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.

किस स्थिति में असमानता का चिन्ह उलट जाता है?

In which situation does the inequality sign reverse?

Explanation opens after your attempt
Correct Answer

A. दोनों पक्षों को ऋणात्मक संख्या से गुणा करने परWhen both sides are multiplied by a negative number

Step 1

Concept

Multiplying or dividing by a negative number reverses the inequality direction. This is the most common mistake in linear inequalities.

Step 2

Why this answer is correct

The correct answer is A. दोनों पक्षों को ऋणात्मक संख्या से गुणा करने पर / When both sides are multiplied by a negative number. Multiplying or dividing by a negative number reverses the inequality direction. This is the most common mistake in linear inequalities.

Step 3

Exam Tip

ऋणात्मक संख्या से गुणा या भाग करने पर असमानता की दिशा बदलती है। यह रैखिक असमानताओं में सबसे सामान्य गलती है।

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असमानता (2(3x+1)\geq 4x+10) का हल चुनिए।

Choose the solution of (2(3x+1)\geq 4x+10).

Explanation opens after your attempt
Correct Answer

A. \(x\geq 4\)

Step 1

Concept

\(6x+2\geq 4x+10\) gives \(2x\geq 8\), so \(x\geq 4\). Multiply every term while opening brackets.

Step 2

Why this answer is correct

The correct answer is A. \(x\geq 4\). \(6x+2\geq 4x+10\) gives \(2x\geq 8\), so \(x\geq 4\). Multiply every term while opening brackets.

Step 3

Exam Tip

\(6x+2\geq 4x+10\) से \(2x\geq 8\), इसलिए \(x\geq 4\)। कोष्ठक खोलते समय हर पद पर गुणा करें।

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असमानता (3(x-2)>12) का हल क्या होगा?

What will be the solution of (3(x-2)>12)?

Explanation opens after your attempt
Correct Answer

A. (x>6)

Step 1

Concept

From (x-2>4), we get (x>6). Expanding brackets or dividing by positive (3) both work.

Step 2

Why this answer is correct

The correct answer is A. (x>6). From (x-2>4), we get (x>6). Expanding brackets or dividing by positive (3) both work.

Step 3

Exam Tip

(x-2>4) से (x>6) मिलता है। पहले कोष्ठक खोलना या धनात्मक (3) से भाग देना दोनों सही हैं।

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असमानता \(6x+1\leq 2x+17\) का सबसे बड़ा पूर्णांक हल क्या है?

What is the greatest integer solution of \(6x+1\leq 2x+17\)?

Explanation opens after your attempt
Correct Answer

A. (4)

Step 1

Concept

From \(4x\leq 16\), we get \(x\leq 4\). Hence the greatest integer solution is (4).

Step 2

Why this answer is correct

The correct answer is A. (4). From \(4x\leq 16\), we get \(x\leq 4\). Hence the greatest integer solution is (4).

Step 3

Exam Tip

\(4x\leq 16\) से \(x\leq 4\) मिलता है। इसलिए सबसे बड़ा पूर्णांक हल (4) है।

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कौन सा चिह्न कठोर असमानता को दर्शाता है?

Which symbol represents a strict inequality?

Explanation opens after your attempt
Correct Answer

A.

Step 1

Concept

(<) and (>) are strict inequalities because equality is not included. \(\leq\) and \(\geq\) include equality.

Step 2

Why this answer is correct

The correct answer is A. . (<) and (>) are strict inequalities because equality is not included. \(\leq\) and \(\geq\) include equality.

Step 3

Exam Tip

(<) और (>) कठोर असमानताएं हैं क्योंकि बराबरी शामिल नहीं होती। \(\leq\) और \(\geq\) में बराबरी शामिल होती है।

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यदि (x) वास्तविक संख्या है, तो \(x^2\geq 0\) किस प्रकार का कथन है?

If (x) is a real number, what type of statement is \(x^2\geq 0\)?

Explanation opens after your attempt
Correct Answer

A. हमेशा सत्यAlways true

Step 1

Concept

The square of any real number is never negative. This is a basic inequality concept.

Step 2

Why this answer is correct

The correct answer is A. हमेशा सत्य / Always true. The square of any real number is never negative. This is a basic inequality concept.

Step 3

Exam Tip

किसी भी वास्तविक संख्या का वर्ग ऋणात्मक नहीं होता। यह मूलभूत असमानता अवधारणा है।

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असमानता (4x-5<2x+7) का हल क्या है?

