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Mathematics algebraic solution of linear inequalities in one variable MCQ Questions for Class 11 General

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01 Practice Topic Graphical solution of linear inequalities in two variables 575 MCQs 02 Practice Topic Introduction to inequalities 591 MCQs 03 Practice Topic representation on number line 592 MCQs

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Question 541/584 Expert Mathematics Linear Inequalities algebraic solution of linear inequalities in one variable Class 11 Level 45

युग्म असमानता \(-3\le \frac{7-2x}{5}<1\) का हल समुच्चय क्या है?

What is the solution set of the compound inequality \(-3\le \frac{7-2x}{5}<1\)?

Explanation opens after your attempt
Correct Answer

A. \(1<x\le 11\)

Explanation

Simple Explanation

दोनों भाग हल करने पर \(x\le 11\) और (x>1) मिलता है। इसलिए संयुक्त हल \(1<x\le 11\) है। / Solving both parts gives \(x\le 11\) and (x>1). Therefore the combined solution is \(1<x\le 11\).

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Question 542/584 Expert Mathematics Linear Inequalities algebraic solution of linear inequalities in one variable Class 11 Level 45

असमानता \(\frac{5x-1}{3}-\frac{x+4}{2}\ge 2\) का हल क्या है?

What is the solution of the inequality \(\frac{5x-1}{3}-\frac{x+4}{2}\ge 2\)?

Explanation opens after your attempt
Correct Answer

C. \(x\ge \frac{26}{7}\)

Explanation

Simple Explanation

हर हटाने पर \(7x-14\ge 12\), अतः \(x\ge \frac{26}{7}\)। भिन्नों में पहले लघुत्तम समापवर्त्य से गुणा करें। / Clearing denominators gives \(7x-14\ge 12\), hence \(x\ge \frac{26}{7}\). For fractions, multiply by the LCM first.

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Question 543/584 Expert Mathematics Linear Inequalities algebraic solution of linear inequalities in one variable Class 11 Level 45

असमानता \(\frac{2x+7}{4}<\frac{3x-1}{6}+\frac{5}{3}\) का हल समुच्चय क्या है?

What is the solution set of the inequality \(\frac{2x+7}{4}<\frac{3x-1}{6}+\frac{5}{3}\)?

Explanation opens after your attempt
Correct Answer

A. \(\varnothing\)

Explanation

Simple Explanation

हर हटाने पर (6x+21<6x+18), जो असत्य है। यदि चर हट जाए और कथन असत्य हो, तो हल रिक्त होता है। / After clearing denominators, (6x+21<6x+18), which is false. If the variable cancels and the statement is false, the solution is empty.

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Question 544/584 Expert Mathematics Linear Inequalities algebraic solution of linear inequalities in one variable Class 11 Level 45

असमानता (4(x-2)-3(2-x)\ge 5x+1) को हल कीजिए।

Solve the inequality (4(x-2)-3(2-x)\ge 5x+1).

Explanation opens after your attempt
Correct Answer

B. \(x\ge \frac{15}{2}\)

Explanation

Simple Explanation

सरलीकरण से \(2x\ge 15\) मिलता है, इसलिए \(x\ge \frac{15}{2}\)। कोष्ठक खोलते समय ऋण चिह्न ध्यान से लगाएँ। / Simplification gives \(2x\ge 15\), so \(x\ge \frac{15}{2}\). Apply the negative sign carefully while opening brackets.

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Question 545/584 Expert Mathematics Linear Inequalities algebraic solution of linear inequalities in one variable Class 11 Level 45

असमानता (\frac{2}{3}(3x-6)-\frac{1}{5}(10x+5)\le x-8) का हल क्या है?

What is the solution of (\frac{2}{3}(3x-6)-\frac{1}{5}(10x+5)\le x-8)?

