Class 11 Chapter Practice

Mathematics Linear Inequalities MCQ Questions for Class 11

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.

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Class 11 Mathematics Linear Inequalities Practice

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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.

representation on number line
592 MCQs
Introduction to inequalities
590 MCQs
algebraic solution of linear inequalities in one variable
583 MCQs
Graphical solution of linear inequalities in two variables
575 MCQs

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Mathematics Linear Inequalities MCQ Questions

Question 1/50 Easy Mathematics Linear Inequalities Introduction to inequalities Class 11 Level 40

यदि (a<b) है तो यह क्या बताता है?

If (a<b), what does it mean?

Explanation opens after your attempt

Correct Answer

A. (a) संख्या (b) से छोटी है(a) is less than (b)

Step 1

Concept

The symbol (<) shows the smaller value. In exams read the direction of the sign carefully.

Step 2

Why this answer is correct

The correct answer is A. (a) संख्या (b) से छोटी है / (a) is less than (b). The symbol (<) shows the smaller value. In exams read the direction of the sign carefully.

Step 3

Exam Tip

चिह्न (<) छोटी संख्या को दर्शाता है। परीक्षा में चिह्न की दिशा ध्यान से देखें।

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Question 2/50 Easy Mathematics Linear Inequalities Introduction to inequalities Class 11 Level 40

असमानता \(x\ge 7\) का सही अर्थ क्या है?

What is the correct meaning of the inequality \(x\ge 7\)?

Explanation opens after your attempt

Correct Answer

B. (x) (7) से बड़ा या बराबर है(x) is greater than or equal to (7)

Step 1

Concept

The symbol \(\ge\) also includes equality. Remember the difference between open and closed points.

Step 2

Why this answer is correct

The correct answer is B. (x) (7) से बड़ा या बराबर है / (x) is greater than or equal to (7). The symbol \(\ge\) also includes equality. Remember the difference between open and closed points.

Step 3

Exam Tip

चिह्न \(\ge\) में बराबर होना भी शामिल है। खुले और बंद बिंदु का अंतर याद रखें।

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Question 3/50 Easy Mathematics Linear Inequalities Introduction to inequalities Class 11 Level 40

इनमें से कौन सी रैखिक असमानता है?

Which of the following is a linear inequality?

Explanation opens after your attempt

Correct Answer

A. (2x+3<9)

Step 1

Concept

In (2x+3<9), the variable has power (1), so it is linear. A linear inequality does not contain \(x^2\) or (xy).

Step 2

Why this answer is correct

The correct answer is A. (2x+3<9). In (2x+3<9), the variable has power (1), so it is linear. A linear inequality does not contain \(x^2\) or (xy).

Step 3

Exam Tip

(2x+3<9) में चर की घात (1) है इसलिए यह रैखिक है। रैखिक असमानता में \(x^2\) या (xy) नहीं होता।

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Question 4/50 Easy Mathematics Linear Inequalities Introduction to inequalities Class 11 Level 40

कौन सा मान (x<4) को संतुष्ट करता है?

Which value satisfies (x<4)?

Explanation opens after your attempt

Correct Answer

C. (3)

Step 1

Concept

Since (3<4) is true, (x=3) is a solution. Substitution is the simplest checking method.

Step 2

Why this answer is correct

The correct answer is C. (3). Since (3<4) is true, (x=3) is a solution. Substitution is the simplest checking method.

Step 3

Exam Tip

(3<4) सत्य है इसलिए (x=3) समाधान है। मान रखकर जाँच करना सबसे सरल तरीका है।

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Question 5/50 Easy Mathematics Linear Inequalities Introduction to inequalities Class 11 Level 40

असमानता \(x\le 2\) में (x=2) के लिए कथन कैसा है?

For (x=2), how is the statement \(x\le 2\)?

Explanation opens after your attempt

Correct Answer

A. सत्यTrue

Step 1

Concept

The sign \(\le\) includes equality, so \(2\le 2\) is true. In exams distinguish \(\le\) from (<).

Step 2

Why this answer is correct

The correct answer is A. सत्य / True. The sign \(\le\) includes equality, so \(2\le 2\) is true. In exams distinguish \(\le\) from (<).

Step 3

Exam Tip

\(\le\) में बराबरी शामिल होती है इसलिए \(2\le 2\) सत्य है। परीक्षा में \(\le\) और (<) को अलग रखें।

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Question 6/50 Easy Mathematics Linear Inequalities Introduction to inequalities Class 11 Level 40

वाक्य (y) (10) से अधिक है को असमानता में कैसे लिखेंगे?

How do we write the sentence (y) is more than (10) as an inequality?

Explanation opens after your attempt

Correct Answer

B. (y>10)

Step 1

Concept

More than means (>). When translating language to symbols, identify the key phrase.

Step 2

Why this answer is correct

The correct answer is B. (y>10). More than means (>). When translating language to symbols, identify the key phrase.

