असमानता (4x+6>22) का हल कौन सा है?
Which is the solution of the inequality (4x+6>22)?
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A (x>4)
B (x<4)
C \(x\geq 4\)
D \(x\leq 4\)
Explanation opens after your attempt
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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असमानता \(5x-3\leq 17\) का सही हल चुनिए।
Choose the correct solution of \(5x-3\leq 17\).
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A \(x\leq 4\)
B \(x\geq 4\)
C (x<4)
D (x>4)
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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यदि (-6x>18), तो (x) के लिए सही असमानता क्या है?
If (-6x>18), what is the correct inequality for (x)?
#linear inequalities
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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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कौन सा कथन (a<b) के लिए हमेशा सही है?
Which statement is always true for (a<b)?
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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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अंतराल ([-4,3)) को असमानता के रूप में कैसे लिखेंगे?
How will the interval ([-4,3)) be written as an inequality?
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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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असमानता \(x+9\geq 2\) का अंतराल रूप क्या है?
What is the interval form of \(x+9\geq 2\)?
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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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असमानता \(11-4x\leq -1\) को हल कीजिए।
Solve the inequality \(11-4x\leq -1\).
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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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कौन सा मान (3x-2<13) का हल नहीं है?
Which value is not a solution of (3x-2<13)?
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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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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?
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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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असमानता \(8x-11\geq 5x+10\) का हल क्या है?
What is the solution of \(8x-11\geq 5x+10\)?
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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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असमानता \(\frac{x}{4}-1>2\) का हल कौन सा है?
Which is the solution of \(\frac{x}{4}-1>2\)?
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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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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
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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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किस असमानता का हल (\(-\infty,2]\) है?
Which inequality has the solution (\(-\infty,2]\)?
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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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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
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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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असमानता \(-8<2x+4\leq 12\) को हल कीजिए।
Solve the inequality \(-8<2x+4\leq 12\).
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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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कौन सा अंतराल (x>-5) को दर्शाता है?
Which interval represents (x>-5)?
#linear inequalities
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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 (6x+5<4x+19) का हल क्या है?
What is the solution of (6x+5<4x+19)?
#linear inequalities
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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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यदि (x) वास्तविक संख्या है, तो कौन सा कथन हमेशा सही है?
If (x) is a real number, which statement is always true?
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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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कौन सा चिह्न बराबरी सहित असमानता को दर्शाता है?
Which symbol represents an inequality including equality?
#linear inequalities
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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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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
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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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असमानता (4(x+1)>28) का हल क्या होगा?
What will be the solution of (4(x+1)>28)?
#linear inequalities
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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 (3(2x-5)\geq x+10) का हल चुनिए।
Choose the solution of (3(2x-5)\geq x+10).
#linear inequalities
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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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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
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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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कौन सा मान \(-3\leq x<2\) को संतुष्ट करता है?
Which value satisfies \(-3\leq x<2\)?
#linear inequalities
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#class 11
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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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असमानता (15-5x<0) का हल क्या है?
What is the solution of (15-5x<0)?
#linear inequalities
#introduction
#class 11
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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 अंतराल \(x\leq -4\) को सही दर्शाता है?
Which interval correctly represents \(x\leq -4\)?
#linear inequalities
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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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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
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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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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
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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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किस संख्या रेखा पर \(x\leq 1\) दिखेगा?
Which number line representation shows \(x\leq 1\)?
#linear inequalities
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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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असमानता \(12\geq 3x+3\) का हल कौन सा है?
Which is the solution of \(12\geq 3x+3\)?
#linear inequalities
#introduction
#class 11
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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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असमानता \(\frac{3x-2}{4}\geq 4\) को हल कीजिए।
Solve the inequality \(\frac{3x-2}{4}\geq 4\).
#linear inequalities
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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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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
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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 (14<2x+4) का हल क्या है?
What is the solution of (14<2x+4)?
