असमानता \(y\ge 0\) में (y=0) के लिए कथन कैसा है?
For (y=0), how is the statement \(y\ge 0\)?
#linear inequalities
#greater equal
#boundary value
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A सत्य / True
B असत्य / False
C निर्धारित नहीं / Not determined
D कोई हल नहीं / No solution
Explanation opens after your attempt
Correct Answer
A. सत्य / True
Step 1
Concept
The sign \(\ge\) includes equality, so \(0\ge 0\) is true. Always check the boundary value carefully.
Step 2
Why this answer is correct
The correct answer is A. सत्य / True. The sign \(\ge\) includes equality, so \(0\ge 0\) is true. Always check the boundary value carefully.
Step 3
Exam Tip
\(\ge\) में बराबरी शामिल होती है इसलिए \(0\ge 0\) सत्य है। सीमा मान को हमेशा ध्यान से जाँचें।
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वाक्य (m) कम से कम (50) है को असमानता में कैसे लिखेंगे?
How do we write the sentence (m) is at least (50) as an inequality?
#linear inequalities
#translation
#at least
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A (m>50)
B \(m\ge 50\)
C (m<50)
D \(m\le 50\)
Explanation opens after your attempt
Correct Answer
B. \(m\ge 50\)
Step 1
Concept
At least (50) means (50) or more. Therefore the correct inequality is \(m\ge 50\).
Step 2
Why this answer is correct
The correct answer is B. \(m\ge 50\). At least (50) means (50) or more. Therefore the correct inequality is \(m\ge 50\).
Step 3
Exam Tip
कम से कम (50) का अर्थ (50) या उससे अधिक है। इसलिए सही असमानता \(m\ge 50\) है।
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वाक्य (c) (75) से अधिक नहीं है का सही रूप कौन सा है?
What is the correct form of the sentence (c) is not more than (75)?
#linear inequalities
#translation
#at most
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A (c<75)
B \(c\le 75\)
C (c>75)
D \(c\ge 75\)
Explanation opens after your attempt
Correct Answer
B. \(c\le 75\)
Step 1
Concept
Not more than means at most (75). A maximum-type sentence includes equality.
Step 2
Why this answer is correct
The correct answer is B. \(c\le 75\). Not more than means at most (75). A maximum-type sentence includes equality.
Step 3
Exam Tip
अधिक नहीं है का अर्थ अधिकतम (75) है। अधिकतम वाले वाक्य में बराबरी शामिल होती है।
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यदि \(b\ge 10\) है तो दोनों ओर (6) घटाने पर क्या होगा?
If \(b\ge 10\), what happens after subtracting (6) from both sides?
#linear inequalities
#subtraction property
#greater equal
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A \(b-6\ge 4\)
B \(b-6\le 4\)
C \(b+6\ge 4\)
D \(6b\ge 4\)
Explanation opens after your attempt
Correct Answer
A. \(b-6\ge 4\)
Step 1
Concept
Subtracting the same number does not change the sign. In subtraction the direction remains the same.
Step 2
Why this answer is correct
The correct answer is A. \(b-6\ge 4\). Subtracting the same number does not change the sign. In subtraction the direction remains the same.
Step 3
Exam Tip
समान संख्या घटाने से चिह्न नहीं बदलता। घटाव में दिशा वही रहती है।
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यदि (p>6) है तो दोनों ओर (3) से गुणा करने पर सही परिणाम क्या है?
If (p>6), what is the correct result after multiplying both sides by (3)?
#linear inequalities
#positive multiplication
#property
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A (3p>18)
B (3p<18)
C (p>18)
D (p<18)
Explanation opens after your attempt
Correct Answer
A. (3p>18)
Step 1
Concept
Multiplying by the positive number (3) does not reverse the sign. The direction changes only in negative multiplication.
Step 2
Why this answer is correct
The correct answer is A. (3p>18). Multiplying by the positive number (3) does not reverse the sign. The direction changes only in negative multiplication.
Step 3
Exam Tip
धनात्मक संख्या (3) से गुणा करने पर चिह्न नहीं पलटता। ऋणात्मक गुणा में ही दिशा बदलती है।
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यदि (q>2) है तो दोनों ओर (-4) से गुणा करने पर क्या मिलेगा?
If (q>2), what do we get after multiplying both sides by (-4)?
#linear inequalities
#negative multiplication
#sign reversal
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A (-4q>-8)
B (-4q<-8)
C (4q<-8)
D (-q>8)
Explanation opens after your attempt
Correct Answer
B. (-4q<-8)
Step 1
Concept
Multiplying by a negative number reverses the inequality sign. Therefore (-4q<-8) is correct.
Step 2
Why this answer is correct
The correct answer is B. (-4q<-8). Multiplying by a negative number reverses the inequality sign. Therefore (-4q<-8) is correct.
Step 3
Exam Tip
ऋणात्मक संख्या से गुणा करने पर असमानता का चिह्न पलट जाता है। इसलिए (-4q<-8) सही है।
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असमानता \(x+9\le 15\) का हल क्या है?
What is the solution of \(x+9\le 15\)?
#linear inequalities
#solve
#one step
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A \(x\le 6\)
B \(x\ge 6\)
C \(x\le 24\)
D \(x\ge 24\)
Explanation opens after your attempt
Correct Answer
A. \(x\le 6\)
Step 1
Concept
Subtracting (9) from both sides gives \(x\le 6\). Addition or subtraction does not change the sign.
