#standard-form
#coefficient-b
#medium
A (12)
B (-7)
C (7)
D (1)
Explanation opens after your attempt
Step 1
Concept
In proper order, the equation is \(x^2-7x+12=0\). So the coefficient of (x) is (b=-7).
Step 2
Why this answer is correct
The correct answer is B. (-7). In proper order, the equation is \(x^2-7x+12=0\). So the coefficient of (x) is (b=-7).
Step 3
Exam Tip
सही क्रम में समीकरण \(x^2-7x+12=0\) है। इसलिए (x) का गुणांक (b=-7) है।
Login to save your score, XP, coins and progress.
Question 348/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
समीकरण \(6x^2-13x+5=0\) के लिए (2a+b-c) का मान क्या है?
For the equation \(6x^2-13x+5=0\), what is the value of (2a+b-c)?
#quadratic-equations
#coefficients
#signs
#medium
A (-6)
B (4)
C (30)
D (-30)
Explanation opens after your attempt
Step 1
Concept
Here (a=6), (b=-13), (c=5). Hence (2a+b-c=12-13-5=-6).
Step 2
Why this answer is correct
The correct answer is A. (-6). Here (a=6), (b=-13), (c=5). Hence (2a+b-c=12-13-5=-6).
Step 3
Exam Tip
यहाँ (a=6), (b=-13), (c=5) हैं। इसलिए (2a+b-c=12-13-5=-6) है।
Login to save your score, XP, coins and progress.
Question 349/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
यदि ((5-p)x-2 +2x+9=0) द्विघात समीकरण है, तो (p) के लिए सही शर्त क्या है?
If ((5-p)x-2 +2x+9=0) is a quadratic equation, what is the correct condition for (p)?
#quadratic-equations
#parameter
#condition
#medium
A (p=5)
B \(p\neq 5\)
C (p=0)
D \(p\neq -5\)
Explanation opens after your attempt
Correct Answer
B. \(p\neq 5\)
Step 1
Concept
For a quadratic equation, the coefficient of \(x^2\) must not be (0). Thus \(5-p\neq0\), so \(p\neq5\).
Step 2
Why this answer is correct
The correct answer is B. \(p\neq 5\). For a quadratic equation, the coefficient of \(x^2\) must not be (0). Thus \(5-p\neq0\), so \(p\neq5\).
Step 3
Exam Tip
द्विघात समीकरण के लिए \(x^2\) का गुणांक (0) नहीं होना चाहिए। इसलिए \(5-p\neq0\), अर्थात \(p\neq5\)।
Login to save your score, XP, coins and progress.
Question 350/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
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।
Login to save your score, XP, coins and progress.
Question 351/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
यदि (x=-4) समीकरण \(x^2+tx-8=0\) का मूल है, तो (t) का मान क्या होगा?
If (x=-4) is a root of \(x^2+tx-8=0\), what is the value of (t)?
#quadratic-equations
#parameter
#root-substitution
#medium
A (2)
B (-2)
C (6)
D (-6)
Explanation opens after your attempt
Step 1
Concept
Putting (x=-4) gives (16-4t-8=0), so (t=2). When a root is given, substitute it directly.
Step 2
Why this answer is correct
The correct answer is A. (2). Putting (x=-4) gives (16-4t-8=0), so (t=2). When a root is given, substitute it directly.
Step 3
Exam Tip
(x=-4) रखने पर (16-4t-8=0) मिलता है, इसलिए (t=2) है। मूल दिया हो तो सीधे प्रतिस्थापन करें।
Login to save your score, XP, coins and progress.
Question 352/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
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।
Login to save your score, XP, coins and progress.
Question 353/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
समीकरण \(x^2+12x+36=0\) को किस पूर्ण वर्ग रूप में लिखा जा सकता है?
In which perfect square form can \(x^2+12x+36=0\) be written?