Step 3

Exam Tip

अधिक है का अर्थ (>) होता है। भाषा को प्रतीक में बदलते समय मुख्य शब्द पहचानें।

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Question 7/50 Easy Mathematics Linear Inequalities Introduction to inequalities Class 11 Level 40

वाक्य (p) (12) से अधिक नहीं है का सही रूप क्या है?

What is the correct form of the sentence (p) is not more than (12)?

Explanation opens after your attempt

Correct Answer

C. \(p\le 12\)

Step 1

Concept

Not more than means at most (12), so \(p\le 12\). Such phrases often include equality.

Step 2

Why this answer is correct

The correct answer is C. \(p\le 12\). Not more than means at most (12), so \(p\le 12\). Such phrases often include equality.

Step 3

Exam Tip

अधिक नहीं है का अर्थ अधिकतम (12) है यानी \(p\le 12\)। ऐसे शब्दों में बराबरी अक्सर शामिल होती है।

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Question 8/50 Easy Mathematics Linear Inequalities Introduction to inequalities Class 11 Level 40

यदि (x>3) है तो दोनों ओर (2) जोड़ने पर क्या मिलेगा?

If (x>3), what do we get after adding (2) to both sides?

Explanation opens after your attempt

Correct Answer

A. (x+2>5)

Step 1

Concept

Adding the same number to both sides does not change the inequality direction. In addition or subtraction the sign stays the same.

Step 2

Why this answer is correct

The correct answer is A. (x+2>5). Adding the same number to both sides does not change the inequality direction. In addition or subtraction the sign stays the same.

Step 3

Exam Tip

दोनों ओर समान संख्या जोड़ने से असमानता की दिशा नहीं बदलती। जोड़ या घटाव में चिह्न वैसा ही रहता है।

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Question 9/50 Easy Mathematics Linear Inequalities Introduction to inequalities Class 11 Level 40

यदि (m<6) है तो दोनों ओर (4) से गुणा करने पर क्या होगा?

If (m<6), what happens after multiplying both sides by (4)?

Explanation opens after your attempt

Correct Answer

A. (4m<24)

Step 1

Concept

Multiplying by a positive number does not reverse the sign. The sign reverses only with negative multiplication or division.

Step 2

Why this answer is correct

The correct answer is A. (4m<24). Multiplying by a positive number does not reverse the sign. The sign reverses only with negative multiplication or division.

Step 3

Exam Tip

धनात्मक संख्या से गुणा करने पर चिह्न नहीं पलटता। केवल ऋणात्मक गुणा या भाग में चिह्न पलटता है।

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Question 10/50 Easy Mathematics Linear Inequalities Introduction to inequalities Class 11 Level 40

यदि (x>5) है तो दोनों ओर (-1) से गुणा करने पर सही असमानता कौन सी है?

If (x>5), which inequality is correct after multiplying both sides by (-1)?

Explanation opens after your attempt

Correct Answer

B. (-x< -5)

Step 1

Concept

When multiplying by a negative number, the inequality sign reverses. This is a very common mistake.

Step 2

Why this answer is correct

The correct answer is B. (-x< -5). When multiplying by a negative number, the inequality sign reverses. This is a very common mistake.

Step 3

Exam Tip

ऋणात्मक संख्या से गुणा करने पर असमानता का चिह्न पलट जाता है। यह बहुत सामान्य गलती है।

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Question 11/50 Easy Mathematics Linear Inequalities Introduction to inequalities Class 11 Level 40

असमानता (x+4<9) का हल क्या है?

What is the solution of (x+4<9)?

Explanation opens after your attempt

Correct Answer

A. (x<5)

Step 1

Concept

Subtracting (4) from both sides gives (x<5). Use the balance method for simple inequalities.

Step 2

Why this answer is correct

The correct answer is A. (x<5). Subtracting (4) from both sides gives (x<5). Use the balance method for simple inequalities.

Step 3

Exam Tip

दोनों ओर (4) घटाने पर (x<5) मिलता है। सरल असमानताओं में संतुलन विधि अपनाएँ।

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Question 12/50 Easy Mathematics Linear Inequalities Introduction to inequalities Class 11 Level 40

असमानता \(x-3\le 7\) का हल कौन सा है?

Which is the solution of \(x-3\le 7\)?

Explanation opens after your attempt

Correct Answer

B. \(x\le 10\)

Step 1

Concept

Adding (3) to both sides gives \(x\le 10\). The sign \(\le\) does not change by addition.

Step 2

Why this answer is correct

The correct answer is B. \(x\le 10\). Adding (3) to both sides gives \(x\le 10\). The sign \(\le\) does not change by addition.

Step 3

Exam Tip

दोनों ओर (3) जोड़ने पर \(x\le 10\) मिलता है। \(\le\) का चिह्न जोड़ने से नहीं बदलता।

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Question 13/50 Easy Mathematics Linear Inequalities Introduction to inequalities Class 11 Level 40

असमानता (2x>10) का हल क्या है?

