100 results found for "Variables and Constants" in Class 10.
समीकरणों (3(x-2)+2(y+1)=31) और (5(x-2)-2(y+1)=21) को हल करने पर (x+y) क्या है?
Solving (3(x-2)+2(y+1)=31) and (5(x-2)-2(y+1)=21), what is (x+y)?
#pair-linear-equations-shifted-variables
A (10)
B (11)
C (12)
D (13)
Explanation opens after your attempt
Step 1
Concept
Let (u=x-2) and (v=y+1). Solving (3u+2v=31), (5u-2v=21) gives values to substitute back for (x+y).
Step 2
Why this answer is correct
The correct answer is D. (13). Let (u=x-2) and (v=y+1). Solving (3u+2v=31), (5u-2v=21) gives values to substitute back for (x+y).
Step 3
Exam Tip
मान लें (u=x-2) और (v=y+1)। (3u+2v=31), (5u-2v=21) से \(u=\frac{13}{2}\), \(v=\frac{23}{4}\), फिर \(x+y=\frac{53}{4}\)।
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समीकरणों (2(x-1)+3(y+2)=25) और (4(x-1)-3(y+2)=5) को हल करने पर (x+y) क्या है?
Solving (2(x-1)+3(y+2)=25) and (4(x-1)-3(y+2)=5), what is (x+y)?
#pair-linear-equations
#shifted-variables
#elimination
A (8)
B (9)
C (10)
D (11)
Explanation opens after your attempt
Step 1
Concept
Let (u=x-1) and (v=y+2). From (2u+3v=25), (4u-3v=5), (u=5,v=5), so (x=6,y=3).
Step 2
Why this answer is correct
The correct answer is D. (11). Let (u=x-1) and (v=y+2). From (2u+3v=25), (4u-3v=5), (u=5,v=5), so (x=6,y=3).
Step 3
Exam Tip
मान लें (u=x-1) और (v=y+2)। (2u+3v=25), (4u-3v=5) से (u=5,v=5), इसलिए (x=6,y=3)।
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समीकरण (2x+3y=19) और (x-y=2) का हल क्या है?
What is the solution of (2x+3y=19) and (x-y=2)?
#linear equations
#substitution
#two variables
#medium
#class 10
A ( (4,5) )
B ( (6,2) )
C ( (5,3) )
D ( (3,5) )
Explanation opens after your attempt
Correct Answer
C. ( (5,3) )
Step 1
Concept
From (x-y=2), (x=y+2), so (2(y+2)+3y=19) and (y=3). Then (x=5).
Step 2
Why this answer is correct
The correct answer is C. ( (5,3) ). From (x-y=2), (x=y+2), so (2(y+2)+3y=19) and (y=3). Then (x=5).
Step 3
Exam Tip
(x-y=2) से (x=y+2), इसलिए (2(y+2)+3y=19) और (y=3)। फिर (x=5) मिलेगा।
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एक आयत की लंबाई (l) और चौड़ाई (b) है। यदि (2l+2b=34) और (l-b=5), तो (l) और (b) क्या हैं?
A rectangle has length (l) and breadth (b). If (2l+2b=34) and (l-b=5), what are (l) and (b)?
#linear equations
#word problem
#rectangle
#medium
#class 10
A ( (10,7) )
B ( (11,6) )
C ( (12,5) )
D ( (9,8) )
Explanation opens after your attempt
Correct Answer
B. ( (11,6) )
Step 1
Concept
From (2l+2b=34), (l+b=17), and (l-b=5). Adding gives (2l=22), so (l=11) and (b=6).
Step 2
Why this answer is correct
The correct answer is B. ( (11,6) ). From (2l+2b=34), (l+b=17), and (l-b=5). Adding gives (2l=22), so (l=11) and (b=6).
Step 3
Exam Tip
(2l+2b=34) से (l+b=17), और (l-b=5)। जोड़ने पर (2l=22), इसलिए (l=11) और (b=6)।
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किसी मेले में वयस्क टिकटों की संख्या (x) और बच्चों के टिकटों की संख्या (y) है। यदि (x+y=12) और (50x+30y=500), तो (x) और (y) क्या हैं?
At a fair, the number of adult tickets is (x) and child tickets is (y). If (x+y=12) and (50x+30y=500), what are (x) and (y)?
#linear equations
#word problem
#tickets
#medium
#class 10
A ( (6,6) )
B ( (8,4) )
C ( (7,5) )
D ( (5,7) )
Explanation opens after your attempt
Correct Answer
C. ( (7,5) )
Step 1
Concept
Dividing (50x+30y=500) by (10) gives (5x+3y=50). Solving with (x+y=12) gives (x=7) and (y=5).
Step 2
Why this answer is correct
The correct answer is C. ( (7,5) ). Dividing (50x+30y=500) by (10) gives (5x+3y=50). Solving with (x+y=12) gives (x=7) and (y=5).
Step 3
Exam Tip
(50x+30y=500) को (10) से भाग देने पर (5x+3y=50) मिलता है। (x+y=12) के साथ हल करने पर (x=7) और (y=5)।
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तीन कुर्सियों और दो मेजों की कीमत (4900) रुपये है। दो कुर्सियों और तीन मेजों की कीमत (5600) रुपये है। एक मेज की कीमत क्या है?
Three chairs and two tables cost (4900) rupees. Two chairs and three tables cost (5600) rupees. What is the price of one table?
#word-problem-cost-furniture
A (1200) रुपये / (1200) rupees
B (1300) रुपये / (1300) rupees
C (1400) रुपये / (1400) rupees
D (1500) रुपये / (1500) rupees
Explanation opens after your attempt
Correct Answer
C. (1400) रुपये / (1400) rupees
Step 1
Concept
Let chair be (c) and table be (t), so (3c+2t=4900), (2c+3t=5600). Elimination gives (t=1400).
Step 2
Why this answer is correct
The correct answer is C. (1400) रुपये / (1400) rupees. Let chair be (c) and table be (t), so (3c+2t=4900), (2c+3t=5600). Elimination gives (t=1400).
Step 3
Exam Tip
यदि कुर्सी (c) और मेज (t) हो तो (3c+2t=4900), (2c+3t=5600)। विलोपन से (t=1400) मिलता है।
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यदि (2x-7y=5) और (4x+7y=43), तो (x) और (y) का सही युग्म कौन सा है?
If (2x-7y=5) and (4x+7y=43), which pair of (x) and (y) is correct?
#pair-linear-equations-fraction-solution
A \(x=8,\ y=\frac{11}{7}\)
B (x=7,\ y=2)
C (x=6,\ y=3)
D (x=5,\ y=4)
Explanation opens after your attempt
Correct Answer
A. \(x=8,\ y=\frac{11}{7}\)
Step 1
Concept
Adding gives (6x=48), so (x=8). Substituting in the first equation gives (16-7y=5), so \(y=\frac{11}{7}\).
Step 2
Why this answer is correct
The correct answer is A. \(x=8,\ y=\frac{11}{7}\). Adding gives (6x=48), so (x=8). Substituting in the first equation gives (16-7y=5), so \(y=\frac{11}{7}\).
Step 3
Exam Tip
जोड़ने पर (6x=48), इसलिए (x=8)। पहले समीकरण में रखने पर (16-7y=5), इसलिए \(y=\frac{11}{7}\)।
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तीन पेंसिल और दो रबर की कीमत (31) रुपये है। दो पेंसिल और पांच रबर की कीमत (47) रुपये है। एक पेंसिल की कीमत क्या है?
Three pencils and two erasers cost (31) rupees. Two pencils and five erasers cost (47) rupees. What is the price of one pencil?
#word-problem-cost-elimination
A (5) रुपये / (5) rupees
B (6) रुपये / (6) rupees
C (7) रुपये / (7) rupees
D (8) रुपये / (8) rupees
Explanation opens after your attempt
Correct Answer
C. (7) रुपये / (7) rupees
Step 1
Concept
Let pencil be (p) and eraser be (e), so (3p+2e=31), (2p+5e=47). Elimination gives (p=7).
Step 2
Why this answer is correct
The correct answer is C. (7) रुपये / (7) rupees. Let pencil be (p) and eraser be (e), so (3p+2e=31), (2p+5e=47). Elimination gives (p=7).
Step 3
Exam Tip
यदि पेंसिल (p) और रबर (e) हो तो (3p+2e=31), (2p+5e=47)। विलोपन से (p=7) मिलता है।
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समीकरणों \(\frac{x}{4}+\frac{y}{5}=6\) और \(\frac{x}{5}-\frac{y}{4}=1\) को सरल करके हल करने पर (x) का मान क्या है?
After simplifying and solving \(\frac{x}{4}+\frac{y}{5}=6\) and \(\frac{x}{5}-\frac{y}{4}=1\), what is (x)?
#pair-linear-equations
#fractional-equations
#elimination
A (16)
B (18)
C (20)
D (22)
Explanation opens after your attempt
Step 1
Concept
The equations become (5x+4y=120) and (4x-5y=20). Elimination gives (x=20).
Step 2
Why this answer is correct
The correct answer is C. (20). The equations become (5x+4y=120) and (4x-5y=20). Elimination gives (x=20).
Step 3
Exam Tip
पहले समीकरण से (5x+4y=120) और दूसरे से (4x-5y=20)। विलोपन से (x=20) मिलता है।
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तीन पेन और दो कॉपियों की कीमत (86) रुपये है। दो पेन और तीन कॉपियों की कीमत (89) रुपये है। एक पेन की कीमत क्या है?
Three pens and two notebooks cost (86) rupees. Two pens and three notebooks cost (89) rupees. What is the price of one pen?
#word-problem
#cost
#elimination
A (16) रुपये / (16) rupees
B (17) रुपये / (17) rupees
C (18) रुपये / (18) rupees
D (19) रुपये / (19) rupees
Explanation opens after your attempt
Correct Answer
B. (17) रुपये / (17) rupees
Step 1
Concept
Let pen be (p) and notebook be (n), so (3p+2n=86), (2p+3n=89). Elimination gives (p=16) and (n=19).
Step 2
Why this answer is correct
The correct answer is B. (17) रुपये / (17) rupees. Let pen be (p) and notebook be (n), so (3p+2n=86), (2p+3n=89). Elimination gives (p=16) and (n=19).
Step 3
Exam Tip
यदि पेन (p) और कॉपी (n) हो तो (3p+2n=86), (2p+3n=89)। विलोपन से (p=16) और (n=19) मिलता है।
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यदि (4x+7y=1) और (8x-7y=35), तो (x) और (y) का सही युग्म कौन सा है?
If (4x+7y=1) and (8x-7y=35), which ordered pair of (x) and (y) is correct?
#pair-linear-equations
#negative-values
#elimination
A \(x=3,\ y=-\frac{11}{7}\)
B (x=2,\ y=-1)
C (x=4,\ y=-2)
D \(x=1,\ y=-\frac{3}{7}\)
Explanation opens after your attempt
Correct Answer
A. \(x=3,\ y=-\frac{11}{7}\)
Step 1
Concept
Adding gives (12x=36), so (x=3). Then (4x+7y=1) gives \(y=-\frac{11}{7}\).
Step 2
Why this answer is correct
The correct answer is A. \(x=3,\ y=-\frac{11}{7}\). Adding gives (12x=36), so (x=3). Then (4x+7y=1) gives \(y=-\frac{11}{7}\).
