यदि (a<b) है तो यह क्या बताता है?
If (a<b), what does it mean?
#linear inequalities
#introduction
#symbols
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A (a) संख्या (b) से छोटी है / (a) is less than (b)
B (a) संख्या (b) के बराबर है / (a) is equal to (b)
C (a) संख्या (b) से बड़ी है / (a) is greater than (b)
D (a) और (b) विपरीत हैं / (a) and (b) are opposite
Explanation opens after your attempt
Correct Answer
A. (a) संख्या (b) से छोटी है / (a) is less than (b)
Step 1
Concept
The symbol (<) shows the smaller value. In exams read the direction of the sign carefully.
Step 2
Why this answer is correct
The correct answer is A. (a) संख्या (b) से छोटी है / (a) is less than (b). The symbol (<) shows the smaller value. In exams read the direction of the sign carefully.
Step 3
Exam Tip
चिह्न (<) छोटी संख्या को दर्शाता है। परीक्षा में चिह्न की दिशा ध्यान से देखें।
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असमानता \(x\ge 7\) का सही अर्थ क्या है?
What is the correct meaning of the inequality \(x\ge 7\)?
#linear inequalities
#greater equal
#basic meaning
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A (x) केवल (7) से बड़ा है / (x) is only greater than (7)
B (x) (7) से बड़ा या बराबर है / (x) is greater than or equal to (7)
C (x) (7) से छोटा है / (x) is less than (7)
D (x) (7) के बराबर नहीं है / (x) is not equal to (7)
Explanation opens after your attempt
Correct Answer
B. (x) (7) से बड़ा या बराबर है / (x) is greater than or equal to (7)
Step 1
Concept
The symbol \(\ge\) also includes equality. Remember the difference between open and closed points.
Step 2
Why this answer is correct
The correct answer is B. (x) (7) से बड़ा या बराबर है / (x) is greater than or equal to (7). The symbol \(\ge\) also includes equality. Remember the difference between open and closed points.
Step 3
Exam Tip
चिह्न \(\ge\) में बराबर होना भी शामिल है। खुले और बंद बिंदु का अंतर याद रखें।
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इनमें से कौन सी रैखिक असमानता है?
Which of the following is a linear inequality?
#linear inequalities
#identify
#easy
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A (2x+3<9)
B \(x^2<4\)
C \(\sqrt{x}<5\)
D (xy>6)
Explanation opens after your attempt
Correct Answer
A. (2x+3<9)
Step 1
Concept
In (2x+3<9), the variable has power (1), so it is linear. A linear inequality does not contain \(x^2\) or (xy).
Step 2
Why this answer is correct
The correct answer is A. (2x+3<9). In (2x+3<9), the variable has power (1), so it is linear. A linear inequality does not contain \(x^2\) or (xy).
Step 3
Exam Tip
(2x+3<9) में चर की घात (1) है इसलिए यह रैखिक है। रैखिक असमानता में \(x^2\) या (xy) नहीं होता।
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कौन सा मान (x<4) को संतुष्ट करता है?
Which value satisfies (x<4)?
#linear inequalities
#solution check
#substitution
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A (4)
B (5)
C (3)
D (6)
Explanation opens after your attempt
Step 1
Concept
Since (3<4) is true, (x=3) is a solution. Substitution is the simplest checking method.
Step 2
Why this answer is correct
The correct answer is C. (3). Since (3<4) is true, (x=3) is a solution. Substitution is the simplest checking method.
Step 3
Exam Tip
(3<4) सत्य है इसलिए (x=3) समाधान है। मान रखकर जाँच करना सबसे सरल तरीका है।
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असमानता \(x\le 2\) में (x=2) के लिए कथन कैसा है?
For (x=2), how is the statement \(x\le 2\)?
#linear inequalities
#less equal
#equality
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A सत्य / True
B असत्य / False
C निर्धारित नहीं / Not determined
D केवल धनात्मक / Only positive
Explanation opens after your attempt
Correct Answer
A. सत्य / True
Step 1
Concept
The sign \(\le\) includes equality, so \(2\le 2\) is true. In exams distinguish \(\le\) from (<).
Step 2
Why this answer is correct
The correct answer is A. सत्य / True. The sign \(\le\) includes equality, so \(2\le 2\) is true. In exams distinguish \(\le\) from (<).
Step 3
Exam Tip
\(\le\) में बराबरी शामिल होती है इसलिए \(2\le 2\) सत्य है। परीक्षा में \(\le\) और (<) को अलग रखें।
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वाक्य (y) (10) से अधिक है को असमानता में कैसे लिखेंगे?
How do we write the sentence (y) is more than (10) as an inequality?
#linear inequalities
#translation
#word statement
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A (y<10)
B (y>10)
C (y=10)
D \(y\le 10\)
Explanation opens after your attempt
Step 1
Concept
More than means (>). When translating language to symbols, identify the key phrase.
Step 2
Why this answer is correct
The correct answer is B. (y>10). More than means (>). When translating language to symbols, identify the key phrase.
Step 3
Exam Tip
अधिक है का अर्थ (>) होता है। भाषा को प्रतीक में बदलते समय मुख्य शब्द पहचानें।
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वाक्य (p) (12) से अधिक नहीं है का सही रूप क्या है?
What is the correct form of the sentence (p) is not more than (12)?
