Concept-wise Practice

class 11 MCQ Questions for Class 11

class 11 se related questions ko ek jagah revise karein. Har question me bilingual content, answer feedback aur explanation available hai.

Practice Questions

2918 questions tagged with class 11.

असमानता \(5x-3\leq 17\) का सही हल चुनिए।

Choose the correct solution of \(5x-3\leq 17\).

Explanation opens after your attempt
Correct Answer

A. \(x\leq 4\)

Step 1

Concept

Since \(5x\leq 20\), \(x\leq 4\). In \(\leq\), the boundary value is also included.

Step 2

Why this answer is correct

The correct answer is A. \(x\leq 4\). Since \(5x\leq 20\), \(x\leq 4\). In \(\leq\), the boundary value is also included.

Step 3

Exam Tip

\(5x\leq 20\) इसलिए \(x\leq 4\) है। \(\leq\) में सीमा मान भी शामिल होता है।

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असमानता (4x+6>22) का हल कौन सा है?

Which is the solution of the inequality (4x+6>22)?

Explanation opens after your attempt
Correct Answer

A. (x>4)

Step 1

Concept

From (4x>16), we get (x>4). Dividing by a positive number does not change the inequality sign.

Step 2

Why this answer is correct

The correct answer is A. (x>4). From (4x>16), we get (x>4). Dividing by a positive number does not change the inequality sign.

Step 3

Exam Tip

(4x>16) से (x>4) मिलता है। धनात्मक संख्या से भाग देने पर असमानता का चिन्ह नहीं बदलता।

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किसी संख्या के (2) गुने में (5) जोड़ने पर परिणाम (19) से अधिक नहीं है। (x) के लिए सही हल क्या है?

Twice a number increased by (5) is not more than (19). What is the correct solution for (x)?

Explanation opens after your attempt
Correct Answer

A. \(x\leq 7\)

Step 1

Concept

Not more than means \(\leq\), so \(2x+5\leq 19\) gives \(x\leq 7\). In word problems, first convert the sentence into an inequality.

Step 2

Why this answer is correct

The correct answer is A. \(x\leq 7\). Not more than means \(\leq\), so \(2x+5\leq 19\) gives \(x\leq 7\). In word problems, first convert the sentence into an inequality.

Step 3

Exam Tip

अधिक नहीं है का अर्थ \(\leq\) होता है, इसलिए \(2x+5\leq 19\) से \(x\leq 7\) मिलता है। शब्द प्रश्नों में वाक्य को पहले असमानता में बदलें।

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एक विद्यार्थी को परीक्षा पास करने के लिए कम से कम (40) अंक चाहिए। यदि उसे पहले से (27) अंक मिल चुके हैं, तो अतिरिक्त अंकों (m) के लिए सही असमानता क्या है?

A student needs at least (40) marks to pass. If the student already has (27) marks, what is the correct inequality for extra marks (m)?

Explanation opens after your attempt
Correct Answer

A. \(27+m\geq 40\)

Step 1

Concept

At least means \(\geq\), so \(27+m\geq 40\) is correct. In word problems, first identify the mathematical symbol for the key phrase.

Step 2

Why this answer is correct

The correct answer is A. \(27+m\geq 40\). At least means \(\geq\), so \(27+m\geq 40\) is correct. In word problems, first identify the mathematical symbol for the key phrase.

Step 3

Exam Tip

कम से कम का अर्थ \(\geq\) होता है, इसलिए \(27+m\geq 40\) सही है। शब्द प्रश्नों में पहले मुख्य शब्द का गणितीय चिह्न पहचानें।

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कौन सा विकल्प \(x\in\mathbb{R}\) और \(x\geq 0\) को दर्शाता है?

Which option represents \(x\in\mathbb{R}\) and \(x\geq 0\)?

Explanation opens after your attempt
Correct Answer

A. \([0,\infty\))

Step 1

Concept

\(x\geq 0\) includes (0) and all positive real numbers. Therefore \([0,\infty\)) is correct.

Step 2

Why this answer is correct

The correct answer is A. \([0,\infty\)). \(x\geq 0\) includes (0) and all positive real numbers. Therefore \([0,\infty\)) is correct.

Step 3

Exam Tip

\(x\geq 0\) में (0) और सभी धनात्मक वास्तविक संख्याएं शामिल हैं। इसलिए \([0,\infty\)) सही है।

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असमानता \(7\leq x+4<12\) का हल क्या है?

