यदि \(-2<x\leq 5\), तो सही अंतराल रूप क्या है?
If \(-2<x\leq 5\), what is the correct interval form?
#linear inequalities
#introduction
#class 11
A ((-2,5])
B ([-2,5))
C ((-2,5))
D ([-2,5])
Explanation opens after your attempt
Correct Answer
A. ((-2,5])
Step 1
Concept
(-2) is not included, so use a round bracket, and (5) is included, so use a square bracket. Check both boundaries separately.
Step 2
Why this answer is correct
The correct answer is A. ((-2,5]). (-2) is not included, so use a round bracket, and (5) is included, so use a square bracket. Check both boundaries separately.
Step 3
Exam Tip
(-2) शामिल नहीं है इसलिए गोल कोष्ठक और (5) शामिल है इसलिए वर्ग कोष्ठक लगेगा। दोनों सीमाओं को अलग जांचें।
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असमानता \(\frac{3x-2}{4}\geq 4\) को हल कीजिए।
Solve the inequality \(\frac{3x-2}{4}\geq 4\).
#linear inequalities
#introduction
#class 11
A \(x\geq 6\)
B \(x\leq 6\)
C (x>6)
D (x<6)
Explanation opens after your attempt
Correct Answer
A. \(x\geq 6\)
Step 1
Concept
Multiplying by positive (4) gives \(3x-2\geq 16\), so \(x\geq 6\). A positive denominator does not reverse the sign.
Step 2
Why this answer is correct
The correct answer is A. \(x\geq 6\). Multiplying by positive (4) gives \(3x-2\geq 16\), so \(x\geq 6\). A positive denominator does not reverse the sign.
Step 3
Exam Tip
धनात्मक (4) से गुणा करने पर \(3x-2\geq 16\), इसलिए \(x\geq 6\)। धनात्मक हर से चिन्ह नहीं बदलता।
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असमानता \(12\geq 3x+3\) का हल कौन सा है?
Which is the solution of \(12\geq 3x+3\)?
#linear inequalities
#introduction
#class 11
A \(x\leq 3\)
B \(x\geq 3\)
C (x<3)
D (x>3)
Explanation opens after your attempt
Correct Answer
A. \(x\leq 3\)
Step 1
Concept
From \(9\geq 3x\), we get \(3\geq x\), that is \(x\leq 3\). Reading the direction correctly is important.
Step 2
Why this answer is correct
The correct answer is A. \(x\leq 3\). From \(9\geq 3x\), we get \(3\geq x\), that is \(x\leq 3\). Reading the direction correctly is important.
Step 3
Exam Tip
\(9\geq 3x\) से \(3\geq x\), यानी \(x\leq 3\) मिलता है। दिशा को ठीक से पढ़ना जरूरी है।
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किस संख्या रेखा पर \(x\leq 1\) दिखेगा?
Which number line representation shows \(x\leq 1\)?
#linear inequalities
#introduction
#class 11
A (1) पर बंद वृत्त और बाईं ओर छाया / Closed circle at (1) and shading to the left
B (1) पर खुला वृत्त और बाईं ओर छाया / Open circle at (1) and shading to the left
C (1) पर बंद वृत्त और दाईं ओर छाया / Closed circle at (1) and shading to the right
D (1) पर खुला वृत्त और दाईं ओर छाया / Open circle at (1) and shading to the right
Explanation opens after your attempt
Correct Answer
A. (1) पर बंद वृत्त और बाईं ओर छाया / Closed circle at (1) and shading to the left
Step 1
Concept
In \(x\leq 1\), (1) is included and smaller values are needed. So a closed circle and left-side shading are correct.
Step 2
Why this answer is correct
The correct answer is A. (1) पर बंद वृत्त और बाईं ओर छाया / Closed circle at (1) and shading to the left. In \(x\leq 1\), (1) is included and smaller values are needed. So a closed circle and left-side shading are correct.
Step 3
Exam Tip
\(x\leq 1\) में (1) शामिल है और छोटे मान चाहिए। इसलिए बंद वृत्त और बाईं ओर छाया सही है।
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वाक्य किसी संख्या का (6) से बड़ा होना किस रूप में लिखा जाएगा?
How is the statement a number is greater than (6) written?