#linear inequalities
#at most
#translation
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A (p>12)
B \(p\ge 12\)
C \(p\le 12\)
D (p<12)
Explanation opens after your attempt
Correct Answer
C. \(p\le 12\)
Step 1
Concept
Not more than means at most (12), so \(p\le 12\). Such phrases often include equality.
Step 2
Why this answer is correct
The correct answer is C. \(p\le 12\). Not more than means at most (12), so \(p\le 12\). Such phrases often include equality.
Step 3
Exam Tip
अधिक नहीं है का अर्थ अधिकतम (12) है यानी \(p\le 12\)। ऐसे शब्दों में बराबरी अक्सर शामिल होती है।
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यदि (x>3) है तो दोनों ओर (2) जोड़ने पर क्या मिलेगा?
If (x>3), what do we get after adding (2) to both sides?
#linear inequalities
#addition property
#basic rules
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A (x+2>5)
B (x+2<5)
C (x-2>5)
D (2x>5)
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Correct Answer
A. (x+2>5)
Step 1
Concept
Adding the same number to both sides does not change the inequality direction. In addition or subtraction the sign stays the same.
Step 2
Why this answer is correct
The correct answer is A. (x+2>5). Adding the same number to both sides does not change the inequality direction. In addition or subtraction the sign stays the same.
Step 3
Exam Tip
दोनों ओर समान संख्या जोड़ने से असमानता की दिशा नहीं बदलती। जोड़ या घटाव में चिह्न वैसा ही रहता है।
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यदि (m<6) है तो दोनों ओर (4) से गुणा करने पर क्या होगा?
If (m<6), what happens after multiplying both sides by (4)?
#linear inequalities
#multiplication positive
#rule
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A (4m<24)
B (4m>24)
C (m<24)
D (m>24)
Explanation opens after your attempt
Correct Answer
A. (4m<24)
Step 1
Concept
Multiplying by a positive number does not reverse the sign. The sign reverses only with negative multiplication or division.
Step 2
Why this answer is correct
The correct answer is A. (4m<24). Multiplying by a positive number does not reverse the sign. The sign reverses only with negative multiplication or division.
Step 3
Exam Tip
धनात्मक संख्या से गुणा करने पर चिह्न नहीं पलटता। केवल ऋणात्मक गुणा या भाग में चिह्न पलटता है।
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यदि (x>5) है तो दोनों ओर (-1) से गुणा करने पर सही असमानता कौन सी है?
If (x>5), which inequality is correct after multiplying both sides by (-1)?
#linear inequalities
#negative multiplication
#sign reversal
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A (-x> -5)
B (-x< -5)
C (x< -5)
D (-x>5)
Explanation opens after your attempt
Correct Answer
B. (-x< -5)
Step 1
Concept
When multiplying by a negative number, the inequality sign reverses. This is a very common mistake.
Step 2
Why this answer is correct
The correct answer is B. (-x< -5). When multiplying by a negative number, the inequality sign reverses. This is a very common mistake.
Step 3
Exam Tip
ऋणात्मक संख्या से गुणा करने पर असमानता का चिह्न पलट जाता है। यह बहुत सामान्य गलती है।
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असमानता (x+4<9) का हल क्या है?
What is the solution of (x+4<9)?
#linear inequalities
#solve
#addition inverse
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A (x<5)
B (x>5)
C (x<13)
D (x>13)
Explanation opens after your attempt
Step 1
Concept
Subtracting (4) from both sides gives (x<5). Use the balance method for simple inequalities.
Step 2
Why this answer is correct
The correct answer is A. (x<5). Subtracting (4) from both sides gives (x<5). Use the balance method for simple inequalities.
Step 3
Exam Tip
दोनों ओर (4) घटाने पर (x<5) मिलता है। सरल असमानताओं में संतुलन विधि अपनाएँ।
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असमानता \(x-3\le 7\) का हल कौन सा है?
Which is the solution of \(x-3\le 7\)?
#linear inequalities
#solve
#less equal
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A \(x\le 4\)
B \(x\le 10\)
C \(x\ge 10\)
D (x<10)
Explanation opens after your attempt
Correct Answer
B. \(x\le 10\)
Step 1
Concept
Adding (3) to both sides gives \(x\le 10\). The sign \(\le\) does not change by addition.
Step 2
Why this answer is correct
The correct answer is B. \(x\le 10\). Adding (3) to both sides gives \(x\le 10\). The sign \(\le\) does not change by addition.
Step 3
Exam Tip
दोनों ओर (3) जोड़ने पर \(x\le 10\) मिलता है। \(\le\) का चिह्न जोड़ने से नहीं बदलता।
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असमानता (2x>10) का हल क्या है?
What is the solution of (2x>10)?
#linear inequalities
#solve
#division positive
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A (x>5)
B (x<5)
C (x>20)
D (x<20)
Explanation opens after your attempt
Step 1
Concept
Dividing both sides by (2) gives (x>5). Division by a positive number does not reverse the sign.
Step 2
Why this answer is correct
The correct answer is A. (x>5). Dividing both sides by (2) gives (x>5). Division by a positive number does not reverse the sign.
Step 3
Exam Tip
दोनों ओर (2) से भाग देने पर (x>5) मिलता है। धनात्मक भाग में चिह्न नहीं बदलता।
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असमानता (-2x<8) का सही हल कौन सा है?
Which is the correct solution of (-2x<8)?