What is the solution of \(7\leq x+4<12\)?

Explanation opens after your attempt
Correct Answer

A. \(3\leq x<8\)

Step 1

Concept

Subtracting (4) from all parts gives \(3\leq x<8\). Apply the same operation to every part of a compound inequality.

Step 2

Why this answer is correct

The correct answer is A. \(3\leq x<8\). Subtracting (4) from all parts gives \(3\leq x<8\). Apply the same operation to every part of a compound inequality.

Step 3

Exam Tip

सभी भागों से (4) घटाने पर \(3\leq x<8\) मिलता है। संयुक्त असमानता में हर भाग पर समान क्रिया करें।

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एक संख्या में (3) जोड़ने पर परिणाम (10) से बड़ा है। सही असमानता क्या है?

A number increased by (3) is greater than (10). What is the correct inequality?

Explanation opens after your attempt
Correct Answer

A. (x+3>10)

Step 1

Concept

Increasing by (3) means (x+3), and greater than means (>). In word problems, define the variable first.

Step 2

Why this answer is correct

The correct answer is A. (x+3>10). Increasing by (3) means (x+3), and greater than means (>). In word problems, define the variable first.

Step 3

Exam Tip

वाक्य में (3) जोड़ना (x+3) और बड़ा है (>) को दर्शाता है। शब्द आधारित प्रश्नों में पहले चर तय करें।

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असमानता \(4- \frac{x}{2}>1\) का हल क्या है?

What is the solution of \(4-\frac{x}{2}>1\)?

Explanation opens after your attempt
Correct Answer

A. (x<6)

Step 1

Concept

\(-\frac{x}{2}>-3\), and removing the negative factor gives (x<6). Identify when the sign must be reversed.

Step 2

Why this answer is correct

The correct answer is A. (x<6). \(-\frac{x}{2}>-3\), and removing the negative factor gives (x<6). Identify when the sign must be reversed.

Step 3

Exam Tip

\(-\frac{x}{2}>-3\) और ऋणात्मक गुणक हटाने पर (x<6) मिलता है। चिन्ह बदलने की स्थिति पहचानें।

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यदि \(2\leq x\leq 6\), तो निम्न में से कौन सा मान हल है?

If \(2\leq x\leq 6\), which of the following is a solution?

Explanation opens after your attempt
Correct Answer

A. (x=6)

Step 1

Concept

Both boundaries include equality, so (2) and (6) are included. Among the options, (x=6) is correct.

Step 2

Why this answer is correct

The correct answer is A. (x=6). Both boundaries include equality, so (2) and (6) are included. Among the options, (x=6) is correct.

Step 3

Exam Tip

दोनों सीमाओं में बराबरी है, इसलिए (2) और (6) शामिल हैं। दिए गए विकल्पों में (x=6) सही है।

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कौन सा विकल्प ({x:x>1}) का अंतराल रूप है?

Which option is the interval form of ({x:x>1})?

Explanation opens after your attempt
Correct Answer

A. (\(1,\infty\))

Step 1

Concept

In (x>1), (1) is not included and values to the right are taken. Hence (\(1,\infty\)) is correct.

Step 2

Why this answer is correct

The correct answer is A. (\(1,\infty\)). In (x>1), (1) is not included and values to the right are taken. Hence (\(1,\infty\)) is correct.

Step 3

Exam Tip

(x>1) में (1) शामिल नहीं है और दाईं ओर के मान आते हैं। इसलिए (\(1,\infty\)) सही है।

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असमानता \(-5x\geq 15\) को हल कीजिए।

Solve the inequality \(-5x\geq 15\).

Explanation opens after your attempt
Correct Answer

A. \(x\leq -3\)

Step 1

Concept

Dividing by (-5) reverses the inequality sign. Therefore \(x\leq -3\) is obtained.

Step 2

Why this answer is correct

The correct answer is A. \(x\leq -3\). Dividing by (-5) reverses the inequality sign. Therefore \(x\leq -3\) is obtained.

Step 3

Exam Tip

(-5) से भाग देने पर असमानता का चिन्ह उलटता है। इसलिए \(x\leq -3\) मिलता है।

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यदि \(5x\leq -20\), तो सही हल क्या है?

If \(5x\leq -20\), what is the correct solution?