#linear inequalities
#introduction
#class 11
A (x>6)
B (x<6)
C \(x\geq 6\)
D \(x\leq 6\)
Explanation opens after your attempt
Step 1
Concept
Greater than means (>). In a word-based question, identifying the correct inequality sign is the first step.
Step 2
Why this answer is correct
The correct answer is A. (x>6). Greater than means (>). In a word-based question, identifying the correct inequality sign is the first step.
Step 3
Exam Tip
से बड़ा का अर्थ (>) होता है। वाक्य आधारित प्रश्न में सही असमानता चिह्न पहचानना पहला कदम है।
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यदि (4x-1>15) और \(x\in\mathbb{Z}\), तो सबसे छोटा पूर्णांक हल कौन सा है?
If (4x-1>15) and \(x\in\mathbb{Z}\), what is the smallest integer solution?
#linear inequalities
#introduction
#class 11
A (5)
B (4)
C (6)
D (3)
Explanation opens after your attempt
Step 1
Concept
The inequality gives (x>4). Among integers, the smallest value greater than this is (5).
Step 2
Why this answer is correct
The correct answer is A. (5). The inequality gives (x>4). Among integers, the smallest value greater than this is (5).
Step 3
Exam Tip
असमानता से (x>4) मिलता है। पूर्णांकों में इससे बड़ा सबसे छोटा मान (5) है।
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कौन सा अंतराल \(x\leq -4\) को सही दर्शाता है?
Which interval correctly represents \(x\leq -4\)?
#linear inequalities
#introduction
#class 11
A (\(-\infty,-4]\)
B (\(-\infty,-4\))
C \([-4,\infty\))
D (\(-4,\infty\))
Explanation opens after your attempt
Correct Answer
A. (\(-\infty,-4]\)
Step 1
Concept
In \(x\leq -4\), (-4) is included and all smaller values are included. Hence (\(-\infty,-4]\) is correct.
Step 2
Why this answer is correct
The correct answer is A. (\(-\infty,-4]\). In \(x\leq -4\), (-4) is included and all smaller values are included. Hence (\(-\infty,-4]\) is correct.
Step 3
Exam Tip
\(x\leq -4\) में (-4) शामिल है और सभी छोटे मान शामिल हैं। इसलिए (\(-\infty,-4]\) सही है।
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असमानता (15-5x<0) का हल क्या है?
What is the solution of (15-5x<0)?
#linear inequalities
#introduction
#class 11
A (x>3)
B (x<3)
C \(x\geq 3\)
D \(x\leq 3\)
Explanation opens after your attempt
Step 1
Concept
(-5x<-15), and dividing by (-5) gives (x>3). The sign must change when dividing by a negative.
Step 2
Why this answer is correct
The correct answer is A. (x>3). (-5x<-15), and dividing by (-5) gives (x>3). The sign must change when dividing by a negative.
Step 3
Exam Tip
(-5x<-15) और (-5) से भाग देने पर (x>3) मिलता है। ऋणात्मक भाग में चिन्ह अवश्य बदलता है।
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कौन सा मान \(-3\leq x<2\) को संतुष्ट करता है?
Which value satisfies \(-3\leq x<2\)?
#linear inequalities
#introduction
#class 11
A (x=-3)
B (x=2)
C (x=3)
D (x=-4)
Explanation opens after your attempt
Step 1
Concept
(-3) is included because \(\leq\) is given. (2) is not included because (<) is given.
Step 2
Why this answer is correct
The correct answer is A. (x=-3). (-3) is included because \(\leq\) is given. (2) is not included because (<) is given.
Step 3
Exam Tip
(-3) शामिल है क्योंकि \(\leq\) दिया है। (2) शामिल नहीं है क्योंकि (<) दिया है।
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यदि दोनों पक्षों को (-3) से गुणा किया जाए, तो असमानता (p<q) क्या बनेगी?
If both sides are multiplied by (-3), what will the inequality (p<q) become?
#linear inequalities
#introduction
#class 11
A (-3p>-3q)
B (-3p<-3q)
C (-3p=-3q)
D (3p>3q)
Explanation opens after your attempt
Correct Answer
A. (-3p>-3q)
Step 1
Concept
Multiplying by a negative number reverses the inequality sign. Hence (<) changes to (>).