#linear inequalities
#introduction
#class 11
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A (x>5)
B (x<5)
C \(x\geq 5\)
D \(x\leq 5\)
Explanation opens after your attempt
Step 1
Concept
From (10<2x), we get (5<x), that is (x>5). (5<x) and (x>5) are the same.
Step 2
Why this answer is correct
The correct answer is A. (x>5). From (10<2x), we get (5<x), that is (x>5). (5<x) and (x>5) are the same.
Step 3
Exam Tip
(10<2x) से (5<x), अर्थात (x>5) मिलता है। (5<x) और (x>5) समान हैं।
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यदि (x-2<5) और \(x\in\mathbb{Z}\) तथा \(x\geq 2\), तो संभावित मान कौन से हैं?
If (x-2<5), \(x\in\mathbb{Z}\), and \(x\geq 2\), which values are possible?
#linear inequalities
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A ({2,3,4,5,6})
B ({2,3,4,5,6,7})
C ({1,2,3,4,5,6})
D ({3,4,5,6,7})
Explanation opens after your attempt
Correct Answer
A. ({2,3,4,5,6})
Step 1
Concept
(x-2<5) gives (x<7), and \(x\geq 2\). Therefore the integer values are ({2,3,4,5,6}).
Step 2
Why this answer is correct
The correct answer is A. ({2,3,4,5,6}). (x-2<5) gives (x<7), and \(x\geq 2\). Therefore the integer values are ({2,3,4,5,6}).
Step 3
Exam Tip
(x-2<5) से (x<7) और \(x\geq 2\) है। इसलिए पूर्णांक मान ({2,3,4,5,6}) होंगे।
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कौन सा कथन (x< -2) के बारे में सही है?
Which statement about (x<-2) is correct?
#linear inequalities
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A (-2) हल में शामिल नहीं है / (-2) is not included in the solution
B (-2) हल में शामिल है / (-2) is included in the solution
C केवल (x=-2) हल है / Only (x=-2) is the solution
D केवल (x>-2) हल है / Only (x>-2) is the solution
Explanation opens after your attempt
Correct Answer
A. (-2) हल में शामिल नहीं है / (-2) is not included in the solution
Step 1
Concept
The strict inequality (<) does not include the boundary value. On the number line, an open circle is drawn at (-2).
Step 2
Why this answer is correct
The correct answer is A. (-2) हल में शामिल नहीं है / (-2) is not included in the solution. The strict inequality (<) does not include the boundary value. On the number line, an open circle is drawn at (-2).
Step 3
Exam Tip
कठोर असमानता (<) सीमा मान को शामिल नहीं करती। संख्या रेखा पर (-2) पर खुला वृत्त बनेगा।
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असमानता (5x+1>2x+16) का हल चुनिए।
Choose the solution of (5x+1>2x+16).
#linear inequalities
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A (x>5)
B (x<5)
C \(x\geq 5\)
D \(x\leq 5\)
Explanation opens after your attempt
Step 1
Concept
From (3x>15), we get (x>5). Since equality is not present, (5) will not be included.
Step 2
Why this answer is correct
The correct answer is A. (x>5). From (3x>15), we get (x>5). Since equality is not present, (5) will not be included.
Step 3
Exam Tip
(3x>15) से (x>5) मिलता है। बराबरी नहीं है इसलिए (5) शामिल नहीं होगा।
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यदि (x>0), तो (-2x) के बारे में क्या सही है?
If (x>0), what is true about (-2x)?
#linear inequalities
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A (-2x<0)
B (-2x>0)
C (-2x=0)
D \(-2x\geq 0\)
Explanation opens after your attempt
Correct Answer
A. (-2x<0)
Step 1
Concept
Multiplying positive (x) by negative (-2) gives a negative result. Therefore (-2x<0) is correct.
Step 2
Why this answer is correct
The correct answer is A. (-2x<0). Multiplying positive (x) by negative (-2) gives a negative result. Therefore (-2x<0) is correct.