What is the solution of (2x>10)?

Explanation opens after your attempt

Correct Answer

A. (x>5)

Step 1

Concept

Dividing both sides by (2) gives (x>5). Division by a positive number does not reverse the sign.

Step 2

Why this answer is correct

The correct answer is A. (x>5). Dividing both sides by (2) gives (x>5). Division by a positive number does not reverse the sign.

Step 3

Exam Tip

दोनों ओर (2) से भाग देने पर (x>5) मिलता है। धनात्मक भाग में चिह्न नहीं बदलता।

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Question 14/50 Easy Mathematics Linear Inequalities Introduction to inequalities Class 11 Level 40

असमानता (-2x<8) का सही हल कौन सा है?

Which is the correct solution of (-2x<8)?

Explanation opens after your attempt

Correct Answer

B. (x> -4)

Step 1

Concept

Dividing by (-2) reverses the sign, so (x>-4). Do not forget sign reversal in negative division.

Step 2

Why this answer is correct

The correct answer is B. (x> -4). Dividing by (-2) reverses the sign, so (x>-4). Do not forget sign reversal in negative division.

Step 3

Exam Tip

दोनों ओर (-2) से भाग देने पर चिह्न पलटेगा इसलिए (x>-4)। ऋणात्मक भाग में दिशा बदलना न भूलें।

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Question 15/50 Easy Mathematics Linear Inequalities Introduction to inequalities Class 11 Level 40

कौन सा (x) असमानता \(3x\le 12\) का समाधान है?

Which (x) is a solution of \(3x\le 12\)?

Explanation opens after your attempt

Correct Answer

B. (4)

Step 1

Concept

For (x=4), \(3\cdot 4\le 12\) is true. Substitute options for a quick check.

Step 2

Why this answer is correct

The correct answer is B. (4). For (x=4), \(3\cdot 4\le 12\) is true. Substitute options for a quick check.

Step 3

Exam Tip

(x=4) रखने पर \(3\cdot 4\le 12\) सत्य है। विकल्पों में मान रखकर जल्दी जाँच करें।

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Question 16/50 Easy Mathematics Linear Inequalities Introduction to inequalities Class 11 Level 40

कौन सा मान (2x+1>9) को संतुष्ट करता है?

Which value satisfies (2x+1>9)?

Explanation opens after your attempt

Correct Answer

C. (5)

Step 1

Concept

The solution is (x>4), so (5) satisfies it. First find the boundary, then choose the option.

Step 2

Why this answer is correct

The correct answer is C. (5). The solution is (x>4), so (5) satisfies it. First find the boundary, then choose the option.

Step 3

Exam Tip

हल (x>4) है इसलिए (5) संतुष्ट करता है। पहले सीमा निकालें फिर विकल्प चुनें।

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Question 17/50 Easy Mathematics Linear Inequalities Introduction to inequalities Class 11 Level 40

असमानता \(x\ge -2\) के लिए संख्या रेखा पर कौन सा चित्र सही होगा?

For \(x\ge -2\), which number line representation is correct?

Explanation opens after your attempt

Correct Answer

B. (-2) पर बंद बिंदु और दाईं ओरClosed circle at (-2) and right side

Step 1

Concept

The sign \(\ge\) includes (-2), and greater numbers are to the right. A closed circle shows equality.

Step 2

Why this answer is correct

The correct answer is B. (-2) पर बंद बिंदु और दाईं ओर / Closed circle at (-2) and right side. The sign \(\ge\) includes (-2), and greater numbers are to the right. A closed circle shows equality.

Step 3

Exam Tip

\(\ge\) में (-2) शामिल है और बड़ी संख्याएँ दाईं ओर हैं। बंद बिंदु बराबरी को दिखाता है।

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Question 18/50 Easy Mathematics Linear Inequalities Introduction to inequalities Class 11 Level 40

अंतराल (\(-\infty,5\)) किस असमानता को दर्शाता है?

Which inequality is represented by the interval (\(-\infty,5\))?

Explanation opens after your attempt

Correct Answer

A. (x<5)

Step 1

Concept

The parenthesis at (5) shows that (5) is not included. (\(-\infty,5\)) means (x<5).

Step 2

Why this answer is correct

The correct answer is A. (x<5). The parenthesis at (5) shows that (5) is not included. (\(-\infty,5\)) means (x<5).

Step 3

Exam Tip

कोष्ठक ((5)) बताता है कि (5) शामिल नहीं है। (\(-\infty,5\)) का अर्थ (x<5) है।

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Question 19/50 Easy Mathematics Linear Inequalities Introduction to inequalities Class 11 Level 40

अंतराल \([2,\infty\)) का सही असमानता रूप क्या है?

What is the correct inequality form of the interval \([2,\infty\))?