Step 2
Why this answer is correct
The correct answer is A. \(x\le 6\). Subtracting (9) from both sides gives \(x\le 6\). Addition or subtraction does not change the sign.
Step 3
Exam Tip
दोनों ओर (9) घटाने पर \(x\le 6\) मिलता है। जोड़ या घटाव से चिह्न नहीं बदलता।
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असमानता (x-8>2) का सही हल कौन सा है?
Which is the correct solution of (x-8>2)?
#linear inequalities
#solve
#greater than
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A (x>10)
B (x<10)
C (x>6)
D (x<6)
Explanation opens after your attempt
Step 1
Concept
Adding (8) to both sides gives (x>10). Add the same number to remove the subtracted term.
Step 2
Why this answer is correct
The correct answer is A. (x>10). Adding (8) to both sides gives (x>10). Add the same number to remove the subtracted term.
Step 3
Exam Tip
दोनों ओर (8) जोड़ने पर (x>10) मिलता है। घटे हुए पद को हटाने के लिए वही संख्या जोड़ें।
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असमानता \(4x\ge 20\) का हल क्या है?
What is the solution of \(4x\ge 20\)?
#linear inequalities
#division positive
#solve
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A \(x\ge 5\)
B \(x\le 5\)
C \(x\ge 16\)
D \(x\le 16\)
Explanation opens after your attempt
Correct Answer
A. \(x\ge 5\)
Step 1
Concept
Dividing both sides by (4) gives \(x\ge 5\). Division by a positive number does not change the direction.
Step 2
Why this answer is correct
The correct answer is A. \(x\ge 5\). Dividing both sides by (4) gives \(x\ge 5\). Division by a positive number does not change the direction.
Step 3
Exam Tip
दोनों ओर (4) से भाग देने पर \(x\ge 5\) मिलता है। धनात्मक भाग में दिशा नहीं बदलती।
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कौन सा मान (3x+2<14) को संतुष्ट करता है?
Which value satisfies (3x+2<14)?
#linear inequalities
#solution check
#substitution
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A (x=4)
B (x=5)
C (x=3)
D (x=6)
Explanation opens after your attempt
Step 1
Concept
For (x=3), \(3\cdot3+2=11\), and (11<14) is true. Check an option by substituting it in the original inequality.
Step 2
Why this answer is correct
The correct answer is C. (x=3). For (x=3), \(3\cdot3+2=11\), and (11<14) is true. Check an option by substituting it in the original inequality.
Step 3
Exam Tip
(x=3) रखने पर \(3\cdot3+2=11\) और (11<14) सत्य है। विकल्प को मूल असमानता में रखकर जाँचें।
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कौन सा मान \(5x-1\ge 24\) को संतुष्ट करता है?
Which value satisfies \(5x-1\ge 24\)?
#linear inequalities
#solution check
#greater equal
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A (x=4)
B (x=5)
C (x=3)
D (x=2)
Explanation opens after your attempt
Step 1
Concept
For (x=5), \(5\cdot5-1=24\), and \(24\ge 24\) is true. The sign \(\ge\) includes the boundary value.
Step 2
Why this answer is correct
The correct answer is B. (x=5). For (x=5), \(5\cdot5-1=24\), and \(24\ge 24\) is true. The sign \(\ge\) includes the boundary value.
Step 3
Exam Tip
(x=5) रखने पर \(5\cdot5-1=24\) और \(24\ge 24\) सत्य है। \(\ge\) में सीमा मान शामिल होता है।
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असमानता (x>2) को संख्या रेखा पर कैसे दिखाया जाता है?
How is (x>2) shown on the number line?
#linear inequalities
#number line
#open circle
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A (2) पर खुला बिंदु और दाईं ओर रेखा / Open circle at (2) and line to the right
B (2) पर बंद बिंदु और बाईं ओर रेखा / Closed circle at (2) and line to the left
C (2) पर बंद बिंदु और दाईं ओर रेखा / Closed circle at (2) and line to the right
D (2) पर खुला बिंदु और बाईं ओर रेखा / Open circle at (2) and line to the left
Explanation opens after your attempt
Correct Answer
A. (2) पर खुला बिंदु और दाईं ओर रेखा / Open circle at (2) and line to the right
Step 1
Concept
In (x>2), (2) is not included and greater numbers lie to the right. So use an open circle and shade right.
Step 2
Why this answer is correct
The correct answer is A. (2) पर खुला बिंदु और दाईं ओर रेखा / Open circle at (2) and line to the right. In (x>2), (2) is not included and greater numbers lie to the right. So use an open circle and shade right.
Step 3
Exam Tip
(x>2) में (2) शामिल नहीं है और बड़ी संख्याएँ दाईं ओर होती हैं। इसलिए खुला बिंदु और दाईं ओर रेखा बनेगी।
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असमानता \(x\le -4\) के लिए संख्या रेखा पर सही रूप कौन सा है?
Which number line form is correct for \(x\le -4\)?
#linear inequalities
#number line
#closed circle
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A (-4) पर खुला बिंदु और दाईं ओर / Open circle at (-4) and right side
B (-4) पर बंद बिंदु और बाईं ओर / Closed circle at (-4) and left side
C (-4) पर खुला बिंदु और बाईं ओर / Open circle at (-4) and left side
D (-4) पर बंद बिंदु और दाईं ओर / Closed circle at (-4) and right side
Explanation opens after your attempt
Correct Answer
B. (-4) पर बंद बिंदु और बाईं ओर / Closed circle at (-4) and left side
Step 1
Concept
The sign \(\le\) includes the boundary, and smaller numbers lie to the left. So use a closed circle at (-4) and shade left.