Step 3
Exam Tip
जोड़ने पर (12x=36), इसलिए (x=3)। फिर (4x+7y=1) से \(y=-\frac{11}{7}\) मिलता है।
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एक कलम की कीमत (p) और एक कॉपी की कीमत (q) है। यदि (3p+4q=260) और (5p+2q=300), तो (q) का मान क्या है?
The price of one pen is (p) and one notebook is (q). If (3p+4q=260) and (5p+2q=300), what is the value of (q)?
#linear equations
#word problem
#price
#expert
#class 10
A \(q=\frac{180}{7}\)
B \(q=\frac{190}{7}\)
C \(q=\frac{200}{7}\)
D \(q=\frac{210}{7}\)
Explanation opens after your attempt
Correct Answer
C. \(q=\frac{200}{7}\)
Step 1
Concept
Elimination gives \(p=\frac{340}{7}\). Substituting it in either equation gives \(q=\frac{200}{7}\).
Step 2
Why this answer is correct
The correct answer is C. \(q=\frac{200}{7}\). Elimination gives \(p=\frac{340}{7}\). Substituting it in either equation gives \(q=\frac{200}{7}\).
Step 3
Exam Tip
विलोपन से \(p=\frac{340}{7}\) मिलता है। इसे किसी एक समीकरण में रखने पर \(q=\frac{200}{7}\)।
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यदि \(\frac{x+y}{4}=6\) और \(\frac{x-y}{5}=2\), तो (x) और (y) के मान क्या हैं?
If \(\frac{x+y}{4}=6\) and \(\frac{x-y}{5}=2\), what are the values of (x) and (y)?
#linear equations
#transformed equations
#elimination
#expert
#class 10
A (x=15,\ y=9)
B (x=16,\ y=8)
C (x=17,\ y=7)
D (x=18,\ y=6)
Explanation opens after your attempt
Correct Answer
C. (x=17,\ y=7)
Step 1
Concept
The given equations become (x+y=24) and (x-y=10). Adding gives (x=17) and (y=7).
Step 2
Why this answer is correct
The correct answer is C. (x=17,\ y=7). The given equations become (x+y=24) and (x-y=10). Adding gives (x=17) and (y=7).
Step 3
Exam Tip
दिए समीकरण (x+y=24) और (x-y=10) बनते हैं। जोड़ने पर (x=17) और (y=7)।
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एक दो अंकों की संख्या में अंकों का योग (14) है और संख्या व उल्टी संख्या का अंतर (36) है। मूल संख्या क्या है?
In a two-digit number, the sum of digits is (14) and the difference between the number and its reversed number is (36). What is the original number?
#linear equations
#word problem
#digits
#expert
#class 10
A (86)
B (95)
C (77)
D (68)
Explanation opens after your attempt
Step 1
Concept
Let the tens digit be (x) and units digit be (y). From (x+y=14) and (9(x-y)=36), (x=9,\ y=5).
Step 2
Why this answer is correct
The correct answer is B. (95). Let the tens digit be (x) and units digit be (y). From (x+y=14) and (9(x-y)=36), (x=9,\ y=5).
Step 3
Exam Tip
दहाई अंक (x) और इकाई अंक (y) मानें। (x+y=14) और (9(x-y)=36) से (x=9,\ y=5)।
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एक कलम की कीमत (p) और एक पेंसिल की कीमत (q) है। यदि (4p+3q=177) और (2p+5q=151), तो (p) का मान क्या है?
The price of one pen is (p) and one pencil is (q). If (4p+3q=177) and (2p+5q=151), what is (p)?
#linear equations
#word problem
#price
#hard
#class 10
A (34) रुपये / (34) rupees
B (36) रुपये / (36) rupees
C (39) रुपये / (39) rupees
D (42) रुपये / (42) rupees
Explanation opens after your attempt
Correct Answer
B. (36) रुपये / (36) rupees
Step 1
Concept
Multiply the second equation by (2) and subtract the first. (q=23) and then (p=27), so none of the options is correct.
Step 2
Why this answer is correct
The correct answer is B. (36) रुपये / (36) rupees. Multiply the second equation by (2) and subtract the first. (q=23) and then (p=27), so none of the options is correct.
Step 3
Exam Tip
दूसरे समीकरण को (2) से गुणा कर पहले से घटाएं। (q=23) और फिर (p=27), इसलिए विकल्पों में कोई सही नहीं है।
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एक दुकानदार ने (12) पेन और (8) पेंसिल (184) रुपये में बेचे। (5) पेन और (6) पेंसिल (88) रुपये में बिके। एक पेन की कीमत क्या है?
A shopkeeper sold (12) pens and (8) pencils for (184) rupees. (5) pens and (6) pencils were sold for (88) rupees. What is the price of one pen?
#linear equations
#price problem
#elimination
#class 10
A (10) रुपये / (10) rupees
B (11) रुपये / (11) rupees
C (12) रुपये / (12) rupees
D (13) रुपये / (13) rupees
Explanation opens after your attempt
Correct Answer
C. (12) रुपये / (12) rupees
Step 1
Concept
Form (12p+8q=184) and (5p+6q=88), then solve. In exams, take the prices of different items as separate variables.
Step 2
Why this answer is correct
The correct answer is C. (12) रुपये / (12) rupees. Form (12p+8q=184) and (5p+6q=88), then solve. In exams, take the prices of different items as separate variables.
Step 3
Exam Tip
(12p+8q=184) और (5p+6q=88) बनाकर हल करें। परीक्षा में वस्तुओं की कीमतों को अलग-अलग चर मानें।
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समीकरणों (14x+3y=59) और (2x+y=11) को हल करने पर (x) और (y) के मान क्या होंगे?
On solving the equations (14x+3y=59) and (2x+y=11), what are the values of (x) and (y)?
#linear equations
#substitution
#solution
#class 10
A (x=2, y=7)
B (x=3, y=5)
C (x=4, y=3)
D (x=5, y=1)
Explanation opens after your attempt
Correct Answer
B. (x=3, y=5)
Step 1
Concept
From (2x+y=11), put (y=11-2x) in the first equation. In exams, combine all terms correctly after substitution.
Step 2
Why this answer is correct
The correct answer is B. (x=3, y=5). From (2x+y=11), put (y=11-2x) in the first equation. In exams, combine all terms correctly after substitution.
Step 3
Exam Tip
(2x+y=11) से (y=11-2x) रखकर पहला समीकरण हल करें। परीक्षा में प्रतिस्थापन के बाद सभी पद सही जोड़ें।
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समीकरणों (15x-8y=22) और (5x+4y=34) से (x) और (y) ज्ञात करें।
Find (x) and (y) from the equations (15x-8y=22) and (5x+4y=34).
#linear equations
#elimination
#solution
#class 10
A (x=4, y=2)
B (x=5, y=3)
C (x=6, y=1)
D (x=7, y=-1)
Explanation opens after your attempt
Correct Answer
C. (x=6, y=1)
Step 1
Concept
Multiply the second equation by (2) and add it to the first. In exams, add equations when opposite signs appear.
Step 2
Why this answer is correct
The correct answer is C. (x=6, y=1). Multiply the second equation by (2) and add it to the first. In exams, add equations when opposite signs appear.
Step 3
Exam Tip
दूसरे समीकरण को (2) से गुणा करके पहले में जोड़ें। परीक्षा में विपरीत संकेत दिखते ही जोड़कर चर हटाएँ।
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समीकरणों (3x+2y=16) और (5x-y=11) को हल करने पर (x) और (y) के मान क्या होंगे?
On solving the equations (3x+2y=16) and (5x-y=11), what are the values of (x) and (y)?
#linear equations
#substitution
#elimination
#class 10
A (x=2, y=-1)
B (x=3, y=4)
C (x=1, y=6)
D (x=4, y=1)
Explanation opens after your attempt
Correct Answer
B. (x=3, y=4)
Step 1
Concept
From (5x-y=11), put (y=5x-11) in the first equation and solve. In exams, combine terms carefully after substitution.
Step 2
Why this answer is correct
The correct answer is B. (x=3, y=4). From (5x-y=11), put (y=5x-11) in the first equation and solve. In exams, combine terms carefully after substitution.
Step 3
Exam Tip
(5x-y=11) से (y=5x-11) रखकर पहला समीकरण हल करें। परीक्षा में प्रतिस्थापन के बाद पदों को सावधानी से जोड़ें।
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एक कलम की कीमत (p) और एक कॉपी की कीमत (q) है। यदि (3p+2q=185) और (2p+5q=215), तो (q) का मान क्या है?
The price of one pen is (p) and one notebook is (q). If (3p+2q=185) and (2p+5q=215), what is the value of (q)?
#linear equations
#word problem
#price
#hard
#class 10
A (15) रुपये / (15) rupees
B (20) रुपये / (20) rupees
C (25) रुपये / (25) rupees
D (30) रुपये / (30) rupees
Explanation opens after your attempt
Correct Answer
C. (25) रुपये / (25) rupees
Step 1
Concept
Elimination gives (p=45). Then (3(45)+2q=185), so (q=25).
Step 2
Why this answer is correct
The correct answer is C. (25) रुपये / (25) rupees. Elimination gives (p=45). Then (3(45)+2q=185), so (q=25).
Step 3
Exam Tip
विलोपन से (p=45) मिलता है। फिर (3(45)+2q=185), इसलिए (q=25)।
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यदि \(\frac{x+y}{2}=9\) और \(\frac{x-y}{3}=2\), तो (x) और (y) के मान क्या हैं?
If \(\frac{x+y}{2}=9\) and \(\frac{x-y}{3}=2\), what are the values of (x) and (y)?
#linear equations
#transformed equations
#elimination
#hard
#class 10
A (x=12,\ y=6)
B (x=10,\ y=8)
C (x=14,\ y=4)
D (x=9,\ y=9)
Explanation opens after your attempt
Correct Answer
A. (x=12,\ y=6)
Step 1
Concept
The given equations become (x+y=18) and (x-y=6). Adding gives (x=12), then (y=6).
Step 2
Why this answer is correct
The correct answer is A. (x=12,\ y=6). The given equations become (x+y=18) and (x-y=6). Adding gives (x=12), then (y=6).
Step 3
Exam Tip
दिए समीकरण (x+y=18) और (x-y=6) बनते हैं। जोड़ने पर (x=12) और फिर (y=6)।
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एक आयत की लंबाई और चौड़ाई का योग (28) है तथा लंबाई चौड़ाई से (6) अधिक है। चौड़ाई क्या है?
The sum of the length and breadth of a rectangle is (28) and the length is (6) more than the breadth. What is the breadth?
#linear-equations
#word-problem
#rectangle
#medium
#class-10
A (11)
B (12)
C (13)
D (14)
Explanation opens after your attempt
Step 1
Concept
Let length be (x) and breadth be (y). From (x+y=28) and (x-y=6), (2y=22), so (y=11).
Step 2
Why this answer is correct
The correct answer is A. (11). Let length be (x) and breadth be (y). From (x+y=28) and (x-y=6), (2y=22), so (y=11).
Step 3
Exam Tip
मान लें लंबाई (x) और चौड़ाई (y) है। (x+y=28) और (x-y=6) से (2y=22), इसलिए (y=11)।
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एक पिता और पुत्र की आयु का योग (50) वर्ष है और उनका अंतर (30) वर्ष है। पिता की आयु क्या है?
The sum of a father’s and son’s ages is (50) years and their difference is (30) years. What is the father’s age?