Explanation opens after your attempt
Correct Answer

A. \(x\leq -4\)

Step 1

Concept

Dividing by positive (5) does not change the sign. Hence \(x\leq -4\) is correct.

Step 2

Why this answer is correct

The correct answer is A. \(x\leq -4\). Dividing by positive (5) does not change the sign. Hence \(x\leq -4\) is correct.

Step 3

Exam Tip

धनात्मक (5) से भाग देने पर चिन्ह नहीं बदलता। इसलिए \(x\leq -4\) सही है।

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किस असमानता का हल \(x\leq -3\) है?

Which inequality has the solution \(x\leq -3\)?

Explanation opens after your attempt
Correct Answer

A. \(x+3\leq 0\)

Step 1

Concept

\(x+3\leq 0\) gives \(x\leq -3\). Solving each option and matching is a quick method.

Step 2

Why this answer is correct

The correct answer is A. \(x+3\leq 0\). \(x+3\leq 0\) gives \(x\leq -3\). Solving each option and matching is a quick method.

Step 3

Exam Tip

\(x+3\leq 0\) से \(x\leq -3\) मिलता है। विकल्पों को हल करके मिलान करना तेज तरीका है।

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असमानता \(2x+5\leq x+9\) में सीमा मान क्या है?

What is the boundary value in the inequality \(2x+5\leq x+9\)?

Explanation opens after your attempt
Correct Answer

A. (4)

Step 1

Concept

The boundary value is found by using equality: (2x+5=x+9), so (x=4). The boundary value decides the open or closed endpoint.

Step 2

Why this answer is correct

The correct answer is A. (4). The boundary value is found by using equality: (2x+5=x+9), so (x=4). The boundary value decides the open or closed endpoint.

Step 3

Exam Tip

सीमा मान बराबरी लगाकर मिलता है: (2x+5=x+9), इसलिए (x=4)। सीमा मान से खुला या बंद सिरा तय होता है।

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यदि (x) एक वास्तविक संख्या है और (x<0), तो (-x) के बारे में क्या सही है?

If (x) is a real number and (x<0), what is true about (-x)?

Explanation opens after your attempt
Correct Answer

A. (-x>0)

Step 1

Concept

The opposite of a negative number is positive. Therefore, if (x<0), then (-x>0).

Step 2

Why this answer is correct

The correct answer is A. (-x>0). The opposite of a negative number is positive. Therefore, if (x<0), then (-x>0).

Step 3

Exam Tip

ऋणात्मक संख्या का विपरीत धनात्मक होता है। इसलिए (x<0) होने पर (-x>0) है।

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असमानता (3x-2> x+8) का हल चुनिए।

Choose the solution of (3x-2>x+8).

Explanation opens after your attempt
Correct Answer

A. (x>5)

Step 1

Concept

From (2x>10), we get (x>5). There is no equality, so (5) will not be included.

Step 2

Why this answer is correct

The correct answer is A. (x>5). From (2x>10), we get (x>5). There is no equality, so (5) will not be included.

Step 3

Exam Tip

(2x>10) से (x>5) मिलता है। बराबरी नहीं है, इसलिए (5) शामिल नहीं होगा।

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कौन सा कथन \(x\geq 5\) के बारे में सही है?

Which statement about \(x\geq 5\) is correct?

Explanation opens after your attempt
Correct Answer

A. (5) हल में शामिल है(5) is included in the solution

Step 1

Concept

\(\geq\) means greater than or equal to, so (5) is included. On the number line, use a closed circle at (5).

Step 2

Why this answer is correct

The correct answer is A. (5) हल में शामिल है / (5) is included in the solution. \(\geq\) means greater than or equal to, so (5) is included. On the number line, use a closed circle at (5).

Step 3

Exam Tip

\(\geq\) का अर्थ बड़ा या बराबर होता है, इसलिए (5) शामिल है। संख्या रेखा पर (5) पर बंद वृत्त बनेगा।

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यदि (x+5<12), तो (x) के कौन से पूर्णांक मान \(0\leq x\) के साथ संभव हैं?

If (x+5<12), which integer values of (x) are possible with \(0\leq x\)?

Explanation opens after your attempt
Correct Answer

A. ({0,1,2,3,4,5,6})

Step 1

Concept

(x+5<12) gives (x<7), and \(0\leq x\) is given. So the integer values are ({0,1,2,3,4,5,6}).

