Related questions grouped automatically for chapter-wise practice. Topics include Methods of Solving Quadratic Equations, Nature of Roots, Roots of a Quadratic Equation, Word Problems and Applications, Introduction to Quadratic Equations.
Related questions grouped automatically for chapter-wise practice.
Mathematics Quadratic Equations ke topic-wise MCQs yahan grouped context me milenge. jo aap ko Exam ki preparation me madad milegi. Ye questions exam-oriented hai and students ko concept clarity, quick revision aur board exam preparation kaafi madad karenge. Sabhi se jude MCQs important topics ke anusar arranged hai, taaki aap Quadratic Equations ko easy tarike se practice aur revise kar sake.
Difficulty select karke Mathematics / Quadratic Equations chapter-filtered timed practice karein. Har button me live question count show hoga.
Which of the following equations is a quadratic equation?
A. \(x^2+3x+2=0\)
द्विघात समीकरण में (x) की सबसे बड़ी घात (2) होती है। परीक्षा में सबसे पहले घात देखें। / A quadratic equation has highest power (2) of (x). In exams first check the degree.
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What is the value of (a) in the equation \(5x^2-2x+9=0\)?
A. (5)
मानक रूप \(ax^2+bx+c=0\) में (a) \(x^2\) का गुणांक होता है। यहां (a=5) है। / In \(ax^2+bx+c=0\), (a) is the coefficient of \(x^2\). Here (a=5).
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What is the value of (b) in \(3x^2+7x-4=0\)?
B. (7)
मानक रूप में (b) (x) का गुणांक होता है। इसलिए (b=7) है। / In standard form, (b) is the coefficient of (x). So (b=7).
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What is the value of (c) in \(4x^2-8x+1=0\)?
C. (1)
मानक रूप में (c) स्थिर पद होता है। यहां स्थिर पद (1) है। / In standard form, (c) is the constant term. Here the constant term is (1).
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What is the value of (c) in \(x^2-6x=0\)?
C. (0)
इसे \(x^2-6x+0=0\) लिखा जा सकता है। अतः (c=0) है। / It can be written as \(x^2-6x+0=0\). Hence (c=0).
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What is the value of \(x\) in \(9x^2+11=0\)?
C. (0)
इसे \(9x^2+0x+11=0\) लिखा जाता है। इसलिए \(x=0\) है। / It is written as \(9x^2+0x+11=0\). So \(x=0\).
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Under which condition is \(ax^2+bx+c=0\) called a quadratic equation?
B. \(a\neq0\)
द्विघात पद बना रहे इसलिए \(a\neq0\) होना चाहिए। परीक्षा में (a=0) होने पर यह रैखिक बन सकता है। / The quadratic term must remain, so \(a\neq0\). If (a=0), it may become linear.
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What is the standard form of \(2x^2+5x=3\)?
B. \(2x^2+5x-3=0\)
सभी पद एक तरफ लाने पर \(2x^2+5x-3=0\) मिलता है। चिन्ह बदलना न भूलें। / Bringing all terms to one side gives \(2x^2+5x-3=0\). Do not forget the sign change.
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Which is the standard form of \(x^2=4x+12\)?
A. \(x^2-4x-12=0\)
दाईं ओर के पदों को बाईं ओर लाने पर चिन्ह बदलते हैं। इसलिए \(x^2-4x-12=0\) सही है। / When terms from the right side move left, their signs change. Thus \(x^2-4x-12=0\) is correct.
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Which equation is in the standard form \(ax^2+bx+c=0\)?
A. \(x^2+2x+1=0\)
मानक रूप में दाईं ओर (0) होता है। विकल्प (A) इसी रूप में है। / In standard form the right side is (0). Option (A) matches this form.
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If (x=2), what is the left side of \(x^2-5x+6=0\)?
A. (0)
रखने पर \(2^2-5\cdot2+6=0\) मिलता है। इसलिए (x=2) समीकरण का हल है। / Substitution gives \(2^2-5\cdot2+6=0\). So (x=2) is a solution.
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Which value is one solution of \(x^2-9=0\)?