#linear inequalities
#solve
#negative division
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A (x< -4)
B (x> -4)
C (x<4)
D (x>4)
Explanation opens after your attempt
Correct Answer
B. (x> -4)
Step 1
Concept
Dividing by (-2) reverses the sign, so (x>-4). Do not forget sign reversal in negative division.
Step 2
Why this answer is correct
The correct answer is B. (x> -4). Dividing by (-2) reverses the sign, so (x>-4). Do not forget sign reversal in negative division.
Step 3
Exam Tip
दोनों ओर (-2) से भाग देने पर चिह्न पलटेगा इसलिए (x>-4)। ऋणात्मक भाग में दिशा बदलना न भूलें।
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कौन सा (x) असमानता \(3x\le 12\) का समाधान है?
Which (x) is a solution of \(3x\le 12\)?
#linear inequalities
#solution check
#numerical
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A (5)
B (4)
C (6)
D (7)
Explanation opens after your attempt
Step 1
Concept
For (x=4), \(3\cdot 4\le 12\) is true. Substitute options for a quick check.
Step 2
Why this answer is correct
The correct answer is B. (4). For (x=4), \(3\cdot 4\le 12\) is true. Substitute options for a quick check.
Step 3
Exam Tip
(x=4) रखने पर \(3\cdot 4\le 12\) सत्य है। विकल्पों में मान रखकर जल्दी जाँच करें।
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कौन सा मान (2x+1>9) को संतुष्ट करता है?
Which value satisfies (2x+1>9)?
#linear inequalities
#solution check
#two step
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A (3)
B (4)
C (5)
D (0)
Explanation opens after your attempt
Step 1
Concept
The solution is (x>4), so (5) satisfies it. First find the boundary, then choose the option.
Step 2
Why this answer is correct
The correct answer is C. (5). The solution is (x>4), so (5) satisfies it. First find the boundary, then choose the option.
Step 3
Exam Tip
हल (x>4) है इसलिए (5) संतुष्ट करता है। पहले सीमा निकालें फिर विकल्प चुनें।
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असमानता \(x\ge -2\) के लिए संख्या रेखा पर कौन सा चित्र सही होगा?
For \(x\ge -2\), which number line representation is correct?
#linear inequalities
#number line
#closed circle
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A (-2) पर खुला बिंदु और बाईं ओर / Open circle at (-2) and left side
B (-2) पर बंद बिंदु और दाईं ओर / Closed circle at (-2) and right side
C (-2) पर खुला बिंदु और दाईं ओर / Open circle at (-2) and right side
D (-2) पर बंद बिंदु और बाईं ओर / Closed circle at (-2) and left side
Explanation opens after your attempt
Correct Answer
B. (-2) पर बंद बिंदु और दाईं ओर / Closed circle at (-2) and right side
Step 1
Concept
The sign \(\ge\) includes (-2), and greater numbers are to the right. A closed circle shows equality.
Step 2
Why this answer is correct
The correct answer is B. (-2) पर बंद बिंदु और दाईं ओर / Closed circle at (-2) and right side. The sign \(\ge\) includes (-2), and greater numbers are to the right. A closed circle shows equality.
Step 3
Exam Tip
\(\ge\) में (-2) शामिल है और बड़ी संख्याएँ दाईं ओर हैं। बंद बिंदु बराबरी को दिखाता है।
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अंतराल (\(-\infty,5\)) किस असमानता को दर्शाता है?
Which inequality is represented by the interval (\(-\infty,5\))?
#linear inequalities
#interval notation
#open interval
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A (x<5)
B \(x\le 5\)
C (x>5)
D \(x\ge 5\)
Explanation opens after your attempt
Step 1
Concept
The parenthesis at (5) shows that (5) is not included. (\(-\infty,5\)) means (x<5).
Step 2
Why this answer is correct
The correct answer is A. (x<5). The parenthesis at (5) shows that (5) is not included. (\(-\infty,5\)) means (x<5).
Step 3
Exam Tip
कोष्ठक ((5)) बताता है कि (5) शामिल नहीं है। (\(-\infty,5\)) का अर्थ (x<5) है।
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अंतराल \([2,\infty\)) का सही असमानता रूप क्या है?
What is the correct inequality form of the interval \([2,\infty\))?
#linear inequalities
#interval notation
#closed endpoint
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A (x>2)
B \(x\ge 2\)
C (x<2)
D \(x\le 2\)
Explanation opens after your attempt
Correct Answer
B. \(x\ge 2\)
Step 1
Concept
The square bracket at (2) shows that (2) is included. Moving right means \(x\ge 2\).
Step 2
Why this answer is correct
The correct answer is B. \(x\ge 2\). The square bracket at (2) shows that (2) is included. Moving right means \(x\ge 2\).
Step 3
Exam Tip
वर्ग कोष्ठक ([2) बताता है कि (2) शामिल है। दाईं ओर जाने का अर्थ \(x\ge 2\) है।
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असमानता \(0\le x\le 6\) में कौन सा मान शामिल नहीं है?
Which value is not included in \(0\le x\le 6\)?
#linear inequalities
#compound inequality
#closed interval
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A (0)
B (6)
C (3)
D (7)
Explanation opens after your attempt
Step 1
Concept
The number (7) is greater than (6), so it is not included. The sign \(\le\) includes values only up to the boundary.
Step 2
Why this answer is correct
The correct answer is D. (7). The number (7) is greater than (6), so it is not included. The sign \(\le\) includes values only up to the boundary.
