Practice focused topic-wise MCQs with answers and explanations for quick revision and exam preparation.
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A. (a) संख्या (b) से छोटी है(a) is less than (b)
चिह्न (<) छोटी संख्या को दर्शाता है। परीक्षा में चिह्न की दिशा ध्यान से देखें। / The symbol (<) shows the smaller value. In exams read the direction of the sign carefully.
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What is the correct meaning of the inequality \(x\ge 7\)?
B. (x) (7) से बड़ा या बराबर है(x) is greater than or equal to (7)
चिह्न \(\ge\) में बराबर होना भी शामिल है। खुले और बंद बिंदु का अंतर याद रखें। / The symbol \(\ge\) also includes equality. Remember the difference between open and closed points.
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Which of the following is a linear inequality?
A. (2x+3<9)
(2x+3<9) में चर की घात (1) है इसलिए यह रैखिक है। रैखिक असमानता में \(x^2\) या (xy) नहीं होता। / In (2x+3<9), the variable has power (1), so it is linear. A linear inequality does not contain \(x^2\) or (xy).
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C. (3)
(3<4) सत्य है इसलिए (x=3) समाधान है। मान रखकर जाँच करना सबसे सरल तरीका है। / Since (3<4) is true, (x=3) is a solution. Substitution is the simplest checking method.
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For (x=2), how is the statement \(x\le 2\)?
A. सत्यTrue
\(\le\) में बराबरी शामिल होती है इसलिए \(2\le 2\) सत्य है। परीक्षा में \(\le\) और (<) को अलग रखें। / The sign \(\le\) includes equality, so \(2\le 2\) is true. In exams distinguish \(\le\) from (<).
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How do we write the sentence (y) is more than (10) as an inequality?
B. (y>10)
अधिक है का अर्थ (>) होता है। भाषा को प्रतीक में बदलते समय मुख्य शब्द पहचानें। / More than means (>). When translating language to symbols, identify the key phrase.
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What is the correct form of the sentence (p) is not more than (12)?
C. \(p\le 12\)
अधिक नहीं है का अर्थ अधिकतम (12) है यानी \(p\le 12\)। ऐसे शब्दों में बराबरी अक्सर शामिल होती है। / Not more than means at most (12), so \(p\le 12\). Such phrases often include equality.
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If (x>3), what do we get after adding (2) to both sides?
A. (x+2>5)
दोनों ओर समान संख्या जोड़ने से असमानता की दिशा नहीं बदलती। जोड़ या घटाव में चिह्न वैसा ही रहता है। / Adding the same number to both sides does not change the inequality direction. In addition or subtraction the sign stays the same.
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If (m<6), what happens after multiplying both sides by (4)?
A. (4m<24)
धनात्मक संख्या से गुणा करने पर चिह्न नहीं पलटता। केवल ऋणात्मक गुणा या भाग में चिह्न पलटता है। / Multiplying by a positive number does not reverse the sign. The sign reverses only with negative multiplication or division.
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If (x>5), which inequality is correct after multiplying both sides by (-1)?
B. (-x< -5)
ऋणात्मक संख्या से गुणा करने पर असमानता का चिह्न पलट जाता है। यह बहुत सामान्य गलती है। / When multiplying by a negative number, the inequality sign reverses. This is a very common mistake.
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