Level 51 • 50/50 questions • 40 seconds per question.
Login to save your score, XP, coins and progress.
What is the (y)-intercept used to draw (x+3y=12)?
C. (4)
For the (y)-intercept, put (x=0). Then (3y=12), so (y=4).
The correct answer is C. (4). For the (y)-intercept, put (x=0). Then (3y=12), so (y=4).
(y)-अंतःखंड के लिए (x=0) रखें। तब (3y=12), इसलिए (y=4)।
Login to save your score, XP, coins and progress.
Which point lies in the solution region of \(x+y\leq 5\)?
C. ((1,2))
Substituting ((1,2)) gives \(3\leq 5\), which is true. Check options by substitution.
The correct answer is C. ((1,2)). Substituting ((1,2)) gives \(3\leq 5\), which is true. Check options by substitution.
((1,2)) रखने पर \(3\leq 5\) सत्य है। विकल्पों में बिंदु रखकर जाँचें।
Login to save your score, XP, coins and progress.
D. (1000)
Total choices are \(5\times5\times5\times8=1000\). In mixed codes, write choices for each position separately.
The correct answer is D. (1000). Total choices are \(5\times5\times5\times8=1000\). In mixed codes, write choices for each position separately.
कुल विकल्प \(5\times5\times5\times8=1000\) हैं। मिश्रित कोड में हर स्थान का विकल्प अलग लिखें।
Login to save your score, XP, coins and progress.
Which point lies in the solution region of (x+2y>8)?
B. ((2,3))
Substitution must make the expression strictly greater than (8). Here no equality is allowed in a strict inequality.
The correct answer is B. ((2,3)). Substitution must make the expression strictly greater than (8). Here no equality is allowed in a strict inequality.
((2,3)) रखने पर (2+6>8) अर्थात (8>8) नहीं, इसलिए ध्यान दें। सही जाँच में कोई बराबरी नहीं चाहिए।
Login to save your score, XP, coins and progress.
How many total outcomes are possible when a coin is tossed and a die is rolled?
A. (12)
A coin has (2) outcomes and a die has (6), so \(2\times6=12\). Multiply when two experiments are performed together.
The correct answer is A. (12). A coin has (2) outcomes and a die has (6), so \(2\times6=12\). Multiply when two experiments are performed together.
सिक्के के (2) और पासे के (6) परिणाम हैं इसलिए \(2\times6=12\)। दो प्रयोग साथ हों तो गुणन करें।
Login to save your score, XP, coins and progress.
Which point truly lies in the solution region of (x+2y>8)?
D. ((2,4))
Substituting ((2,4)) gives (2+8>8), which is true. Do not choose an equal boundary point in a strict inequality.
The correct answer is D. ((2,4)). Substituting ((2,4)) gives (2+8>8), which is true. Do not choose an equal boundary point in a strict inequality.
((2,4)) रखने पर (2+8>8) सत्य है। कठोर असमानता में बराबर वाला बिंदु न चुनें।
Login to save your score, XP, coins and progress.
Two distinct coins are tossed. How many total outcomes are possible?
B. (4)
Each coin has (2) outcomes, so \(2\times2=4\). Treat distinct coins as separate stages.
The correct answer is B. (4). Each coin has (2) outcomes, so \(2\times2=4\). Treat distinct coins as separate stages.
हर सिक्के के (2) परिणाम हैं इसलिए \(2\times2=4\)। अलग-अलग सिक्कों को अलग चरण मानें।
Login to save your score, XP, coins and progress.
What is the status of ((3,1)) for \(2x+y\leq 7\)?
A. हल में हैIn the solution
Substituting ((3,1)) gives \(6+1\leq 7\), which is true. It lies on the boundary line.
The correct answer is A. हल में है / In the solution. Substituting ((3,1)) gives \(6+1\leq 7\), which is true. It lies on the boundary line.
((3,1)) रखने पर \(6+1\leq 7\) सत्य है। यह सीमा रेखा पर स्थित है।
Login to save your score, XP, coins and progress.
Two dice are rolled together. How many ordered outcomes are possible?
C. (36)
The first die has (6) outcomes and the second has (6), so \(6\times6=36\). In ordered outcomes, the roles of both dice are distinct.