Step 3
Exam Tip
(7) संख्या (6) से बड़ी है इसलिए शामिल नहीं है। \(\le\) में केवल सीमा तक के मान आते हैं।
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इनमें से कौन सा कथन सत्य है?
Which of the following statements is true?
#linear inequalities
#true false
#basic comparison
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A (5<2)
B \(3\le 3\)
C (7>9)
D \(4\ne 4\)
Explanation opens after your attempt
Correct Answer
B. \(3\le 3\)
Step 1
Concept
The statement \(3\le 3\) is true because equality is included. Check each option separately in such questions.
Step 2
Why this answer is correct
The correct answer is B. \(3\le 3\). The statement \(3\le 3\) is true because equality is included. Check each option separately in such questions.
Step 3
Exam Tip
\(3\le 3\) सत्य है क्योंकि बराबरी शामिल है। ऐसे प्रश्नों में हर विकल्प अलग से जाँचें।
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यदि \(r\le 9\) है तो इनमें से कौन सा मान निश्चित रूप से संभव है?
If \(r\le 9\), which value is definitely possible?
#linear inequalities
#boundary value
#solution set
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A (10)
B (12)
C (9)
D (15)
Explanation opens after your attempt
Step 1
Concept
In \(r\le 9\), (9) and numbers smaller than (9) are included. With equality signs, the boundary value is also a solution.
Step 2
Why this answer is correct
The correct answer is C. (9). In \(r\le 9\), (9) and numbers smaller than (9) are included. With equality signs, the boundary value is also a solution.
Step 3
Exam Tip
\(r\le 9\) में (9) और उससे छोटी संख्याएँ आती हैं। बराबरी वाले चिह्न में सीमा मान भी समाधान होता है।
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किसी परीक्षा में पास होने के लिए अंक (40) या अधिक चाहिए। यदि अंक (s) हैं तो सही असमानता क्या है?
To pass an exam, marks must be (40) or more. If the marks are (s), what is the correct inequality?
#linear inequalities
#application
#marks
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A (s>40)
B \(s\ge 40\)
C (s<40)
D \(s\le 40\)
Explanation opens after your attempt
Correct Answer
B. \(s\ge 40\)
Step 1
Concept
(40) or more means \(s\ge 40\). The phrase or more includes equality.
Step 2
Why this answer is correct
The correct answer is B. \(s\ge 40\). (40) or more means \(s\ge 40\). The phrase or more includes equality.
Step 3
Exam Tip
(40) या अधिक का अर्थ \(s\ge 40\) है। शब्द या अधिक बराबरी को शामिल करता है।
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एक बैग का वजन (15) किलोग्राम से अधिक नहीं होना चाहिए। यदि वजन (w) है तो सही असमानता क्या है?
A bag weight should not exceed (15) kilograms. If the weight is (w), what is the correct inequality?
#linear inequalities
#application
#maximum
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A (w<15)
B \(w\le 15\)
C (w>15)
D \(w\ge 15\)
Explanation opens after your attempt
Correct Answer
B. \(w\le 15\)
Step 1
Concept
Not exceed means at most (15), so \(w\le 15\). In real-life statements, maximum gives \(\le\).
Step 2
Why this answer is correct
The correct answer is B. \(w\le 15\). Not exceed means at most (15), so \(w\le 15\). In real-life statements, maximum gives \(\le\).
Step 3
Exam Tip
से अधिक नहीं का अर्थ अधिकतम (15) है इसलिए \(w\le 15\)। वास्तविक जीवन में अधिकतम शब्द \(\le\) देता है।
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किसी टिकट की कीमत (100) रुपये से कम है। यदि कीमत (p) है तो सही असमानता कौन सी है?
A ticket price is less than (100) rupees. If the price is (p), which inequality is correct?
#linear inequalities
#application
#less than
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A (p<100)
B \(p\le 100\)
C (p>100)
D \(p\ge 100\)
Explanation opens after your attempt
Correct Answer
A. (p<100)
Step 1
Concept
Less than means strictly smaller, so (p<100). If equality is included, we use \(\le\).
Step 2
Why this answer is correct
The correct answer is A. (p<100). Less than means strictly smaller, so (p<100). If equality is included, we use \(\le\).
Step 3
Exam Tip
से कम का अर्थ सख्त रूप से कम है इसलिए (p<100)। यदि बराबर भी शामिल हो तो \(\le\) लिखा जाता है।
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किसी क्लब में प्रवेश के लिए आयु (18) वर्ष से कम नहीं होनी चाहिए। यदि आयु (a) है तो सही असमानता क्या है?
For entry to a club, age must not be less than (18) years. If age is (a), what is the correct inequality?
#linear inequalities
#application
#at least
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A (a<18)
B \(a\le 18\)
C \(a\ge 18\)
D (a>18)
Explanation opens after your attempt
Correct Answer
C. \(a\ge 18\)
Step 1
Concept
Not less than means at least (18), so \(a\ge 18\). At least is always linked with \(\ge\).
Step 2
Why this answer is correct
The correct answer is C. \(a\ge 18\). Not less than means at least (18), so \(a\ge 18\). At least is always linked with \(\ge\).
Step 3
Exam Tip
कम नहीं का अर्थ कम से कम (18) है इसलिए \(a\ge 18\)। कम से कम हमेशा \(\ge\) से जुड़ा होता है।
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यदि (x=2) है तो कौन सी असमानता सत्य है?