Step 2
Why this answer is correct
The correct answer is B. (-4) पर बंद बिंदु और बाईं ओर / Closed circle at (-4) and left side. The sign \(\le\) includes the boundary, and smaller numbers lie to the left. So use a closed circle at (-4) and shade left.
Step 3
Exam Tip
\(\le\) में सीमा शामिल होती है और छोटी संख्याएँ बाईं ओर होती हैं। इसलिए (-4) पर बंद बिंदु और बाईं ओर रेखा होगी।
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अंतराल (\(-\infty,3]\) किस असमानता को दर्शाता है?
Which inequality is represented by the interval (\(-\infty,3]\)?
#linear inequalities
#interval notation
#closed endpoint
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A (x<3)
B \(x\le 3\)
C (x>3)
D \(x\ge 3\)
Explanation opens after your attempt
Correct Answer
B. \(x\le 3\)
Step 1
Concept
The square bracket (]) shows that (3) is included. Therefore (\(-\infty,3]\) means \(x\le 3\).
Step 2
Why this answer is correct
The correct answer is B. \(x\le 3\). The square bracket (]) shows that (3) is included. Therefore (\(-\infty,3]\) means \(x\le 3\).
Step 3
Exam Tip
वर्ग कोष्ठक (]) बताता है कि (3) शामिल है। इसलिए (\(-\infty,3]\) का अर्थ \(x\le 3\) है।
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अंतराल \([-1,\infty\)) का असमानता रूप क्या है?
What is the inequality form of the interval \([-1,\infty\))?
#linear inequalities
#interval notation
#greater equal
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A (x>-1)
B \(x\ge -1\)
C (x<-1)
D \(x\le -1\)
Explanation opens after your attempt
Correct Answer
B. \(x\ge -1\)
Step 1
Concept
The square bracket shows that (-1) is included and values lie to the right. Therefore \(x\ge -1\) is correct.
Step 2
Why this answer is correct
The correct answer is B. \(x\ge -1\). The square bracket shows that (-1) is included and values lie to the right. Therefore \(x\ge -1\) is correct.
Step 3
Exam Tip
वर्ग कोष्ठक बताता है कि (-1) शामिल है और मान दाईं ओर हैं। इसलिए \(x\ge -1\) सही है।
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असमानता \(-1\le x<4\) में कौन सा मान शामिल है?
Which value is included in \(-1\le x<4\)?
#linear inequalities
#compound inequality
#included value
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A (4)
B (5)
C (0)
D (-2)
Explanation opens after your attempt
Step 1
Concept
The number (0) lies between (-1) and (4). This inequality includes (-1) but excludes (4).
Step 2
Why this answer is correct
The correct answer is C. (0). The number (0) lies between (-1) and (4). This inequality includes (-1) but excludes (4).
Step 3
Exam Tip
(0) संख्या (-1) और (4) के बीच है। इस असमानता में (-1) शामिल है पर (4) शामिल नहीं है।
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यदि \(r\ge -2\) है तो इनमें से कौन सा मान संभव है?
If \(r\ge -2\), which of the following values is possible?
#linear inequalities
#possible value
#boundary
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A (-5)
B (-4)
C (-2)
D (-6)
Explanation opens after your attempt
Step 1
Concept
In \(r\ge -2\), (-2) and greater numbers are included. With an equality sign, the boundary value is also a solution.
Step 2
Why this answer is correct
The correct answer is C. (-2). In \(r\ge -2\), (-2) and greater numbers are included. With an equality sign, the boundary value is also a solution.
Step 3
Exam Tip
\(r\ge -2\) में (-2) और उससे बड़ी संख्याएँ आती हैं। बराबरी वाले चिह्न में सीमा मान भी हल होता है।
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किसी परीक्षा में छात्र को (45) या अधिक अंक चाहिए। यदि अंक (s) हैं तो सही असमानता क्या है?
A student needs (45) or more marks in an exam. If the marks are (s), what is the correct inequality?
#linear inequalities
#word problem
#marks
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A (s>45)
B \(s\ge 45\)
C (s<45)
D \(s\le 45\)
Explanation opens after your attempt
Correct Answer
B. \(s\ge 45\)
Step 1
Concept
(45) or more means \(s\ge 45\). A phrase with or more includes equality.
Step 2
Why this answer is correct
The correct answer is B. \(s\ge 45\). (45) or more means \(s\ge 45\). A phrase with or more includes equality.
Step 3
Exam Tip
(45) या अधिक का अर्थ \(s\ge 45\) है। या अधिक वाले वाक्य में बराबरी शामिल होती है।
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एक पैकेट का भार (12) किलोग्राम से अधिक नहीं होना चाहिए। यदि भार (w) है तो सही असमानता क्या है?
A packet weight should not be more than (12) kilograms. If the weight is (w), what is the correct inequality?
#linear inequalities
#word problem
#maximum
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A (w<12)
B \(w\le 12\)
C (w>12)
D \(w\ge 12\)
Explanation opens after your attempt
Correct Answer
B. \(w\le 12\)
Step 1
Concept
Not more than means at most (12), so \(w\le 12\). A maximum limit includes equality.