Step 2

Why this answer is correct

The correct answer is A. ({0,1,2,3,4,5,6}). (x+5<12) gives (x<7), and \(0\leq x\) is given. So the integer values are ({0,1,2,3,4,5,6}).

Step 3

Exam Tip

(x+5<12) से (x<7) और \(0\leq x\) दिया है। इसलिए पूर्णांक मान ({0,1,2,3,4,5,6}) होंगे।

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असमानता (10<3x+1) का हल क्या है?

What is the solution of (10<3x+1)?

Explanation opens after your attempt
Correct Answer

A. (x>3)

Step 1

Concept

From (9<3x), we get (3<x), meaning (x>3). (3<x) and (x>3) mean the same thing.

Step 2

Why this answer is correct

The correct answer is A. (x>3). From (9<3x), we get (3<x), meaning (x>3). (3<x) and (x>3) mean the same thing.

Step 3

Exam Tip

(9<3x) से (3<x), यानी (x>3) मिलता है। (3<x) और (x>3) समान अर्थ रखते हैं।

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कौन सा विकल्प \(x\leq 0\) का उदाहरण है?

Which option is an example of \(x\leq 0\)?

Explanation opens after your attempt
Correct Answer

A. (x=-3)

Step 1

Concept

\(x\leq 0\) includes zero and all smaller values. (x=-3) is one such value.

Step 2

Why this answer is correct

The correct answer is A. (x=-3). \(x\leq 0\) includes zero and all smaller values. (x=-3) is one such value.

Step 3

Exam Tip

\(x\leq 0\) में शून्य या उससे छोटे मान आते हैं। (x=-3) ऐसे मानों में से एक है।

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यदि \(-1\leq x<4\), तो सही अंतराल रूप क्या है?

If \(-1\leq x<4\), what is the correct interval form?

Explanation opens after your attempt
Correct Answer

A. ([-1,4))

Step 1

Concept

(-1) is included, so use a square bracket; (4) is not included, so use a round bracket. Check both endpoints separately while writing intervals.

Step 2

Why this answer is correct

The correct answer is A. ([-1,4)). (-1) is included, so use a square bracket; (4) is not included, so use a round bracket. Check both endpoints separately while writing intervals.

Step 3

Exam Tip

(-1) शामिल है इसलिए वर्ग कोष्ठक और (4) शामिल नहीं है इसलिए गोल कोष्ठक लगेगा। अंतराल लिखते समय दोनों सिरों को अलग जांचें।

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

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

Explanation opens after your attempt
Correct Answer

A. \(x\leq 7\)

Step 1

Concept

Multiplying by positive (5) gives \(2x+1\leq 15\), so \(x\leq 7\). A positive denominator does not reverse the sign.

Step 2

Why this answer is correct

The correct answer is A. \(x\leq 7\). Multiplying by positive (5) gives \(2x+1\leq 15\), so \(x\leq 7\). A positive denominator does not reverse the sign.

Step 3

Exam Tip

धनात्मक (5) से गुणा करने पर \(2x+1\leq 15\), इसलिए \(x\leq 7\)। धनात्मक हर होने पर चिन्ह नहीं बदलता।

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असमानता \(8\leq 2x+4\) का हल कौन सा है?

Which is the solution of \(8\leq 2x+4\)?

Explanation opens after your attempt
Correct Answer

A. \(x\geq 2\)

Step 1

Concept

From \(4\leq 2x\), we get \(2\leq x\), that is \(x\geq 2\). Pay attention to direction while reading inequalities.

Step 2

Why this answer is correct

The correct answer is A. \(x\geq 2\). From \(4\leq 2x\), we get \(2\leq x\), that is \(x\geq 2\). Pay attention to direction while reading inequalities.

Step 3

Exam Tip

\(4\leq 2x\) से \(2\leq x\), अर्थात \(x\geq 2\)। असमानता को पढ़ते समय दिशा का ध्यान रखें।

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किस संख्या रेखा पर (x>2) दिखेगा?

Which number line representation shows (x>2)?

Explanation opens after your attempt
Correct Answer

A. (2) पर खुला वृत्त और दाईं ओर छायाOpen circle at (2) and shading to the right

Step 1

Concept

In (x>2), (2) is not included and greater values are needed. So an open circle and right-side shading are correct.