If (x=2), which inequality is true?
#linear inequalities
#substitution
#true option
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A (x>5)
B (x<1)
C \(x\le 2\)
D \(x\ge 4\)
Explanation opens after your attempt
Correct Answer
C. \(x\le 2\)
Step 1
Concept
\(2\le 2\) is true because equality is included. Put the given value in place of (x).
Step 2
Why this answer is correct
The correct answer is C. \(x\le 2\). \(2\le 2\) is true because equality is included. Put the given value in place of (x).
Step 3
Exam Tip
\(2\le 2\) सत्य है क्योंकि बराबरी शामिल है। विकल्प में (x) की जगह दिया मान रखें।
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असमानता \(x+1\ge 6\) का हल कौन सा है?
Which is the solution of \(x+1\ge 6\)?
#linear inequalities
#solve
#greater equal
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A \(x\ge 5\)
B \(x\le 5\)
C (x>7)
D (x<7)
Explanation opens after your attempt
Correct Answer
A. \(x\ge 5\)
Step 1
Concept
Subtracting (1) from both sides gives \(x\ge 5\). In addition or subtraction, the direction stays the same.
Step 2
Why this answer is correct
The correct answer is A. \(x\ge 5\). Subtracting (1) from both sides gives \(x\ge 5\). In addition or subtraction, the direction stays the same.
Step 3
Exam Tip
दोनों ओर (1) घटाने पर \(x\ge 5\) मिलता है। जोड़ घटाव में दिशा वही रहती है।
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असमानता (5-x>2) का सही हल क्या है?
What is the correct solution of (5-x>2)?
#linear inequalities
#solve
#sign reversal
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A (x<3)
B (x>3)
C (x<7)
D (x>7)
Explanation opens after your attempt
Step 1
Concept
From (5-x>2), we get (-x>-3), and dividing by a negative gives (x<3). When (-x) appears, remember to reverse the sign.
Step 2
Why this answer is correct
The correct answer is A. (x<3). From (5-x>2), we get (-x>-3), and dividing by a negative gives (x<3). When (-x) appears, remember to reverse the sign.
Step 3
Exam Tip
(5-x>2) से (-x>-3) और ऋणात्मक से भाग देने पर (x<3)। (-x) आने पर चिह्न पलटना याद रखें।
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असमानता \(4x+2\le 14\) का हल कौन सा है?
Which is the solution of \(4x+2\le 14\)?
#linear inequalities
#two step
#solve
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A \(x\le 3\)
B \(x\ge 3\)
C \(x\le 4\)
D \(x\ge 4\)
Explanation opens after your attempt
Correct Answer
A. \(x\le 3\)
Step 1
Concept
First subtract (2), then divide by (4), giving \(x\le 3\). Keep the order correct in two-step questions.
Step 2
Why this answer is correct
The correct answer is A. \(x\le 3\). First subtract (2), then divide by (4), giving \(x\le 3\). Keep the order correct in two-step questions.
Step 3
Exam Tip
पहले (2) घटाएँ फिर (4) से भाग दें तो \(x\le 3\)। दो चरणों वाले प्रश्न में क्रम सही रखें।
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असमानता \(3-2x\le 9\) का सही हल क्या है?
What is the correct solution of \(3-2x\le 9\)?
#linear inequalities
#negative coefficient
#solve
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A \(x\ge -3\)
B \(x\le -3\)
C \(x\ge 3\)
D \(x\le 3\)
Explanation opens after your attempt
Correct Answer
A. \(x\ge -3\)
Step 1
Concept
From \(3-2x\le 9\), we get \(-2x\le 6\), and division by (-2) gives \(x\ge -3\). Negative division reverses the direction.
Step 2
Why this answer is correct
The correct answer is A. \(x\ge -3\). From \(3-2x\le 9\), we get \(-2x\le 6\), and division by (-2) gives \(x\ge -3\). Negative division reverses the direction.
Step 3
Exam Tip
\(3-2x\le 9\) से \(-2x\le 6\) और (-2) से भाग देने पर \(x\ge -3\)। ऋणात्मक भाग दिशा पलटता है।
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कौन सा कथन \(x\le -1\) के लिए सही है?
Which statement is correct for \(x\le -1\)?
#linear inequalities
#number line
#negative boundary
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A समाधान (-1) से दाईं ओर हैं / Solutions are to the right of (-1)
B समाधान (-1) और उससे बाईं ओर हैं / Solutions are (-1) and to its left
C केवल (x=0) समाधान है / Only (x=0) is a solution
D कोई वास्तविक समाधान नहीं है / There is no real solution
Explanation opens after your attempt
Correct Answer
B. समाधान (-1) और उससे बाईं ओर हैं / Solutions are (-1) and to its left
Step 1
Concept
The sign \(\le\) includes the boundary and smaller numbers. On the number line, smaller numbers are to the left.
Step 2
Why this answer is correct
The correct answer is B. समाधान (-1) और उससे बाईं ओर हैं / Solutions are (-1) and to its left. The sign \(\le\) includes the boundary and smaller numbers. On the number line, smaller numbers are to the left.
Step 3
Exam Tip
\(\le\) में सीमा और उससे छोटी संख्याएँ शामिल होती हैं। संख्या रेखा पर छोटी संख्याएँ बाईं ओर होती हैं।
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असमानता (x>-4) का अंतराल रूप क्या है?