The correct answer is C. (36). The first die has (6) outcomes and the second has (6), so \(6\times6=36\). In ordered outcomes, the roles of both dice are distinct.
पहले पासे के (6) और दूसरे के (6) परिणाम हैं इसलिए \(6\times6=36\)। क्रमित परिणाम में दोनों पासों की भूमिका अलग रहती है।
Login to save your score, XP, coins and progress.
D. (12)
One color and one shape are needed, so \(4\times3=12\). Multiply two independent attributes.
The correct answer is D. (12). One color and one shape are needed, so \(4\times3=12\). Multiply two independent attributes.
एक रंग और एक आकार चाहिए इसलिए \(4\times3=12\)। दो स्वतंत्र विशेषताओं को गुणा करें।
Login to save your score, XP, coins and progress.
For which inequality is the boundary line included in the graph?
C. \(2x+y\leq 9\)
The boundary line is included for \(\leq\) and \(\geq\). Choose by checking the inequality sign.
The correct answer is C. \(2x+y\leq 9\). The boundary line is included for \(\leq\) and \(\geq\). Choose by checking the inequality sign.
\(\leq\) और \(\geq\) में सीमा रेखा शामिल होती है। प्रश्न में चिह्न देखकर उत्तर चुनें।
Login to save your score, XP, coins and progress.
A. (12)
The first stage has (3) choices and the second has (4), so \(3\times4=12\). Fill password positions in order.
The correct answer is A. (12). The first stage has (3) choices and the second has (4), so \(3\times4=12\). Fill password positions in order.
पहले चरण में (3) और दूसरे में (4) विकल्प हैं इसलिए \(3\times4=12\)। पासवर्ड के स्थानों को क्रम से भरें।
Login to save your score, XP, coins and progress.
For which inequality is the boundary line not included in the graph?
D. (y<x+2)
For (<) and (>), the boundary line is not included. So a dashed line is drawn.
The correct answer is D. (y<x+2). For (<) and (>), the boundary line is not included. So a dashed line is drawn.
(<) और (>) में सीमा रेखा शामिल नहीं होती। इसलिए टूटी हुई रेखा बनाई जाती है।
Login to save your score, XP, coins and progress.
B. (11)
Only one topic is to be chosen, so (5+6=11). Add when option groups are separate and not chosen together.
The correct answer is B. (11). Only one topic is to be chosen, so (5+6=11). Add when option groups are separate and not chosen together.
केवल एक विषय चुनना है इसलिए (5+6=11)। विकल्प समूह अलग हों और साथ नहीं चुने जाते हों तो जोड़ें।
Login to save your score, XP, coins and progress.
Why is the origin in the solution of \(x+y\leq 1\)?
A. क्योंकि \(0\leq 1\)Because \(0\leq 1\)
Substituting the origin gives \(0\leq 1\), which is true. Hence, the side with the origin is the solution.
The correct answer is A. क्योंकि \(0\leq 1\) / Because \(0\leq 1\). Substituting the origin gives \(0\leq 1\), which is true. Hence, the side with the origin is the solution.
मूल बिंदु रखने पर \(0\leq 1\) सत्य मिलता है। इसलिए मूल बिंदु वाला पक्ष हल है।
Login to save your score, XP, coins and progress.
C. (7)
The place will be a museum or a park, so (3+4=7). Use the addition rule for separate “or” choices.
The correct answer is C. (7). The place will be a museum or a park, so (3+4=7). Use the addition rule for separate “or” choices.
स्थान संग्रहालय या पार्क में से होगा इसलिए (3+4=7)। “या” वाले अलग चयन में योग का नियम लगाएँ।
Login to save your score, XP, coins and progress.
Is the origin in the solution of \(x+y\geq -3\)?
A. हाँYes
Substituting ((0,0)) gives \(0\geq -3\), which is true. So the origin is in the solution region.
The correct answer is A. हाँ / Yes. Substituting ((0,0)) gives \(0\geq -3\), which is true. So the origin is in the solution region.
((0,0)) रखने पर \(0\geq -3\) सत्य है। इसलिए मूल बिंदु हल-क्षेत्र में है।
Login to save your score, XP, coins and progress.