Step 2

Why this answer is correct

The correct answer is A. (2) पर खुला वृत्त और दाईं ओर छाया / Open circle at (2) and shading to the right. In (x>2), (2) is not included and greater values are needed. So an open circle and right-side shading are correct.

Step 3

Exam Tip

(x>2) में (2) शामिल नहीं है और उससे बड़े मान चाहिए। इसलिए खुला वृत्त और दाईं ओर छाया सही है।

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वाक्य (x) का (4) से कम या बराबर होना किस रूप में लिखा जाएगा?

How is the statement (x) is less than or equal to (4) written?

Explanation opens after your attempt
Correct Answer

A. \(x\leq 4\)

Step 1

Concept

The symbol \(\leq\) is used for less than or equal to. Translating words into mathematical symbols is an important exam skill.

Step 2

Why this answer is correct

The correct answer is A. \(x\leq 4\). The symbol \(\leq\) is used for less than or equal to. Translating words into mathematical symbols is an important exam skill.

Step 3

Exam Tip

कम या बराबर के लिए \(\leq\) चिह्न प्रयोग होता है। शब्दों को गणितीय चिह्नों में बदलना परीक्षा में जरूरी कौशल है।

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यदि (2x+3>11) और \(x\in\mathbb{Z}\), तो सबसे छोटा पूर्णांक हल कौन सा है?

If (2x+3>11) and \(x\in\mathbb{Z}\), what is the smallest integer solution?

Explanation opens after your attempt
Correct Answer

A. (5)

Step 1

Concept

The inequality gives (x>4). Among integers, the smallest solution is (5).

Step 2

Why this answer is correct

The correct answer is A. (5). The inequality gives (x>4). Among integers, the smallest solution is (5).

Step 3

Exam Tip

असमानता से (x>4) मिलता है। पूर्णांकों में सबसे छोटा हल (5) है।

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कौन सा अंतराल (x< -1) को सही दर्शाता है?

Which interval correctly represents (x<-1)?

Explanation opens after your attempt
Correct Answer

A. (\(-\infty,-1\))

Step 1

Concept

In (x<-1), (-1) is not included and all smaller values are included. Hence the open bracket is correct.

Step 2

Why this answer is correct

The correct answer is A. (\(-\infty,-1\)). In (x<-1), (-1) is not included and all smaller values are included. Hence the open bracket is correct.

Step 3

Exam Tip

(x<-1) में (-1) शामिल नहीं है और सभी छोटे मान शामिल हैं। इसलिए खुला कोष्ठक सही है।

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असमानता (9-3x<0) का हल क्या है?

What is the solution of (9-3x<0)?

Explanation opens after your attempt
Correct Answer

A. (x>3)

Step 1

Concept

(-3x<-9), and dividing by (-3) gives (x>3). Always reverse the sign when dividing by a negative.

Step 2

Why this answer is correct

The correct answer is A. (x>3). (-3x<-9), and dividing by (-3) gives (x>3). Always reverse the sign when dividing by a negative.

Step 3

Exam Tip

(-3x<-9) और (-3) से भाग देने पर (x>3) मिलता है। ऋणात्मक भाग में चिन्ह जरूर उलटें।

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कौन सा मान असमानता \(-2<x\leq 3\) को संतुष्ट करता है?

Which value satisfies the inequality \(-2<x\leq 3\)?

Explanation opens after your attempt
Correct Answer

A. (x=3)

Step 1

Concept

(-2) is not included, but (3) is included. Hence (x=3) is a correct value.

Step 2

Why this answer is correct

The correct answer is A. (x=3). (-2) is not included, but (3) is included. Hence (x=3) is a correct value.

Step 3

Exam Tip

(-2) शामिल नहीं है लेकिन (3) शामिल है। इसलिए (x=3) सही मान है।

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यदि (a>b) और (c<0), तो कौन सा निष्कर्ष सही है?

If (a>b) and (c<0), which conclusion is correct?

Explanation opens after your attempt
Correct Answer

A. (ac<bc)

Step 1

Concept

Multiplying by negative (c) changes (>) to (<). Therefore (ac<bc) is correct.

Step 2

Why this answer is correct

The correct answer is A. (ac<bc). Multiplying by negative (c) changes (>) to (<). Therefore (ac<bc) is correct.

Step 3

Exam Tip

ऋणात्मक (c) से गुणा करने पर (>) बदलकर (<) हो जाता है। इसलिए (ac<bc) सही है।

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