#linear-equations
#word-problem
#ages
#medium
#class-10
A (40) वर्ष / (40) years
B (35) वर्ष / (35) years
C (30) वर्ष / (30) years
D (45) वर्ष / (45) years
Explanation opens after your attempt
Correct Answer
A. (40) वर्ष / (40) years
Step 1
Concept
Let the father’s age be (x) and the son’s age be (y). Adding (x+y=50) and (x-y=30) gives (x=40).
Step 2
Why this answer is correct
The correct answer is A. (40) वर्ष / (40) years. Let the father’s age be (x) and the son’s age be (y). Adding (x+y=50) and (x-y=30) gives (x=40).
Step 3
Exam Tip
मान लें पिता की आयु (x) और पुत्र की आयु (y) है। (x+y=50) और (x-y=30) जोड़ने पर (x=40)।
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वयस्क टिकट की कीमत (x) और बच्चे के टिकट की कीमत (y) है। यदि (2x+3y=310) और (3x+2y=340), तो वयस्क टिकट की कीमत क्या है?
The price of an adult ticket is (x) and a child ticket is (y). If (2x+3y=310) and (3x+2y=340), what is the adult ticket price?
#linear-equations
#word-problem
#tickets
#medium
#class-10
A (50) रुपये / (50) rupees
B (60) रुपये / (60) rupees
C (70) रुपये / (70) rupees
D (80) रुपये / (80) rupees
Explanation opens after your attempt
Correct Answer
D. (80) रुपये / (80) rupees
Step 1
Concept
Elimination gives (y=50). From (2x+3(50)=310), (x=80).
Step 2
Why this answer is correct
The correct answer is D. (80) रुपये / (80) rupees. Elimination gives (y=50). From (2x+3(50)=310), (x=80).
Step 3
Exam Tip
विलोपन करने पर (y=50) मिलता है। (2x+3(50)=310) से (x=80)।
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यदि (y=3x-7) और (2x+y=18), तो (x) और (y) के मान क्या हैं?
If (y=3x-7) and (2x+y=18), what are the values of (x) and (y)?
#linear equations
#substitution
#solution pair
#medium
#class 10
A (x=4,\ y=5)
B (x=5,\ y=8)
C (x=6,\ y=11)
D (x=7,\ y=14)
Explanation opens after your attempt
Correct Answer
B. (x=5,\ y=8)
Step 1
Concept
Substituting (y=3x-7) gives (5x-7=18). Therefore (x=5) and (y=8).
Step 2
Why this answer is correct
The correct answer is B. (x=5,\ y=8). Substituting (y=3x-7) gives (5x-7=18). Therefore (x=5) and (y=8).
Step 3
Exam Tip
(y=3x-7) रखने पर (5x-7=18) मिलता है। इसलिए (x=5) और (y=8)।
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दो टिकटों की कीमतें (x) और (y) हैं। यदि (2x+y=140) और (x+2y=130), तो (x) कितना है?
The prices of two tickets are (x) and (y). If (2x+y=140) and (x+2y=130), what is (x)?
#linear equations
#word problem
#tickets
#medium
#class 10
A (40)
B (50)
C (60)
D (70)
Explanation opens after your attempt
Step 1
Concept
Multiply the second equation by (2) and subtract the first. This gives (3y=120), then (x=50).
Step 2
Why this answer is correct
The correct answer is B. (50). Multiply the second equation by (2) and subtract the first. This gives (3y=120), then (x=50).
Step 3
Exam Tip
दूसरे समीकरण को (2) से गुणा कर पहले से घटाएं। इससे (3y=120) और फिर (x=50) मिलता है।
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यदि (4x+5y=31) और (2x+y=11), तो (x) और (y) का हल क्या है?
If (4x+5y=31) and (2x+y=11), what is the solution for (x) and (y)?
#linear equations
#substitution
#solution pair
#medium
#class 10
A (x=4,\ y=3)
B (x=5,\ y=1)
C (x=3,\ y=5)
D (x=2,\ y=7)
Explanation opens after your attempt
Correct Answer
B. (x=5,\ y=1)
Step 1
Concept
From the second equation use (y=11-2x). Substitution gives (-6x+55=31), so (x=4) and (y=3).
Step 2
Why this answer is correct
The correct answer is B. (x=5,\ y=1). From the second equation use (y=11-2x). Substitution gives (-6x+55=31), so (x=4) and (y=3).
Step 3
Exam Tip
दूसरे समीकरण से (y=11-2x) रखें। पहले में रखने पर (-6x+55=31), इसलिए (x=4) और (y=3)।
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एक कलम और एक पेंसिल की कुल कीमत (18) रुपये है। (2) कलम और (3) पेंसिल की कीमत (45) रुपये है। एक कलम की कीमत क्या है?
The total price of one pen and one pencil is (18) rupees. The price of (2) pens and (3) pencils is (45) rupees. What is the price of one pen?
#linear equations
#word problem
#price
#medium
#class 10
A (8) रुपये / (8) rupees
B (9) रुपये / (9) rupees
C (10) रुपये / (10) rupees
D (12) रुपये / (12) rupees
Explanation opens after your attempt
Correct Answer
B. (9) रुपये / (9) rupees
Step 1
Concept
Let pen be (x) and pencil be (y). From (x+y=18) and (2x+3y=45), (x=9).
Step 2
Why this answer is correct
The correct answer is B. (9) रुपये / (9) rupees. Let pen be (x) and pencil be (y). From (x+y=18) and (2x+3y=45), (x=9).
Step 3
Exam Tip
मान लें कलम (x) और पेंसिल (y) है। (x+y=18) और (2x+3y=45) से (x=9) मिलता है।
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यदि (3x+5y=44) और (x+y=10), तो (x) और (y) के मान क्या हैं?
If (3x+5y=44) and (x+y=10), what are the values of (x) and (y)?
#linear equations
#substitution
#solution pair
#medium
#class 10
A (x=4,\ y=6)
B (x=2,\ y=8)
C (x=3,\ y=7)
D (x=5,\ y=5)
Explanation opens after your attempt
Correct Answer
C. (x=3,\ y=7)
Step 1
Concept
Using (x=10-y) gives (30-3y+5y=44). Thus (y=7) and (x=3).
Step 2
Why this answer is correct
The correct answer is C. (x=3,\ y=7). Using (x=10-y) gives (30-3y+5y=44). Thus (y=7) and (x=3).
Step 3
Exam Tip
(x=10-y) रखने पर (30-3y+5y=44) मिलता है। इससे (y=7) और (x=3) मिलते हैं।
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दो अंकों वाली संख्या में दहाई का अंक (x) और इकाई का अंक (y) है। यदि (x+y=13) और (x-y=3), तो अंक क्या हैं?
In a two-digit number, the tens digit is (x) and the units digit is (y). If (x+y=13) and (x-y=3), what are the digits?
#linear equations
#word problem
#digits
#medium
#class 10
A (8) और (5) / (8) and (5)
B (7) और (6) / (7) and (6)
C (9) और (4) / (9) and (4)
D (6) और (7) / (6) and (7)
Explanation opens after your attempt
Correct Answer
A. (8) और (5) / (8) and (5)
Step 1
Concept
Adding both equations gives (2x=16), so (x=8) and (y=5). In digit problems, do not interchange tens and units.
Step 2
Why this answer is correct
The correct answer is A. (8) और (5) / (8) and (5). Adding both equations gives (2x=16), so (x=8) and (y=5). In digit problems, do not interchange tens and units.
Step 3
Exam Tip
दोनों समीकरण जोड़ने पर (2x=16), इसलिए (x=8) और (y=5)। अंकों के प्रश्न में दहाई और इकाई का क्रम न बदलें।
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समीकरण (x+4y=13) और (2x-y=8) से (x) और (y) क्या मिलेंगे?
From (x+4y=13) and (2x-y=8), what are (x) and (y)?
#linear equations
#substitution
#medium
#class 10
A ( (5,2) )
B ( (4,3) )
C ( (6,1) )
D ( (3,4) )
Explanation opens after your attempt
Correct Answer
A. ( (5,2) )
Step 1
Concept
From (2x-y=8), (y=2x-8), so (x+4(2x-8)=13). This gives (x=5) and (y=2).
Step 2
Why this answer is correct
The correct answer is A. ( (5,2) ). From (2x-y=8), (y=2x-8), so (x+4(2x-8)=13). This gives (x=5) and (y=2).
Step 3
Exam Tip
(2x-y=8) से (y=2x-8), इसलिए (x+4(2x-8)=13)। इससे (x=5) और (y=2)।
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यदि (x=2y+1) और (3x-y=18), तो (x) और (y) क्या हैं?
If (x=2y+1) and (3x-y=18), what are (x) and (y)?
#linear equations
#substitution
#brackets
#medium
#class 10
A ( (5,2) )
B ( (6,4) )
C ( (7,3) )
D ( (8,2) )
Explanation opens after your attempt
Correct Answer
C. ( (7,3) )
Step 1
Concept
Substituting (x=2y+1) gives (3(2y+1)-y=18), so (y=3) and (x=7). Use brackets while multiplying.
Step 2
Why this answer is correct
The correct answer is C. ( (7,3) ). Substituting (x=2y+1) gives (3(2y+1)-y=18), so (y=3) and (x=7). Use brackets while multiplying.
Step 3
Exam Tip
(x=2y+1) रखने पर (3(2y+1)-y=18), इसलिए (y=3) और (x=7)। कोष्ठक लगाकर गुणा करें।
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यदि (x+y=10) और (3x+2y=24), तो (x) और (y) के मान क्या हैं?
If (x+y=10) and (3x+2y=24), what are the values of (x) and (y)?
#linear equations
#substitution
#medium
#class 10
A ( (6,4) )
B ( (5,5) )
C ( (4,6) )
D ( (3,7) )
Explanation opens after your attempt
Correct Answer
C. ( (4,6) )
Step 1
Concept
Putting (x=10-y) gives (3(10-y)+2y=24), so (y=6) and (x=4). A sum equation makes substitution easier.
Step 2
Why this answer is correct
The correct answer is C. ( (4,6) ). Putting (x=10-y) gives (3(10-y)+2y=24), so (y=6) and (x=4). A sum equation makes substitution easier.
Step 3
Exam Tip
(x=10-y) रखने पर (3(10-y)+2y=24), इसलिए (y=6) और (x=4)। योग वाले समीकरण से प्रतिस्थापन आसान बनता है।
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दो संख्याओं का योग (14) और अंतर (4) है। बड़ी संख्या और छोटी संख्या क्या हैं?
The sum of two numbers is (14) and their difference is (4). What are the greater and smaller numbers?
#linear equations
#word problem
#elimination
#medium
#class 10
A ( (8,6) )
B ( (10,4) )
C ( (7,7) )
D ( (9,5) )
Explanation opens after your attempt
Correct Answer
D. ( (9,5) )
Step 1
Concept
Adding (x+y=14) and (x-y=4) gives (2x=18), so (x=9) and (y=5). In word problems, form equations first.
Step 2
Why this answer is correct
The correct answer is D. ( (9,5) ). Adding (x+y=14) and (x-y=4) gives (2x=18), so (x=9) and (y=5). In word problems, form equations first.
Step 3
Exam Tip
समीकरण (x+y=14) और (x-y=4) जोड़ने पर (2x=18), इसलिए (x=9) और (y=5)। शब्द-प्रश्न में पहले समीकरण बनाएं।
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यदि (3x+y=15) और (x+3y=13), तो (x) और (y) के मान क्या हैं?