Step 2
Why this answer is correct
The correct answer is A. (-3p>-3q). Multiplying by a negative number reverses the inequality sign. Hence (<) changes to (>).
Step 3
Exam Tip
ऋणात्मक संख्या से गुणा करने पर असमानता का चिन्ह उलट जाता है। इसलिए (<) बदलकर (>) होगा।
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असमानता (3(2x-5)\geq x+10) का हल चुनिए।
Choose the solution of (3(2x-5)\geq x+10).
#linear inequalities
#introduction
#class 11
A \(x\geq 5\)
B \(x\leq 5\)
C (x>5)
D (x<5)
Explanation opens after your attempt
Correct Answer
A. \(x\geq 5\)
Step 1
Concept
\(6x-15\geq x+10\) gives \(5x\geq 25\), so \(x\geq 5\). Multiply every term while opening brackets.
Step 2
Why this answer is correct
The correct answer is A. \(x\geq 5\). \(6x-15\geq x+10\) gives \(5x\geq 25\), so \(x\geq 5\). Multiply every term while opening brackets.
Step 3
Exam Tip
\(6x-15\geq x+10\) से \(5x\geq 25\) इसलिए \(x\geq 5\)। कोष्ठक खोलते समय हर पद पर गुणा करें।
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असमानता (4(x+1)>28) का हल क्या होगा?
What will be the solution of (4(x+1)>28)?
#linear inequalities
#introduction
#class 11
A (x>6)
B (x<6)
C (x>7)
D (x<7)
Explanation opens after your attempt
Step 1
Concept
From (x+1>7), we get (x>6). Removing a positive multiplier keeps the direction unchanged.
Step 2
Why this answer is correct
The correct answer is A. (x>6). From (x+1>7), we get (x>6). Removing a positive multiplier keeps the direction unchanged.
Step 3
Exam Tip
(x+1>7) से (x>6) मिलता है। धनात्मक गुणक हटाने पर दिशा वही रहती है।
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असमानता \(9x-4\leq 5x+20\) का सबसे बड़ा पूर्णांक हल क्या है?
What is the greatest integer solution of \(9x-4\leq 5x+20\)?
#linear inequalities
#introduction
#class 11
A (6)
B (5)
C (7)
D (4)
Explanation opens after your attempt
Step 1
Concept
From \(4x\leq 24\), we get \(x\leq 6\). Hence the greatest integer solution is (6).
Step 2
Why this answer is correct
The correct answer is A. (6). From \(4x\leq 24\), we get \(x\leq 6\). Hence the greatest integer solution is (6).
Step 3
Exam Tip
\(4x\leq 24\) से \(x\leq 6\) मिलता है। इसलिए सबसे बड़ा पूर्णांक हल (6) है।
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कौन सा चिह्न बराबरी सहित असमानता को दर्शाता है?
Which symbol represents an inequality including equality?
#linear inequalities
#introduction
#class 11
A \(\geq\)
B
C \(\neq\)
D
Explanation opens after your attempt
Correct Answer
A. \(\geq\)
Step 1
Concept
\(\geq\) means greater than or equal to. Therefore it includes the boundary value.
Step 2
Why this answer is correct
The correct answer is A. \(\geq\). \(\geq\) means greater than or equal to. Therefore it includes the boundary value.
Step 3
Exam Tip
\(\geq\) का अर्थ बड़ा या बराबर होता है। इसलिए इसमें सीमा मान भी शामिल होता है।
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यदि (x) वास्तविक संख्या है, तो कौन सा कथन हमेशा सही है?
If (x) is a real number, which statement is always true?
#linear inequalities
#introduction
#class 11
A \(x^2+1>0\)
B \(x^2-1>0\)
C \(x^2<0\)
D (x+1>0)
Explanation opens after your attempt
Correct Answer
A. \(x^2+1>0\)
Step 1
Concept
Since \(x^2\geq 0\), \(x^2+1>0\) is always true. Remember basic properties in such questions.
Step 2
Why this answer is correct
The correct answer is A. \(x^2+1>0\). Since \(x^2\geq 0\), \(x^2+1>0\) is always true. Remember basic properties in such questions.
Step 3
Exam Tip
\(x^2\geq 0\) होता है इसलिए \(x^2+1>0\) हमेशा सत्य है। ऐसे प्रश्नों में मूल गुण याद रखें।
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असमानता (6x+5<4x+19) का हल क्या है?