Explanation opens after your attempt

Correct Answer

B. \(x\ge 2\)

Step 1

Concept

The square bracket at (2) shows that (2) is included. Moving right means \(x\ge 2\).

Step 2

Why this answer is correct

The correct answer is B. \(x\ge 2\). The square bracket at (2) shows that (2) is included. Moving right means \(x\ge 2\).

Step 3

Exam Tip

वर्ग कोष्ठक ([2) बताता है कि (2) शामिल है। दाईं ओर जाने का अर्थ \(x\ge 2\) है।

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Question 20/50 Easy Mathematics Linear Inequalities Introduction to inequalities Class 11 Level 40

असमानता \(0\le x\le 6\) में कौन सा मान शामिल नहीं है?

Which value is not included in \(0\le x\le 6\)?

Explanation opens after your attempt

Correct Answer

D. (7)

Step 1

Concept

The number (7) is greater than (6), so it is not included. The sign \(\le\) includes values only up to the boundary.

Step 2

Why this answer is correct

The correct answer is D. (7). The number (7) is greater than (6), so it is not included. The sign \(\le\) includes values only up to the boundary.

Step 3

Exam Tip

(7) संख्या (6) से बड़ी है इसलिए शामिल नहीं है। \(\le\) में केवल सीमा तक के मान आते हैं।

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Question 21/50 Easy Mathematics Linear Inequalities Introduction to inequalities Class 11 Level 40

इनमें से कौन सा कथन सत्य है?

Which of the following statements is true?

Explanation opens after your attempt

Correct Answer

B. \(3\le 3\)

Step 1

Concept

The statement \(3\le 3\) is true because equality is included. Check each option separately in such questions.

Step 2

Why this answer is correct

The correct answer is B. \(3\le 3\). The statement \(3\le 3\) is true because equality is included. Check each option separately in such questions.

Step 3

Exam Tip

\(3\le 3\) सत्य है क्योंकि बराबरी शामिल है। ऐसे प्रश्नों में हर विकल्प अलग से जाँचें।

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Question 22/50 Easy Mathematics Linear Inequalities Introduction to inequalities Class 11 Level 40

यदि \(r\le 9\) है तो इनमें से कौन सा मान निश्चित रूप से संभव है?

If \(r\le 9\), which value is definitely possible?

Explanation opens after your attempt

Correct Answer

C. (9)

Step 1

Concept

In \(r\le 9\), (9) and numbers smaller than (9) are included. With equality signs, the boundary value is also a solution.

Step 2

Why this answer is correct

The correct answer is C. (9). In \(r\le 9\), (9) and numbers smaller than (9) are included. With equality signs, the boundary value is also a solution.

Step 3

Exam Tip

\(r\le 9\) में (9) और उससे छोटी संख्याएँ आती हैं। बराबरी वाले चिह्न में सीमा मान भी समाधान होता है।

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Question 23/50 Easy Mathematics Linear Inequalities Introduction to inequalities Class 11 Level 40

किसी परीक्षा में पास होने के लिए अंक (40) या अधिक चाहिए। यदि अंक (s) हैं तो सही असमानता क्या है?

To pass an exam, marks must be (40) or more. If the marks are (s), what is the correct inequality?

Explanation opens after your attempt

Correct Answer

B. \(s\ge 40\)

Step 1

Concept

(40) or more means \(s\ge 40\). The phrase or more includes equality.

Step 2

Why this answer is correct

The correct answer is B. \(s\ge 40\). (40) or more means \(s\ge 40\). The phrase or more includes equality.

Step 3

Exam Tip

(40) या अधिक का अर्थ \(s\ge 40\) है। शब्द या अधिक बराबरी को शामिल करता है।

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Question 24/50 Easy Mathematics Linear Inequalities Introduction to inequalities Class 11 Level 40

एक बैग का वजन (15) किलोग्राम से अधिक नहीं होना चाहिए। यदि वजन (w) है तो सही असमानता क्या है?

A bag weight should not exceed (15) kilograms. If the weight is (w), what is the correct inequality?

Explanation opens after your attempt

Correct Answer

B. \(w\le 15\)

Step 1

Concept

Not exceed means at most (15), so \(w\le 15\). In real-life statements, maximum gives \(\le\).

Step 2

Why this answer is correct

The correct answer is B. \(w\le 15\). Not exceed means at most (15), so \(w\le 15\). In real-life statements, maximum gives \(\le\).

Step 3

Exam Tip

से अधिक नहीं का अर्थ अधिकतम (15) है इसलिए \(w\le 15\)। वास्तविक जीवन में अधिकतम शब्द \(\le\) देता है।

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Question 25/50 Easy Mathematics Linear Inequalities Introduction to inequalities Class 11 Level 40

किसी टिकट की कीमत (100) रुपये से कम है। यदि कीमत (p) है तो सही असमानता कौन सी है?

A ticket price is less than (100) rupees. If the price is (p), which inequality is correct?