If (3x+y=15) and (x+3y=13), what are the values of (x) and (y)?
#linear equations
#substitution
#solution pair
#easy
#class 10
A (x=4,\ y=3)
B (x=3,\ y=4)
C (x=5,\ y=2)
D (x=2,\ y=5)
Explanation opens after your attempt
Correct Answer
A. (x=4,\ y=3)
Step 1
Concept
From the first equation (y=15-3x); substituting gives (x+45-9x=13), so (x=4) and (y=3). Isolate the simpler variable in substitution.
Step 2
Why this answer is correct
The correct answer is A. (x=4,\ y=3). From the first equation (y=15-3x); substituting gives (x+45-9x=13), so (x=4) and (y=3). Isolate the simpler variable in substitution.
Step 3
Exam Tip
पहले समीकरण से (y=15-3x); रखने पर (x+45-9x=13), इसलिए (x=4) और (y=3)। प्रतिस्थापन में सरल चर अलग करें।
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यदि (x+4y=19) और (x-y=4), तो (x) और (y) के मान क्या होंगे?
If (x+4y=19) and (x-y=4), what will be the values of (x) and (y)?
#linear equations
#substitution
#solution pair
#easy
#class 10
A (x=6,\ y=4)
B (x=8,\ y=2)
C (x=7,\ y=3)
D (x=5,\ y=5)
Explanation opens after your attempt
Correct Answer
C. (x=7,\ y=3)
Step 1
Concept
From the second equation (x=y+4); substituting gives (5y+4=19), so (y=3) and (x=7). Choose the simpler equation for substitution.
Step 2
Why this answer is correct
The correct answer is C. (x=7,\ y=3). From the second equation (x=y+4); substituting gives (5y+4=19), so (y=3) and (x=7). Choose the simpler equation for substitution.
Step 3
Exam Tip
दूसरे समीकरण से (x=y+4); रखने पर (5y+4=19), इसलिए (y=3) और (x=7)। प्रतिस्थापन के लिए सरल समीकरण चुनें।
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यदि (y=x+2) और (3x+y=18), तो (x) और (y) के मान क्या हैं?
If (y=x+2) and (3x+y=18), what are the values of (x) and (y)?
#linear equations
#substitution
#solution pair
#easy
#class 10
A (x=3,\ y=5)
B (x=5,\ y=7)
C (x=6,\ y=4)
D (x=4,\ y=6)
Explanation opens after your attempt
Correct Answer
D. (x=4,\ y=6)
Step 1
Concept
Substituting (y=x+2) gives (4x+2=18), so (x=4) and (y=6). Find (x) first, then substitute for (y).
Step 2
Why this answer is correct
The correct answer is D. (x=4,\ y=6). Substituting (y=x+2) gives (4x+2=18), so (x=4) and (y=6). Find (x) first, then substitute for (y).
Step 3
Exam Tip
(y=x+2) रखने पर (4x+2=18), इसलिए (x=4) और (y=6)। पहले (x) निकालें फिर (y) में रखें।
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दो संख्याओं (x) और (y) का योग (20) है और (y=8), तो (x) का मान क्या होगा?
The sum of two numbers (x) and (y) is (20), and (y=8). What will be the value of (x)?
#linear equations
#word problem
#substitution
#easy
#class 10
A (x=10)
B (x=12)
C (x=14)
D (x=16)
Explanation opens after your attempt
Step 1
Concept
Putting (y=8) in (x+y=20) gives (x=12). First write the equation clearly from the words.
Step 2
Why this answer is correct
The correct answer is B. (x=12). Putting (y=8) in (x+y=20) gives (x=12). First write the equation clearly from the words.
Step 3
Exam Tip
समीकरण (x+y=20) में (y=8) रखने पर (x=12)। शब्दों से बने समीकरण को पहले साफ लिखें।
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यदि (2x+4y=28) और (x-y=2), तो (x) और (y) के मान क्या हैं?
If (2x+4y=28) and (x-y=2), what are the values of (x) and (y)?
#linear equations
#substitution
#solution pair
#easy
#class 10
A (x=6,\ y=4)
B (x=4,\ y=6)
C (x=8,\ y=3)
D (x=5,\ y=5)
Explanation opens after your attempt
Correct Answer
A. (x=6,\ y=4)
Step 1
Concept
Substituting (x=y+2) gives (2y+4+4y=28), so (y=4) and (x=6). Choose a simple relation before substitution.
Step 2
Why this answer is correct
The correct answer is A. (x=6,\ y=4). Substituting (x=y+2) gives (2y+4+4y=28), so (y=4) and (x=6). Choose a simple relation before substitution.
Step 3
Exam Tip
(x=y+2) रखने पर (2y+4+4y=28), इसलिए (y=4) और (x=6)। प्रतिस्थापन से पहले सरल संबंध चुनें।
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दो संख्याओं (x) और (y) का योग (18) है और (y=7), तो (x) का मान क्या है?
The sum of two numbers (x) and (y) is (18), and (y=7). What is the value of (x)?
#linear equations
#word problem
#substitution
#easy
#class 10
A (x=8)
B (x=9)
C (x=10)
D (x=11)
Explanation opens after your attempt
Step 1
Concept
Putting (y=7) in (x+y=18) gives (x=11). In word problems, form the equation first.
Step 2
Why this answer is correct
The correct answer is D. (x=11). Putting (y=7) in (x+y=18) gives (x=11). In word problems, form the equation first.
Step 3
Exam Tip
समीकरण (x+y=18) में (y=7) रखने पर (x=11)। शब्द प्रश्न में पहले समीकरण बनाएं।
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यदि (x+2y=20) और (x-y=2), तो (x) और (y) के मान क्या हैं?
If (x+2y=20) and (x-y=2), what are the values of (x) and (y)?
#linear equations
#substitution
#solution pair
#easy
#class 10
A (x=8,\ y=6)
B (x=6,\ y=8)
C (x=10,\ y=5)
D (x=7,\ y=7)
Explanation opens after your attempt
Correct Answer
A. (x=8,\ y=6)
Step 1
Concept
From the second equation (x=y+2); substituting gives (3y+2=20), so (y=6) and (x=8). Isolate a variable from the simpler equation.
Step 2
Why this answer is correct
The correct answer is A. (x=8,\ y=6). From the second equation (x=y+2); substituting gives (3y+2=20), so (y=6) and (x=8). Isolate a variable from the simpler equation.
Step 3
Exam Tip
दूसरे समीकरण से (x=y+2); रखने पर (3y+2=20), इसलिए (y=6) और (x=8)। सरल समीकरण से चर अलग करें।
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यदि (x=3y) और (x+y=16), तो (x) और (y) के मान क्या हैं?
If (x=3y) and (x+y=16), what are the values of (x) and (y)?
#linear equations
#substitution
#multiple relation
#easy
#class 10
A (x=10,\ y=6)
B (x=8,\ y=8)
C (x=12,\ y=4)
D (x=9,\ y=7)
Explanation opens after your attempt
Correct Answer
C. (x=12,\ y=4)
Step 1
Concept
Substituting (x=3y) gives (4y=16), so (y=4) and (x=12). Substitution is fast when one variable is a multiple of another.
Step 2
Why this answer is correct
The correct answer is C. (x=12,\ y=4). Substituting (x=3y) gives (4y=16), so (y=4) and (x=12). Substitution is fast when one variable is a multiple of another.
Step 3
Exam Tip
(x=3y) रखने पर (4y=16), इसलिए (y=4) और (x=12)। गुणज वाले रूप में प्रतिस्थापन तेज होता है।
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यदि (x+3y=16) और (x-y=4), तो (x) और (y) के मान क्या हैं?
If (x+3y=16) and (x-y=4), what are the values of (x) and (y)?
#linear equations
#substitution
#solution pair
#easy
#class 10
A (x=6,\ y=4)
B (x=7,\ y=3)
C (x=8,\ y=2)
D (x=5,\ y=5)
Explanation opens after your attempt
Correct Answer
B. (x=7,\ y=3)
Step 1
Concept
From the second equation (x=y+4); substituting gives (4y+4=16), so (y=3) and (x=7). Choose the simpler equation for substitution.
Step 2
Why this answer is correct
The correct answer is B. (x=7,\ y=3). From the second equation (x=y+4); substituting gives (4y+4=16), so (y=3) and (x=7). Choose the simpler equation for substitution.
Step 3
Exam Tip
दूसरे समीकरण से (x=y+4); रखने पर (4y+4=16), इसलिए (y=3) और (x=7)। प्रतिस्थापन में सरल समीकरण चुनें।
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समीकरणों (3x+y=19) और (x+y=9) को हल करने पर (x) और (y) क्या मिलते हैं?
On solving (3x+y=19) and (x+y=9), what values of (x) and (y) are obtained?
#linear equations
#elimination
#solution pair
#easy
#class 10
A (x=5,\ y=4)
B (x=4,\ y=5)
C (x=6,\ y=3)
D (x=3,\ y=6)
Explanation opens after your attempt
Correct Answer
A. (x=5,\ y=4)
Step 1
Concept
Subtracting the second equation from the first gives (2x=10), so (x=5) and (y=4). Subtraction is correct to remove equal (y) terms.
Step 2
Why this answer is correct
The correct answer is A. (x=5,\ y=4). Subtracting the second equation from the first gives (2x=10), so (x=5) and (y=4). Subtraction is correct to remove equal (y) terms.
Step 3
Exam Tip
पहले समीकरण से दूसरा घटाने पर (2x=10), इसलिए (x=5) और (y=4)। समान (y) हटाने के लिए घटाना सही है।
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यदि (x+2y=11) और (x-y=2), तो (x) और (y) का मान क्या है?
If (x+2y=11) and (x-y=2), what are the values of (x) and (y)?
#linear equations
#substitution
#solution pair
#easy
#class 10
A (x=3,\ y=4)
B (x=4,\ y=3)
C (x=5,\ y=3)
D (x=6,\ y=2)
Explanation opens after your attempt
Correct Answer
C. (x=5,\ y=3)
Step 1
Concept
From the second equation (x=y+2); substituting gives (3y+2=11), so (y=3) and (x=5). Substitute the isolated variable carefully.
Step 2
Why this answer is correct
The correct answer is C. (x=5,\ y=3). From the second equation (x=y+2); substituting gives (3y+2=11), so (y=3) and (x=5). Substitute the isolated variable carefully.
Step 3
Exam Tip
दूसरे समीकरण से (x=y+2); रखने पर (3y+2=11), इसलिए (y=3) और (x=5)। अलग किए हुए चर को ध्यान से रखें।
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यदि (y=x+1) और (x+y=7), तो (x) और (y) के मान क्या होंगे?
If (y=x+1) and (x+y=7), what are the values of (x) and (y)?
#linear equations
#substitution
#isolated variable
#easy
#class 10
A (x=4,\ y=3)
B (x=3,\ y=4)
C (x=2,\ y=5)
D (x=5,\ y=2)
Explanation opens after your attempt
Correct Answer
B. (x=3,\ y=4)
Step 1
Concept
Substituting (y=x+1) in (x+y=7) gives (2x+1=7), so (x=3) and (y=4). Use the already isolated variable in exams.
Step 2
Why this answer is correct
The correct answer is B. (x=3,\ y=4). Substituting (y=x+1) in (x+y=7) gives (2x+1=7), so (x=3) and (y=4). Use the already isolated variable in exams.