What is the solution of (4x-5<2x+7)?

Explanation opens after your attempt
Correct Answer

A. (x<6)

Step 1

Concept

From (2x<12), we get (x<6). Combine like terms to form a simple linear inequality.

Step 2

Why this answer is correct

The correct answer is A. (x<6). From (2x<12), we get (x<6). Combine like terms to form a simple linear inequality.

Step 3

Exam Tip

(2x<12) से (x<6) मिलता है। समान पदों को मिलाकर सरल रैखिक असमानता बनाएं।

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कौन सा अंतराल \(x\geq -2\) को दर्शाता है?

Which interval represents \(x\geq -2\)?

Explanation opens after your attempt
Correct Answer

A. \([-2,\infty\))

Step 1

Concept

In \(x\geq -2\), (-2) is included and values go to the right. So \([-2,\infty\)) is correct.

Step 2

Why this answer is correct

The correct answer is A. \([-2,\infty\)). In \(x\geq -2\), (-2) is included and values go to the right. So \([-2,\infty\)) is correct.

Step 3

Exam Tip

\(x\geq -2\) में (-2) शामिल है और मान दाईं ओर जाते हैं। इसलिए \([-2,\infty\)) सही है।

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असमानता \(-3\leq x+2<8\) को हल कीजिए।

Solve the inequality \(-3\leq x+2<8\).

Explanation opens after your attempt
Correct Answer

A. \(-5\leq x<6\)

Step 1

Concept

Subtracting (2) from all parts gives \(-5\leq x<6\). The equality sign remains on the same boundary.

Step 2

Why this answer is correct

The correct answer is A. \(-5\leq x<6\). Subtracting (2) from all parts gives \(-5\leq x<6\). The equality sign remains on the same boundary.

Step 3

Exam Tip

सभी भागों से (2) घटाने पर \(-5\leq x<6\) मिलता है। बराबरी वाला चिन्ह उसी तरफ बना रहता है।

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संयुक्त असमानता \(1<2x+3\leq 11\) का हल क्या है?

What is the solution of the compound inequality \(1<2x+3\leq 11\)?

Explanation opens after your attempt
Correct Answer

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

Step 1

Concept

Subtracting (3) from all parts gives \(-2<2x\leq 8\), so \(-1<x\leq 4\). Handle both bounds together in compound inequalities.

Step 2

Why this answer is correct

The correct answer is A. \(-1<x\leq 4\). Subtracting (3) from all parts gives \(-2<2x\leq 8\), so \(-1<x\leq 4\). Handle both bounds together in compound inequalities.

Step 3

Exam Tip

सभी भागों से (3) घटाने पर \(-2<2x\leq 8\), इसलिए \(-1<x\leq 4\)। संयुक्त असमानता में दोनों सीमाएं साथ संभालें।

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किस असमानता का हल (\(-\infty,6\)) है?

Which inequality has the solution (\(-\infty,6\))?

Explanation opens after your attempt
Correct Answer

A. (x<6)

Step 1

Concept

(\(-\infty,6\)) means all real values less than (6). Since (6) is not included, (x<6) is correct.

Step 2

Why this answer is correct

The correct answer is A. (x<6). (\(-\infty,6\)) means all real values less than (6). Since (6) is not included, (x<6) is correct.

Step 3

Exam Tip

(\(-\infty,6\)) का अर्थ (6) से छोटे सभी वास्तविक मान हैं। (6) शामिल नहीं है, इसलिए (x<6) सही है।

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यदि \(\frac{x-1}{2}\geq 4\), तो (x) का न्यूनतम पूर्णांक मान क्या है?

If \(\frac{x-1}{2}\geq 4\), what is the least integer value of (x)?

Explanation opens after your attempt
Correct Answer

A. (9)

Step 1

Concept

From \(\frac{x-1}{2}\geq 4\), we get \(x\geq 9\). Hence the least integer is (9).

Step 2

Why this answer is correct

The correct answer is A. (9). From \(\frac{x-1}{2}\geq 4\), we get \(x\geq 9\). Hence the least integer is (9).

Step 3

Exam Tip

\(\frac{x-1}{2}\geq 4\) से \(x\geq 9\) मिलता है। इसलिए न्यूनतम पूर्णांक (9) है।

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असमानता \(\frac{x}{3}+2<5\) का हल कौन सा है?

