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

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Question 491/584 Expert Mathematics Linear Inequalities algebraic solution of linear inequalities in one variable Class 11 Level 44

यदि ( -2(3x-4)>5-x ) हो तो (x) का हल-समुच्चय क्या है?

If ( -2(3x-4)>5-x ), what is the solution set of (x)?

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Correct Answer

A. \(x<\frac{3}{5}\)

Explanation

Simple Explanation

सरलीकरण से (-5x>-3) मिलता है और ऋणात्मक से भाग देने पर चिह्न बदलता है। परीक्षा में इसी स्टेप पर सबसे अधिक गलती होती है। / Simplification gives (-5x>-3) and division by a negative reverses the sign. This is the most common exam error.

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Question 492/584 Expert Mathematics Linear Inequalities algebraic solution of linear inequalities in one variable Class 11 Level 44

दोहरी असमानता \( -2<\frac{5-3x}{4}\leq 1 \) का सही हल-अंतराल क्या है?

What is the correct solution interval of the double inequality \( -2<\frac{5-3x}{4}\leq 1 \)?

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Correct Answer

C. \( \frac{1}{3}\leq x<\frac{13}{3} \)

Explanation

Simple Explanation

(-3) से भाग देने पर दोनों असमानता-चिह्न उलटते हैं। इसलिए हल \( \frac{1}{3}\leq x<\frac{13}{3} \) है। / Dividing by (-3) reverses both inequality signs. Hence the solution is \( \frac{1}{3}\leq x<\frac{13}{3} \).

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Question 493/584 Expert Mathematics Linear Inequalities algebraic solution of linear inequalities in one variable Class 11 Level 44

यदि ( ax+7<1 ) का हल (x>3) है, तो (a) का मान क्या होगा?

If the solution of ( ax+7<1 ) is (x>3), what is the value of (a)?

Explanation opens after your attempt
Correct Answer

D. (-2)

Explanation

Simple Explanation

(ax<-6) से (x>3) तभी मिलेगा जब (a) ऋणात्मक हो। \(\frac{-6}{a}=3\) से (a=-2) मिलता है। / From (ax<-6), (x>3) occurs only when (a) is negative. Using \(\frac{-6}{a}=3\), we get (a=-2).

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Question 494/584 Expert Mathematics Linear Inequalities algebraic solution of linear inequalities in one variable Class 11 Level 44

दोहरी असमानता \( -3\leq 2x+5<11 \) का हल कौन-सा है?

Which is the solution of the double inequality \( -3\leq 2x+5<11 \)?

Explanation opens after your attempt
Correct Answer

A. \( -4\leq x<3 \)

Explanation

Simple Explanation

सभी भागों से (5) घटाकर फिर (2) से भाग दें। बंद और खुले सिरों को वैसा ही रखें। / Subtract (5) from all parts and then divide by (2). Keep closed and open endpoints exactly as given.

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Question 495/584 Expert Mathematics Linear Inequalities algebraic solution of linear inequalities in one variable Class 11 Level 44

यदि \(x\in \mathbb{Z}\), \( \frac{2x-7}{3}<5 \) और \( 4-\frac{x}{2}\leq 1 \), तो (x) के कितने पूर्णांक मान संभव हैं?

If \(x\in \mathbb{Z}\), \( \frac{2x-7}{3}<5 \), and \( 4-\frac{x}{2}\leq 1 \), how many integer values of (x) are possible?

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Correct Answer

A. (5)

Explanation

Simple Explanation

पहली असमानता से (x<11) और दूसरी से \(x\geq 6\) मिलता है। पूर्णांक (6,7,8,9,10) हैं, इसलिए कुल (5) मान हैं। / The first inequality gives (x<11), and the second gives \(x\geq 6\). The integers are (6,7,8,9,10), so there are (5) values.

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Question 496/584 Expert Mathematics Linear Inequalities algebraic solution of linear inequalities in one variable Class 11 Level 44

यदि \( \frac{2x-3}{4}\geq \frac{x+5}{6} \), तो सबसे छोटा पूर्णांक (x) क्या होगा?

If \( \frac{2x-3}{4}\geq \frac{x+5}{6} \), what is the smallest integer (x)?

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Correct Answer

B. (7)

Explanation

Simple Explanation

(12) से गुणा करने पर \(6x-9\geq 2x+10\) और \(x\geq \frac{19}{4}\) मिलता है। इसलिए सबसे छोटा पूर्णांक (7) है। / Multiplying by (12) gives \(6x-9\geq 2x+10\) and \(x\geq \frac{19}{4}\). Therefore the smallest integer is (7).

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Question 497/584 Expert Mathematics Linear Inequalities algebraic solution of linear inequalities in one variable Class 11 Level 44

असमानता \( 4-\frac{3x+2}{5}>1+\frac{x-6}{2} \) का हल है:

The solution of \( 4-\frac{3x+2}{5}>1+\frac{x-6}{2} \) is:

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Correct Answer

A. \(x<\frac{29}{11}\)

Explanation

Simple Explanation

(10) से गुणा करने पर (40-6x-4>10+5x-30) मिलता है। अतः (66-11x>0) से (x<6) नहीं बल्कि \(x<\frac{66}{11}=6\) आता है। / Multiplying by (10) gives (40-6x-4>10+5x-30). Thus (66-11x>0) gives (x<6).

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Question 498/584 Expert Mathematics Linear Inequalities algebraic solution of linear inequalities in one variable Class 11 Level 44

असमानता ( 5(2-x)\leq 3(4-x)-8 ) का हल-समुच्चय क्या है?

What is the solution set of ( 5(2-x)\leq 3(4-x)-8 )?

Explanation opens after your attempt
Correct Answer

A. \(x\geq 3\)

Explanation

Simple Explanation

सरलीकरण से \(10-5x\leq 4-3x\) और \(6\leq 2x\) मिलता है। इसलिए \(x\geq 3\) है। / Simplification gives \(10-5x\leq 4-3x\) and \(6\leq 2x\). Therefore \(x\geq 3\).

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Question 499/584 Expert Mathematics Linear Inequalities algebraic solution of linear inequalities in one variable Class 11 Level 44

यदि \( 7-2x\leq 3x+12<22-2x \), तो (x) का अंतराल क्या है?

If \( 7-2x\leq 3x+12<22-2x \), what is the interval of (x)?

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Correct Answer

A. \(x\geq -1\) और (x<2)\(x\geq -1\) and (x<2)

Explanation

Simple Explanation

दोनों भाग अलग-अलग हल करने पर \(x\geq -1\) और (x<2) मिलता है। संयुक्त हल ([-1,2)) है। / Solving both parts separately gives \(x\geq -1\) and (x<2). The combined solution is ([-1,2)).

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Question 500/584 Expert Mathematics Linear Inequalities algebraic solution of linear inequalities in one variable Class 11 Level 44

असमानता \( \frac{5-2x}{3}\geq x-4 \) का हल है:

The solution of \( \frac{5-2x}{3}\geq x-4 \) is:

Explanation opens after your attempt
Correct Answer

A. \(x\leq \frac{17}{5}\)

Explanation

Simple Explanation

(3) से गुणा करने पर \(5-2x\geq 3x-12\) मिलता है। इससे \(17\geq 5x\) अर्थात \(x\leq \frac{17}{5}\) है। / Multiplying by (3) gives \(5-2x\geq 3x-12\). This gives \(17\geq 5x\), so \(x\leq \frac{17}{5}\).

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