What is the interval form of (x>-4)?
#linear inequalities
#interval form
#greater than
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A (\(-4,\infty\))
B \([-4,\infty\))
C (\(-\infty,-4\))
D (\(-\infty,-4]\)
Explanation opens after your attempt
Correct Answer
A. (\(-4,\infty\))
Step 1
Concept
In (x>-4), (-4) is not included and values lie to the right. So the interval is (\(-4,\infty\)).
Step 2
Why this answer is correct
The correct answer is A. (\(-4,\infty\)). In (x>-4), (-4) is not included and values lie to the right. So the interval is (\(-4,\infty\)).
Step 3
Exam Tip
(x>-4) में (-4) शामिल नहीं है और मान दाईं ओर हैं। इसलिए अंतराल (\(-4,\infty\)) है।
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असमानता \(x\le 0\) का अंतराल रूप कौन सा है?
Which is the interval form of \(x\le 0\)?
#linear inequalities
#interval form
#less equal
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A (\(0,\infty\))
B \([0,\infty\))
C (\(-\infty,0]\)
D (\(-\infty,0\))
Explanation opens after your attempt
Correct Answer
C. (\(-\infty,0]\)
Step 1
Concept
In \(x\le 0\), (0) is included and smaller numbers are to the left. So (\(-\infty,0]\) is correct.
Step 2
Why this answer is correct
The correct answer is C. (\(-\infty,0]\). In \(x\le 0\), (0) is included and smaller numbers are to the left. So (\(-\infty,0]\) is correct.
Step 3
Exam Tip
\(x\le 0\) में (0) शामिल है और छोटी संख्याएँ बाईं ओर हैं। इसलिए (\(-\infty,0]\) सही है।
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कौन सा विकल्प \(2\le x<5\) को सही बताता है?
Which option correctly describes \(2\le x<5\)?
#linear inequalities
#compound inequality
#interpretation
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A (x) (2) से बड़ा है और (5) से बड़ा है / (x) is greater than (2) and greater than (5)
B (x) (2) से छोटा है और (5) से बड़ा है / (x) is less than (2) and greater than (5)
C (x) (2) या उससे बड़ा और (5) से छोटा है / (x) is (2) or more and less than (5)
D (x) केवल (5) के बराबर है / (x) is only equal to (5)
Explanation opens after your attempt
Correct Answer
C. (x) (2) या उससे बड़ा और (5) से छोटा है / (x) is (2) or more and less than (5)
Step 1
Concept
In \(2\le x<5\), (2) is included but (5) is not. Read a compound inequality in two parts.
Step 2
Why this answer is correct
The correct answer is C. (x) (2) या उससे बड़ा और (5) से छोटा है / (x) is (2) or more and less than (5). In \(2\le x<5\), (2) is included but (5) is not. Read a compound inequality in two parts.
Step 3
Exam Tip
\(2\le x<5\) में (2) शामिल है पर (5) शामिल नहीं है। संयुक्त असमानता को दो भागों में पढ़ें।
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यदि (x) एक प्राकृतिक संख्या है और (x<4) है तो संभावित मान कौन से हैं?
If (x) is a natural number and (x<4), what are the possible values?
#linear inequalities
#natural numbers
#solution set
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A \(x\in{1,2,3}\)
B \(x\in{0,1,2,3}\)
C \(x\in{4,5,6}\)
D \(x\in{1,2,3,4}\)
Explanation opens after your attempt
Correct Answer
A. \(x\in{1,2,3}\)
Step 1
Concept
Natural numbers are taken from (1), and (4) is not included. Therefore the values are (1,2,3).
Step 2
Why this answer is correct
The correct answer is A. \(x\in{1,2,3}\). Natural numbers are taken from (1), and (4) is not included. Therefore the values are (1,2,3).
Step 3
Exam Tip
प्राकृतिक संख्याएँ (1) से शुरू मानी जाती हैं और (4) शामिल नहीं है। इसलिए मान (1,2,3) हैं।
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यदि (x) एक पूर्णांक है और \(-2<x\le 2\) है तो (x) के मान क्या हैं?
If (x) is an integer and \(-2<x\le 2\), what are the values of (x)?
#linear inequalities
#integers
#compound inequality
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A \(x\in{-2,-1,0,1,2}\)
B \(x\in{-1,0,1,2}\)
C \(x\in{-1,0,1}\)
D \(x\in{-2,-1,0,1}\)
Explanation opens after your attempt
Correct Answer
B. \(x\in{-1,0,1,2}\)
Step 1
Concept
The value (-2) is not included, but (2) is included. The integer values are (-1,0,1,2).
Step 2
Why this answer is correct
The correct answer is B. \(x\in{-1,0,1,2}\). The value (-2) is not included, but (2) is included. The integer values are (-1,0,1,2).
Step 3
Exam Tip
(-2) शामिल नहीं है पर (2) शामिल है। पूर्णांक मान (-1,0,1,2) होंगे।
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कौन सी असमानता (x) के कम से कम (6) होने को दिखाती है?
Which inequality shows that (x) is at least (6)?
#linear inequalities
#at least
#language
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A (x<6)
B \(x\le 6\)
C \(x\ge 6\)
D (x>6)
Explanation opens after your attempt
Correct Answer
C. \(x\ge 6\)
Step 1
Concept
At least (6) means (6) or more. Therefore the correct sign is \(\ge\).