Which is the solution of \(\frac{x}{3}+2<5\)?

Explanation opens after your attempt
Correct Answer

A. (x<9)

Step 1

Concept

\(\frac{x}{3}<3\), so (x<9). Multiplying by positive (3) does not change the sign.

Step 2

Why this answer is correct

The correct answer is A. (x<9). \(\frac{x}{3}<3\), so (x<9). Multiplying by positive (3) does not change the sign.

Step 3

Exam Tip

\(\frac{x}{3}<3\) इसलिए (x<9) है। धनात्मक (3) से गुणा करने पर चिन्ह नहीं बदलता।

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असमानता \(7x+3\geq 3x+15\) का हल क्या है?

What is the solution of \(7x+3\geq 3x+15\)?

Explanation opens after your attempt
Correct Answer

A. \(x\geq 3\)

Step 1

Concept

From \(4x\geq 12\), we get \(x\geq 3\). Bringing variable terms to one side is a simple method.

Step 2

Why this answer is correct

The correct answer is A. \(x\geq 3\). From \(4x\geq 12\), we get \(x\geq 3\). Bringing variable terms to one side is a simple method.

Step 3

Exam Tip

\(4x\geq 12\) से \(x\geq 3\) मिलता है। चर वाले पदों को एक तरफ लाना सरल तरीका है।

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यदि \(x\in\mathbb{N}\) और (x<5), तो हल समुच्चय क्या होगा?

If \(x\in\mathbb{N}\) and (x<5), what is the solution set?

Explanation opens after your attempt
Correct Answer

A. ({1,2,3,4})

Step 1

Concept

Usually, \(\mathbb{N}\) means \(1,2,3,\ldots\). Thus the natural numbers less than (5) are ({1,2,3,4}).

Step 2

Why this answer is correct

The correct answer is A. ({1,2,3,4}). Usually, \(\mathbb{N}\) means \(1,2,3,\ldots\). Thus the natural numbers less than (5) are ({1,2,3,4}).

Step 3

Exam Tip

\(\mathbb{N}\) में सामान्यतः \(1,2,3,\ldots\) लिए जाते हैं। इसलिए (5) से छोटे प्राकृतिक मान ({1,2,3,4}) हैं।

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कौन सा मान (2x+1<9) का हल नहीं है?

Which value is not a solution of (2x+1<9)?

Explanation opens after your attempt
Correct Answer

A. (x=4)

Step 1

Concept

The inequality gives (x<4), so (x=4) is not included. In a strict inequality, the boundary value is not a solution.

Step 2

Why this answer is correct

The correct answer is A. (x=4). The inequality gives (x<4), so (x=4) is not included. In a strict inequality, the boundary value is not a solution.

Step 3

Exam Tip

असमानता से (x<4) मिलता है, इसलिए (x=4) शामिल नहीं है। कठोर असमानता में सीमा मान हल नहीं होता।

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असमानता \(5-2x\geq 1\) को हल कीजिए।

Solve the inequality \(5-2x\geq 1\).

Explanation opens after your attempt
Correct Answer

A. \(x\leq 2\)

Step 1

Concept

\(-2x\geq -4\), and dividing by a negative gives \(x\leq 2\). Reversing the sign is the key step here.

Step 2

Why this answer is correct

The correct answer is A. \(x\leq 2\). \(-2x\geq -4\), and dividing by a negative gives \(x\leq 2\). Reversing the sign is the key step here.

Step 3

Exam Tip

\(-2x\geq -4\) और ऋणात्मक से भाग देने पर \(x\leq 2\) मिलता है। ऐसे प्रश्नों में चिन्ह पलटना सबसे महत्वपूर्ण है।

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असमानता \(x-4\geq 6\) का हल समुच्चय क्या है?

What is the solution set of \(x-4\geq 6\)?

Explanation opens after your attempt
Correct Answer

A. \([10,\infty\))

Step 1

Concept

We get \(x\geq 10\), so the interval is \([10,\infty\)). With \(\geq\), (10) is included.

Step 2

Why this answer is correct

The correct answer is A. \([10,\infty\)). We get \(x\geq 10\), so the interval is \([10,\infty\)). With \(\geq\), (10) is included.

Step 3

Exam Tip

\(x\geq 10\) मिलता है, इसलिए अंतराल \([10,\infty\)) है। \(\geq\) होने पर (10) शामिल रहेगा।

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अंतराल ((2,7]) को असमानता के रूप में कैसे लिखेंगे?