Explanation opens after your attempt

Correct Answer

A. (p<100)

Step 1

Concept

Less than means strictly smaller, so (p<100). If equality is included, we use \(\le\).

Step 2

Why this answer is correct

The correct answer is A. (p<100). Less than means strictly smaller, so (p<100). If equality is included, we use \(\le\).

Step 3

Exam Tip

से कम का अर्थ सख्त रूप से कम है इसलिए (p<100)। यदि बराबर भी शामिल हो तो \(\le\) लिखा जाता है।

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Question 26/50 Easy Mathematics Linear Inequalities Introduction to inequalities Class 11 Level 40

किसी क्लब में प्रवेश के लिए आयु (18) वर्ष से कम नहीं होनी चाहिए। यदि आयु (a) है तो सही असमानता क्या है?

For entry to a club, age must not be less than (18) years. If age is (a), what is the correct inequality?

Explanation opens after your attempt

Correct Answer

C. \(a\ge 18\)

Step 1

Concept

Not less than means at least (18), so \(a\ge 18\). At least is always linked with \(\ge\).

Step 2

Why this answer is correct

The correct answer is C. \(a\ge 18\). Not less than means at least (18), so \(a\ge 18\). At least is always linked with \(\ge\).

Step 3

Exam Tip

कम नहीं का अर्थ कम से कम (18) है इसलिए \(a\ge 18\)। कम से कम हमेशा \(\ge\) से जुड़ा होता है।

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Question 27/50 Easy Mathematics Linear Inequalities Introduction to inequalities Class 11 Level 40

यदि (x=2) है तो कौन सी असमानता सत्य है?

If (x=2), which inequality is true?

Explanation opens after your attempt

Correct Answer

C. \(x\le 2\)

Step 1

Concept

\(2\le 2\) is true because equality is included. Put the given value in place of (x).

Step 2

Why this answer is correct

The correct answer is C. \(x\le 2\). \(2\le 2\) is true because equality is included. Put the given value in place of (x).

Step 3

Exam Tip

\(2\le 2\) सत्य है क्योंकि बराबरी शामिल है। विकल्प में (x) की जगह दिया मान रखें।

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Question 28/50 Easy Mathematics Linear Inequalities Introduction to inequalities Class 11 Level 40

असमानता \(x+1\ge 6\) का हल कौन सा है?

Which is the solution of \(x+1\ge 6\)?

Explanation opens after your attempt

Correct Answer

A. \(x\ge 5\)

Step 1

Concept

Subtracting (1) from both sides gives \(x\ge 5\). In addition or subtraction, the direction stays the same.

Step 2

Why this answer is correct

The correct answer is A. \(x\ge 5\). Subtracting (1) from both sides gives \(x\ge 5\). In addition or subtraction, the direction stays the same.

Step 3

Exam Tip

दोनों ओर (1) घटाने पर \(x\ge 5\) मिलता है। जोड़ घटाव में दिशा वही रहती है।

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Question 29/50 Easy Mathematics Linear Inequalities Introduction to inequalities Class 11 Level 40

असमानता (5-x>2) का सही हल क्या है?

What is the correct solution of (5-x>2)?

Explanation opens after your attempt

Correct Answer

A. (x<3)

Step 1

Concept

From (5-x>2), we get (-x>-3), and dividing by a negative gives (x<3). When (-x) appears, remember to reverse the sign.

Step 2

Why this answer is correct

The correct answer is A. (x<3). From (5-x>2), we get (-x>-3), and dividing by a negative gives (x<3). When (-x) appears, remember to reverse the sign.

Step 3

Exam Tip

(5-x>2) से (-x>-3) और ऋणात्मक से भाग देने पर (x<3)। (-x) आने पर चिह्न पलटना याद रखें।

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Question 30/50 Easy Mathematics Linear Inequalities Introduction to inequalities Class 11 Level 40

असमानता \(4x+2\le 14\) का हल कौन सा है?

Which is the solution of \(4x+2\le 14\)?

Explanation opens after your attempt

Correct Answer

A. \(x\le 3\)

Step 1

Concept

First subtract (2), then divide by (4), giving \(x\le 3\). Keep the order correct in two-step questions.

Step 2

Why this answer is correct

The correct answer is A. \(x\le 3\). First subtract (2), then divide by (4), giving \(x\le 3\). Keep the order correct in two-step questions.

Step 3

Exam Tip

पहले (2) घटाएँ फिर (4) से भाग दें तो \(x\le 3\)। दो चरणों वाले प्रश्न में क्रम सही रखें।

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Question 31/50 Easy Mathematics Linear Inequalities Introduction to inequalities Class 11 Level 40

असमानता \(3-2x\le 9\) का सही हल क्या है?

What is the correct solution of \(3-2x\le 9\)?

Explanation opens after your attempt

Correct Answer

A. \(x\ge -3\)

Step 1

Concept

From \(3-2x\le 9\), we get \(-2x\le 6\), and division by (-2) gives \(x\ge -3\). Negative division reverses the direction.