Step 2
Why this answer is correct
The correct answer is C. \(x\ge 6\). At least (6) means (6) or more. Therefore the correct sign is \(\ge\).
Step 3
Exam Tip
कम से कम (6) का अर्थ (6) या उससे अधिक है। इसलिए सही चिह्न \(\ge\) है।
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कौन सी असमानता (n) के अधिकतम (20) होने को दिखाती है?
Which inequality shows that (n) is at most (20)?
#linear inequalities
#at most
#language
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A \(n\le 20\)
B (n<20)
C (n>20)
D \(n\ge 20\)
Explanation opens after your attempt
Correct Answer
A. \(n\le 20\)
Step 1
Concept
At most (20) means (20) or less. Therefore \(n\le 20\) is correct.
Step 2
Why this answer is correct
The correct answer is A. \(n\le 20\). At most (20) means (20) or less. Therefore \(n\le 20\) is correct.
Step 3
Exam Tip
अधिकतम (20) का अर्थ (20) या उससे कम है। इसलिए \(n\le 20\) सही है।
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यदि (a>b) और (k>0) है तो कौन सा कथन सही है?
If (a>b) and (k>0), which statement is correct?
#linear inequalities
#positive multiplier
#property
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A (ak>bk)
B (ak<bk)
C (a+k<b+k)
D (a-k<b-k)
Explanation opens after your attempt
Correct Answer
A. (ak>bk)
Step 1
Concept
Multiplication by a positive number keeps the direction the same. The condition (k>0) is important.
Step 2
Why this answer is correct
The correct answer is A. (ak>bk). Multiplication by a positive number keeps the direction the same. The condition (k>0) is important.
Step 3
Exam Tip
धनात्मक संख्या से गुणा करने पर दिशा वही रहती है। (k>0) होने की शर्त जरूरी है।
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असमानता (x+7>7) का हल क्या है?
What is the solution of (x+7>7)?
#linear inequalities
#solve
#simple transformation
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A (x>0)
B (x<0)
C (x>14)
D (x<14)
Explanation opens after your attempt
Step 1
Concept
Subtracting (7) from both sides gives (x>0). Remove equal terms to get the simple form.
Step 2
Why this answer is correct
The correct answer is A. (x>0). Subtracting (7) from both sides gives (x>0). Remove equal terms to get the simple form.
Step 3
Exam Tip
दोनों ओर (7) घटाने पर (x>0) मिलता है। समान पद हटाकर सरल रूप बनाइए।
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असमानता \(\frac{x}{3}\le 2\) का हल क्या है?
What is the solution of \(\frac{x}{3}\le 2\)?
#linear inequalities
#fraction
#solve
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A \(x\le 6\)
B \(x\ge 6\)
C \(x\le \frac{2}{3}\)
D \(x\ge \frac{2}{3}\)
Explanation opens after your attempt
Correct Answer
A. \(x\le 6\)
Step 1
Concept
Multiplying both sides by (3) gives \(x\le 6\). Positive multiplication does not reverse the sign.
Step 2
Why this answer is correct
The correct answer is A. \(x\le 6\). Multiplying both sides by (3) gives \(x\le 6\). Positive multiplication does not reverse the sign.
Step 3
Exam Tip
दोनों ओर (3) से गुणा करने पर \(x\le 6\) मिलता है। धनात्मक गुणा में चिह्न नहीं पलटता।
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असमानता \(\frac{x}{-4}>1\) का सही हल क्या है?
What is the correct solution of \(\frac{x}{-4}>1\)?
#linear inequalities
#fraction
#negative multiplier
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A (x>-4)
B (x<-4)
C (x>4)
D (x<4)
Explanation opens after your attempt
Step 1
Concept
Multiplying both sides by (-4) reverses the sign, so (x<-4). Negative multiplication changes the direction.
Step 2
Why this answer is correct
The correct answer is B. (x<-4). Multiplying both sides by (-4) reverses the sign, so (x<-4). Negative multiplication changes the direction.
Step 3
Exam Tip
दोनों ओर (-4) से गुणा करने पर चिह्न पलटेगा इसलिए (x<-4)। ऋणात्मक गुणा में दिशा बदलती है।
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असमानता (6<2x) का हल कौन सा है?
Which is the solution of (6<2x)?
#linear inequalities
#solve
#rewrite
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A (x>3)
B (x<3)
C (x>12)
D (x<12)
Explanation opens after your attempt
Step 1
Concept
Dividing both sides by (2) gives (3<x), that is (x>3). When rewriting, check the meaning of the sign direction.
Step 2
Why this answer is correct
The correct answer is A. (x>3). Dividing both sides by (2) gives (3<x), that is (x>3). When rewriting, check the meaning of the sign direction.
Step 3
Exam Tip
दोनों ओर (2) से भाग देने पर (3<x) यानी (x>3) मिलता है। रूप बदलते समय चिह्न की दिशा अर्थ से जाँचें।
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कौन सा मान असमानता (2x-1<7) को संतुष्ट करता है?
Which value satisfies the inequality (2x-1<7)?
#linear inequalities
#strict inequality
#solution check
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A (x=5)
B (x=4)
C (x=6)
D (x=7)
Explanation opens after your attempt
Step 1
Concept
From (2x-1<7), we get (2x<8) and (x<4), so (x=4) does not satisfy the strict inequality. Check strict signs carefully while testing options.