Step 2
Why this answer is correct
The correct answer is B. \(w\le 12\). Not more than means at most (12), so \(w\le 12\). A maximum limit includes equality.
Step 3
Exam Tip
अधिक नहीं का अर्थ अधिकतम (12) है इसलिए \(w\le 12\)। अधिकतम सीमा में बराबरी शामिल होती है।
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किसी पेन की कीमत (30) रुपये से कम है। यदि कीमत (p) है तो असमानता क्या होगी?
The price of a pen is less than (30) rupees. If the price is (p), what is the inequality?
#linear inequalities
#word problem
#price
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A (p<30)
B \(p\le 30\)
C (p>30)
D \(p\ge 30\)
Explanation opens after your attempt
Step 1
Concept
Less than means strictly smaller, so (p<30). If equality is included, we write \(\le\).
Step 2
Why this answer is correct
The correct answer is A. (p<30). Less than means strictly smaller, so (p<30). If equality is included, we write \(\le\).
Step 3
Exam Tip
से कम का अर्थ सख्त रूप से कम है इसलिए (p<30)। बराबरी शामिल हो तो \(\le\) लिखा जाता है।
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बस में बैठने के लिए आयु कम से कम (5) वर्ष होनी चाहिए। यदि आयु (a) है तो सही असमानता कौन सी है?
To sit in the bus, age must be at least (5) years. If age is (a), which inequality is correct?
#linear inequalities
#word problem
#at least
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A (a<5)
B \(a\le 5\)
C \(a\ge 5\)
D (a>5)
Explanation opens after your attempt
Correct Answer
C. \(a\ge 5\)
Step 1
Concept
At least (5) means (5) or more. Therefore \(a\ge 5\) is correct.
Step 2
Why this answer is correct
The correct answer is C. \(a\ge 5\). At least (5) means (5) or more. Therefore \(a\ge 5\) is correct.
Step 3
Exam Tip
कम से कम (5) का अर्थ (5) या उससे अधिक है। इसलिए \(a\ge 5\) सही है।
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यदि (x=-1) है तो कौन सी असमानता सत्य है?
If (x=-1), which inequality is true?
#linear inequalities
#substitution
#true option
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A (x<-3)
B \(x\le -1\)
C (x>2)
D \(x\ge 0\)
Explanation opens after your attempt
Correct Answer
B. \(x\le -1\)
Step 1
Concept
\(-1\le -1\) is true because equality is included. Substitute the given value in each option.
Step 2
Why this answer is correct
The correct answer is B. \(x\le -1\). \(-1\le -1\) is true because equality is included. Substitute the given value in each option.
Step 3
Exam Tip
\(-1\le -1\) सत्य है क्योंकि बराबरी शामिल है। दिए गए मान को हर विकल्प में रखकर जाँचें।
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असमानता \(x+4\ge 13\) का हल कौन सा है?
Which is the solution of \(x+4\ge 13\)?
#linear inequalities
#solve
#greater equal
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A \(x\ge 9\)
B \(x\le 9\)
C (x>17)
D (x<17)
Explanation opens after your attempt
Correct Answer
A. \(x\ge 9\)
Step 1
Concept
Subtracting (4) from both sides gives \(x\ge 9\). Addition or subtraction does not change the direction.
Step 2
Why this answer is correct
The correct answer is A. \(x\ge 9\). Subtracting (4) from both sides gives \(x\ge 9\). Addition or subtraction does not change the direction.
Step 3
Exam Tip
दोनों ओर (4) घटाने पर \(x\ge 9\) मिलता है। जोड़ या घटाव से दिशा नहीं बदलती।
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असमानता (9-x<4) का सही हल क्या है?
What is the correct solution of (9-x<4)?
#linear inequalities
#negative coefficient
#solve
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A (x>5)
B (x<5)
C (x>13)
D (x<13)
Explanation opens after your attempt
Step 1
Concept
From (9-x<4), we get (-x<-5), and dividing by a negative gives (x>5). The sign reverses when removing (-x).
Step 2
Why this answer is correct
The correct answer is A. (x>5). From (9-x<4), we get (-x<-5), and dividing by a negative gives (x>5). The sign reverses when removing (-x).
Step 3
Exam Tip
(9-x<4) से (-x<-5) और ऋणात्मक से भाग देने पर (x>5)। (-x) हटाते समय चिह्न पलटता है।
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असमानता \(2x+5\le 17\) का हल कौन सा है?
Which is the solution of \(2x+5\le 17\)?
#linear inequalities
#two step
#solve
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A \(x\le 6\)
B \(x\ge 6\)
C \(x\le 11\)
D \(x\ge 11\)
Explanation opens after your attempt
Correct Answer
A. \(x\le 6\)
Step 1
Concept
First subtract (5), then divide by (2), giving \(x\le 6\). Keep the order correct in two-step questions.
Step 2
Why this answer is correct
The correct answer is A. \(x\le 6\). First subtract (5), then divide by (2), giving \(x\le 6\). Keep the order correct in two-step questions.
Step 3
Exam Tip
पहले (5) घटाएँ फिर (2) से भाग दें तो \(x\le 6\)। दो चरणों वाले प्रश्न में क्रम सही रखें।
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असमानता \(15-3x\ge 6\) का सही हल क्या है?
What is the correct solution of \(15-3x\ge 6\)?