Step 3
Exam Tip
धनात्मक (x) को ऋणात्मक (-2) से गुणा करने पर परिणाम ऋणात्मक होता है। इसलिए (-2x<0) सही है।
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असमानता \(3x+7\leq x+19\) में सीमा मान क्या है?
What is the boundary value in the inequality \(3x+7\leq x+19\)?
#linear inequalities
#introduction
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A (6)
B (7)
C (8)
D (5)
Explanation opens after your attempt
Step 1
Concept
The boundary value is found by using equality: (3x+7=x+19), so (x=6). The boundary value decides the final interval.
Step 2
Why this answer is correct
The correct answer is A. (6). The boundary value is found by using equality: (3x+7=x+19), so (x=6). The boundary value decides the final interval.
Step 3
Exam Tip
सीमा मान बराबरी लगाकर मिलता है: (3x+7=x+19), इसलिए (x=6)। सीमा मान से अंतिम अंतराल तय होता है।
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किस असमानता का हल \(x\geq -1\) है?
Which inequality has the solution \(x\geq -1\)?
#linear inequalities
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A \(x+1\geq 0\)
B \(x-1\geq 0\)
C \(x+1\leq 0\)
D \(x-1\leq 0\)
Explanation opens after your attempt
Correct Answer
A. \(x+1\geq 0\)
Step 1
Concept
\(x+1\geq 0\) gives \(x\geq -1\). Solving and matching the options is a useful method.
Step 2
Why this answer is correct
The correct answer is A. \(x+1\geq 0\). \(x+1\geq 0\) gives \(x\geq -1\). Solving and matching the options is a useful method.
Step 3
Exam Tip
\(x+1\geq 0\) से \(x\geq -1\) मिलता है। विकल्पों को हल करके मिलान करना उपयोगी तरीका है।
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यदि \(7x\geq -21\), तो सही हल क्या है?
If \(7x\geq -21\), what is the correct solution?
#linear inequalities
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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
Dividing by positive (7) does not change the direction of the inequality. Therefore \(x\geq -3\).
Step 2
Why this answer is correct
The correct answer is A. \(x\geq -3\). Dividing by positive (7) does not change the direction of the inequality. Therefore \(x\geq -3\).
Step 3
Exam Tip
धनात्मक (7) से भाग देने पर असमानता की दिशा नहीं बदलती। इसलिए \(x\geq -3\) है।
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असमानता \(-7x\leq 28\) को हल कीजिए।
Solve the inequality \(-7x\leq 28\).
#linear inequalities
#introduction
#class 11
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A \(x\geq -4\)
B \(x\leq -4\)
C (x>-4)
D (x<-4)
Explanation opens after your attempt
Correct Answer
A. \(x\geq -4\)
Step 1
Concept
Dividing by (-7) reverses the sign to \(\geq\). Therefore \(x\geq -4\) is obtained.
Step 2
Why this answer is correct
The correct answer is A. \(x\geq -4\). Dividing by (-7) reverses the sign to \(\geq\). Therefore \(x\geq -4\) is obtained.
Step 3
Exam Tip
(-7) से भाग देने पर चिन्ह उलटकर \(\geq\) हो जाता है। इसलिए \(x\geq -4\) मिलता है।
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कौन सा विकल्प \({x:x\leq 8}\) का अंतराल रूप है?
Which option is the interval form of \({x:x\leq 8}\)?
#linear inequalities
#introduction
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A (\(-\infty,8]\)
B (\(-\infty,8\))
C \([8,\infty\))
D (\(8,\infty\))
Explanation opens after your attempt
Correct Answer
A. (\(-\infty,8]\)
Step 1
Concept
In \(x\leq 8\), (8) is included and all smaller values are taken. Hence (\(-\infty,8]\) is correct.
Step 2
Why this answer is correct
The correct answer is A. (\(-\infty,8]\). In \(x\leq 8\), (8) is included and all smaller values are taken. Hence (\(-\infty,8]\) is correct.