D. (8)
Both selections are made together, so \(4\times2=8\). Multiply independent setting options.
The correct answer is D. (8). Both selections are made together, so \(4\times2=8\). Multiply independent setting options.
दोनों चयन साथ करने हैं इसलिए \(4\times2=8\)। सेटिंग्स के स्वतंत्र विकल्पों को गुणा करें।
Login to save your score, XP, coins and progress.
What does the origin test give for \(x-y\leq 2\)?
A. \(0\leq 2\) सत्य\(0\leq 2\) true
Putting the origin gives left side (0). Hence, the test is true.
The correct answer is A. \(0\leq 2\) सत्य / \(0\leq 2\) true. Putting the origin gives left side (0). Hence, the test is true.
मूल बिंदु रखने पर बायाँ पक्ष (0) है। इसलिए परीक्षण सत्य है।
Login to save your score, XP, coins and progress.
A. (30)
Total ways are \(2\times5\times3=30\). Multiply when one item is chosen from each category.
The correct answer is A. (30). Total ways are \(2\times5\times3=30\). Multiply when one item is chosen from each category.
कुल तरीके \(2\times5\times3=30\) हैं। एक-एक चीज़ अलग श्रेणियों से हो तो गुणा करें।
Login to save your score, XP, coins and progress.
What does the origin test show for \(x-y\geq 2\)?
B. मूल बिंदु हल में नहीं हैOrigin is not in solution
Substituting ((0,0)) gives \(0\geq 2\), which is false. So the side with the origin is not chosen.
The correct answer is B. मूल बिंदु हल में नहीं है / Origin is not in solution. Substituting ((0,0)) gives \(0\geq 2\), which is false. So the side with the origin is not chosen.
((0,0)) रखने पर \(0\geq 2\) असत्य है। इसलिए मूल बिंदु वाला पक्ष नहीं चुना जाएगा।
Login to save your score, XP, coins and progress.
B. (500)
The two digit positions have (10) and (10) choices, and the letter has (5) choices. Total ways are \(10\times10\times5=500\).
The correct answer is B. (500). The two digit positions have (10) and (10) choices, and the letter has (5) choices. Total ways are \(10\times10\times5=500\).
दो अंक स्थानों के (10) और (10) विकल्प तथा अक्षर के (5) विकल्प हैं। कुल \(10\times10\times5=500\) हैं।
Login to save your score, XP, coins and progress.
If the boundary line is (x+2y=6) and the inequality is \(x+2y\leq 6\), what type of line is drawn?
B. ठोस रेखाSolid line
For \(\leq\), the boundary line is included. Therefore, a solid line is drawn.
The correct answer is B. ठोस रेखा / Solid line. For \(\leq\), the boundary line is included. Therefore, a solid line is drawn.
\(\leq\) में सीमा रेखा शामिल होती है। इसलिए ठोस रेखा बनती है।
Login to save your score, XP, coins and progress.
B. (1296)
Each position has (6) choices, so \(6^4=1296\). When the same choices repeat, using powers is faster.
The correct answer is B. (1296). Each position has (6) choices, so \(6^4=1296\). When the same choices repeat, using powers is faster.
प्रत्येक स्थान के (6) विकल्प हैं इसलिए \(6^4=1296\)। समान विकल्प बार-बार हों तो घात का प्रयोग तेज होता है।
Login to save your score, XP, coins and progress.
For the inequality (x+2y>6), which statement about the boundary line is correct?
B. रेखा टूटी हुई होगीThe line will be dashed
For (>), the boundary line is not included in the solution. So a dashed line is drawn.
The correct answer is B. रेखा टूटी हुई होगी / The line will be dashed. For (>), the boundary line is not included in the solution. So a dashed line is drawn.
(>) में सीमा रेखा हल में शामिल नहीं होती। इसलिए टूटी हुई रेखा खींची जाती है।
Login to save your score, XP, coins and progress.
How many (4)-digit numbers can be formed from digits (1,2,3,4) without repetition?
C. (24)
The four positions have (4,3,2,1) choices, so \(4\times3\times2\times1=24\). If all digits are used, choices decrease step by step.