#quadratic-equations
#perfect-square
#identity
#medium
A ((x+6)2 =0)
B ((x-6)2 =0)
C ((x+12)2 =0)
D ((x-12)2 =0)
Explanation opens after your attempt
Correct Answer
A. ((x+6)2 =0)
Step 1
Concept
(x-2 +12x+36=(x+6)2 ). To identify a perfect square, match the middle term with (2ab).
Step 2
Why this answer is correct
The correct answer is A. ((x+6)2 =0). (x-2 +12x+36=(x+6)2 ). To identify a perfect square, match the middle term with (2ab).
Step 3
Exam Tip
(x-2 +12x+36=(x+6)2 ) होता है। पूर्ण वर्ग पहचानने के लिए मध्य पद (2ab) से मिलाएं।
Login to save your score, XP, coins and progress.
Question 354/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
एक वर्ग का क्षेत्रफल उसकी भुजा के (8) गुने से (15) अधिक है। यदि भुजा (x) है, तो समीकरण कौन-सा है?
The area of a square is (15) more than (8) times its side. If the side is (x), which equation is correct?
#quadratic-equations
#word-problem
#square-area
#medium
A \(x^2-8x-15=0\)
B \(x^2+8x+15=0\)
C \(x^2-15x-8=0\)
D \(8x^2-x+15=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-8x-15=0\)
Step 1
Concept
The area is \(x^2\), and it is given that \(x^2=8x+15\). Therefore \(x^2-8x-15=0\) is correct.
Step 2
Why this answer is correct
The correct answer is A. \(x^2-8x-15=0\). The area is \(x^2\), and it is given that \(x^2=8x+15\). Therefore \(x^2-8x-15=0\) is correct.
Step 3
Exam Tip
क्षेत्रफल \(x^2\) है और दिया है \(x^2=8x+15\)। इसलिए \(x^2-8x-15=0\) सही है।
Login to save your score, XP, coins and progress.
Question 355/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
यदि \(x^2+sx+18=0\) के मूल (-3) और (-6) हैं, तो (s) का मान क्या है?
If the roots of \(x^2+sx+18=0\) are (-3) and (-6), what is the value of (s)?
#quadratic-equations
#parameter
#roots
#medium
A (9)
B (-9)
C (18)
D (-18)
Explanation opens after your attempt
Step 1
Concept
The sum of roots is (-9), and in \(x^2+sx+18=0\) the sum is (-s). Therefore (s=9).
Step 2
Why this answer is correct
The correct answer is A. (9). The sum of roots is (-9), and in \(x^2+sx+18=0\) the sum is (-s). Therefore (s=9).
Step 3
Exam Tip
मूलों का योग (-9) है और \(x^2+sx+18=0\) में योग (-s) होता है। इसलिए (s=9) है।
Login to save your score, XP, coins and progress.
Question 356/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
समीकरण \(x^2-13x+42=0\) के गुणनखंड पहचानने के लिए कौन-सी संख्या जोड़ी उपयोगी है?
Which pair of numbers is useful to identify the factors of \(x^2-13x+42=0\)?
#quadratic-equations
#factorisation
#number-pair
#medium
A (6) और (7) / (6) and (7)
B (3) और (14) / (3) and (14)
C (2) और (21) / (2) and (21)
D (1) और (42) / (1) and (42)
Explanation opens after your attempt
Correct Answer
A. (6) और (7) / (6) and (7)
Step 1
Concept
\(6\cdot7=42\) and (6+7=13). Because the middle term is negative, the factors are ((x-6)(x-7)).
Step 2
Why this answer is correct
The correct answer is A. (6) और (7) / (6) and (7). \(6\cdot7=42\) and (6+7=13). Because the middle term is negative, the factors are ((x-6)(x-7)).
Step 3
Exam Tip
\(6\cdot7=42\) और (6+7=13) होता है। ऋण मध्य पद के कारण गुणनखंड ((x-6)(x-7)) बनते हैं।
Login to save your score, XP, coins and progress.
Question 357/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
यदि \(6x^2-18x+12=0\) को (6) से भाग दें, तो सरल समीकरण कौन-सा होगा?