B. (3)
\(3^2-9=0\) इसलिए (3) हल है। आसान प्रश्नों में मान रखकर जांच करें। / Since \(3^2-9=0\), (3) is a solution. For easy questions, check by substitution.
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What do we get by putting (x=2) in \(x^2-4x+4=0\)?
A. (0=0)
\(2^2-4\cdot2+4=0\) है। अतः (x=2) सही हल है। / We get \(2^2-4\cdot2+4=0\). Hence (x=2) is a correct solution.
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Which of the following is a quadratic polynomial?
B. \(x^2-3x+2\)
द्विघात बहुपद की घात (2) होती है। \(x^2-3x+2\) में सबसे बड़ी घात (2) है। / A quadratic polynomial has degree (2). In \(x^2-3x+2\), the highest power is (2).
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Which equation is not quadratic?
C. \(x^3+x+1=0\)
\(x^3+x+1=0\) की घात (3) है। इसलिए यह द्विघात समीकरण नहीं है। / The degree of \(x^3+x+1=0\) is (3). So it is not a quadratic equation.
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For \(6x^2=0\), what are (a), (b), (c) respectively?
A. (6,0,0)
इसे \(6x^2+0x+0=0\) लिखा जाता है। इसलिए (a=6), (b=0), (c=0) हैं। / It is written as \(6x^2+0x+0=0\). Therefore (a=6), (b=0), (c=0).
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Write (x(x+5)=0) in standard form.
A. \(x^2+5x=0\)
गुणा करने पर \(x^2+5x=0\) मिलता है। कोष्ठक खोलते समय हर पद से गुणा करें। / Multiplying gives \(x^2+5x=0\). While opening brackets, multiply each term.
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What is the expanded form of ((x+2)(x+3)=0)?
A. \(x^2+5x+6=0\)
विस्तार से \(x^2+3x+2x+6=0\) मिलता है। समान पद जोड़कर \(x^2+5x+6=0\) बनता है। / Expansion gives \(x^2+3x+2x+6=0\). Combining like terms gives \(x^2+5x+6=0\).
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Which is the standard form of ((x-4)(x+1)=0)?
A. \(x^2-3x-4=0\)
विस्तार करने पर \(x^2+x-4x-4=0\) मिलता है। इसलिए \(x^2-3x-4=0\) सही है। / Expanding gives \(x^2+x-4x-4=0\). So \(x^2-3x-4=0\) is correct.
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What is the coefficient of \(x^2\) in \(x^2+8x+16=0\)?
B. (1)
जब \(x^2\) के आगे कोई संख्या नहीं लिखी होती तब गुणांक (1) होता है। यह सामान्य परीक्षा गलती है। / When no number is written before \(x^2\), its coefficient is (1). This is a common exam mistake.
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What is the value of (a) in \(-x^2+3x+10=0\)?
B. \(-1\)
\(-x^2\) का गुणांक (-1) होता है। इसलिए (a=-1) है। / The coefficient of \(-x^2\) is (-1). So (a=-1).
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Which option shows \(x^2+6x+9=0\) in factor form?
A. \((x+3)^2=0\)
\(x^2+6x+9\) एक पूर्ण वर्ग है। यह ((x+3)2) के बराबर है। / \(x^2+6x+9\) is a perfect square. It equals ((x+3)2).
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Which value is a solution of \(x^2+x-6=0\)?
B. (2)
\(2^2+2-6=0\) है। इसलिए (x=2) इस समीकरण का हल है। / Since \(2^2+2-6=0\), (x=2) is a solution of the equation.
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If an equation in (x) has degree (2), what is it called?
B. द्विघात समीकरणQuadratic equation
घात (2) वाले समीकरण को द्विघात समीकरण कहते हैं। नाम याद रखने के लिए द्वि का अर्थ (2) समझें। / An equation of degree (2) is called a quadratic equation. Remember that quadratic means degree (2).
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Which of the following contains the \(x^2\) term?
C. \(x^2-2=0\)
द्विघात समीकरण के लिए \(x^2\) पद आवश्यक है। विकल्प (C) में यह पद है। / The \(x^2\) term is necessary for a quadratic equation. Option (C) has this term.