Explanation opens after your attempt
Correct Answer

C. \(x\ge 3\)

Explanation

Simple Explanation

बायाँ पक्ष (-5) बनता है, इसलिए \(-5\le x-8\) और \(x\ge 3\)। चर कटने पर बचे स्थिर पद को सही तरफ रखें। / The left side becomes (-5), so \(-5\le x-8\) and \(x\ge 3\). When variables cancel, place the remaining constant correctly.

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Question 546/584 Expert Mathematics Linear Inequalities algebraic solution of linear inequalities in one variable Class 11 Level 45

असमानता (-3(2x+1)+5\ge 4(1-x)-2x) का हल समुच्चय क्या है?

What is the solution set of (-3(2x+1)+5\ge 4(1-x)-2x)?

Explanation opens after your attempt
Correct Answer

D. \(\varnothing\)

Explanation

Simple Explanation

सरलीकरण के बाद \(2\ge 4\) मिलता है, जो असत्य है। असत्य स्थिर असमानता का हल रिक्त समुच्चय होता है। / After simplification, \(2\ge 4\), which is false. A false constant inequality has an empty solution set.

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Question 547/584 Expert Mathematics Linear Inequalities algebraic solution of linear inequalities in one variable Class 11 Level 45

असमानता \(\frac{x-2}{7}+\frac{x+3}{5}>1\) को हल कीजिए।

Solve the inequality \(\frac{x-2}{7}+\frac{x+3}{5}>1\).

Explanation opens after your attempt
Correct Answer

A. (x>2)

Explanation

Simple Explanation

हर हटाने पर (12x+11>35), इसलिए (x>2)। धनात्मक लघुत्तम समापवर्त्य से गुणा करने पर चिह्न नहीं बदलता। / Clearing denominators gives (12x+11>35), so (x>2). Multiplying by a positive LCM does not change the sign.

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Question 548/584 Expert Mathematics Linear Inequalities algebraic solution of linear inequalities in one variable Class 11 Level 45

असमानता \(6-\frac{3x-4}{2}\le \frac{5-x}{3}\) का हल क्या है?

What is the solution of \(6-\frac{3x-4}{2}\le \frac{5-x}{3}\)?

Explanation opens after your attempt
Correct Answer

B. \(x\ge \frac{38}{7}\)

Explanation

Simple Explanation

हर हटाने और सरलीकरण पर \(38\le 7x\) मिलता है। इसलिए \(x\ge \frac{38}{7}\) सही हल है। / After clearing denominators and simplifying, \(38\le 7x\). Therefore \(x\ge \frac{38}{7}\) is the correct solution.

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Question 549/584 Expert Mathematics Linear Inequalities algebraic solution of linear inequalities in one variable Class 11 Level 45

असमानता (\frac{2}{5}(5x-3)-\frac{1}{4}(8x+4)<\frac{5}{2}) का हल समुच्चय क्या है?

What is the solution set of (\frac{2}{5}(5x-3)-\frac{1}{4}(8x+4)<\frac{5}{2})?

Explanation opens after your attempt
Correct Answer

C. \(x\in\mathbb{R}\)

Explanation

Simple Explanation

बायाँ पक्ष \(-\frac{11}{5}\) बनता है और \(-\frac{11}{5}<\frac{5}{2}\) सत्य है। इसलिए हर वास्तविक (x) हल है। / The left side becomes \(-\frac{11}{5}\), and \(-\frac{11}{5}<\frac{5}{2}\) is true. Therefore every real (x) is a solution.

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Question 550/584 Expert Mathematics Linear Inequalities algebraic solution of linear inequalities in one variable Class 11 Level 45

युग्म असमानता \(4\le 2x+6<14\) को हल कीजिए।

Solve the compound inequality \(4\le 2x+6<14\).

Explanation opens after your attempt
Correct Answer

A. \(-1\le x<4\)

Explanation

Simple Explanation

सभी भागों से (6) घटाकर \(-2\le 2x<8\) मिलता है। फिर (2) से भाग देने पर \(-1\le x<4\) आता है। / Subtracting (6) from all parts gives \(-2\le 2x<8\). Dividing by (2) gives \(-1\le x<4\).

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