#linear inequalities
#negative division
#two step
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A \(x\le 3\)
B \(x\ge 3\)
C \(x\le -3\)
D \(x\ge -3\)
Explanation opens after your attempt
Correct Answer
A. \(x\le 3\)
Step 1
Concept
From \(15-3x\ge 6\), we get \(-3x\ge -9\), and division by (-3) gives \(x\le 3\). Negative division changes the direction.
Step 2
Why this answer is correct
The correct answer is A. \(x\le 3\). From \(15-3x\ge 6\), we get \(-3x\ge -9\), and division by (-3) gives \(x\le 3\). Negative division changes the direction.
Step 3
Exam Tip
\(15-3x\ge 6\) से \(-3x\ge -9\) और (-3) से भाग देने पर \(x\le 3\)। ऋणात्मक भाग में दिशा बदलती है।
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कौन सा कथन (x>-3) के लिए सही है?
Which statement is correct for (x>-3)?
#linear inequalities
#number line
#strict greater
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A समाधान (-3) से बाईं ओर हैं / Solutions are to the left of (-3)
B समाधान (-3) से दाईं ओर हैं और (-3) शामिल नहीं है / Solutions are to the right of (-3) and (-3) is not included
C केवल (x=-3) समाधान है / Only (x=-3) is a solution
D कोई वास्तविक समाधान नहीं है / There is no real solution
Explanation opens after your attempt
Correct Answer
B. समाधान (-3) से दाईं ओर हैं और (-3) शामिल नहीं है / Solutions are to the right of (-3) and (-3) is not included
Step 1
Concept
In (x>-3), (-3) is not included and greater numbers lie to the right. Use an open circle on the number line.
Step 2
Why this answer is correct
The correct answer is B. समाधान (-3) से दाईं ओर हैं और (-3) शामिल नहीं है / Solutions are to the right of (-3) and (-3) is not included. In (x>-3), (-3) is not included and greater numbers lie to the right. Use an open circle on the number line.
Step 3
Exam Tip
(x>-3) में (-3) शामिल नहीं होता और बड़ी संख्याएँ दाईं ओर होती हैं। संख्या रेखा पर खुला बिंदु लगाएँ।
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असमानता \(x\le 4\) का अंतराल रूप क्या है?
What is the interval form of \(x\le 4\)?
#linear inequalities
#interval form
#less equal
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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 \(x\le 4\), (4) is included and values go to the left. Therefore (\(-\infty,4]\) is correct.
Step 2
Why this answer is correct
The correct answer is A. (\(-\infty,4]\). In \(x\le 4\), (4) is included and values go to the left. Therefore (\(-\infty,4]\) is correct.
Step 3
Exam Tip
\(x\le 4\) में (4) शामिल है और मान बाईं ओर जाते हैं। इसलिए (\(-\infty,4]\) सही है।
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असमानता (x>6) का अंतराल रूप कौन सा है?
Which is the interval form of (x>6)?
#linear inequalities
#interval form
#greater than
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A (\(6,\infty\))
B \([6,\infty\))
C (\(-\infty,6\))
D (\(-\infty,6]\)
Explanation opens after your attempt
Correct Answer
A. (\(6,\infty\))
Step 1
Concept
In (x>6), (6) is not included and values lie to the right. So (\(6,\infty\)) is correct.
Step 2
Why this answer is correct
The correct answer is A. (\(6,\infty\)). In (x>6), (6) is not included and values lie to the right. So (\(6,\infty\)) is correct.
Step 3
Exam Tip
(x>6) में (6) शामिल नहीं है और मान दाईं ओर हैं। इसलिए (\(6,\infty\)) सही है।
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कौन सा विकल्प \(0\le x<10\) को सही बताता है?
Which option correctly describes \(0\le x<10\)?
#linear inequalities
#compound inequality
#interpretation
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A (x) (0) या उससे बड़ा और (10) से छोटा है / (x) is (0) or more and less than (10)
B (x) (0) से छोटा और (10) से बड़ा है / (x) is less than (0) and greater than (10)
C (x) केवल (10) के बराबर है / (x) is only equal to (10)
D (x) केवल (0) से छोटा है / (x) is only less than (0)
Explanation opens after your attempt
Correct Answer
A. (x) (0) या उससे बड़ा और (10) से छोटा है / (x) is (0) or more and less than (10)
Step 1
Concept
In \(0\le x<10\), (0) is included but (10) is not included. Read a compound inequality from both sides.
Step 2
Why this answer is correct
The correct answer is A. (x) (0) या उससे बड़ा और (10) से छोटा है / (x) is (0) or more and less than (10). In \(0\le x<10\), (0) is included but (10) is not included. Read a compound inequality from both sides.
Step 3
Exam Tip
\(0\le x<10\) में (0) शामिल है पर (10) शामिल नहीं है। संयुक्त असमानता को दोनों तरफ से पढ़ें।
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यदि (x) एक पूर्णांक है और \(-4<x\le 1\) है तो (x) के मान क्या हैं?
If (x) is an integer and \(-4<x\le 1\), what are the values of (x)?
#linear inequalities
#integers
#compound inequality
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A \(x\in{-4,-3,-2,-1,0,1}\)
B \(x\in{-3,-2,-1,0,1}\)
C \(x\in{-3,-2,-1,0}\)
D \(x\in{-2,-1,0,1,2}\)
Explanation opens after your attempt
Correct Answer
B. \(x\in{-3,-2,-1,0,1}\)
Step 1
Concept
The value (-4) is not included but (1) is included. The integer values are (-3,-2,-1,0,1).