What is the solution of (6x+5<4x+19)?
#linear inequalities
#introduction
#class 11
A (x<7)
B (x>7)
C \(x\leq 7\)
D \(x\geq 7\)
Explanation opens after your attempt
Step 1
Concept
From (2x<14), we get (x<7). Simplify the inequality by subtracting like terms from both sides.
Step 2
Why this answer is correct
The correct answer is A. (x<7). From (2x<14), we get (x<7). Simplify the inequality by subtracting like terms from both sides.
Step 3
Exam Tip
(2x<14) से (x<7) मिलता है। दोनों पक्षों के समान पद घटाकर असमानता सरल करें।
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कौन सा अंतराल (x>-5) को दर्शाता है?
Which interval represents (x>-5)?
#linear inequalities
#introduction
#class 11
A (\(-5,\infty\))
B \([-5,\infty\))
C (\(-\infty,-5\))
D (\(-\infty,-5]\)
Explanation opens after your attempt
Correct Answer
A. (\(-5,\infty\))
Step 1
Concept
In (x>-5), (-5) is not included and values go to the right. So an open bracket is used.
Step 2
Why this answer is correct
The correct answer is A. (\(-5,\infty\)). In (x>-5), (-5) is not included and values go to the right. So an open bracket is used.
Step 3
Exam Tip
(x>-5) में (-5) शामिल नहीं है और मान दाईं ओर जाते हैं। इसलिए खुला कोष्ठक लगेगा।
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असमानता \(-8<2x+4\leq 12\) को हल कीजिए।
Solve the inequality \(-8<2x+4\leq 12\).
#linear inequalities
#introduction
#class 11
A \(-6<x\leq 4\)
B \(-6\leq x<4\)
C \(-4<x\leq 6\)
D \(-2<x\leq 8\)
Explanation opens after your attempt
Correct Answer
A. \(-6<x\leq 4\)
Step 1
Concept
Subtracting (4) from all parts and dividing by (2) gives \(-6<x\leq 4\). Identify open and closed boundaries separately.
Step 2
Why this answer is correct
The correct answer is A. \(-6<x\leq 4\). Subtracting (4) from all parts and dividing by (2) gives \(-6<x\leq 4\). Identify open and closed boundaries separately.
Step 3
Exam Tip
सभी भागों से (4) घटाकर (2) से भाग देने पर \(-6<x\leq 4\) मिलता है। खुली और बंद सीमा अलग पहचानें।
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संयुक्त असमानता \(2\leq 3x-1<14\) का हल क्या है?
What is the solution of the compound inequality \(2\leq 3x-1<14\)?
#linear inequalities
#introduction
#class 11
A \(1\leq x<5\)
B \(1<x\leq 5\)
C \(2\leq x<14\)
D \(-1\leq x<4\)
Explanation opens after your attempt
Correct Answer
A. \(1\leq x<5\)
Step 1
Concept
Adding (1) to all parts gives \(3\leq 3x<15\), so \(1\leq x<5\). Apply the same operation to every part of a compound inequality.
Step 2
Why this answer is correct
The correct answer is A. \(1\leq x<5\). Adding (1) to all parts gives \(3\leq 3x<15\), so \(1\leq x<5\). Apply the same operation to every part of a compound inequality.
Step 3
Exam Tip
सभी भागों में (1) जोड़ने पर \(3\leq 3x<15\), इसलिए \(1\leq x<5\)। संयुक्त असमानता में हर भाग पर समान क्रिया करें।
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किस असमानता का हल (\(-\infty,2]\) है?
Which inequality has the solution (\(-\infty,2]\)?
#linear inequalities
#introduction
#class 11
A \(x\leq 2\)
B (x<2)
C \(x\geq 2\)
D (x>2)
Explanation opens after your attempt
Correct Answer
A. \(x\leq 2\)
Step 1
Concept
(\(-\infty,2]\) means all values up to (2). Since (2) is included, \(\leq\) is used.
Step 2
Why this answer is correct
The correct answer is A. \(x\leq 2\). (\(-\infty,2]\) means all values up to (2). Since (2) is included, \(\leq\) is used.