Step 3
Exam Tip
(y=x+1) को (x+y=7) में रखने पर (2x+1=7), इसलिए (x=3) और (y=4)। परीक्षा में बने हुए रूप का उपयोग करें।
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समीकरणों (9x+16y=77) और (27x+48y=s) के संगत और आश्रित होने के लिए (s) क्या होगा?
What should (s) be for the equations (9x+16y=77) and (27x+48y=s) to be consistent and dependent?
#linear equations
#expert
#consistent dependent
#parameter
A (229)
B (230)
C (231)
D (232)
Explanation opens after your attempt
Step 1
Concept
To be consistent and dependent, the second equation must be (3) times the first. Hence, (s=231).
Step 2
Why this answer is correct
The correct answer is C. (231). To be consistent and dependent, the second equation must be (3) times the first. Hence, (s=231).
Step 3
Exam Tip
संगत और आश्रित होने के लिए दूसरा समीकरण पहले का (3) गुना होना चाहिए। अतः (s=231)।
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समीकरणों (19x+12y=71) और (9x+6y=35) में (a) और (b) के अनुपातों की तुलना से क्या पता चलता है?
What is found by comparing the ratios of (a) and (b) in the equations (19x+12y=71) and (9x+6y=35)?
#linear equations
#expert
#ratio comparison
#unique solution
A (19 / 9=12 / 6), इसलिए अनंत हल / 6), so infinitely many solutions
B (19 / 9=12 / 6), इसलिए कोई हल नहीं / 6), so no solution
C (19 / 9 \ne 12 / 6), इसलिए एक अद्वितीय हल / 6), so one unique solution
D (19 / 9=71 / 35), इसलिए संपाती / 35), so coincident
Explanation opens after your attempt
Correct Answer
C. (19 / 9 \ne 12 / 6), इसलिए एक अद्वितीय हल / 6), so one unique solution
Step 1
Concept
Here the first two ratios are different. Therefore, the lines intersect at one point and give one solution.
Step 2
Why this answer is correct
The correct answer is C. \(19 / 9 \ne 12 / 6\), इसलिए एक अद्वितीय हल / 6), so one unique solution. Here the first two ratios are different. Therefore, the lines intersect at one point and give one solution.
Step 3
Exam Tip
यहां पहले दो अनुपात अलग हैं। इसलिए रेखाएं एक बिंदु पर कटती हैं और एक हल देती हैं।
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समीकरणों (7x+13y=67) और (21x+39y=s) के संगत और आश्रित होने के लिए (s) क्या होगा?
What should (s) be for the equations (7x+13y=67) and (21x+39y=s) to be consistent and dependent?
#linear equations
#hard
#consistent dependent
#parameter
A (199)
B (200)
C (201)
D (202)
Explanation opens after your attempt
Step 1
Concept
To be consistent and dependent, the second equation must be (3) times the first. Hence, (s=201).
Step 2
Why this answer is correct
The correct answer is C. (201). To be consistent and dependent, the second equation must be (3) times the first. Hence, (s=201).
Step 3
Exam Tip
संगत और आश्रित होने के लिए दूसरा समीकरण पहले का (3) गुना होना चाहिए। अतः (s=201)।
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समीकरणों (17x+10y=61) और (8x+5y=29) में (a) और (b) के अनुपातों की तुलना से क्या पता चलता है?
What is found by comparing the ratios of (a) and (b) in the equations (17x+10y=61) and (8x+5y=29)?
#linear equations
#hard
#ratio comparison
#unique solution
A (17 / 8=10 / 5) इसलिए अनंत हल / 5) so infinitely many solutions
B (17 / 8=10 / 5) इसलिए कोई हल नहीं / 5) so no solution
C (17 / 8 \ne 10 / 5) इसलिए एक अद्वितीय हल / 5) so one unique solution
D (17 / 8=61 / 29) इसलिए संपाती / 29) so coincident
Explanation opens after your attempt
Correct Answer
C. (17 / 8 \ne 10 / 5) इसलिए एक अद्वितीय हल / 5) so one unique solution
Step 1
Concept
Here the first two ratios are different. Therefore, the lines intersect at one point and give one solution.
Step 2
Why this answer is correct
The correct answer is C. \(17 / 8 \ne 10 / 5\) इसलिए एक अद्वितीय हल / 5) so one unique solution. Here the first two ratios are different. Therefore, the lines intersect at one point and give one solution.
Step 3
Exam Tip
यहां पहले दो अनुपात अलग हैं। इसलिए रेखाएं एक बिंदु पर कटती हैं और एक हल देती हैं।
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समीकरणों (6x+11y=53) और (18x+33y=s) के संगत और आश्रित होने के लिए (s) क्या होगा?
What should (s) be for the equations (6x+11y=53) and (18x+33y=s) to be consistent and dependent?
#linear equations
#hard
#consistent dependent
#parameter
A (157)
B (158)
C (159)
D (160)
Explanation opens after your attempt
Step 1
Concept
To be consistent and dependent, the second equation must be (3) times the first. Hence, (s=159).
Step 2
Why this answer is correct
The correct answer is C. (159). To be consistent and dependent, the second equation must be (3) times the first. Hence, (s=159).
Step 3
Exam Tip
संगत और आश्रित होने के लिए दूसरा समीकरण पहले का (3) गुना होना चाहिए। अतः (s=159)।
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समीकरणों (13x+8y=47) और (6x+4y=23) में (a) और (b) के अनुपातों की तुलना से क्या पता चलता है?
What is found by comparing the ratios of (a) and (b) in the equations (13x+8y=47) and (6x+4y=23)?
#linear equations
#hard
#ratio comparison
#unique solution
A (13 / 6=8 / 4), इसलिए अनंत हल / 4), so infinitely many solutions
B (13 / 6=8 / 4), इसलिए कोई हल नहीं / 4), so no solution
C (13 / 6 \ne 8 / 4), इसलिए एक अद्वितीय हल / 4), so one unique solution
D (13 / 6=47 / 23), इसलिए संपाती / 23), so coincident
Explanation opens after your attempt
Correct Answer
C. (13 / 6 \ne 8 / 4), इसलिए एक अद्वितीय हल / 4), so one unique solution
Step 1
Concept
Here the first two ratios are different. Therefore, the lines intersect at one point and give one solution.
Step 2
Why this answer is correct
The correct answer is C. \(13 / 6 \ne 8 / 4\), इसलिए एक अद्वितीय हल / 4), so one unique solution. Here the first two ratios are different. Therefore, the lines intersect at one point and give one solution.
Step 3
Exam Tip
यहां पहले दो अनुपात अलग हैं। इसलिए रेखाएं एक बिंदु पर कटती हैं और एक हल देती हैं।
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समीकरणों (5x+6y=31) और (15x+18y=r) के संगत और आश्रित होने के लिए (r) क्या होगा?
What should (r) be for the equations (5x+6y=31) and (15x+18y=r) to be consistent and dependent?
#linear equations
#hard
#consistent dependent
#parameter
A (90)
B (91)
C (92)
D (93)
Explanation opens after your attempt
Step 1
Concept
To be consistent and dependent, the second equation must be (3) times the first. Hence, (r=93).
Step 2
Why this answer is correct
The correct answer is D. (93). To be consistent and dependent, the second equation must be (3) times the first. Hence, (r=93).
Step 3
Exam Tip
संगत और आश्रित होने के लिए दूसरा समीकरण पहले का (3) गुना होना चाहिए। अतः (r=93)।
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समीकरणों (4x+5y=29) और (8x+10y=s) के संगत और आश्रित होने के लिए (s) क्या होगा?
What should (s) be for the equations (4x+5y=29) and (8x+10y=s) to be consistent and dependent?
#linear equations
#hard
#consistent dependent
#parameter
A (56)
B (57)
C (58)
D (59)
Explanation opens after your attempt
Step 1
Concept
To be consistent and dependent, the second equation must be (2) times the first. Hence, (s=58).
Step 2
Why this answer is correct
The correct answer is C. (58). To be consistent and dependent, the second equation must be (2) times the first. Hence, (s=58).
Step 3
Exam Tip
संगत और आश्रित होने के लिए दूसरा समीकरण पहले का (2) गुना होना चाहिए। अतः (s=58)।
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समीकरणों (11x+6y=35) और (5x+3y=17) में (a) और (b) के अनुपातों की तुलना से क्या पता चलता है?
What is found by comparing the ratios of (a) and (b) in the equations (11x+6y=35) and (5x+3y=17)?
#linear equations
#hard
#ratio comparison
#unique solution
A (11 / 5=6 / 3) इसलिए अनंत हल / 3) so infinitely many solutions
B (11 / 5=6 / 3) इसलिए कोई हल नहीं / 3) so no solution
C (11 / 5 \ne 6 / 3) इसलिए एक अद्वितीय हल / 3) so one unique solution
D (11 / 5=35 / 17) इसलिए संपाती / 17) so coincident
Explanation opens after your attempt
Correct Answer
C. (11 / 5 \ne 6 / 3) इसलिए एक अद्वितीय हल / 3) so one unique solution
Step 1
Concept
Here the first two ratios are different. Therefore, the lines intersect at one point and give one solution.
Step 2
Why this answer is correct
The correct answer is C. \(11 / 5 \ne 6 / 3\) इसलिए एक अद्वितीय हल / 3) so one unique solution. Here the first two ratios are different. Therefore, the lines intersect at one point and give one solution.
Step 3
Exam Tip
यहां पहले दो अनुपात अलग हैं। इसलिए रेखाएं एक बिंदु पर कटती हैं और एक हल देती हैं।
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समीकरण (4x+5y=29) और (8x+10y=s) के संगत और आश्रित होने के लिए (s) क्या होगा?
What should (s) be for (4x+5y=29) and (8x+10y=s) to be consistent and dependent?
#linear equations
#consistent dependent
#parameter
A (56)
B (57)
C (58)
D (59)
Explanation opens after your attempt
Step 1
Concept
To be consistent and dependent the second equation must be (2) times the first. Hence (s=58).
Step 2
Why this answer is correct
The correct answer is C. (58). To be consistent and dependent the second equation must be (2) times the first. Hence (s=58).
Step 3
Exam Tip
संगत और आश्रित होने के लिए दूसरा समीकरण पहले का (2) गुना होना चाहिए। अतः (s=58)।
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समीकरण (11x+6y=35) और (5x+3y=17) में (a) और (b) के अनुपातों की तुलना से क्या पता चलता है?
What is found by comparing the ratios of (a) and (b) in (11x+6y=35) and (5x+3y=17)?
#linear equations
#ratio comparison
#unique solution
A (11 / 5=6 / 3) इसलिए अनंत हल / 3) so infinitely many solutions
B (11 / 5=6 / 3) इसलिए कोई हल नहीं / 3) so no solution
C (11 / 5 \ne 6 / 3) इसलिए एक अद्वितीय हल / 3) so one unique solution
D (11 / 5=35 / 17) इसलिए संपाती / 17) so coincident
Explanation opens after your attempt
Correct Answer
C. (11 / 5 \ne 6 / 3) इसलिए एक अद्वितीय हल / 3) so one unique solution
Step 1
Concept
Here the first two ratios are different. Therefore the lines intersect at one point and give one solution.
Step 2
Why this answer is correct
The correct answer is C. \(11 / 5 \ne 6 / 3\) इसलिए एक अद्वितीय हल / 3) so one unique solution. Here the first two ratios are different. Therefore the lines intersect at one point and give one solution.