Step 2
Why this answer is correct
The correct answer is B. \(x\in{-3,-2,-1,0,1}\). The value (-4) is not included but (1) is included. The integer values are (-3,-2,-1,0,1).
Step 3
Exam Tip
(-4) शामिल नहीं है पर (1) शामिल है। पूर्णांक मान (-3,-2,-1,0,1) होंगे।
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कौन सी असमानता (n) के न्यूनतम (18) होने को दिखाती है?
Which inequality shows that (n) is minimum (18)?
#linear inequalities
#minimum
#language
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A \(n\le 18\)
B (n<18)
C \(n\ge 18\)
D (n>18)
Explanation opens after your attempt
Correct Answer
C. \(n\ge 18\)
Step 1
Concept
Minimum (18) means (18) or more. Therefore \(n\ge 18\) is correct.
Step 2
Why this answer is correct
The correct answer is C. \(n\ge 18\). Minimum (18) means (18) or more. Therefore \(n\ge 18\) is correct.
Step 3
Exam Tip
न्यूनतम (18) का अर्थ (18) या उससे अधिक है। इसलिए \(n\ge 18\) सही है।
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कौन सी असमानता (u) के (25) से कम या बराबर होने को दिखाती है?
Which inequality shows that (u) is less than or equal to (25)?
#linear inequalities
#less equal
#translation
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A (u<25)
B \(u\le 25\)
C (u>25)
D \(u\ge 25\)
Explanation opens after your attempt
Correct Answer
B. \(u\le 25\)
Step 1
Concept
The symbol for less than or equal to is \(\le\). Therefore \(u\le 25\) is correct.
Step 2
Why this answer is correct
The correct answer is B. \(u\le 25\). The symbol for less than or equal to is \(\le\). Therefore \(u\le 25\) is correct.
Step 3
Exam Tip
से कम या बराबर का प्रतीक \(\le\) होता है। इसलिए \(u\le 25\) सही है।
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यदि (a>b) और दोनों ओर (5) जोड़ा जाए तो कौन सा कथन हमेशा सही है?
If (a>b) and (5) is added to both sides, which statement is always true?
#linear inequalities
#addition property
#general rule
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A (a+5>b+5)
B (a+5<b+5)
C (a-5<b-5)
D (5a<b+5)
Explanation opens after your attempt
Correct Answer
A. (a+5>b+5)
Step 1
Concept
Adding the same number to both sides does not change the direction. Therefore (a+5>b+5) is always true.
Step 2
Why this answer is correct
The correct answer is A. (a+5>b+5). Adding the same number to both sides does not change the direction. Therefore (a+5>b+5) is always true.
Step 3
Exam Tip
दोनों ओर समान संख्या जोड़ने से दिशा नहीं बदलती। इसलिए (a+5>b+5) हमेशा 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 inequality direction the same. The condition (k>0) is necessary.
Step 2
Why this answer is correct
The correct answer is A. (ak<bk). Multiplication by a positive number keeps the inequality direction the same. The condition (k>0) is necessary.
Step 3
Exam Tip
धनात्मक संख्या से गुणा करने पर असमानता की दिशा वही रहती है। (k>0) की शर्त जरूरी है।
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यदि (a>b) और (k<0) है तो सही कथन कौन सा है?
If (a>b) and (k<0), which statement is correct?
#linear inequalities
#negative multiplier
#property
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A (ak>bk)
B (ak<bk)
C (a+k<b+k)
D \(\frac{a}{k}>\frac{b}{k}\)
Explanation opens after your attempt
Correct Answer
B. (ak<bk)
Step 1
Concept
Multiplying by a negative number reverses the inequality. Therefore (ak<bk) is correct.
Step 2
Why this answer is correct
The correct answer is B. (ak<bk). Multiplying by a negative number reverses the inequality. Therefore (ak<bk) is correct.
Step 3
Exam Tip
ऋणात्मक संख्या से गुणा करने पर असमानता उलट जाती है। इसलिए (ak<bk) सही है।
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असमानता (x+11>11) का हल क्या है?
What is the solution of (x+11>11)?
#linear inequalities
#solve
#simple transformation
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A (x>0)
B (x<0)
C (x>22)
D (x<22)
Explanation opens after your attempt
Step 1
Concept
Subtracting (11) 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 (11) from both sides gives (x>0). Remove equal terms to get the simple form.
Step 3
Exam Tip
दोनों ओर (11) घटाने पर (x>0) मिलता है। समान पद हटाकर सरल रूप बनाइए।
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असमानता \(\frac{x}{6}\le 2\) का हल क्या है?
What is the solution of \(\frac{x}{6}\le 2\)?
#linear inequalities
#fraction
#solve
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A \(x\le 12\)
B \(x\ge 12\)
C \(x\le \frac{1}{3}\)
D \(x\ge \frac{1}{3}\)
Explanation opens after your attempt
Correct Answer
A. \(x\le 12\)
Step 1
Concept
Multiplying both sides by (6) gives \(x\le 12\). Positive multiplication does not reverse the sign.
Step 2
Why this answer is correct
The correct answer is A. \(x\le 12\). Multiplying both sides by (6) gives \(x\le 12\). Positive multiplication does not reverse the sign.
Step 3
Exam Tip
दोनों ओर (6) से गुणा करने पर \(x\le 12\) मिलता है। धनात्मक गुणा में चिह्न नहीं पलटता।
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असमानता \(\frac{x}{-5}>3\) का सही हल क्या है?