Step 2

Why this answer is correct

The correct answer is A. \(x\ge -3\). From \(3-2x\le 9\), we get \(-2x\le 6\), and division by (-2) gives \(x\ge -3\). Negative division reverses the direction.

Step 3

Exam Tip

\(3-2x\le 9\) से \(-2x\le 6\) और (-2) से भाग देने पर \(x\ge -3\)। ऋणात्मक भाग दिशा पलटता है।

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Question 32/50 Easy Mathematics Linear Inequalities Introduction to inequalities Class 11 Level 40

कौन सा कथन \(x\le -1\) के लिए सही है?

Which statement is correct for \(x\le -1\)?

Explanation opens after your attempt

Correct Answer

B. समाधान (-1) और उससे बाईं ओर हैंSolutions are (-1) and to its left

Step 1

Concept

The sign \(\le\) includes the boundary and smaller numbers. On the number line, smaller numbers are to the left.

Step 2

Why this answer is correct

The correct answer is B. समाधान (-1) और उससे बाईं ओर हैं / Solutions are (-1) and to its left. The sign \(\le\) includes the boundary and smaller numbers. On the number line, smaller numbers are to the left.

Step 3

Exam Tip

\(\le\) में सीमा और उससे छोटी संख्याएँ शामिल होती हैं। संख्या रेखा पर छोटी संख्याएँ बाईं ओर होती हैं।

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Question 33/50 Easy Mathematics Linear Inequalities Introduction to inequalities Class 11 Level 40

असमानता (x>-4) का अंतराल रूप क्या है?

What is the interval form of (x>-4)?

Explanation opens after your attempt

Correct Answer

A. (\(-4,\infty\))

Step 1

Concept

In (x>-4), (-4) is not included and values lie to the right. So the interval is (\(-4,\infty\)).

Step 2

Why this answer is correct

The correct answer is A. (\(-4,\infty\)). In (x>-4), (-4) is not included and values lie to the right. So the interval is (\(-4,\infty\)).

Step 3

Exam Tip

(x>-4) में (-4) शामिल नहीं है और मान दाईं ओर हैं। इसलिए अंतराल (\(-4,\infty\)) है।

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Question 34/50 Easy Mathematics Linear Inequalities Introduction to inequalities Class 11 Level 40

असमानता \(x\le 0\) का अंतराल रूप कौन सा है?

Which is the interval form of \(x\le 0\)?

Explanation opens after your attempt

Correct Answer

C. (\(-\infty,0]\)

Step 1

Concept

In \(x\le 0\), (0) is included and smaller numbers are to the left. So (\(-\infty,0]\) is correct.

Step 2

Why this answer is correct

The correct answer is C. (\(-\infty,0]\). In \(x\le 0\), (0) is included and smaller numbers are to the left. So (\(-\infty,0]\) is correct.

Step 3

Exam Tip

\(x\le 0\) में (0) शामिल है और छोटी संख्याएँ बाईं ओर हैं। इसलिए (\(-\infty,0]\) सही है।

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Question 35/50 Easy Mathematics Linear Inequalities Introduction to inequalities Class 11 Level 40

कौन सा विकल्प \(2\le x<5\) को सही बताता है?

Which option correctly describes \(2\le x<5\)?

Explanation opens after your attempt

Correct Answer

C. (x) (2) या उससे बड़ा और (5) से छोटा है(x) is (2) or more and less than (5)

Step 1

Concept

In \(2\le x<5\), (2) is included but (5) is not. Read a compound inequality in two parts.

Step 2

Why this answer is correct

The correct answer is C. (x) (2) या उससे बड़ा और (5) से छोटा है / (x) is (2) or more and less than (5). In \(2\le x<5\), (2) is included but (5) is not. Read a compound inequality in two parts.

Step 3

Exam Tip

\(2\le x<5\) में (2) शामिल है पर (5) शामिल नहीं है। संयुक्त असमानता को दो भागों में पढ़ें।

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Question 36/50 Easy Mathematics Linear Inequalities Introduction to inequalities Class 11 Level 40

यदि (x) एक प्राकृतिक संख्या है और (x<4) है तो संभावित मान कौन से हैं?

If (x) is a natural number and (x<4), what are the possible values?

Explanation opens after your attempt

Correct Answer

A. \(x\in{1,2,3}\)

Step 1

Concept

Natural numbers are taken from (1), and (4) is not included. Therefore the values are (1,2,3).

Step 2

Why this answer is correct

The correct answer is A. \(x\in{1,2,3}\). Natural numbers are taken from (1), and (4) is not included. Therefore the values are (1,2,3).

Step 3

Exam Tip

प्राकृतिक संख्याएँ (1) से शुरू मानी जाती हैं और (4) शामिल नहीं है। इसलिए मान (1,2,3) हैं।

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Question 37/50 Easy Mathematics Linear Inequalities Introduction to inequalities Class 11 Level 40

यदि (x) एक पूर्णांक है और \(-2<x\le 2\) है तो (x) के मान क्या हैं?

