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 351-360 of 591 questions.
What is the correct solution of (4-7x>18)?
A. (x<-2)
(4-7x>18) से (-7x>14) और (x<-2) मिलता है। ऋणात्मक (-7) से भाग देते समय चिन्ह पलटना न भूलें। / From (4-7x>18), we get (-7x>14), hence (x<-2). Do not forget to reverse the sign when dividing by negative (-7).
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If (7-4x>19), which solution for (x) is correct?
A. (x<-3)
(7-4x>19) से (-4x>12) और (x<-3) मिलता है। ऋणात्मक संख्या से भाग देते समय असमता का चिन्ह पलटता है। / From (7-4x>19), we get (-4x>12), so (x<-3). The inequality sign reverses when dividing by a negative number.
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If \(x\in\mathbb{R}\) and \(-7<2x+5\leq 13\), which solution for (x) is correct?
A. \(-6<x\leq 4\)
(5) घटाने पर \(-12<2x\leq 8\) और फिर \(-6<x\leq 4\) मिलता है। संयुक्त असमता में हर भाग पर समान क्रिया करें। / Subtracting (5) gives \(-12<2x\leq 8\), then \(-6<x\leq 4\). Apply the same operation to every part of a compound inequality.
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If \(x\in\mathbb{R}\) and \(\frac{5-2x}{3}\geq \frac{x+1}{6}\), which solution for (x) is correct?
A. \(x\leq 3\)
(6) से गुणा करने पर \(10-4x\geq x+1\) और \(9\geq 5x\) मिलता है। इसलिए \(x\leq \frac{9}{5}\) होता है, अतः सही विकल्पों में कोई नहीं होना चाहिए। / Multiplying by (6) gives \(10-4x\geq x+1\), so \(9\geq 5x\). Therefore \(x\leq \frac{9}{5}\), so none of the listed options should be correct.
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What is the solution of (5(2x-3)\leq 3x+20)?
A. \(x\leq 5\)
सरलीकरण से \(10x-15\leq 3x+20\) और \(7x\leq 35\) मिलता है। कोष्ठक खोलने के बाद समान पदों को सही ओर रखें। / Simplifying gives \(10x-15\leq 3x+20\), so \(7x\leq 35\). After opening brackets, place like terms correctly.
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What is the solution of \(\frac{3-x}{-4}<2\)?
A. (x<11)
(-4) से गुणा करने पर चिन्ह पलटकर (3-x>-8) मिलता है। इससे (-x>-11) और (x<11) प्राप्त होता है। / Multiplying by (-4) reverses the sign and gives (3-x>-8). This gives (-x>-11), so (x<11).
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If \(x\in\mathbb{Z}\) and (4x+9<1), what is the greatest possible (x)?
C. (-2)
असमता से (4x<-8) इसलिए (x<-2) मिलता है। सबसे बड़ा पूर्णांक हल (-3) नहीं बल्कि (-3) से पहले जांचें और सही मान (-3) होगा। / The inequality gives (4x<-8), so (x<-2). The greatest integer less than (-2) is (-3).
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A. \(2x-5\geq x+3,\ x\geq 8\)
कम नहीं है का अर्थ \(\geq\) होता है। \(2x-5\geq x+3\) से \(x\geq 8\) मिलता है। / Not less than means \(\geq\). From \(2x-5\geq x+3\), we get \(x\geq 8\).
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How is the interval (\(-\infty,-6]\) written as an inequality?
B. \(x\leq -6\)
दायां सिरा (-6) बंद है इसलिए (-6) शामिल होगा। अतः असमता \(x\leq -6\) है। / The right endpoint (-6) is closed, so (-6) is included. Therefore the inequality is \(x\leq -6\).
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If \(x\in\mathbb{Z}\) and \(-2\leq \frac{x-1}{3}<3\), how many integer solutions are there?
B. (15)
(3) से गुणा करने पर \(-6\leq x-1<9\), इसलिए \(-5\leq x<10\) मिलता है। पूर्णांक (-5) से (9) तक हैं, कुल (15)। / Multiplying by (3) gives \(-6\leq x-1<9\), so \(-5\leq x<10\). The integers from (-5) to (9) are (15) in total.
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