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What is the linear term in \(2x^2+0x-7=0\)?
B. (0x)
रैखिक पद (x) वाला पद होता है। यहां वह (0x) है। / The linear term is the term containing (x). Here it is (0x).
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Which equation is equivalent to \(x^2+2x+1=0\)?
A. \((x+1)^2=0\)
((x+1)2=x-2+2x+1) होता है। पूर्ण वर्ग पहचानना तेजी से हल कराने में मदद करता है। / ((x+1)2=x-2+2x+1). Recognising perfect squares helps solve faster.
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How do we write \(x^2-16=0\) in factor form?
A. \((x-4)(x+4)=0\)
\(x^2-16\) वर्गों का अंतर है। इसलिए यह ((x-4)(x+4)) बनता है। / \(x^2-16\) is a difference of squares. Hence it becomes ((x-4)(x+4)).
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If (x=1), what is the left side of \(x^2+2x-3=0\)?
A. (0)
रखने पर \(1^2+2\cdot1-3=0\) मिलता है। इसलिए (1) एक हल है। / Substituting gives \(1^2+2\cdot1-3=0\). So (1) is a solution.
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What are (a), (b), (c) in \(7x^2-14=0\)?
A. (7,0,-14)
इसे \(7x^2+0x-14=0\) लिखें। इससे (a=7), (b=0), (c=-14) मिलते हैं। / Write it as \(7x^2+0x-14=0\). Then (a=7), (b=0), (c=-14).
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Which equation is quadratic in (x) but not in (y)?
A. \(x^2+5x+6=0\)
विकल्प (A) में चर (x) की घात (2) है। इसलिए यह (x) में द्विघात है। / In option (A), the variable (x) has degree (2). So it is quadratic in (x).
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What is the standard form of (3x(x-2)=0)?
A. \(3x^2-6x=0\)
(3x) को दोनों पदों से गुणा करने पर \(3x^2-6x=0\) मिलता है। चिन्ह पर ध्यान दें। / Multiplying (3x) by both terms gives \(3x^2-6x=0\). Watch the sign.
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If (p(x)=x-2-1), what is (p(1))?
A. (0)
(p(1)=12-1=0) है। जब (p(a)=0) हो तो (a) शून्यक कहलाता है। / (p(1)=12-1=0). When (p(a)=0), (a) is called a zero.
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Which option is the constant term in \(2x^2+3x+1=0\)?
C. (1)
स्थिर पद में (x) नहीं होता। इसलिए (1) स्थिर पद है। / The constant term does not contain (x). Hence (1) is the constant term.
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Which term is absent in \(x^2+10x=0\)?
C. स्थिर पदConstant term
इसे \(x^2+10x+0=0\) माना जाता है। इसलिए स्थिर पद अनुपस्थित है। / It is treated as \(x^2+10x+0=0\). So the constant term is absent.
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Which equation is a pure quadratic like \(x^2+5=0\)?
A. \(x^2-9=0\)
शुद्ध द्विघात में (x) वाला रैखिक पद नहीं होता। \(x^2-9=0\) ऐसा ही है। / A pure quadratic has no linear (x) term. \(x^2-9=0\) is of that type.
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What happens when (x=-2) is put in \(x^2+4x+4=0\)?
A. समीकरण संतुष्ट होता हैThe equation is satisfied
((-2)2+4(-2)+4=0) है। अतः (x=-2) हल है। / ((-2)2+4(-2)+4=0). Hence (x=-2) is a solution.
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Which form represents (a=2), (b=-5), (c=3) in \(ax^2+bx+c=0\)?
A. \(2x^2-5x+3=0\)
दिए गए मान सीधे मानक रूप में रखने पर \(2x^2-5x+3=0\) मिलता है। (b) का चिन्ह ध्यान रखें। / Putting the given values in standard form gives \(2x^2-5x+3=0\). Keep the sign of (b) carefully.
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If (a=1), (b=0), (c=-25), what is the equation?
A. \(x^2-25=0\)
\(ax^2+bx+c=0\) में रखने पर \(x^2+0x-25=0\) मिलता है। इसे \(x^2-25=0\) लिखते हैं। / Substituting in \(ax^2+bx+c=0\) gives \(x^2+0x-25=0\). This is written as \(x^2-25=0\).