Step 2
Why this answer is correct
The correct answer is B. (x=4). From (2x-1<7), we get (2x<8) and (x<4), so (x=4) does not satisfy the strict inequality. Check strict signs carefully while testing options.
Step 3
Exam Tip
(2x-1<7) से (2x<8) और (x<4) मिलता है इसलिए सीमा के पास (x=4) संतुष्ट नहीं करता बल्कि सही जाँच में \(2\cdot4-1=7\) है इसलिए यह सख्त नहीं है। सही विकल्प को जाँचते समय सख्त चिह्न का ध्यान रखें।
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यदि (x) पूर्णांक है और \(3\le x<7\) है तो कुल कितने मान संभव हैं?
If (x) is an integer and \(3\le x<7\), how many values are possible?
#linear inequalities
#integers
#counting solutions
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A (3)
B (4)
C (5)
D (7)
Explanation opens after your attempt
Step 1
Concept
The possible integers are (3,4,5,6), so there are (4) values. The sign \(\le\) includes the left endpoint but (<) excludes the right endpoint.
Step 2
Why this answer is correct
The correct answer is B. (4). The possible integers are (3,4,5,6), so there are (4) values. The sign \(\le\) includes the left endpoint but (<) excludes the right endpoint.
Step 3
Exam Tip
संभव पूर्णांक (3,4,5,6) हैं इसलिए कुल (4) मान हैं। \(\le\) में बायां सिरा शामिल है पर (<) में दायां सिरा शामिल नहीं है।
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असमानता \(7-3x\ge 1\) का हल कौन सा है?
Which is the solution of \(7-3x\ge 1\)?
#linear inequalities
#negative coefficient
#solve
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A \(x\le 2\)
B \(x\ge 2\)
C (x<2)
D (x>2)
Explanation opens after your attempt
Correct Answer
A. \(x\le 2\)
Step 1
Concept
From \(7-3x\ge 1\), we get \(-3x\ge -6\), and dividing by (-3) gives \(x\le 2\). The sign reverses when dividing by a negative number.
Step 2
Why this answer is correct
The correct answer is A. \(x\le 2\). From \(7-3x\ge 1\), we get \(-3x\ge -6\), and dividing by (-3) gives \(x\le 2\). The sign reverses when dividing by a negative number.
Step 3
Exam Tip
\(7-3x\ge 1\) से \(-3x\ge -6\) और (-3) से भाग देने पर \(x\le 2\) मिलता है। ऋणात्मक संख्या से भाग देते समय चिह्न पलटता है।
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अंतराल ((1,6]) को असमानता के रूप में कैसे लिखेंगे?
How do we write the interval ((1,6]) as an inequality?
#linear inequalities
#interval notation
#compound inequality
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A \(1<x\le 6\)
B \(1\le x<6\)
C (1<x<6)
D \(1\le x\le 6\)
Explanation opens after your attempt
Correct Answer
A. \(1<x\le 6\)
Step 1
Concept
The symbol ((1) shows that (1) is not included and (6]) shows that (6) is included. Therefore \(1<x\le 6\) is correct.
Step 2
Why this answer is correct
The correct answer is A. \(1<x\le 6\). The symbol ((1) shows that (1) is not included and (6]) shows that (6) is included. Therefore \(1<x\le 6\) is correct.
Step 3
Exam Tip
((1) बताता है कि (1) शामिल नहीं है और (6]) बताता है कि (6) शामिल है। इसलिए \(1<x\le 6\) सही है।
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किसी कक्षा में विद्यार्थियों की संख्या (n) कम से कम (25) और अधिकतम (40) है। सही असमानता कौन सी है?
In a class, the number of students (n) is at least (25) and at most (40). Which inequality is correct?
#linear inequalities
#word problem
#compound inequality
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A (25<n<40)
B \(25\le n\le 40\)
C \(25\ge n\ge 40\)
D (n<25)
Explanation opens after your attempt
Correct Answer
B. \(25\le n\le 40\)
Step 1
Concept
At least (25) means \(n\ge 25\), and at most (40) means \(n\le 40\). Combining both gives \(25\le n\le 40\).
Step 2
Why this answer is correct
The correct answer is B. \(25\le n\le 40\). At least (25) means \(n\ge 25\), and at most (40) means \(n\le 40\). Combining both gives \(25\le n\le 40\).
Step 3
Exam Tip
कम से कम (25) का अर्थ \(n\ge 25\) और अधिकतम (40) का अर्थ \(n\le 40\) है। दोनों को मिलाकर \(25\le n\le 40\) मिलता है।
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असमानता (9<3x+3) का सही हल क्या है?
What is the correct solution of the inequality (9<3x+3)?
#linear inequalities
#solve
#rewrite inequality
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A (x>2)
B (x<2)
C (x>4)
D (x<4)
Explanation opens after your attempt
Step 1
Concept
First subtract (3) from both sides to get (6<3x), then divide by (3) to get (x>2). When rewriting an inequality, always check the meaning of its direction.
Step 2
Why this answer is correct
The correct answer is A. (x>2). First subtract (3) from both sides to get (6<3x), then divide by (3) to get (x>2). When rewriting an inequality, always check the meaning of its direction.
Step 3
Exam Tip
पहले दोनों ओर (3) घटाएँ तो (6<3x) मिलता है और फिर (3) से भाग देने पर (x>2) आता है। असमानता को पलटकर लिखते समय दिशा का अर्थ जरूर जाँचें।
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