What is the correct solution of \(\frac{x}{-5}>3\)?
#linear inequalities
#fraction
#negative multiplier
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A (x> -15)
B (x< -15)
C (x>15)
D (x<15)
Explanation opens after your attempt
Correct Answer
B. (x< -15)
Step 1
Concept
Multiplying both sides by (-5) reverses the sign, so (x<-15). Negative multiplication changes the direction.
Step 2
Why this answer is correct
The correct answer is B. (x< -15). Multiplying both sides by (-5) reverses the sign, so (x<-15). Negative multiplication changes the direction.
Step 3
Exam Tip
दोनों ओर (-5) से गुणा करने पर चिह्न पलटेगा इसलिए (x<-15)। ऋणात्मक गुणा में दिशा बदलती है।
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असमानता (18<6x) का हल कौन सा है?
Which is the solution of (18<6x)?
#linear inequalities
#solve
#rewrite
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A (x>3)
B (x<3)
C (x>24)
D (x<24)
Explanation opens after your attempt
Step 1
Concept
Dividing both sides by (6) gives (3<x), that is (x>3). When rewriting, check the meaning of the direction.
Step 2
Why this answer is correct
The correct answer is A. (x>3). Dividing both sides by (6) gives (3<x), that is (x>3). When rewriting, check the meaning of the direction.
Step 3
Exam Tip
दोनों ओर (6) से भाग देने पर (3<x) यानी (x>3) मिलता है। रूप बदलते समय दिशा का अर्थ जाँचें।
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किसी समूह में सदस्यों की संख्या (g) कम से कम (12) और अधिकतम (28) है। सही असमानता कौन सी है?
In a group, the number of members (g) is at least (12) and at most (28). Which inequality is correct?
#linear inequalities
#word problem
#compound inequality
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A (12<g<28)
B \(12\le g\le 28\)
C \(12\ge g\ge 28\)
D (g<12)
Explanation opens after your attempt
Correct Answer
B. \(12\le g\le 28\)
Step 1
Concept
At least (12) means \(g\ge 12\), and at most (28) means \(g\le 28\). Combining both gives \(12\le g\le 28\).
Step 2
Why this answer is correct
The correct answer is B. \(12\le g\le 28\). At least (12) means \(g\ge 12\), and at most (28) means \(g\le 28\). Combining both gives \(12\le g\le 28\).
Step 3
Exam Tip
कम से कम (12) का अर्थ \(g\ge 12\) और अधिकतम (28) का अर्थ \(g\le 28\) है। दोनों को मिलाकर \(12\le g\le 28\) मिलता है।
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असमानता \(6x-5\ge 19\) का हल क्या है?
What is the solution of the inequality \(6x-5\ge 19\)?
#linear inequalities
#two step
#solve
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A \(x\ge 4\)
B \(x\le 4\)
C \(x\ge 14\)
D \(x\le 14\)
Explanation opens after your attempt
Correct Answer
A. \(x\ge 4\)
Step 1
Concept
First add (5) to both sides to get \(6x\ge 24\), then divide by (6). Division by a positive number does not change the sign.
Step 2
Why this answer is correct
The correct answer is A. \(x\ge 4\). First add (5) to both sides to get \(6x\ge 24\), then divide by (6). Division by a positive number does not change the sign.
Step 3
Exam Tip
पहले दोनों ओर (5) जोड़ें तो \(6x\ge 24\) मिलता है फिर (6) से भाग दें। धनात्मक भाग में चिह्न नहीं बदलता।
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असमानता (3(x-2)<15) का सही हल कौन सा है?
Which is the correct solution of (3(x-2)<15)?
#linear inequalities
#bracket
#solve
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A (x<7)
B (x>7)
C (x<5)
D (x>5)
Explanation opens after your attempt
Step 1
Concept
First divide by (3) to get (x-2<5), then (x<7). Keep the order correct in bracket questions.
Step 2
Why this answer is correct
The correct answer is A. (x<7). First divide by (3) to get (x-2<5), then (x<7). Keep the order correct in bracket questions.
Step 3
Exam Tip
पहले (3) से भाग देने पर (x-2<5) मिलता है और फिर (x<7)। कोष्ठक वाले प्रश्न में क्रम सही रखें।
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यदि (x) पूर्णांक है और \(2\le x<8\) है तो कुल कितने मान संभव हैं?
If (x) is an integer and \(2\le x<8\), how many values are possible?
#linear inequalities
#integers
#counting solutions
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A (5)
B (6)
C (7)
D (8)
Explanation opens after your attempt
Step 1
Concept
The possible integers are (2,3,4,5,6,7), so there are (6) values. The sign \(\le\) includes the endpoint but (<) does not.
Step 2
Why this answer is correct
The correct answer is B. (6). The possible integers are (2,3,4,5,6,7), so there are (6) values. The sign \(\le\) includes the endpoint but (<) does not.
Step 3
Exam Tip
संभव पूर्णांक (2,3,4,5,6,7) हैं इसलिए कुल (6) मान हैं। \(\le\) सीमा को शामिल करता है पर (<) सीमा को नहीं।
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अंतराल ((-3,5]) को असमानता के रूप में कैसे लिखेंगे?
How do we write the interval ((-3,5]) as an inequality?