Step 3
Exam Tip
\(x\leq 8\) में (8) शामिल है और उससे छोटे सभी मान आते हैं। इसलिए (\(-\infty,8]\) सही है।
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यदि \(0<x\leq 4\), तो निम्न में से कौन सा मान हल है?
If \(0<x\leq 4\), which of the following is a solution?
#linear inequalities
#introduction
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A (x=4)
B (x=0)
C (x=5)
D (x=-1)
Explanation opens after your attempt
Step 1
Concept
(0) is not included, but (4) is included. Therefore (x=4) is correct among the given options.
Step 2
Why this answer is correct
The correct answer is A. (x=4). (0) is not included, but (4) is included. Therefore (x=4) is correct among the given options.
Step 3
Exam Tip
(0) शामिल नहीं है लेकिन (4) शामिल है। इसलिए दिए गए विकल्पों में (x=4) सही है।
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असमानता \(6-\frac{x}{3}\geq 2\) का हल क्या है?
What is the solution of \(6-\frac{x}{3}\geq 2\)?
#linear inequalities
#introduction
#class 11
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A \(x\leq 12\)
B \(x\geq 12\)
C (x<12)
D (x>12)
Explanation opens after your attempt
Correct Answer
A. \(x\leq 12\)
Step 1
Concept
\(-\frac{x}{3}\geq -4\), and removing the negative factor gives \(x\leq 12\). Identify when the sign must be reversed.
Step 2
Why this answer is correct
The correct answer is A. \(x\leq 12\). \(-\frac{x}{3}\geq -4\), and removing the negative factor gives \(x\leq 12\). Identify when the sign must be reversed.
Step 3
Exam Tip
\(-\frac{x}{3}\geq -4\) से ऋणात्मक गुणक हटाने पर \(x\leq 12\) मिलता है। चिन्ह बदलने की स्थिति पहचानें।
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किसी संख्या में (8) जोड़ने पर परिणाम (15) से कम है। सही असमानता क्या है?
A number increased by (8) is less than (15). What is the correct inequality?
#linear inequalities
#introduction
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A (x+8<15)
B (x+8>15)
C (8x<15)
D (x-8<15)
Explanation opens after your attempt
Correct Answer
A. (x+8<15)
Step 1
Concept
Increasing a number by (8) is (x+8), and less than means (<). Identify the main operation in word problems.
Step 2
Why this answer is correct
The correct answer is A. (x+8<15). Increasing a number by (8) is (x+8), and less than means (<). Identify the main operation in word problems.
Step 3
Exam Tip
संख्या में (8) जोड़ना (x+8) है और से कम का अर्थ (<) होता है। शब्द प्रश्नों में मुख्य क्रिया पहचानें।
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कौन सा कथन (x>9) और \(x\geq 9\) में अंतर बताता है?
Which statement explains the difference between (x>9) and \(x\geq 9\)?
#linear inequalities
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#class 11
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A \(x\geq 9\) में (9) शामिल है / \(x\geq 9\) includes (9)
B (x>9) में (9) शामिल है / (x>9) includes (9)
C दोनों में (9) शामिल नहीं है / (9) is not included in both
D दोनों केवल (9) को दर्शाते हैं / Both represent only (9)
Explanation opens after your attempt
Correct Answer
A. \(x\geq 9\) में (9) शामिल है / \(x\geq 9\) includes (9)
Step 1
Concept
(>) does not include the boundary, but \(\geq\) includes it. This decides the open or closed circle.
Step 2
Why this answer is correct
The correct answer is A. \(x\geq 9\) में (9) शामिल है / \(x\geq 9\) includes (9). (>) does not include the boundary, but \(\geq\) includes it. This decides the open or closed circle.
Step 3
Exam Tip
(>) सीमा को शामिल नहीं करता लेकिन \(\geq\) सीमा को शामिल करता है। इसी से खुला या बंद वृत्त तय होता है।
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असमानता \(5\leq x+2<11\) का हल क्या है?
What is the solution of \(5\leq x+2<11\)?