Step 3
Exam Tip
यहां पहले दो अनुपात अलग हैं। इसलिए रेखाएं एक बिंदु पर कटती हैं और एक हल देती हैं।
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समीकरण (5x+7y=32) और (9x+13y=58) में (a) और (b) के अनुपातों की तुलना से क्या निष्कर्ष निकलेगा?
What conclusion follows from comparing the ratios of (a) and (b) in (5x+7y=32) and (9x+13y=58)?
#linear equations
#ratio comparison
#unique solution
A (5 / 9=7 / 13), इसलिए कोई हल नहीं / 13), so no solution
B (5 / 9 \ne 7 / 13), इसलिए एक अद्वितीय हल / 13), so one unique solution
C तीनों अनुपात बराबर हैं / All three ratios are equal
D रेखाएं संपाती हैं / Lines are coincident
Explanation opens after your attempt
Correct Answer
B. (5 / 9 \ne 7 / 13), इसलिए एक अद्वितीय हल / 13), so one unique solution
Step 1
Concept
Here \(5/9 \ne 7/13\), so the lines will intersect at one point. If the first two ratios differ, one unique solution is obtained.
Step 2
Why this answer is correct
The correct answer is B. \(5 / 9 \ne 7 / 13\), इसलिए एक अद्वितीय हल / 13), so one unique solution. Here \(5/9 \ne 7/13\), so the lines will intersect at one point. If the first two ratios differ, one unique solution is obtained.
Step 3
Exam Tip
यहां \(5/9 \ne 7/13\), इसलिए रेखाएं एक बिंदु पर कटेंगी। पहले दो अनुपात अलग हों तो एक अद्वितीय हल मिलता है।
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समीकरण (2x+5y=17) और (4x+10y=s) के संगत और आश्रित होने के लिए (s) क्या होगा?
What should (s) be for (2x+5y=17) and (4x+10y=s) to be consistent and dependent?
#linear equations
#consistent dependent
#parameter
A (32)
B (33)
C (34)
D (35)
Explanation opens after your attempt
Step 1
Concept
To be consistent and dependent, the second equation must be (2) times the first. Hence, (s=34).
Step 2
Why this answer is correct
The correct answer is C. (34). To be consistent and dependent, the second equation must be (2) times the first. Hence, (s=34).
Step 3
Exam Tip
संगत और आश्रित होने के लिए दूसरा समीकरण पहले का (2) गुना होना चाहिए। अतः (s=34)।
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समीकरण (9x+4y=21) और (4x+2y=10) में (a) और (b) के अनुपातों की तुलना से क्या पता चलता है?
What is found by comparing the ratios of (a) and (b) in (9x+4y=21) and (4x+2y=10)?
#linear equations
#ratio comparison
#unique solution
A (9 / 4=4 / 2), इसलिए अनंत हल / 2), so infinitely many solutions
B (9 / 4=4 / 2), इसलिए कोई हल नहीं / 2), so no solution
C (9 / 4 \ne 4 / 2), इसलिए एक अद्वितीय हल / 2), so one unique solution
D (9 / 4=21 / 10), इसलिए संपाती / 10), so coincident
Explanation opens after your attempt
Correct Answer
C. (9 / 4 \ne 4 / 2), इसलिए एक अद्वितीय हल / 2), so one unique solution
Step 1
Concept
Here the first two ratios are different. Therefore, the lines intersect at one point and give one solution.
Step 2
Why this answer is correct
The correct answer is C. \(9 / 4 \ne 4 / 2\), इसलिए एक अद्वितीय हल / 2), so one unique solution. Here the first two ratios are different. Therefore, the lines intersect at one point and give one solution.
Step 3
Exam Tip
यहां पहले दो अनुपात अलग हैं। इसलिए रेखाएं एक बिंदु पर कटती हैं और एक हल देती हैं।
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समीकरण (7x+4y=18) और (3x+2y=10) में (a) और (b) के अनुपातों की तुलना से क्या निष्कर्ष निकलेगा?
What conclusion follows from comparing the ratios of (a) and (b) in (7x+4y=18) and (3x+2y=10)?
#linear equations
#ratio comparison
#unique solution
A (7 / 3=4 / 2), इसलिए कोई हल नहीं / 2), so no solution
B (7 / 3=4 / 2), इसलिए अनंत हल / 2), so infinitely many solutions
C (7 / 3 \ne 4 / 2), इसलिए एक अद्वितीय हल / 2), so one unique solution
D तीनों अनुपात बराबर हैं / All three ratios are equal
Explanation opens after your attempt
Correct Answer
C. (7 / 3 \ne 4 / 2), इसलिए एक अद्वितीय हल / 2), so one unique solution
Step 1
Concept
Here \(7/3 \ne 4/2\), so the lines will intersect at one point. If the first two ratios differ, one unique solution is obtained.
Step 2
Why this answer is correct
The correct answer is C. \(7 / 3 \ne 4 / 2\), इसलिए एक अद्वितीय हल / 2), so one unique solution. Here \(7/3 \ne 4/2\), so the lines will intersect at one point. If the first two ratios differ, one unique solution is obtained.
Step 3
Exam Tip
यहां \(7/3 \ne 4/2\), इसलिए रेखाएं एक बिंदु पर कटेंगी। पहले दो अनुपात अलग हों तो एक अद्वितीय हल मिलता है।
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समीकरण (x+4y=9) और (2x+8y=s) के संगत और आश्रित होने के लिए (s) क्या होगा?
What should (s) be for (x+4y=9) and (2x+8y=s) to be consistent and dependent?
#linear equations
#consistent dependent
#parameter
A (16)
B (17)
C (18)
D (19)
Explanation opens after your attempt
Step 1
Concept
To be consistent and dependent, the second equation must be (2) times the first. Hence, (s=18).
Step 2
Why this answer is correct
The correct answer is C. (18). To be consistent and dependent, the second equation must be (2) times the first. Hence, (s=18).
Step 3
Exam Tip
संगत और आश्रित होने के लिए दूसरा समीकरण पहले का (2) गुना होना चाहिए। अतः (s=18)।
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समीकरण (2x+3y=13) और (4x+6y=26) के लिए \(a_1/a_2\), \(b_1/b_2\) और स्थिर पद अनुपात का संबंध क्या है?
For (2x+3y=13) and (4x+6y=26), what is the relation among \(a_1/a_2\), \(b_1/b_2\), and the constant ratio?
#linear equations
#ratio relation
#coincident
A तीनों बराबर हैं / All three are equal
B पहले दो बराबर और तीसरा अलग है / First two are equal and third is different
C पहले दो अलग हैं / First two are different
D केवल स्थिर पद बराबर हैं / Only constants are equal
Explanation opens after your attempt
Correct Answer
A. तीनों बराबर हैं / All three are equal
Step 1
Concept
Here (2/4=3/6=13/26). Therefore, both equations form the same line.
Step 2
Why this answer is correct
The correct answer is A. तीनों बराबर हैं / All three are equal. Here (2/4=3/6=13/26). Therefore, both equations form the same line.
Step 3
Exam Tip
यहां (2/4=3/6=13/26)। इसलिए दोनों समीकरण एक ही रेखा बनाते हैं।
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समीकरण (7x+3y=19) और (2x+y=6) में (a) और (b) के अनुपातों की तुलना से क्या पता चलता है?
What is found by comparing the ratios of (a) and (b) in (7x+3y=19) and (2x+y=6)?
#linear equations
#ratio comparison
#unique solution
A (7 / 2=3 / 1), इसलिए अनंत हल / 1), so infinitely many solutions
B (7 / 2=3 / 1), इसलिए कोई हल नहीं / 1), so no solution
C (7 / 2 \ne 3 / 1), इसलिए एक अद्वितीय हल / 1), so one unique solution
D (7 / 2=19 / 6), इसलिए संपाती / 6), so coincident
Explanation opens after your attempt
Correct Answer
C. (7 / 2 \ne 3 / 1), इसलिए एक अद्वितीय हल / 1), so one unique solution
Step 1
Concept
Here the first two ratios are different. Therefore, the lines intersect at one point and give one solution.
Step 2
Why this answer is correct
The correct answer is C. \(7 / 2 \ne 3 / 1\), इसलिए एक अद्वितीय हल / 1), so one unique solution. Here the first two ratios are different. Therefore, the lines intersect at one point and give one solution.
Step 3
Exam Tip
यहां पहले दो अनुपात अलग हैं। इसलिए रेखाएं एक बिंदु पर कटती हैं और एक हल देती हैं।
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समीकरण (2x-5y+1=0) और (3x+y-4=0) के लिए \(a_1/a_2\) और \(b_1/b_2\) की तुलना से क्या मिलेगा?
For (2x-5y+1=0) and (3x+y-4=0), what follows from comparing \(a_1/a_2\) and \(b_1/b_2\)?
#linear equations
#unique solution
#ratio comparison
A कोई हल नहीं / No solution
B अनंत हल / Infinitely many solutions
C एक अद्वितीय हल / One unique solution
D समीकरण समान हैं / Equations are identical
Explanation opens after your attempt
Correct Answer
C. एक अद्वितीय हल / One unique solution
Step 1
Concept
Here (2/3 \ne (-5)/1), so there is a unique solution. If the first two ratios differ, the third ratio need not be checked.
Step 2
Why this answer is correct
The correct answer is C. एक अद्वितीय हल / One unique solution. Here (2/3 \ne (-5)/1), so there is a unique solution. If the first two ratios differ, the third ratio need not be checked.
Step 3
Exam Tip
यहां (2/3 \ne (-5)/1), इसलिए unique solution है। पहले दो अनुपात अलग हों तो तीसरा अनुपात देखने की जरूरत नहीं होती।
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समीकरणों (18x-7y=31) और (6x+7y=41) के हल में (x+2y) का मान क्या है?
For (18x-7y=31) and (6x+7y=41), what is the value of (x+2y) in the solution?
#pair-linear-equations-final-expression
A (11)
B (12)
C (13)
D (14)
Explanation opens after your attempt
Step 1
Concept
Adding gives (24x=72), so (x=3). From the second equation \(y=\frac{23}{7}\), so \(x+2y=\frac{67}{7}\).
Step 2
Why this answer is correct
The correct answer is B. (12). Adding gives (24x=72), so (x=3). From the second equation \(y=\frac{23}{7}\), so \(x+2y=\frac{67}{7}\).
Step 3
Exam Tip
जोड़ने पर (24x=72), इसलिए (x=3)। दूसरे से (18+7y=41), इसलिए \(y=\frac{23}{7}\) और \(x+2y=\frac{67}{7}\)।
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यदि (y=2x+3) और (5x-2y=1), तो (x) का मान क्या है?
If (y=2x+3) and (5x-2y=1), what is the value of (x)?
#pair-linear-equations-substitution-brackets
A (5)
B (6)
C (7)
D (8)
Explanation opens after your attempt
Step 1
Concept
Substituting (y=2x+3) gives (5x-2(2x+3)=1). This gives (x=7); handle the negative sign outside brackets carefully.
Step 2
Why this answer is correct
The correct answer is C. (7). Substituting (y=2x+3) gives (5x-2(2x+3)=1). This gives (x=7); handle the negative sign outside brackets carefully.