Step 3
Exam Tip
(\(-\infty,2]\) का अर्थ (2) तक के सभी मान हैं। (2) शामिल है इसलिए \(\leq\) प्रयोग होगा।
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यदि \(\frac{x+3}{2}>6\), तो (x) का सबसे छोटा पूर्णांक मान क्या है?
If \(\frac{x+3}{2}>6\), what is the least integer value of (x)?
#linear inequalities
#introduction
#class 11
A (10)
B (9)
C (8)
D (12)
Explanation opens after your attempt
Step 1
Concept
From \(\frac{x+3}{2}>6\), we get (x>9). Hence the least integer solution is (10).
Step 2
Why this answer is correct
The correct answer is A. (10). From \(\frac{x+3}{2}>6\), we get (x>9). Hence the least integer solution is (10).
Step 3
Exam Tip
\(\frac{x+3}{2}>6\) से (x>9) मिलता है। इसलिए सबसे छोटा पूर्णांक हल (10) है।
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असमानता \(\frac{x}{4}-1>2\) का हल कौन सा है?
Which is the solution of \(\frac{x}{4}-1>2\)?
#linear inequalities
#introduction
#class 11
A (x>12)
B (x<12)
C \(x\geq 12\)
D \(x\leq 12\)
Explanation opens after your attempt
Step 1
Concept
\(\frac{x}{4}>3\), so (x>12). Multiplying by positive (4) does not change the sign.
Step 2
Why this answer is correct
The correct answer is A. (x>12). \(\frac{x}{4}>3\), so (x>12). Multiplying by positive (4) does not change the sign.
Step 3
Exam Tip
\(\frac{x}{4}>3\) इसलिए (x>12) है। धनात्मक (4) से गुणा करने पर चिन्ह नहीं बदलता।
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असमानता \(8x-11\geq 5x+10\) का हल क्या है?
What is the solution of \(8x-11\geq 5x+10\)?
#linear inequalities
#introduction
#class 11
A \(x\geq 7\)
B \(x\leq 7\)
C (x>7)
D (x<7)
Explanation opens after your attempt
Correct Answer
A. \(x\geq 7\)
Step 1
Concept
From \(3x\geq 21\), we get \(x\geq 7\). Keep variable terms and constant terms on separate sides.
Step 2
Why this answer is correct
The correct answer is A. \(x\geq 7\). From \(3x\geq 21\), we get \(x\geq 7\). Keep variable terms and constant terms on separate sides.
Step 3
Exam Tip
\(3x\geq 21\) से \(x\geq 7\) मिलता है। चर पदों और स्थिर पदों को अलग तरफ रखें।
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यदि \(x\in\mathbb{W}\) और \(x\leq 4\), तो हल समुच्चय क्या है?
If \(x\in\mathbb{W}\) and \(x\leq 4\), what is the solution set?
#linear inequalities
#introduction
#class 11
A ({0,1,2,3,4})
B ({1,2,3,4})
C ({0,1,2,3})
D (\(-\infty,4]\)
Explanation opens after your attempt
Correct Answer
A. ({0,1,2,3,4})
Step 1
Concept
\(\mathbb{W}\) includes (0). Therefore the whole numbers up to (4) are ({0,1,2,3,4}).
Step 2
Why this answer is correct
The correct answer is A. ({0,1,2,3,4}). \(\mathbb{W}\) includes (0). Therefore the whole numbers up to (4) are ({0,1,2,3,4}).
Step 3
Exam Tip
\(\mathbb{W}\) में (0) भी शामिल होता है। इसलिए (4) तक की पूर्ण संख्याएं ({0,1,2,3,4}) हैं।
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कौन सा मान (3x-2<13) का हल नहीं है?
Which value is not a solution of (3x-2<13)?
#linear inequalities
#introduction
#class 11
A (x=5)
B (x=0)
C (x=-1)
D (x=4)
Explanation opens after your attempt
Step 1
Concept
The inequality gives (x<5). In a strict inequality, (x=5) is not included in the solution.
Step 2
Why this answer is correct
The correct answer is A. (x=5). The inequality gives (x<5). In a strict inequality, (x=5) is not included in the solution.
Step 3
Exam Tip
असमानता से (x<5) मिलता है। कठोर असमानता में (x=5) हल में शामिल नहीं होता।
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असमानता \(11-4x\leq -1\) को हल कीजिए।
Solve the inequality \(11-4x\leq -1\).
