Practice focused topic-wise MCQs with answers and explanations for quick revision and exam preparation.
Difficulty select karke sirf is topic ke focused MCQs practice karein. Score, timer aur explanations student-friendly flow me milenge.
Showing 121-130 of 600 questions.
State the nature of roots of \(5x^2-20x+20=0\).
A. वास्तविक और समानReal and equal
इसमें (D=0) है इसलिए दोनों मूल बराबर होंगे। (D=0) का मतलब समान मूल होता है। / Here (D=0), so both roots will be equal. (D=0) means equal roots.
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If a quadratic equation has (D=25), what will be the nature of roots?
A. वास्तविक, परिमेय और भिन्नReal, rational and distinct
(25>0) है और (25) पूर्ण वर्ग है। इसलिए मूल वास्तविक, परिमेय और भिन्न होंगे। / (25>0) and (25) is a perfect square. Therefore the roots are real, rational and distinct.
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If a quadratic equation has (D=5), what is the correct conclusion?
A. मूल वास्तविक, अपरिमेय और भिन्न हैंRoots are real, irrational and distinct
(5>0) है लेकिन (5) पूर्ण वर्ग नहीं है। इसलिए मूल वास्तविक, अपरिमेय और भिन्न होंगे। / (5>0), but (5) is not a perfect square. So the roots are real, irrational and distinct.
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If a quadratic equation has (D=-9), which option is correct?
A. कोई वास्तविक मूल नहींNo real roots
क्योंकि (-9<0) है इसलिए (D<0) होगा। अतः वास्तविक मूल नहीं होंगे। / Because (-9<0), we have (D<0). Hence there will be no real roots.
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If the roots of \(x^2+kx+16=0\) are equal, what is the value of \(k^2\)?
A. (64)
समान मूलों के लिए (D=0) होता है इसलिए \(k^2-64=0\)। अतः \(k^2=64\) है। / For equal roots (D=0), so \(k^2-64=0\). Therefore \(k^2=64\).
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If the roots of \(x^2+kx+16=0\) are equal, which is one possible value of (k)?
A. (8)
\(k^2=64\) से (k=8) या (k=-8) मिलता है। दिए गए विकल्पों में (8) सही है। / From \(k^2=64\), we get (k=8) or (k=-8). Among the given options (8) is correct.
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If the roots of \(x^2+px+6=0\) are real and distinct, which condition is correct for (p)?
A. \(p^2>24\)
वास्तविक और भिन्न मूलों के लिए (D>0) होता है। इसलिए \(p^2-24>0\), अर्थात \(p^2>24\)। / For real and distinct roots (D>0). So \(p^2-24>0\), that is \(p^2>24\).
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If \(x^2+qx+10=0\) has no real roots, what is the correct condition for (q)?
A. \(q^2<40\)
वास्तविक मूल नहीं होने के लिए (D<0) चाहिए। इसलिए \(q^2-40<0\), अर्थात \(q^2<40\)। / For no real roots, (D<0) is needed. So \(q^2-40<0\), that is \(q^2<40\).
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If the roots of \(mx^2+6x+3=0\) are equal, what will be the value of (m)?
A. (3)
समान मूलों के लिए (D=0) है इसलिए (62-4(m)(3)=0)। इससे (m=3) मिलता है। / For equal roots (D=0), so (62-4(m)(3)=0). This gives (m=3).
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If the roots of \(2x^2+nx+8=0\) are equal, what will be \(n^2\)?
A. (64)
(D=0) रखने पर (n-2-4(2)(8)=0) मिलता है। इसलिए \(n^2=64\) है। / Putting (D=0), we get (n-2-4(2)(8)=0). Therefore \(n^2=64\).
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