If (x) is an integer and \(-2<x\le 2\), what are the values of (x)?

Explanation opens after your attempt

Correct Answer

B. \(x\in{-1,0,1,2}\)

Step 1

Concept

The value (-2) is not included, but (2) is included. The integer values are (-1,0,1,2).

Step 2

Why this answer is correct

The correct answer is B. \(x\in{-1,0,1,2}\). The value (-2) is not included, but (2) is included. The integer values are (-1,0,1,2).

Step 3

Exam Tip

(-2) शामिल नहीं है पर (2) शामिल है। पूर्णांक मान (-1,0,1,2) होंगे।

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Question 38/50 Easy Mathematics Linear Inequalities Introduction to inequalities Class 11 Level 40

कौन सी असमानता (x) के कम से कम (6) होने को दिखाती है?

Which inequality shows that (x) is at least (6)?

Explanation opens after your attempt

Correct Answer

C. \(x\ge 6\)

Step 1

Concept

At least (6) means (6) or more. Therefore the correct sign is \(\ge\).

Step 2

Why this answer is correct

The correct answer is C. \(x\ge 6\). At least (6) means (6) or more. Therefore the correct sign is \(\ge\).

Step 3

Exam Tip

कम से कम (6) का अर्थ (6) या उससे अधिक है। इसलिए सही चिह्न \(\ge\) है।

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Question 39/50 Easy Mathematics Linear Inequalities Introduction to inequalities Class 11 Level 40

कौन सी असमानता (n) के अधिकतम (20) होने को दिखाती है?

Which inequality shows that (n) is at most (20)?

Explanation opens after your attempt

Correct Answer

A. \(n\le 20\)

Step 1

Concept

At most (20) means (20) or less. Therefore \(n\le 20\) is correct.

Step 2

Why this answer is correct

The correct answer is A. \(n\le 20\). At most (20) means (20) or less. Therefore \(n\le 20\) is correct.

Step 3

Exam Tip

अधिकतम (20) का अर्थ (20) या उससे कम है। इसलिए \(n\le 20\) सही है।

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Question 40/50 Easy Mathematics Linear Inequalities Introduction to inequalities Class 11 Level 40

यदि (a>b) और (k>0) है तो कौन सा कथन सही है?

If (a>b) and (k>0), which statement is correct?

Explanation opens after your attempt

Correct Answer

A. (ak>bk)

Step 1

Concept

Multiplication by a positive number keeps the direction the same. The condition (k>0) is important.

Step 2

Why this answer is correct

The correct answer is A. (ak>bk). Multiplication by a positive number keeps the direction the same. The condition (k>0) is important.

Step 3

Exam Tip

धनात्मक संख्या से गुणा करने पर दिशा वही रहती है। (k>0) होने की शर्त जरूरी है।

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Question 41/50 Easy Mathematics Linear Inequalities Introduction to inequalities Class 11 Level 40

असमानता (x+7>7) का हल क्या है?

What is the solution of (x+7>7)?

Explanation opens after your attempt

Correct Answer

A. (x>0)

Step 1

Concept

Subtracting (7) from both sides gives (x>0). Remove equal terms to get the simple form.

Step 2

Why this answer is correct

The correct answer is A. (x>0). Subtracting (7) from both sides gives (x>0). Remove equal terms to get the simple form.

Step 3

Exam Tip

दोनों ओर (7) घटाने पर (x>0) मिलता है। समान पद हटाकर सरल रूप बनाइए।

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Question 42/50 Easy Mathematics Linear Inequalities Introduction to inequalities Class 11 Level 40

असमानता \(\frac{x}{3}\le 2\) का हल क्या है?

What is the solution of \(\frac{x}{3}\le 2\)?

Explanation opens after your attempt

Correct Answer

A. \(x\le 6\)

Step 1

Concept

Multiplying both sides by (3) gives \(x\le 6\). Positive multiplication does not reverse the sign.

Step 2

Why this answer is correct

The correct answer is A. \(x\le 6\). Multiplying both sides by (3) gives \(x\le 6\). Positive multiplication does not reverse the sign.

Step 3

Exam Tip

दोनों ओर (3) से गुणा करने पर \(x\le 6\) मिलता है। धनात्मक गुणा में चिह्न नहीं पलटता।

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Question 43/50 Easy Mathematics Linear Inequalities Introduction to inequalities Class 11 Level 40

असमानता \(\frac{x}{-4}>1\) का सही हल क्या है?

What is the correct solution of \(\frac{x}{-4}>1\)?

Explanation opens after your attempt

Correct Answer

B. (x<-4)

Step 1

Concept

Multiplying both sides by (-4) reverses the sign, so (x<-4). Negative multiplication changes the direction.