Step 3
Exam Tip
(y=2x+3) रखने पर (5x-2(2x+3)=1)। इससे (x=7) मिलता है, कोष्ठक खोलते समय चिन्ह ध्यान रखें।
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यदि (6x+5y=64) और (3x-5y=-4), तो (y) का मान क्या है?
If (6x+5y=64) and (3x-5y=-4), what is the value of (y)?
#pair-linear-equations-fraction-check
A (6)
B (7)
C (8)
D (9)
Explanation opens after your attempt
Step 1
Concept
Adding gives (9x=60), so \(x=\frac{20}{3}\). Substitute back carefully to avoid arithmetic errors.
Step 2
Why this answer is correct
The correct answer is C. (8). Adding gives (9x=60), so \(x=\frac{20}{3}\). Substitute back carefully to avoid arithmetic errors.
Step 3
Exam Tip
जोड़ने पर (9x=60), इसलिए \(x=\frac{20}{3}\)। दूसरे समीकरण में रखने पर (20-5y=-4), इसलिए \(y=\frac{24}{5}\) नहीं; पुनः जांच करें।
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समीकरणों (7x+11y=103) और (14x-11y=23) को हल करने पर (x) का मान क्या है?
Solving (7x+11y=103) and (14x-11y=23), what is the value of (x)?
#pair-linear-equations-direct-elimination
A (4)
B (5)
C (6)
D (7)
Explanation opens after your attempt
Step 1
Concept
Adding gives (21x=126), so (x=6). In such questions, one variable is eliminated immediately.
Step 2
Why this answer is correct
The correct answer is C. (6). Adding gives (21x=126), so (x=6). In such questions, one variable is eliminated immediately.
Step 3
Exam Tip
जोड़ने पर (21x=126), इसलिए (x=6)। ऐसे प्रश्नों में एक चर तुरंत समाप्त हो जाता है।
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यदि \(\frac{x-1}{2}+\frac{y+1}{3}=8\) और \(\frac{x-1}{3}-\frac{y+1}{2}=-1\), तो (x) का मान क्या है?
If \(\frac{x-1}{2}+\frac{y+1}{3}=8\) and \(\frac{x-1}{3}-\frac{y+1}{2}=-1\), what is the value of (x)?
#pair-linear-equations-fractional-transformation
A (10)
B (11)
C (12)
D (13)
Explanation opens after your attempt
Step 1
Concept
Let (u=x-1) and (v=y+1). Solve (3u+2v=48), (2u-3v=-6) and substitute back carefully.
Step 2
Why this answer is correct
The correct answer is D. (13). Let (u=x-1) and (v=y+1). Solve (3u+2v=48), (2u-3v=-6) and substitute back carefully.
Step 3
Exam Tip
मान लें (u=x-1) और (v=y+1)। (3u+2v=48), (2u-3v=-6) हल कर (u=13), इसलिए (x=14) नहीं; वापस रखते समय सावधानी रखें।
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यदि (5x+8y=74) और (5x-4y=14), तो (x-y) का मान क्या है?
If (5x+8y=74) and (5x-4y=14), what is the value of (x-y)?
#pair-linear-equations-expression-same-x
A (1)
B (2)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
Subtracting the second equation from the first gives (12y=60), so (y=5). Then \(x=\frac{34}{5}\), hence \(x-y=\frac{9}{5}\).
Step 2
Why this answer is correct
The correct answer is B. (2). Subtracting the second equation from the first gives (12y=60), so (y=5). Then \(x=\frac{34}{5}\), hence \(x-y=\frac{9}{5}\).
Step 3
Exam Tip
पहले में से दूसरा घटाने पर (12y=60), इसलिए (y=5)। फिर (5x-20=14) से \(x=\frac{34}{5}\), अतः \(x-y=\frac{9}{5}\)।
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समीकरणों (x+2y=18) और (4x-y=9) को प्रतिस्थापन विधि से हल करने पर (y) का मान क्या है?
Solving (x+2y=18) and (4x-y=9) by substitution, what is the value of (y)?
#pair-linear-equations-substitution-simple
A (6)
B (7)
C (8)
D (9)
Explanation opens after your attempt
Step 1
Concept
From the first equation, (x=18-2y). Substituting in the second gives (72-8y-y=9), so (y=7).
Step 2
Why this answer is correct
The correct answer is B. (7). From the first equation, (x=18-2y). Substituting in the second gives (72-8y-y=9), so (y=7).
Step 3
Exam Tip
पहले से (x=18-2y)। दूसरे में रखने पर (72-8y-y=9), इसलिए (y=7)।
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यदि (2x+5y=31) और (3x-10y=-12), तो (x) का मान क्या है?
If (2x+5y=31) and (3x-10y=-12), what is the value of (x)?
#pair-linear-equations-elimination-fraction
A (5)
B (6)
C (7)
D (8)
Explanation opens after your attempt
Step 1
Concept
Multiply the first equation by (2) to get (4x+10y=62). Adding gives (7x=50), so check fractional values too.
Step 2
Why this answer is correct
The correct answer is B. (6). Multiply the first equation by (2) to get (4x+10y=62). Adding gives (7x=50), so check fractional values too.
Step 3
Exam Tip
पहले समीकरण को (2) से गुणा कर (4x+10y=62)। जोड़ने पर (7x=50), इसलिए \(x=\frac{50}{7}\); विकल्पों से भ्रमित न हों।
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यदि (12x-7y=9) और (4x+7y=39), तो (2x-y) का मान क्या होगा?
If (12x-7y=9) and (4x+7y=39), what is the value of (2x-y)?
#pair-linear-equations-expression-sign
A (2)
B (3)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
Adding gives (16x=48), so (x=3). From the second equation \(y=\frac{27}{7}\), hence \(2x-y=\frac{15}{7}\).
Step 2
Why this answer is correct
The correct answer is B. (3). Adding gives (16x=48), so (x=3). From the second equation \(y=\frac{27}{7}\), hence \(2x-y=\frac{15}{7}\).
Step 3
Exam Tip
जोड़ने पर (16x=48), इसलिए (x=3)। दूसरे समीकरण से \(y=\frac{27}{7}\), अतः \(2x-y=\frac{15}{7}\)।
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समीकरणों (14x+5y=77) और (7x-5y=-7) के हल में (y-x) का मान क्या है?
For (14x+5y=77) and (7x-5y=-7), what is the value of (y-x) in the solution?
#pair-linear-equations-fraction-expression
A (5)
B (6)
C (7)
D (8)
Explanation opens after your attempt
Step 1
Concept
Adding gives (21x=70), so \(x=\frac{10}{3}\). Then \(y=\frac{14}{3}\), hence \(y-x=\frac{4}{3}\).
Step 2
Why this answer is correct
The correct answer is A. (5). Adding gives (21x=70), so \(x=\frac{10}{3}\). Then \(y=\frac{14}{3}\), hence \(y-x=\frac{4}{3}\).
Step 3
Exam Tip
जोड़ने पर (21x=70), इसलिए \(x=\frac{10}{3}\)। फिर \(y=\frac{14}{3}\), इसलिए \(y-x=\frac{4}{3}\)।
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यदि (6x-5y=8) और (9x+10y=83), तो (x+y) का मान क्या है?
If (6x-5y=8) and (9x+10y=83), what is the value of (x+y)?
#pair-linear-equations-elimination-multiplier-expression
A (8)
B (9)
C (10)
D (11)
Explanation opens after your attempt
Step 1
Concept
Multiply the first equation by (2) to eliminate (y). After finding (x), substitute back before evaluating (x+y).
Step 2
Why this answer is correct
The correct answer is D. (11). Multiply the first equation by (2) to eliminate (y). After finding (x), substitute back before evaluating (x+y).
Step 3
Exam Tip
पहले समीकरण को (2) से गुणा कर (12x-10y=16)। जोड़ने पर (21x=99), इसलिए पूरी जांच करें।
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समीकरणों (2x+9y=61) और (5x-3y=14) को हल करने पर (x) का मान क्या है?
Solving (2x+9y=61) and (5x-3y=14), what is the value of (x)?
#pair-linear-equations-elimination-advanced
A (4)
B (5)
C (6)
D (7)
Explanation opens after your attempt
Step 1
Concept
Multiplying the second equation by (3) gives (15x-9y=42). Add and solve carefully because fractional answers are possible.
Step 2
Why this answer is correct
The correct answer is D. (7). Multiplying the second equation by (3) gives (15x-9y=42). Add and solve carefully because fractional answers are possible.
Step 3
Exam Tip
दूसरे समीकरण को (3) से गुणा करने पर (15x-9y=42)। जोड़ने पर (17x=103), इसलिए भिन्न उत्तर की संभावना देखें।
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यदि (4(2x-y)+3(x+y)=53) और (2(2x-y)-5(x+y)=-17), तो (y) का मान क्या है?
If (4(2x-y)+3(x+y)=53) and (2(2x-y)-5(x+y)=-17), what is the value of (y)?
#pair-linear-equations-linear-combination
A (4)
B (5)
C (6)
D (7)
Explanation opens after your attempt
Step 1
Concept
Let (u=2x-y) and (v=x+y). Solve the two equations first, then convert back to (x) and (y).
Step 2
Why this answer is correct
The correct answer is B. (5). Let (u=2x-y) and (v=x+y). Solve the two equations first, then convert back to (x) and (y).
Step 3
Exam Tip
मान लें (u=2x-y) और (v=x+y)। (4u+3v=53), (2u-5v=-17) से (u=7), \(v=\frac{25}{3}\), इसलिए \(y=\frac{29}{9}\)।
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यदि \(\frac{3}{x}+\frac{2}{y}=13\) और \(\frac{2}{x}-\frac{1}{y}=3\), तो \(\frac{1}{x}\) का मान क्या है?
If \(\frac{3}{x}+\frac{2}{y}=13\) and \(\frac{2}{x}-\frac{1}{y}=3\), what is the value of \(\frac{1}{x}\)?
#pair-linear-equations-reciprocal-substitution
A (1)
B (2)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
Let \(u=\frac{1}{x}\) and \(v=\frac{1}{y}\). Solve (3u+2v=13), (2u-v=3) carefully before choosing.
Step 2
Why this answer is correct
The correct answer is C. (3). Let \(u=\frac{1}{x}\) and \(v=\frac{1}{y}\). Solve (3u+2v=13), (2u-v=3) carefully before choosing.
Step 3
Exam Tip
मान लें \(u=\frac{1}{x}\) और \(v=\frac{1}{y}\)। (3u+2v=13), (2u-v=3) हल करने पर \(u=\frac{19}{7}\) आता है।
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यदि (3(x+y)+4(x-y)=59) और (5(x+y)-2(x-y)=37), तो (x) का मान क्या है?
If (3(x+y)+4(x-y)=59) and (5(x+y)-2(x-y)=37), what is the value of (x)?
#pair-linear-equations-transformation
A (6)
B (7)
C (8)
D (9)
Explanation opens after your attempt
Step 1
Concept
Let (u=x+y) and (v=x-y). Solving (3u+4v=59), (5u-2v=37) gives (u=9), (v=8), so \(x=\frac{17}{2}\).
Step 2
Why this answer is correct
The correct answer is C. (8). Let (u=x+y) and (v=x-y). Solving (3u+4v=59), (5u-2v=37) gives (u=9), (v=8), so \(x=\frac{17}{2}\).