If \(6x^2-18x+12=0\) is divided by (6), which simplified equation is obtained?
#quadratic-equations
#simplification
#common-factor
#medium
A \(x^2-3x+2=0\)
B \(x^2+3x+2=0\)
C \(6x^2-3x+2=0\)
D \(x^2-18x+12=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-3x+2=0\)
Step 1
Concept
Dividing every term by (6) gives \(x^2-3x+2=0\). Dividing by a common nonzero factor does not change the roots.
Step 2
Why this answer is correct
The correct answer is A. \(x^2-3x+2=0\). Dividing every term by (6) gives \(x^2-3x+2=0\). Dividing by a common nonzero factor does not change the roots.
Step 3
Exam Tip
हर पद को (6) से भाग देने पर \(x^2-3x+2=0\) मिलता है। समान अशून्य गुणनखंड से भाग देने पर मूल नहीं बदलते।
Login to save your score, XP, coins and progress.
Question 358/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
किस विकल्प में (x) पद अनुपस्थित है लेकिन समीकरण द्विघात है?
In which option is the (x) term absent but the equation is quadratic?
#quadratic-equations
#missing-linear-term
#pure-quadratic
#medium
A \(3x^2-27=0\)
B (3x-27=0)
C \(3x^3-27=0\)
D \(\frac{3}{x^2}-27=0\)
Explanation opens after your attempt
Correct Answer
A. \(3x^2-27=0\)
Step 1
Concept
In \(3x^2-27=0\), the \(x^2\) term is present and the (x) term is absent. An equation can be quadratic even without the (x) term.
Step 2
Why this answer is correct
The correct answer is A. \(3x^2-27=0\). In \(3x^2-27=0\), the \(x^2\) term is present and the (x) term is absent. An equation can be quadratic even without the (x) term.
Step 3
Exam Tip
\(3x^2-27=0\) में \(x^2\) पद है और (x) पद अनुपस्थित है। (x) पद न होने पर भी समीकरण द्विघात हो सकता है।
Login to save your score, XP, coins and progress.
Question 359/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
समीकरण \(x^2+kx+49=0\) में यदि मूल समान और धनात्मक हैं, तो (k) का संभव मान कौन-सा है?
In \(x^2+kx+49=0\), if the roots are equal and positive, which possible value of (k) is correct?
#quadratic-equations
#equal-positive-roots
#parameter
#medium
A (14)
B (-14)
C (7)
D (-7)
Explanation opens after your attempt
Step 1
Concept
For equal roots, \(k^2=196\), and the equal root is \(-\frac{k}{2}\). For a positive root, (k=-14) is correct.
Step 2
Why this answer is correct
The correct answer is B. (-14). For equal roots, \(k^2=196\), and the equal root is \(-\frac{k}{2}\). For a positive root, (k=-14) is correct.
Step 3
Exam Tip
समान मूलों के लिए \(k^2=196\) और समान मूल \(-\frac{k}{2}\) होगा। धनात्मक मूल के लिए (k=-14) सही है।
Login to save your score, XP, coins and progress.
Question 360/600
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
यदि द्विघात समीकरण \(x^2-14x+k=0\) के मूल समान हैं, तो (k) क्या होगा?
If the roots of \(x^2-14x+k=0\) are equal, what is (k)?
#quadratic-equations
#equal-roots
#discriminant
#medium
A (14)
B (49)
C (98)
D (196)
Explanation opens after your attempt
Step 1
Concept
For equal roots, (D=0), so (196-4k=0) and (k=49). For equal roots, set the discriminant to zero.
Step 2
Why this answer is correct
The correct answer is B. (49). For equal roots, (D=0), so (196-4k=0) and (k=49). For equal roots, set the discriminant to zero.
Step 3
Exam Tip
समान मूलों के लिए (D=0), इसलिए (196-4k=0) और (k=49)। समान मूल की शर्त में विवेचक शून्य रखें।
Login to save your score, XP, coins and progress.
