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 311-320 of 550 questions.
If the roots of \(x^2-6x+k=0\) are real and distinct, what is the correct condition on (k)?
A. (k<9)
भिन्न वास्तविक मूलों के लिए (D>0) चाहिए। यहाँ (36-4k>0), इसलिए (k<9)। / For real and distinct roots, (D>0) is needed. Here (36-4k>0), so (k<9).
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Which equation has discriminant (-15)?
A. \(x^2+x+4=0\)
\(x^2+x+4=0\) के लिए \(D=1^2-4\cdot1\cdot4=-15\) है। विवेचक निकालते समय (4ac) पूरा घटाएं। / For \(x^2+x+4=0\), \(D=1^2-4\cdot1\cdot4=-15\). Subtract the full (4ac) while finding the discriminant.
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If one root of \(x^2+ax+12=0\) is (3), what are the other root and (a)?
A. दूसरा मूल (4), (a=-7)other root (4), (a=-7)
मूलों का गुणनफल (12) है, इसलिए दूसरा मूल (4) होगा। योग (7) है और (-a=7), इसलिए (a=-7)। / The product of roots is (12), so the other root is (4). The sum is (7), and (-a=7), so (a=-7).
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What is the sum of squares of the roots of \(2x^2+7x+3=0\)?
A. \( \frac{37}{4} \)
यदि मूल \(\alpha,\beta\) हैं, तो (\alpha-2+\beta-2=\(\alpha+\beta\)2-2\alpha\beta)। यहाँ (\left\(-\frac{7}{2}\right\)2-2\cdot\frac{3}{2}=\frac{37}{4})। / If the roots are \(\alpha,\beta\), then (\alpha-2+\beta-2=\(\alpha+\beta\)2-2\alpha\beta). Here (\left\(-\frac{7}{2}\right\)2-2\cdot\frac{3}{2}=\frac{37}{4}).
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If \(\alpha\) and \(\beta\) are roots of \(x^2-8x+15=0\), what is (\(\alpha-1\)\(\beta-1\))?
A. (8)
(\(\alpha-1\)\(\beta-1\)=\alpha\beta-\(\alpha+\beta\)+1) होता है। यहाँ (15-8+1=8)। / (\(\alpha-1\)\(\beta-1\)=\alpha\beta-\(\alpha+\beta\)+1). Here (15-8+1=8).
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In which option will the given equation not remain quadratic?
A. ((t-2)x-2+5x+1=0), (t=2)
पहले विकल्प में (t=2) रखने पर \(x^2\) का गुणांक (0) हो जाता है। तब समीकरण रैखिक बन जाता है। / In the first option, putting (t=2) makes the coefficient of \(x^2\) equal to (0). Then the equation becomes linear.
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What is the standard form of ((x+1)(x+2)+(x+3)(x+4)=50)?
A. \(2x^2+10x-36=0\)
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। / The left side is \(x^2+3x+2+x^2+7x+12=2x^2+10x+14\). Subtracting (50) gives \(2x^2+10x-36=0\).
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If the roots of \(x^2+px+q=0\) are (p) and (q) themselves, which relation is correct?
A. (p+q=-p) और (pq=q)(p+q=-p) and (pq=q)
मूलों का योग (-p) और गुणनफल (q) होता है। दिए मूल (p,q) हैं, इसलिए (p+q=-p) और (pq=q)। / The sum of roots is (-p) and the product is (q). Since the roots are (p,q), we get (p+q=-p) and (pq=q).
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Which statement is correct for \(x^2-4x+6=0\)?
A. वास्तविक मूल नहीं हैंIt has no real roots
यहाँ (D=(-4)2-4\cdot1\cdot6=-8<0) है। इसलिए वास्तविक मूल नहीं होंगे। / Here (D=(-4)2-4\cdot1\cdot6=-8<0). Therefore it has no real roots.
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If one root of (x-2-(m+2)x+2m=0) is (2), what is the other root?
A. (m)
गुणनफल (2m) है और एक मूल (2) है। इसलिए दूसरा मूल \(\frac{2m}{2}=m\) है। / The product of roots is (2m) and one root is (2). Hence the other root is \(\frac{2m}{2}=m\).
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