How will the interval ((2,7]) be written as an inequality?

Explanation opens after your attempt
Correct Answer

A. \(2<x\leq 7\)

Step 1

Concept

In ((2,7]), (2) is not included and (7) is included. Identify open and closed brackets carefully.

Step 2

Why this answer is correct

The correct answer is A. \(2<x\leq 7\). In ((2,7]), (2) is not included and (7) is included. Identify open and closed brackets carefully.

Step 3

Exam Tip

((2,7]) में (2) शामिल नहीं और (7) शामिल है। खुले और बंद कोष्ठक को ध्यान से पहचानें।

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यदि (-4x<20), तो सही हल क्या होगा?

If (-4x<20), what is the correct solution?

Explanation opens after your attempt
Correct Answer

A. (x>-5)

Step 1

Concept

Dividing by the negative number (-4) reverses the inequality sign. Hence (x>-5) is correct.

Step 2

Why this answer is correct

The correct answer is A. (x>-5). Dividing by the negative number (-4) reverses the inequality sign. Hence (x>-5) is correct.

Step 3

Exam Tip

ऋणात्मक संख्या (-4) से भाग देने पर असमानता का चिन्ह बदलता है। इसलिए (x>-5) सही है।

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असमानता \(2x-7\leq 9\) का हल चुनिए।

Choose the solution of the inequality \(2x-7\leq 9\).

Explanation opens after your attempt
Correct Answer

A. \(x\leq 8\)

Step 1

Concept

Since \(2x\leq 16\), \(x\leq 8\). In \(\leq\), the boundary value is included.

Step 2

Why this answer is correct

The correct answer is A. \(x\leq 8\). Since \(2x\leq 16\), \(x\leq 8\). In \(\leq\), the boundary value is included.

Step 3

Exam Tip

\(2x\leq 16\) इसलिए \(x\leq 8\) है। \(\leq\) में सीमा भी हल में शामिल होती है।

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असमानता (3x+5>14) का हल कौन सा है?

What is the solution of the inequality (3x+5>14)?

Explanation opens after your attempt
Correct Answer

A. (x>3)

Step 1

Concept

From (3x>9), we get (x>3). In exams, subtracting the same number from both sides keeps the sign unchanged.

Step 2

Why this answer is correct

The correct answer is A. (x>3). From (3x>9), we get (x>3). In exams, subtracting the same number from both sides keeps the sign unchanged.

Step 3

Exam Tip

(3x>9) से (x>3) मिलता है। परीक्षा में दोनों पक्षों से समान संख्या घटाना सुरक्षित रहता है।

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यदि (f(x)=3x-2) और (g(x)=2x-2+1), तो ((f+g)(x)) किसके बराबर है?

If (f(x)=3x-2) and (g(x)=2x-2+1), then ((f+g)(x)) is equal to which expression?

Explanation opens after your attempt
Correct Answer

A. \(5x^2+1\)

Step 1

Concept

((f+g)(x)=3x-2+2x-2+1=5x-2+1). Add terms with the same power.

Step 2

Why this answer is correct

The correct answer is A. \(5x^2+1\). ((f+g)(x)=3x-2+2x-2+1=5x-2+1). Add terms with the same power.

Step 3

Exam Tip

((f+g)(x)=3x-2+2x-2+1=5x-2+1)। समान घात वाले पद जोड़ें।

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यदि (f(x)=x-2-1) और (g(x)=x-2+1), तो ((f+g)(x)) क्या है?

If (f(x)=x-2-1) and (g(x)=x-2+1), what is ((f+g)(x))?

Explanation opens after your attempt
Correct Answer

A. \(2x^2\)

Step 1

Concept

((f+g)(x)=x-2-1+x-2+1=2x-2). The constant terms (-1) and (1) cancel out.

Step 2

Why this answer is correct

The correct answer is A. \(2x^2\). ((f+g)(x)=x-2-1+x-2+1=2x-2). The constant terms (-1) and (1) cancel out.

Step 3

Exam Tip

((f+g)(x)=x-2-1+x-2+1=2x-2)। स्थिर पद (-1) और (1) कट जाते हैं।

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यदि (f(x)=x-2+2x) और (g(x)=x-2-x), तो ((f-g)(x)) क्या है?

If (f(x)=x-2+2x) and (g(x)=x-2-x), what is ((f-g)(x))?