#linear inequalities
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#class 11
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A \(3\leq x<9\)
B \(3<x\leq 9\)
C \(7\leq x<13\)
D \(2\leq x<8\)
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Correct Answer
A. \(3\leq x<9\)
Step 1
Concept
Subtracting (2) from all parts gives \(3\leq x<9\). Apply the same operation to every part of a compound inequality.
Step 2
Why this answer is correct
The correct answer is A. \(3\leq x<9\). Subtracting (2) from all parts gives \(3\leq x<9\). Apply the same operation to every part of a compound inequality.
Step 3
Exam Tip
सभी भागों से (2) घटाने पर \(3\leq x<9\) मिलता है। संयुक्त असमानता में हर भाग पर समान क्रिया करें।
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कौन सा विकल्प \(x\in\mathbb{R}\) और (x<0) को दर्शाता है?
Which option represents \(x\in\mathbb{R}\) and (x<0)?
#linear inequalities
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A (\(-\infty,0\))
B (\(-\infty,0]\)
C \([0,\infty\))
D (\(0,\infty\))
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Correct Answer
A. (\(-\infty,0\))
Step 1
Concept
(x<0) includes all negative real numbers and does not include (0). Therefore (\(-\infty,0\)) is correct.
Step 2
Why this answer is correct
The correct answer is A. (\(-\infty,0\)). (x<0) includes all negative real numbers and does not include (0). Therefore (\(-\infty,0\)) is correct.
Step 3
Exam Tip
(x<0) में सभी ऋणात्मक वास्तविक संख्याएं आती हैं और (0) शामिल नहीं होता। इसलिए (\(-\infty,0\)) सही है।
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एक कोचिंग योजना में प्रवेश शुल्क (150) रुपये और मासिक शुल्क (80m) रुपये है। यदि कुल खर्च (550) रुपये से अधिक नहीं होना चाहिए, तो (m) के लिए सही हल क्या है?
A coaching plan has an admission fee of (150) rupees and a monthly fee of (80m) rupees. If the total cost should not exceed (550) rupees, what is the correct solution for (m)?
#linear inequalities
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A \(m\leq 5\)
B \(m\geq 5\)
C (m<5)
D (m>5)
Explanation opens after your attempt
Correct Answer
A. \(m\leq 5\)
Step 1
Concept
The cost inequality is \(150+80m\leq 550\), which gives \(m\leq 5\). Remember that not exceed means \(\leq\).
Step 2
Why this answer is correct
The correct answer is A. \(m\leq 5\). The cost inequality is \(150+80m\leq 550\), which gives \(m\leq 5\). Remember that not exceed means \(\leq\).
Step 3
Exam Tip
खर्च की असमानता \(150+80m\leq 550\) होगी, जिससे \(m\leq 5\) मिलता है। अधिक नहीं का अर्थ \(\leq\) याद रखें।
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संयुक्त असमानता \(-2<\frac{5-x}{3}\leq 4\) का हल कौन सा है?
Which is the solution of the compound inequality \(-2<\frac{5-x}{3}\leq 4\)?
#linear inequalities
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A \(-7\leq x<11\)
B \(-7<x\leq 11\)
C \(-11<x\leq 7\)
D \(7\leq x<11\)
Explanation opens after your attempt
Correct Answer
A. \(-7\leq x<11\)
Step 1
Concept
After multiplying by positive (3), we get \(-6<5-x\leq 12\), then the direction changes because of the negative part. The correct solution is \(-7\leq x<11\).
Step 2
Why this answer is correct
The correct answer is A. \(-7\leq x<11\). After multiplying by positive (3), we get \(-6<5-x\leq 12\), then the direction changes because of the negative part. The correct solution is \(-7\leq x<11\).
Step 3
Exam Tip
धनात्मक (3) से गुणा करने के बाद \(-6<5-x\leq 12\) मिलता है, फिर ऋणात्मक भाग के कारण दिशा बदलती है। सही हल \(-7\leq x<11\) है।
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