The correct answer is C. (24). The four positions have (4,3,2,1) choices, so \(4\times3\times2\times1=24\). If all digits are used, choices decrease step by step.
चार स्थानों के विकल्प (4,3,2,1) हैं इसलिए \(4\times3\times2\times1=24\)। सभी अंक उपयोग हों तो विकल्प क्रम से घटते हैं।
Login to save your score, XP, coins and progress.
Which inequality has the solution region below the line (y=4)?
C. \(y\leq 4\)
Below the line, (y) is less than or equal to (4). Hence, \(y\leq 4\) is correct.
The correct answer is C. \(y\leq 4\). Below the line, (y) is less than or equal to (4). Hence, \(y\leq 4\) is correct.
रेखा के नीचे (y) का मान (4) से कम या बराबर होता है। इसलिए \(y\leq 4\) सही है।
Login to save your score, XP, coins and progress.
How many (3)-digit even numbers can be formed from digits (0,1,2,3) without repetition?
B. (8)
If the units digit is (0), there are \(3\times2=6\) ways, and if it is (2), there are \(2\times2=4\) ways. Total ways are (6+4=10).
The correct answer is B. (8). If the units digit is (0), there are \(3\times2=6\) ways, and if it is (2), there are \(2\times2=4\) ways. Total ways are (6+4=10).
यदि इकाई (0) है तो \(3\times2=6\) तरीके हैं और यदि इकाई (2) है तो सैकड़े के (2) तथा दहाई के (2) तरीके हैं। कुल (6+4=10) हैं।
Login to save your score, XP, coins and progress.
Which inequality has the solution region to the right of the line (x=-2)?
B. (x>-2)
To the right, (x) is greater than (-2). Therefore, (x>-2) is correct.
The correct answer is B. (x>-2). To the right, (x) is greater than (-2). Therefore, (x>-2) is correct.
दाईं ओर (x) का मान (-2) से बड़ा होता है। इसलिए (x>-2) सही है।
Login to save your score, XP, coins and progress.
C. (9)
Only one drink is chosen, so (3+4+2=9). Add when the groups are alternatives, not simultaneous choices.
The correct answer is C. (9). Only one drink is chosen, so (3+4+2=9). Add when the groups are alternatives, not simultaneous choices.
केवल एक पेय चुनना है इसलिए (3+4+2=9)। एक ही श्रेणी नहीं बल्कि वैकल्पिक समूह हों तो जोड़ें।
Login to save your score, XP, coins and progress.
Which point lies on the line (x+2y=4)?
B. ((2,1))
Substituting ((2,1)) gives (2+2=4). A point on the line must satisfy equality.
The correct answer is B. ((2,1)). Substituting ((2,1)) gives (2+2=4). A point on the line must satisfy equality.
((2,1)) रखने पर (2+2=4) मिलता है। रेखा पर बिंदु के लिए बराबरी सत्य होनी चाहिए।
Login to save your score, XP, coins and progress.
D. (20)
Both color and size are to be selected, so \(5\times4=20\). Multiply when product features are independent.
The correct answer is D. (20). Both color and size are to be selected, so \(5\times4=20\). Multiply when product features are independent.
रंग और आकार दोनों चुनने हैं इसलिए \(5\times4=20\)। उत्पाद की अलग विशेषताएँ स्वतंत्र हों तो गुणा करें।
Login to save your score, XP, coins and progress.
Which point lies on the line (3x+y=9)?
A. ((2,3))
Substituting ((2,3)) gives (6+3=9), which is true. Substitute coordinates directly in point testing.
The correct answer is A. ((2,3)). Substituting ((2,3)) gives (6+3=9), which is true. Substitute coordinates directly in point testing.
((2,3)) रखने पर (6+3=9) सत्य है। बिंदु जाँच में सीधे मान रखें।
Login to save your score, XP, coins and progress.
A. (24)
The three stages are independent, so \(3\times2\times4=24\). In design questions, treat each feature as one stage.
The correct answer is A. (24). The three stages are independent, so \(3\times2\times4=24\). In design questions, treat each feature as one stage.