Explanation opens after your attempt
Correct Answer

A. (3x)

Step 1

Concept

((f-g)(x)=x-2+2x-\(x^2-x\)=3x). The like \(x^2\) terms cancel out.

Step 2

Why this answer is correct

The correct answer is A. (3x). ((f-g)(x)=x-2+2x-\(x^2-x\)=3x). The like \(x^2\) terms cancel out.

Step 3

Exam Tip

((f-g)(x)=x-2+2x-\(x^2-x\)=3x)। समान \(x^2\) पद कट जाते हैं।

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यदि (f(x)=x+4), तो ((2f)(x)) क्या होगा?

If (f(x)=x+4), what is ((2f)(x))?

Explanation opens after your attempt
Correct Answer

A. (2x+8)

Step 1

Concept

((2f)(x)=2f(x)=2(x+4)=2x+8). In scalar multiplication, multiply every term.

Step 2

Why this answer is correct

The correct answer is A. (2x+8). ((2f)(x)=2f(x)=2(x+4)=2x+8). In scalar multiplication, multiply every term.

Step 3

Exam Tip

((2f)(x)=2f(x)=2(x+4)=2x+8)। स्थिर गुणन में हर पद से गुणा करें।

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यदि (f(x)=x-2) और (g(x)=4), तो ((f+g)(2)) का मान क्या है?

If (f(x)=x-2) and (g(x)=4), what is the value of ((f+g)(2))?

Explanation opens after your attempt
Correct Answer

A. (8)

Step 1

Concept

((f+g)(2)=f(2)+g(2)=4+4=8). You may add functions first or substitute directly.

Step 2

Why this answer is correct

The correct answer is A. (8). ((f+g)(2)=f(2)+g(2)=4+4=8). You may add functions first or substitute directly.

Step 3

Exam Tip

((f+g)(2)=f(2)+g(2)=4+4=8)। पहले फलन जोड़ें या सीधे मान रखें।

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यदि (f(x)=2x+6) और (g(x)=2), तो (\left\(\frac{f}{g}\right\)(x)) क्या होगा?

If (f(x)=2x+6) and (g(x)=2), what is (\left\(\frac{f}{g}\right\)(x))?

Explanation opens after your attempt
Correct Answer

A. (x+3)

Step 1

Concept

In division, (\left\(\frac{f}{g}\right\)(x)=\frac{2x+6}{2}=x+3). The denominator must not be zero.

Step 2

Why this answer is correct

The correct answer is A. (x+3). In division, (\left\(\frac{f}{g}\right\)(x)=\frac{2x+6}{2}=x+3). The denominator must not be zero.

Step 3

Exam Tip

भाग में (\left\(\frac{f}{g}\right\)(x)=\frac{2x+6}{2}=x+3)। हर शून्य नहीं होना चाहिए।

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यदि (f(x)=x+1) और (g(x)=x-1), तो ((fg)(x)) क्या है?

If (f(x)=x+1) and (g(x)=x-1), what is ((fg)(x))?

Explanation opens after your attempt
Correct Answer

A. \(x^2-1\)

Step 1

Concept

In multiplication, ((fg)(x)=f(x)g(x)), so ((x+1)(x-1)=x-2-1). Remember the identity \(a^2-b^2\).

Step 2

Why this answer is correct

The correct answer is A. \(x^2-1\). In multiplication, ((fg)(x)=f(x)g(x)), so ((x+1)(x-1)=x-2-1). Remember the identity \(a^2-b^2\).

Step 3

Exam Tip

गुणन में ((fg)(x)=f(x)g(x)), इसलिए ((x+1)(x-1)=x-2-1)। पहचान \(a^2-b^2\) याद रखें।

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यदि (f(x)=5x-1) और (g(x)=2x+4), तो ((f-g)(x)) ज्ञात कीजिए।

If (f(x)=5x-1) and (g(x)=2x+4), find ((f-g)(x)).

Explanation opens after your attempt
Correct Answer

A. (3x-5)

Step 1

Concept

((f-g)(x)=(5x-1)-(2x+4)=3x-5). In subtraction, change every sign of the second function.

Step 2

Why this answer is correct

The correct answer is A. (3x-5). ((f-g)(x)=(5x-1)-(2x+4)=3x-5). In subtraction, change every sign of the second function.

Step 3

Exam Tip

((f-g)(x)=(5x-1)-(2x+4)=3x-5)। घटाने में दूसरे फलन के सभी चिह्न बदलें।

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