Related questions grouped automatically for chapter-wise practice. Topics include representation on number line, Introduction to inequalities, algebraic solution of linear inequalities in one variable, Graphical solution of linear inequalities in two variables.
Related questions grouped automatically for chapter-wise practice.
Mathematics Linear Inequalities 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 Linear Inequalities ko easy tarike se practice aur revise kar sake.
Difficulty select karke Mathematics / Linear Inequalities chapter-filtered timed practice karein. Har button me live question count show hoga.
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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What is the solution of (x+4<9)?
A. (x<5)
दोनों ओर (4) घटाने पर (x<5) मिलता है। सरल असमानताओं में संतुलन विधि अपनाएँ। / Subtracting (4) from both sides gives (x<5). Use the balance method for simple inequalities.
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Which is the solution of \(x-3\le 7\)?
B. \(x\le 10\)
दोनों ओर (3) जोड़ने पर \(x\le 10\) मिलता है। \(\le\) का चिह्न जोड़ने से नहीं बदलता। / Adding (3) to both sides gives \(x\le 10\). The sign \(\le\) does not change by addition.
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What is the solution of (2x>10)?
A. (x>5)
दोनों ओर (2) से भाग देने पर (x>5) मिलता है। धनात्मक भाग में चिह्न नहीं बदलता। / Dividing both sides by (2) gives (x>5). Division by a positive number does not reverse the sign.
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Which is the correct solution of (-2x<8)?
B. (x> -4)
दोनों ओर (-2) से भाग देने पर चिह्न पलटेगा इसलिए (x>-4)। ऋणात्मक भाग में दिशा बदलना न भूलें। / Dividing by (-2) reverses the sign, so (x>-4). Do not forget sign reversal in negative division.
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Which (x) is a solution of \(3x\le 12\)?
B. (4)
(x=4) रखने पर \(3\cdot 4\le 12\) सत्य है। विकल्पों में मान रखकर जल्दी जाँच करें। / For (x=4), \(3\cdot 4\le 12\) is true. Substitute options for a quick check.
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Which value satisfies (2x+1>9)?
C. (5)
हल (x>4) है इसलिए (5) संतुष्ट करता है। पहले सीमा निकालें फिर विकल्प चुनें। / The solution is (x>4), so (5) satisfies it. First find the boundary, then choose the option.
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For \(x\ge -2\), which number line representation is correct?
B. (-2) पर बंद बिंदु और दाईं ओरClosed circle at (-2) and right side
\(\ge\) में (-2) शामिल है और बड़ी संख्याएँ दाईं ओर हैं। बंद बिंदु बराबरी को दिखाता है। / The sign \(\ge\) includes (-2), and greater numbers are to the right. A closed circle shows equality.
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Which inequality is represented by the interval (\(-\infty,5\))?
A. (x<5)
कोष्ठक ((5)) बताता है कि (5) शामिल नहीं है। (\(-\infty,5\)) का अर्थ (x<5) है। / The parenthesis at (5) shows that (5) is not included. (\(-\infty,5\)) means (x<5).
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What is the correct inequality form of the interval \([2,\infty\))?
B. \(x\ge 2\)
वर्ग कोष्ठक ([2) बताता है कि (2) शामिल है। दाईं ओर जाने का अर्थ \(x\ge 2\) है। / The square bracket at (2) shows that (2) is included. Moving right means \(x\ge 2\).
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Which value is not included in \(0\le x\le 6\)?
D. (7)
(7) संख्या (6) से बड़ी है इसलिए शामिल नहीं है। \(\le\) में केवल सीमा तक के मान आते हैं। / The number (7) is greater than (6), so it is not included. The sign \(\le\) includes values only up to the boundary.
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Which of the following statements is true?
B. \(3\le 3\)
\(3\le 3\) सत्य है क्योंकि बराबरी शामिल है। ऐसे प्रश्नों में हर विकल्प अलग से जाँचें। / The statement \(3\le 3\) is true because equality is included. Check each option separately in such questions.
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If \(r\le 9\), which value is definitely possible?
C. (9)
\(r\le 9\) में (9) और उससे छोटी संख्याएँ आती हैं। बराबरी वाले चिह्न में सीमा मान भी समाधान होता है। / In \(r\le 9\), (9) and numbers smaller than (9) are included. With equality signs, the boundary value is also a solution.
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To pass an exam, marks must be (40) or more. If the marks are (s), what is the correct inequality?
B. \(s\ge 40\)
(40) या अधिक का अर्थ \(s\ge 40\) है। शब्द या अधिक बराबरी को शामिल करता है। / (40) or more means \(s\ge 40\). The phrase or more includes equality.
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A bag weight should not exceed (15) kilograms. If the weight is (w), what is the correct inequality?
B. \(w\le 15\)
से अधिक नहीं का अर्थ अधिकतम (15) है इसलिए \(w\le 15\)। वास्तविक जीवन में अधिकतम शब्द \(\le\) देता है। / Not exceed means at most (15), so \(w\le 15\). In real-life statements, maximum gives \(\le\).