तीनों चरण स्वतंत्र हैं इसलिए \(3\times2\times4=24\)। डिज़ाइन प्रश्नों में हर फीचर को एक चरण मानें।
Login to save your score, XP, coins and progress.
In the graph of \(x+y\leq 8\), what is the status of ((8,0))?
A. हल में है और सीमा पर हैIn solution and on boundary
Substituting ((8,0)) gives \(8\leq 8\), which is true. Equality means the point is on the boundary.
The correct answer is A. हल में है और सीमा पर है / In solution and on boundary. Substituting ((8,0)) gives \(8\leq 8\), which is true. Equality means the point is on the boundary.
((8,0)) रखने पर \(8\leq 8\) सत्य है। बराबरी होने से बिंदु सीमा पर भी है।
Login to save your score, XP, coins and progress.
B. (9)
Only one course is to be chosen, so (6+3=9). Add when the options are not taken together.
The correct answer is B. (9). Only one course is to be chosen, so (6+3=9). Add when the options are not taken together.
एक ही कोर्स चुनना है इसलिए (6+3=9)। विकल्पों को एक साथ नहीं लेना हो तो योग करें।
Login to save your score, XP, coins and progress.
C. (20)
One picture and one message are both needed, so \(4\times5=20\). The multiplication principle applies to combined selection.
The correct answer is C. (20). One picture and one message are both needed, so \(4\times5=20\). The multiplication principle applies to combined selection.
एक चित्र और एक संदेश दोनों चाहिए इसलिए \(4\times5=20\)। संयुक्त चयन में गुणा सिद्धांत लागू होता है।
Login to save your score, XP, coins and progress.
What is the (x)-intercept of \(2x+3y\leq 12\)'s boundary line?
C. (6)
The boundary line is (2x+3y=12). Putting (y=0) gives (x=6).
The correct answer is C. (6). The boundary line is (2x+3y=12). Putting (y=0) gives (x=6).
सीमा रेखा (2x+3y=12) है। (y=0) रखने पर (x=6) मिलता है।
Login to save your score, XP, coins and progress.
D. (12)
Total models are \(3\times4=12\). In product models, multiply each independent feature.
The correct answer is D. (12). Total models are \(3\times4=12\). In product models, multiply each independent feature.
कुल मॉडल \(3\times4=12\) होंगे। उत्पाद मॉडल में हर स्वतंत्र विशेषता को गुणा करें।
Login to save your score, XP, coins and progress.
What is the (y)-intercept of the boundary line of \(2x+3y\leq 12\)?
C. (4)
Put (x=0) in the boundary line. Then (3y=12), so (y=4).
The correct answer is C. (4). Put (x=0) in the boundary line. Then (3y=12), so (y=4).
सीमा रेखा में (x=0) रखें। तब (3y=12), इसलिए (y=4)।
Login to save your score, XP, coins and progress.
A. (12)
Two different posts are to be filled, so \(4\times3=12\). Treat selections for different posts as ordered stages.
The correct answer is A. (12). Two different posts are to be filled, so \(4\times3=12\). Treat selections for different posts as ordered stages.
दो अलग पद भरने हैं इसलिए \(4\times3=12\)। अलग पदों के चयन को क्रमबद्ध चरण मानें।
Login to save your score, XP, coins and progress.
Which point is outside the solution region of \(x+y\leq 10\)?
C. ((6,7))
Substituting ((6,7)) gives \(13\leq 10\), which is false. An outside point does not satisfy the inequality.
The correct answer is C. ((6,7)). Substituting ((6,7)) gives \(13\leq 10\), which is false. An outside point does not satisfy the inequality.
((6,7)) रखने पर \(13\leq 10\) असत्य है। बाहर वाला बिंदु असमानता को संतुष्ट नहीं करता।
Login to save your score, XP, coins and progress.
B. (10)
There are (5) choices first and (2) choices next, so \(5\times2=10\). Multiply the stages in a sequential journey.
The correct answer is B. (10). There are (5) choices first and (2) choices next, so \(5\times2=10\). Multiply the stages in a sequential journey.
पहले (5) और फिर (2) विकल्प हैं इसलिए \(5\times2=10\)। क्रम से होने वाली यात्रा में चरणों को गुणा करें।
Login to save your score, XP, coins and progress.