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Which equation becomes \(x^2-7x+10=0\) after writing in standard form?
A. \(x^2-7x=-10\)
\(x^2-7x=-10\) में (-10) को बाईं ओर लाने पर (+10) बनता है। इसलिए मानक रूप \(x^2-7x+10=0\) है। / In \(x^2-7x=-10\), moving (-10) to the left gives (+10). So the standard form is \(x^2-7x+10=0\).
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What is the maximum number of real solutions possible for \(x^2+3x+2=0\)?
B. (2)
द्विघात समीकरण के अधिकतम (2) वास्तविक हल हो सकते हैं। आसान प्रश्न में घात से अधिकतम हल का संकेत मिलता है। / A quadratic equation can have at most (2) real solutions. In easy questions, degree indicates the maximum possible solutions.
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What is the value of (a+b+c) for \(4x^2+4x+1=0\)?
C. (9)
यहां (a=4), (b=4), (c=1) हैं। इसलिए (a+b+c=9) है। / Here (a=4), (b=4), (c=1). Therefore (a+b+c=9).
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What is the value of (a-b+c) for \(2x^2-3x-5=0\)?
A. (0)
यहां (a=2), (b=-3), (c=-5) हैं। इसलिए (a-b+c=2-(-3)-5=0) है। / Here (a=2), (b=-3), (c=-5). Thus (a-b+c=2-(-3)-5=0).
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What is the degree of \(5x^2+2x-1=0\)?
C. (2)
सबसे बड़ी घात (2) है। इसलिए समीकरण द्विघात है। / The highest power is (2). Therefore the equation is quadratic.
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Which option is the factor form of \(x^2-2x-15=0\)?
A. \((x-5)(x+3)=0\)
((x-5)(x+3)) फैलाने पर \(x^2-2x-15\) मिलता है। गुणनखंड जांचने के लिए विस्तार करें। / Expanding ((x-5)(x+3)) gives \(x^2-2x-15\). To check factors, expand them.
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If a rectangle has length (x+3) and width (x), and area (10), what equation is formed?
A. (x(x+3)=10)
क्षेत्रफल लंबाई और चौड़ाई का गुणनफल होता है। इसलिए समीकरण (x(x+3)=10) बनेगा। / Area is the product of length and width. So the equation is (x(x+3)=10).
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A. (x(x+1)=30)
लगातार अगला पूर्णांक (x+1) होगा। गुणनफल (30) है इसलिए (x(x+1)=30) बनेगा। / The next consecutive integer is (x+1). Since the product is (30), the equation is (x(x+1)=30).
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Which option shows the common mistake while converting \(x^2=5x-6\) to standard form?
B. \(x^2-5x-6=0\)
सही रूप \(x^2-5x+6=0\) है। विकल्प (B) में (-6) का चिन्ह नहीं बदला गया। / The correct form is \(x^2-5x+6=0\). In option (B), the sign of (-6) was not changed.
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Which equation has (x=0) as a solution?
A. \(x^2+5x=0\)
(x=0) रखने पर विकल्प (A) में (0=0) मिलता है। हल जांचने का सबसे सरल तरीका प्रत्यक्ष प्रतिस्थापन है। / Putting (x=0) in option (A) gives (0=0). Direct substitution is the simplest way to check a solution.
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If \(x^2+kx+12=0\) is a quadratic equation, then (k) is the coefficient of which term?
B. (x) पद(x) term
मानक रूप \(ax^2+bx+c=0\) में (x) का गुणांक (b) होता है। यहां (kx) में (k) (x) का गुणांक है। / In \(ax^2+bx+c=0\), (b) is the coefficient of (x). Here in (kx), (k) is the coefficient of (x).
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Related questions grouped automatically for chapter-wise practice. Topics include Methods of Solving Quadratic Equations, Nature of Roots, Roots of a Quadratic Equation, Word Problems and Applications, Introduction to Quadratic Equations.
Start with Easy MCQs, review explanations after every answer, then move to Medium, Hard and Expert timed quizzes for stronger exam preparation.
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