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A ticket price is less than (100) rupees. If the price is (p), which inequality is correct?
A. (p<100)
से कम का अर्थ सख्त रूप से कम है इसलिए (p<100)। यदि बराबर भी शामिल हो तो \(\le\) लिखा जाता है। / Less than means strictly smaller, so (p<100). If equality is included, we use \(\le\).
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C. \(a\ge 18\)
कम नहीं का अर्थ कम से कम (18) है इसलिए \(a\ge 18\)। कम से कम हमेशा \(\ge\) से जुड़ा होता है। / Not less than means at least (18), so \(a\ge 18\). At least is always linked with \(\ge\).
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If (x=2), which inequality is true?
C. \(x\le 2\)
\(2\le 2\) सत्य है क्योंकि बराबरी शामिल है। विकल्प में (x) की जगह दिया मान रखें। / \(2\le 2\) is true because equality is included. Put the given value in place of (x).
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Which is the solution of \(x+1\ge 6\)?
A. \(x\ge 5\)
दोनों ओर (1) घटाने पर \(x\ge 5\) मिलता है। जोड़ घटाव में दिशा वही रहती है। / Subtracting (1) from both sides gives \(x\ge 5\). In addition or subtraction, the direction stays the same.
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What is the correct solution of (5-x>2)?
A. (x<3)
(5-x>2) से (-x>-3) और ऋणात्मक से भाग देने पर (x<3)। (-x) आने पर चिह्न पलटना याद रखें। / From (5-x>2), we get (-x>-3), and dividing by a negative gives (x<3). When (-x) appears, remember to reverse the sign.
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Which is the solution of \(4x+2\le 14\)?
A. \(x\le 3\)
पहले (2) घटाएँ फिर (4) से भाग दें तो \(x\le 3\)। दो चरणों वाले प्रश्न में क्रम सही रखें। / First subtract (2), then divide by (4), giving \(x\le 3\). Keep the order correct in two-step questions.
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What is the correct solution of \(3-2x\le 9\)?
A. \(x\ge -3\)
\(3-2x\le 9\) से \(-2x\le 6\) और (-2) से भाग देने पर \(x\ge -3\)। ऋणात्मक भाग दिशा पलटता है। / From \(3-2x\le 9\), we get \(-2x\le 6\), and division by (-2) gives \(x\ge -3\). Negative division reverses the direction.
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Which statement is correct for \(x\le -1\)?
B. समाधान (-1) और उससे बाईं ओर हैंSolutions are (-1) and to its left
\(\le\) में सीमा और उससे छोटी संख्याएँ शामिल होती हैं। संख्या रेखा पर छोटी संख्याएँ बाईं ओर होती हैं। / The sign \(\le\) includes the boundary and smaller numbers. On the number line, smaller numbers are to the left.
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What is the interval form of (x>-4)?
A. (\(-4,\infty\))
(x>-4) में (-4) शामिल नहीं है और मान दाईं ओर हैं। इसलिए अंतराल (\(-4,\infty\)) है। / In (x>-4), (-4) is not included and values lie to the right. So the interval is (\(-4,\infty\)).
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Which is the interval form of \(x\le 0\)?
C. (\(-\infty,0]\)
\(x\le 0\) में (0) शामिल है और छोटी संख्याएँ बाईं ओर हैं। इसलिए (\(-\infty,0]\) सही है। / In \(x\le 0\), (0) is included and smaller numbers are to the left. So (\(-\infty,0]\) is correct.
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Which option correctly describes \(2\le x<5\)?
C. (x) (2) या उससे बड़ा और (5) से छोटा है(x) is (2) or more and less than (5)
\(2\le x<5\) में (2) शामिल है पर (5) शामिल नहीं है। संयुक्त असमानता को दो भागों में पढ़ें। / In \(2\le x<5\), (2) is included but (5) is not. Read a compound inequality in two parts.
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If (x) is a natural number and (x<4), what are the possible values?
A. \(x\in{1,2,3}\)
प्राकृतिक संख्याएँ (1) से शुरू मानी जाती हैं और (4) शामिल नहीं है। इसलिए मान (1,2,3) हैं। / Natural numbers are taken from (1), and (4) is not included. Therefore the values are (1,2,3).
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If (x) is an integer and \(-2<x\le 2\), what are the values of (x)?
B. \(x\in{-1,0,1,2}\)
(-2) शामिल नहीं है पर (2) शामिल है। पूर्णांक मान (-1,0,1,2) होंगे। / The value (-2) is not included, but (2) is included. The integer values are (-1,0,1,2).
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Which inequality shows that (x) is at least (6)?
C. \(x\ge 6\)
कम से कम (6) का अर्थ (6) या उससे अधिक है। इसलिए सही चिह्न \(\ge\) है। / At least (6) means (6) or more. Therefore the correct sign is \(\ge\).
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Which inequality shows that (n) is at most (20)?