In the graph of \(y\geq x\), where does ((2,5)) lie?
A. हल-क्षेत्र मेंIn the solution region
For ((2,5)), \(5\geq 2\) is true. Hence, the point lies in the solution region.
The correct answer is A. हल-क्षेत्र में / In the solution region. For ((2,5)), \(5\geq 2\) is true. Hence, the point lies in the solution region.
((2,5)) में \(5\geq 2\) सत्य है। इसलिए बिंदु हल-क्षेत्र में है।
Login to save your score, XP, coins and progress.
C. (18)
Both choices are independent, so \(3\times6=18\). In profile setup, multiply every required selection.
The correct answer is C. (18). Both choices are independent, so \(3\times6=18\). In profile setup, multiply every required selection.
दोनों चुनाव स्वतंत्र हैं इसलिए \(3\times6=18\)। प्रोफाइल सेटअप में हर अनिवार्य चयन को गुणा करें।
Login to save your score, XP, coins and progress.
D. (24)
Total avatars are \(2\times4\times3=24\). When there are three independent features, multiply all choices.
The correct answer is D. (24). Total avatars are \(2\times4\times3=24\). When there are three independent features, multiply all choices.
कुल अवतार \(2\times4\times3=24\) होंगे। तीन स्वतंत्र फीचर हों तो सभी विकल्पों को गुणा करें।
Login to save your score, XP, coins and progress.
What do we get when \(2x-y\leq 4\) is written in terms of (y)?
A. \(y\geq 2x-4\)
In \(-y\leq 4-2x\), dividing by (-1) reverses the sign. In exams, always reverse the sign when multiplying or dividing by a negative number.
The correct answer is A. \(y\geq 2x-4\). In \(-y\leq 4-2x\), dividing by (-1) reverses the sign. In exams, always reverse the sign when multiplying or dividing by a negative number.
\(-y\leq 4-2x\) में (-1) से भाग देने पर चिह्न बदलता है। परीक्षा में ऋणात्मक से गुणा या भाग करते समय चिह्न जरूर बदलें।
Login to save your score, XP, coins and progress.
Which equation is used to draw the boundary line of (x-2y<6)?
A. (x-2y=6)
For the boundary line, replace the inequality sign with equality. Since the sign is (<), the line will be dashed.
The correct answer is A. (x-2y=6). For the boundary line, replace the inequality sign with equality. Since the sign is (<), the line will be dashed.
सीमा रेखा के लिए असमानता चिह्न को बराबर में बदलते हैं। (<) होने से रेखा टूटी हुई बनेगी।
Login to save your score, XP, coins and progress.
Which point lies in the solution region of \(y\leq -x+3\)?
B. ((2,1))
Substituting ((2,1)) gives \(1\leq 1\), which is true. Boundary points are included for \(\leq\).
The correct answer is B. ((2,1)). Substituting ((2,1)) gives \(1\leq 1\), which is true. Boundary points are included for \(\leq\).
((2,1)) रखने पर \(1\leq 1\) सत्य है। बराबरी वाले बिंदु \(\leq\) में हल में शामिल होते हैं।
Login to save your score, XP, coins and progress.
Which statement about the origin is correct for the graph of (x+y>1)?
C. मूल बिंदु हल-क्षेत्र में नहीं हैThe origin is not in the solution region
Substituting ((0,0)) gives (0>1), which is false. Therefore, the side containing the origin is not shaded.
The correct answer is C. मूल बिंदु हल-क्षेत्र में नहीं है / The origin is not in the solution region. Substituting ((0,0)) gives (0>1), which is false. Therefore, the side containing the origin is not shaded.
((0,0)) रखने पर (0>1) असत्य है। इसलिए मूल बिंदु वाले पक्ष को छायांकित नहीं करेंगे।
Login to save your score, XP, coins and progress.
This level is designed for 50 active questions. Currently 50 questions are available for the selected class and difficulty.
Yes, the timer uses 40 seconds per question for Easy difficulty and shows the total remaining time on the page.
Yes, every question has its own SEO-friendly page with answer, explanation and related practice links.
Use Google login or mobile OTP. Admin can block users and control login providers.