Step 2

Why this answer is correct

The correct answer is B. (x<-4). Multiplying both sides by (-4) reverses the sign, so (x<-4). Negative multiplication changes the direction.

Step 3

Exam Tip

दोनों ओर (-4) से गुणा करने पर चिह्न पलटेगा इसलिए (x<-4)। ऋणात्मक गुणा में दिशा बदलती है।

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Question 44/50 Easy Mathematics Linear Inequalities Introduction to inequalities Class 11 Level 40

असमानता (6<2x) का हल कौन सा है?

Which is the solution of (6<2x)?

Explanation opens after your attempt

Correct Answer

A. (x>3)

Step 1

Concept

Dividing both sides by (2) gives (3<x), that is (x>3). When rewriting, check the meaning of the sign direction.

Step 2

Why this answer is correct

The correct answer is A. (x>3). Dividing both sides by (2) gives (3<x), that is (x>3). When rewriting, check the meaning of the sign direction.

Step 3

Exam Tip

दोनों ओर (2) से भाग देने पर (3<x) यानी (x>3) मिलता है। रूप बदलते समय चिह्न की दिशा अर्थ से जाँचें।

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Question 45/50 Easy Mathematics Linear Inequalities Introduction to inequalities Class 11 Level 40

कौन सा मान असमानता (2x-1<7) को संतुष्ट करता है?

Which value satisfies the inequality (2x-1<7)?

Explanation opens after your attempt

Correct Answer

B. (x=4)

Step 1

Concept

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.

Step 2

Why this answer is correct

The correct answer is B. (x=4). 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.

Step 3

Exam Tip

(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।

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Question 46/50 Easy Mathematics Linear Inequalities Introduction to inequalities Class 11 Level 40

यदि (x) पूर्णांक है और \(3\le x<7\) है तो कुल कितने मान संभव हैं?

If (x) is an integer and \(3\le x<7\), how many values are possible?

Explanation opens after your attempt

Correct Answer

B. (4)

Step 1

Concept

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.

Step 2

Why this answer is correct

The correct answer is B. (4). 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.

Step 3

Exam Tip

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।

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Question 47/50 Easy Mathematics Linear Inequalities Introduction to inequalities Class 11 Level 40

असमानता \(7-3x\ge 1\) का हल कौन सा है?

Which is the solution of \(7-3x\ge 1\)?

Explanation opens after your attempt

Correct Answer

A. \(x\le 2\)

Step 1

Concept

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.

Step 2

Why this answer is correct

The correct answer is A. \(x\le 2\). 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.

Step 3

Exam Tip

\(7-3x\ge 1\) से \(-3x\ge -6\) और (-3) से भाग देने पर \(x\le 2\) मिलता है। ऋणात्मक संख्या से भाग देते समय चिह्न पलटता है।

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Question 48/50 Easy Mathematics Linear Inequalities Introduction to inequalities Class 11 Level 40

अंतराल ((1,6]) को असमानता के रूप में कैसे लिखेंगे?

How do we write the interval ((1,6]) as an inequality?

Explanation opens after your attempt

Correct Answer

A. \(1<x\le 6\)

Step 1

Concept

The symbol ((1) shows that (1) is not included and (6]) shows that (6) is included. Therefore \(1<x\le 6\) is correct.

Step 2

Why this answer is correct

The correct answer is A. \(1<x\le 6\). The symbol ((1) shows that (1) is not included and (6]) shows that (6) is included. Therefore \(1<x\le 6\) is correct.

Step 3

Exam Tip

((1) बताता है कि (1) शामिल नहीं है और (6]) बताता है कि (6) शामिल है। इसलिए \(1<x\le 6\) सही है।

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Question 49/50 Easy Mathematics Linear Inequalities Introduction to inequalities Class 11 Level 40

किसी कक्षा में विद्यार्थियों की संख्या (n) कम से कम (25) और अधिकतम (40) है। सही असमानता कौन सी है?

In a class, the number of students (n) is at least (25) and at most (40). Which inequality is correct?

Explanation opens after your attempt

Correct Answer

B. \(25\le n\le 40\)

Step 1

Concept

At least (25) means \(n\ge 25\), and at most (40) means \(n\le 40\). Combining both gives \(25\le n\le 40\).

Step 2

Why this answer is correct

The correct answer is B. \(25\le n\le 40\). At least (25) means \(n\ge 25\), and at most (40) means \(n\le 40\). Combining both gives \(25\le n\le 40\).

Step 3

Exam Tip

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।

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Question 50/50 Easy Mathematics Linear Inequalities Introduction to inequalities Class 11 Level 40

असमानता (9<3x+3) का सही हल क्या है?

What is the correct solution of the inequality (9<3x+3)?

Explanation opens after your attempt

Correct Answer

A. (x>2)

Step 1

Concept

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.

Step 2

Why this answer is correct

The correct answer is A. (x>2). 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.

Step 3

Exam Tip

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।

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