A. \(n\le 20\)
अधिकतम (20) का अर्थ (20) या उससे कम है। इसलिए \(n\le 20\) सही है। / At most (20) means (20) or less. Therefore \(n\le 20\) is correct.
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If (a>b) and (k>0), which statement is correct?
A. (ak>bk)
धनात्मक संख्या से गुणा करने पर दिशा वही रहती है। (k>0) होने की शर्त जरूरी है। / Multiplication by a positive number keeps the direction the same. The condition (k>0) is important.
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What is the solution of (x+7>7)?
A. (x>0)
दोनों ओर (7) घटाने पर (x>0) मिलता है। समान पद हटाकर सरल रूप बनाइए। / Subtracting (7) from both sides gives (x>0). Remove equal terms to get the simple form.
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What is the solution of \(\frac{x}{3}\le 2\)?
A. \(x\le 6\)
दोनों ओर (3) से गुणा करने पर \(x\le 6\) मिलता है। धनात्मक गुणा में चिह्न नहीं पलटता। / Multiplying both sides by (3) gives \(x\le 6\). Positive multiplication does not reverse the sign.
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What is the correct solution of \(\frac{x}{-4}>1\)?
B. (x<-4)
दोनों ओर (-4) से गुणा करने पर चिह्न पलटेगा इसलिए (x<-4)। ऋणात्मक गुणा में दिशा बदलती है। / Multiplying both sides by (-4) reverses the sign, so (x<-4). Negative multiplication changes the direction.
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Which is the solution of (6<2x)?
A. (x>3)
दोनों ओर (2) से भाग देने पर (3<x) यानी (x>3) मिलता है। रूप बदलते समय चिह्न की दिशा अर्थ से जाँचें। / Dividing both sides by (2) gives (3<x), that is (x>3). When rewriting, check the meaning of the sign direction.
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Which value satisfies the inequality (2x-1<7)?
B. (x=4)
(2x-1<7) से (2x<8) और (x<4) मिलता है इसलिए सीमा के पास (x=4) संतुष्ट नहीं करता बल्कि सही जाँच में \(2\cdot4-1=7\) है इसलिए यह सख्त नहीं है। सही विकल्प को जाँचते समय सख्त चिह्न का ध्यान रखें। / From (2x-1<7), we get (2x<8) and (x<4), so (x=4) does not satisfy the strict inequality. Check strict signs carefully while testing options.
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If (x) is an integer and \(3\le x<7\), how many values are possible?
B. (4)
संभव पूर्णांक (3,4,5,6) हैं इसलिए कुल (4) मान हैं। \(\le\) में बायां सिरा शामिल है पर (<) में दायां सिरा शामिल नहीं है। / The possible integers are (3,4,5,6), so there are (4) values. The sign \(\le\) includes the left endpoint but (<) excludes the right endpoint.
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Which is the solution of \(7-3x\ge 1\)?
A. \(x\le 2\)
\(7-3x\ge 1\) से \(-3x\ge -6\) और (-3) से भाग देने पर \(x\le 2\) मिलता है। ऋणात्मक संख्या से भाग देते समय चिह्न पलटता है। / From \(7-3x\ge 1\), we get \(-3x\ge -6\), and dividing by (-3) gives \(x\le 2\). The sign reverses when dividing by a negative number.
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How do we write the interval ((1,6]) as an inequality?
A. \(1<x\le 6\)
((1) बताता है कि (1) शामिल नहीं है और (6]) बताता है कि (6) शामिल है। इसलिए \(1<x\le 6\) सही है। / The symbol ((1) shows that (1) is not included and (6]) shows that (6) is included. Therefore \(1<x\le 6\) is correct.
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B. \(25\le n\le 40\)
कम से कम (25) का अर्थ \(n\ge 25\) और अधिकतम (40) का अर्थ \(n\le 40\) है। दोनों को मिलाकर \(25\le n\le 40\) मिलता है। / At least (25) means \(n\ge 25\), and at most (40) means \(n\le 40\). Combining both gives \(25\le n\le 40\).
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What is the correct solution of the inequality (9<3x+3)?
A. (x>2)
पहले दोनों ओर (3) घटाएँ तो (6<3x) मिलता है और फिर (3) से भाग देने पर (x>2) आता है। असमानता को पलटकर लिखते समय दिशा का अर्थ जरूर जाँचें। / First subtract (3) from both sides to get (6<3x), then divide by (3) to get (x>2). When rewriting an inequality, always check the meaning of its direction.
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Related questions grouped automatically for chapter-wise practice. Topics include representation on number line, Introduction to inequalities, algebraic solution of linear inequalities in one variable, Graphical solution of linear inequalities in two variables.
Start with Easy MCQs, review explanations after every answer, then move to Medium, Hard and Expert timed quizzes for stronger exam preparation.
Yes, this page includes topic-wise practice such as representation on number line, Introduction to inequalities, algebraic solution of linear inequalities in one variable, Graphical solution of linear inequalities in two variables.
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