#linear inequalities
#interval notation
#compound inequality
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A \(-3<x\le 5\)
B \(-3\le x<5\)
C (-3<x<5)
D \(-3\le x\le 5\)
Explanation opens after your attempt
Correct Answer
A. \(-3<x\le 5\)
Step 1
Concept
The symbol ((-3) shows that (-3) is not included and (5]) shows that (5) is included. Therefore \(-3<x\le 5\) is correct.
Step 2
Why this answer is correct
The correct answer is A. \(-3<x\le 5\). The symbol ((-3) shows that (-3) is not included and (5]) shows that (5) is included. Therefore \(-3<x\le 5\) is correct.
Step 3
Exam Tip
((-3) बताता है कि (-3) शामिल नहीं है और (5]) बताता है कि (5) शामिल है। इसलिए \(-3<x\le 5\) सही है।
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वाक्य किसी संख्या में (4) जोड़ने पर परिणाम (10) से अधिक है को असमानता में कैसे लिखेंगे?
How do we write the sentence adding (4) to a number gives a result greater than (10) as an inequality?
#linear inequalities
#translation
#word statement
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A (x+4>10)
B (x+4<10)
C (x-4>10)
D (4x>10)
Explanation opens after your attempt
Correct Answer
A. (x+4>10)
Step 1
Concept
Adding (4) to a number is written as (x+4), and greater than uses (>). Therefore (x+4>10) is correct.
Step 2
Why this answer is correct
The correct answer is A. (x+4>10). Adding (4) to a number is written as (x+4), and greater than uses (>). Therefore (x+4>10) is correct.
Step 3
Exam Tip
संख्या में (4) जोड़ने का रूप (x+4) है और अधिक है का चिह्न (>) है। इसलिए (x+4>10) सही है।
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असमानता \(\frac{x}{7}>2\) का हल क्या है?
What is the solution of the inequality \(\frac{x}{7}>2\)?
#linear inequalities
#fraction
#positive multiplication
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A (x>14)
B (x<14)
C \(x>\frac{2}{7}\)
D \(x<\frac{2}{7}\)
Explanation opens after your attempt
Step 1
Concept
Multiplying both sides by (7) gives (x>14). Positive multiplication does not change the inequality direction.
Step 2
Why this answer is correct
The correct answer is A. (x>14). Multiplying both sides by (7) gives (x>14). Positive multiplication does not change the inequality direction.
Step 3
Exam Tip
दोनों ओर (7) से गुणा करने पर (x>14) मिलता है। धनात्मक गुणा में असमानता की दिशा नहीं बदलती।
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असमानता \(7-x\ge 2\) का सही हल कौन सा है?
Which is the correct solution of \(7-x\ge 2\)?
#linear inequalities
#negative coefficient
#solve
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A \(x\le 5\)
B \(x\ge 5\)
C (x<9)
D (x>9)
Explanation opens after your attempt
Correct Answer
A. \(x\le 5\)
Step 1
Concept
From \(7-x\ge 2\), we get \(-x\ge -5\), and dividing by a negative gives \(x\le 5\). Reverse the sign when removing (-x).
Step 2
Why this answer is correct
The correct answer is A. \(x\le 5\). From \(7-x\ge 2\), we get \(-x\ge -5\), and dividing by a negative gives \(x\le 5\). Reverse the sign when removing (-x).
Step 3
Exam Tip
\(7-x\ge 2\) से \(-x\ge -5\) मिलता है और ऋणात्मक से भाग देने पर \(x\le 5\)। (-x) हटाते समय चिह्न पलटें।
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यदि \(x\ge -3\) है तो दोनों ओर (-2) से गुणा करने पर कौन सा कथन सही होगा?
If \(x\ge -3\), which statement is correct after multiplying both sides by (-2)?
#linear inequalities
#negative multiplication
#sign reversal
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A \(-2x\ge 6\)
B \(-2x\le 6\)
C \(2x\le 6\)
D \(-2x\le -6\)
Explanation opens after your attempt
Correct Answer
B. \(-2x\le 6\)
Step 1
Concept
Multiplying by the negative number (-2) reverses the inequality sign. Therefore \(-2x\le 6\) is correct.
Step 2
Why this answer is correct
The correct answer is B. \(-2x\le 6\). Multiplying by the negative number (-2) reverses the inequality sign. Therefore \(-2x\le 6\) is correct.
Step 3
Exam Tip
ऋणात्मक संख्या (-2) से गुणा करने पर असमानता का चिह्न पलटता है। इसलिए \(-2x\le 6\) सही है।
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असमानता (2(3-x)\le 8) का सही हल क्या है?
What is the correct solution of the inequality (2(3-x)\le 8)?
#linear inequalities
#bracket
#negative variable
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A \(x\ge -1\)
B \(x\le -1\)
C \(x\ge 1\)
D \(x\le 1\)
Explanation opens after your attempt
Correct Answer
A. \(x\ge -1\)
Step 1
Concept
First divide by (2) to get \(3-x\le 4\), then \(-x\le 1\) gives \(x\ge -1\). Remember to reverse the sign when removing a negative variable.
Step 2
Why this answer is correct
The correct answer is A. \(x\ge -1\). First divide by (2) to get \(3-x\le 4\), then \(-x\le 1\) gives \(x\ge -1\). Remember to reverse the sign when removing a negative variable.
Step 3
Exam Tip
पहले (2) से भाग देने पर \(3-x\le 4\) मिलता है और फिर \(-x\le 1\) से \(x\ge -1\) आता है। ऋणात्मक चर हटाते समय चिह्न पलटना याद रखें।
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