#linear inequalities
#introduction
#class 11
A \(x\geq 3\)
B \(x\leq 3\)
C (x>3)
D (x<3)
Explanation opens after your attempt
Correct Answer
A. \(x\geq 3\)
Step 1
Concept
\(-4x\leq -12\), and dividing by (-4) gives \(x\geq 3\). Do not forget to reverse the sign when dividing by a negative.
Step 2
Why this answer is correct
The correct answer is A. \(x\geq 3\). \(-4x\leq -12\), and dividing by (-4) gives \(x\geq 3\). Do not forget to reverse the sign when dividing by a negative.
Step 3
Exam Tip
\(-4x\leq -12\) और (-4) से भाग देने पर \(x\geq 3\) मिलता है। ऋणात्मक भाग में चिन्ह पलटना न भूलें।
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असमानता \(x+9\geq 2\) का अंतराल रूप क्या है?
What is the interval form of \(x+9\geq 2\)?
#linear inequalities
#introduction
#class 11
A \([-7,\infty\))
B (\(-7,\infty\))
C (\(-\infty,-7]\)
D (\(-\infty,-7\))
Explanation opens after your attempt
Correct Answer
A. \([-7,\infty\))
Step 1
Concept
We get \(x\geq -7\), so the interval is \([-7,\infty\)). With equality, the left endpoint is closed.
Step 2
Why this answer is correct
The correct answer is A. \([-7,\infty\)). We get \(x\geq -7\), so the interval is \([-7,\infty\)). With equality, the left endpoint is closed.
Step 3
Exam Tip
\(x\geq -7\) मिलता है इसलिए अंतराल \([-7,\infty\)) होगा। बराबरी होने पर बायां सिरा बंद रहेगा।
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अंतराल ([-4,3)) को असमानता के रूप में कैसे लिखेंगे?
How will the interval ([-4,3)) be written as an inequality?
#linear inequalities
#introduction
#class 11
A \(-4\leq x<3\)
B \(-4<x\leq 3\)
C (-4<x<3)
D \(-4\leq x\leq 3\)
Explanation opens after your attempt
Correct Answer
A. \(-4\leq x<3\)
Step 1
Concept
In ([-4,3)), (-4) is included and (3) is not included. Write the inequality by checking the brackets.
Step 2
Why this answer is correct
The correct answer is A. \(-4\leq x<3\). In ([-4,3)), (-4) is included and (3) is not included. Write the inequality by checking the brackets.
Step 3
Exam Tip
([-4,3)) में (-4) शामिल है और (3) शामिल नहीं है। कोष्ठक देखकर सही असमानता लिखें।
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कौन सा कथन (a<b) के लिए हमेशा सही है?
Which statement is always true for (a<b)?
#linear inequalities
#introduction
#class 11
A (a-5<b-5)
B (-2a<-2b)
C (3-a<3-b)
D \(a^2<b^2\) हर स्थिति में / \(a^2<b^2\) in every case
Explanation opens after your attempt
Correct Answer
A. (a-5<b-5)
Step 1
Concept
Subtracting the same number from both sides does not change the direction. Negative multiplication and squares need extra care.
Step 2
Why this answer is correct
The correct answer is A. (a-5<b-5). Subtracting the same number from both sides does not change the direction. Negative multiplication and squares need extra care.
Step 3
Exam Tip
दोनों पक्षों से समान संख्या घटाने पर दिशा नहीं बदलती। ऋणात्मक गुणा और वर्ग के मामलों में विशेष सावधानी चाहिए।
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यदि (-6x>18), तो (x) के लिए सही असमानता क्या है?
If (-6x>18), what is the correct inequality for (x)?
#linear inequalities
#introduction
#class 11
A (x<-3)
B (x>-3)
C (x<3)
D (x>3)
Explanation opens after your attempt
Step 1
Concept
Dividing by negative (-6) reverses the sign. Therefore (x<-3) is the correct solution.
Step 2
Why this answer is correct
The correct answer is A. (x<-3). Dividing by negative (-6) reverses the sign. Therefore (x<-3) is the correct solution.
Step 3
Exam Tip
ऋणात्मक (-6) से भाग देने पर चिन्ह उलटता है। इसलिए (x<-3) सही हल है।
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