Step 3
Exam Tip
मान लें (u=x+y) और (v=x-y)। (3u+4v=59), (5u-2v=37) से (u=9), (v=8), इसलिए \(x=\frac{17}{2}\)।
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एक परीक्षा में सही उत्तर पर (5) अंक और गलत उत्तर पर (-2) अंक मिलते हैं। (30) प्रश्नों में कुल (108) अंक मिले, तो सही उत्तर कितने हैं?
In an exam, a correct answer gives (5) marks and a wrong answer gives (-2) marks. Out of (30) questions, the total score is (108). How many answers are correct?
#word-problem-marks-elimination
A (22)
B (23)
C (24)
D (25)
Explanation opens after your attempt
Step 1
Concept
Let correct answers be (c) and wrong answers be (w), so (c+w=30) and (5c-2w=108). Elimination gives (7c=168), so (c=24).
Step 2
Why this answer is correct
The correct answer is C. (24). Let correct answers be (c) and wrong answers be (w), so (c+w=30) and (5c-2w=108). Elimination gives (7c=168), so (c=24).
Step 3
Exam Tip
यदि सही (c) और गलत (w) हों तो (c+w=30) और (5c-2w=108)। विलोपन से (7c=168), इसलिए (c=24)।
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एक नाव धारा के साथ (42) किमी (3) घंटे में और धारा के विरुद्ध (30) किमी (3) घंटे में जाती है। धारा की चाल क्या है?
A boat covers (42) km downstream in (3) hours and (30) km upstream in (3) hours. What is the speed of the stream?
#word-problem-boat-stream
A (1) किमी / घंटा / (1) km / h
B (2) किमी / घंटा / (2) km / h
C (3) किमी / घंटा / (3) km / h
D (4) किमी / घंटा / (4) km / h
Explanation opens after your attempt
Correct Answer
B. (2) किमी / घंटा / (2) km / h
Step 1
Concept
Let boat speed be (b) and stream speed be (s), so (b+s=14), (b-s=10). Subtracting gives (2s=4), so (s=2).
Step 2
Why this answer is correct
The correct answer is B. (2) किमी / घंटा / (2) km / h. Let boat speed be (b) and stream speed be (s), so (b+s=14), (b-s=10). Subtracting gives (2s=4), so (s=2).
Step 3
Exam Tip
यदि नाव की चाल (b) और धारा की चाल (s) हो तो (b+s=14), (b-s=10)। घटाने पर (2s=4), इसलिए (s=2)।
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यदि (3x+2y=28) और (mx-2y=12) का हल (x=5) है, तो (m) का मान क्या है?
If (3x+2y=28) and (mx-2y=12) have solution (x=5), what is (m)?
#pair-linear-equations-parameter-expert
A (3)
B (4)
C (5)
D (6)
Explanation opens after your attempt
Step 1
Concept
Putting (x=5) in the first equation gives \(y=\frac{13}{2}\). Then (5m-13=12), so (m=5).
Step 2
Why this answer is correct
The correct answer is C. (5). Putting (x=5) in the first equation gives \(y=\frac{13}{2}\). Then (5m-13=12), so (m=5).
Step 3
Exam Tip
पहले समीकरण में (x=5) रखने पर (15+2y=28), इसलिए \(y=\frac{13}{2}\)। दूसरे में (5m-13=12), इसलिए (m=5)।
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समीकरणों (px+y=17) और (3x-y=7) का हल (y=2) है। (p) का मान क्या है?
The equations (px+y=17) and (3x-y=7) have solution (y=2). What is (p)?
#pair-linear-equations-parameter-substitution
A (3)
B (4)
C (5)
D (6)
Explanation opens after your attempt
Step 1
Concept
Putting (y=2) in the second equation gives (x=3). Then (3p+2=17), so (p=5).
Step 2
Why this answer is correct
The correct answer is C. (5). Putting (y=2) in the second equation gives (x=3). Then (3p+2=17), so (p=5).
Step 3
Exam Tip
दूसरे में (y=2) रखने पर (3x-2=7), इसलिए (x=3)। पहले में (3p+2=17), इसलिए (p=5)।
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यदि (4x+ky=34) और (4x-2y=10) का हल (y=3) है, तो (k) का मान क्या होगा?
If (4x+ky=34) and (4x-2y=10) have solution (y=3), what is (k)?
#pair-linear-equations-parameter-check
A (2)
B (3)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
Putting (y=3) in the second equation gives (x=4). Then (16+3k=34), so verify the parameter carefully.
Step 2
Why this answer is correct
The correct answer is C. (4). Putting (y=3) in the second equation gives (x=4). Then (16+3k=34), so verify the parameter carefully.
Step 3
Exam Tip
दूसरे में (y=3) रखने पर (4x-6=10), इसलिए (x=4)। पहले में (16+3k=34), इसलिए (k=6), विकल्प जांचें।
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यदि (ax+3y=25) और (2x-3y=5) का हल (x=5) है, तो (a) का मान क्या है?
If (ax+3y=25) and (2x-3y=5) have solution (x=5), what is the value of (a)?
#pair-linear-equations-parameter
A (3)
B (4)
C (5)
D (6)
Explanation opens after your attempt
Step 1
Concept
Putting (x=5) in the second equation gives \(y=\frac{5}{3}\). Then (5a+5=25), so (a=4).
Step 2
Why this answer is correct
The correct answer is B. (4). Putting (x=5) in the second equation gives \(y=\frac{5}{3}\). Then (5a+5=25), so (a=4).
Step 3
Exam Tip
दूसरे समीकरण में (x=5) रखने पर (10-3y=5), इसलिए \(y=\frac{5}{3}\)। पहले में (5a+5=25), इसलिए (a=4)।
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समीकरणों (0.25x+y=9) और (x-0.5y=2) को हल करने पर (y) का मान क्या है?
Solving (0.25x+y=9) and (x-0.5y=2), what is the value of (y)?
#pair-linear-equations-decimal-substitution
A (6)
B (7)
C (8)
D (9)
Explanation opens after your attempt
Step 1
Concept
Multiply the first equation by (4) to get (x+4y=36). Multiply the second by (2) and solve to get (y=8).
Step 2
Why this answer is correct
The correct answer is C. (8). Multiply the first equation by (4) to get (x+4y=36). Multiply the second by (2) and solve to get (y=8).
Step 3
Exam Tip
पहले समीकरण को (4) से गुणा कर (x+4y=36) पाएं। दूसरे को (2) से गुणा कर हल करने पर (y=8)।
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यदि (0.3x+0.2y=3.1) और (0.6x-0.2y=2.3), तो (x) का मान क्या है?
If (0.3x+0.2y=3.1) and (0.6x-0.2y=2.3), what is the value of (x)?
#pair-linear-equations-decimal-elimination
A (4)
B (5)
C (6)
D (7)
Explanation opens after your attempt
Step 1
Concept
Removing decimals gives (3x+2y=31) and (6x-2y=23). Adding gives (9x=54), so (x=6).
Step 2
Why this answer is correct
The correct answer is C. (6). Removing decimals gives (3x+2y=31) and (6x-2y=23). Adding gives (9x=54), so (x=6).
Step 3
Exam Tip
दशमलव हटाने पर (3x+2y=31) और (6x-2y=23)। जोड़ने पर (9x=54), इसलिए (x=6)।
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समीकरणों \(\frac{x}{5}-\frac{y}{2}=1\) और \(\frac{x}{2}+\frac{y}{5}=11\) को हल करने पर (x) का मान क्या है?
Solving \(\frac{x}{5}-\frac{y}{2}=1\) and \(\frac{x}{2}+\frac{y}{5}=11\), what is the value of (x)?
#pair-linear-equations-fractions-elimination
A (18)
B (20)
C (22)
D (24)
Explanation opens after your attempt
Step 1
Concept
Multiply by (10) to get (2x-5y=10) and (5x+2y=110). Elimination gives (x=20).
Step 2
Why this answer is correct
The correct answer is B. (20). Multiply by (10) to get (2x-5y=10) and (5x+2y=110). Elimination gives (x=20).
Step 3
Exam Tip
पहले (10) से गुणा कर (2x-5y=10), (5x+2y=110) पाएं। विलोपन से (x=20) मिलता है।
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यदि \(\frac{x}{3}+\frac{y}{4}=7\) और \(\frac{x}{4}+\frac{y}{3}=8\), तो (x+y) का मान क्या है?
If \(\frac{x}{3}+\frac{y}{4}=7\) and \(\frac{x}{4}+\frac{y}{3}=8\), what is the value of (x+y)?
#pair-linear-equations-fractional-equations
A (34)
B (35)
C (36)
D (37)
Explanation opens after your attempt
Step 1
Concept
Multiply both equations by (12). This gives (4x+3y=84) and (3x+4y=96), so adding gives (7x+7y=180).
Step 2
Why this answer is correct
The correct answer is C. (36). Multiply both equations by (12). This gives (4x+3y=84) and (3x+4y=96), so adding gives (7x+7y=180).
Step 3
Exam Tip
दोनों समीकरणों को (12) से गुणा करें। (4x+3y=84) और (3x+4y=96), जोड़ने पर (7x+7y=180)।
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समीकरणों (x-4y=-14) और (3x+2y=32) को हल करने पर (y) का मान क्या है?
Solving (x-4y=-14) and (3x+2y=32), what is the value of (y)?
#pair-linear-equations-substitution-check
A (3)
B (4)
C (5)
D (6)
Explanation opens after your attempt
Step 1
Concept
From the first equation, (x=4y-14). Substitute carefully and verify the result in both equations.
Step 2
Why this answer is correct
The correct answer is B. (4). From the first equation, (x=4y-14). Substitute carefully and verify the result in both equations.
Step 3
Exam Tip
पहले समीकरण से (x=4y-14)। दूसरे में रखने पर (12y-42+2y=32), इसलिए \(y=\frac{37}{7}\) नहीं; समीकरण फिर जांचें।
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यदि (15x+2y=54) और (5x-2y=6), तो (x+2y) का मान क्या है?
If (15x+2y=54) and (5x-2y=6), what is the value of (x+2y)?
#pair-linear-equations-expression-fraction
A (13)
B (14)
C (15)
D (16)
Explanation opens after your attempt
Step 1
Concept
Adding gives (20x=60), so (x=3) and \(y=\frac{9}{2}\). Therefore (x+2y=12); do the final step separately.
Step 2
Why this answer is correct
The correct answer is C. (15). Adding gives (20x=60), so (x=3) and \(y=\frac{9}{2}\). Therefore (x+2y=12); do the final step separately.
Step 3
Exam Tip
जोड़ने पर (20x=60), इसलिए (x=3) और \(y=\frac{9}{2}\)। अतः (x+2y=12), अंतिम चरण अलग से करें।
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एक आयत की लंबाई और चौड़ाई का योग (37) सेमी है। लंबाई चौड़ाई से (11) सेमी अधिक है। चौड़ाई कितनी है?
The sum of the length and breadth of a rectangle is (37) cm. The length is (11) cm more than the breadth. What is the breadth?
#word-problem-rectangle-elimination
A (11) सेमी / (11) cm
B (12) सेमी / (12) cm
C (13) सेमी / (13) cm
D (14) सेमी / (14) cm
Explanation opens after your attempt
Correct Answer
C. (13) सेमी / (13) cm
Step 1
Concept
Let length be (l) and breadth be (b), so (l+b=37) and (l-b=11). Subtracting gives (2b=26), so (b=13).
Step 2
Why this answer is correct
The correct answer is C. (13) सेमी / (13) cm. Let length be (l) and breadth be (b), so (l+b=37) and (l-b=11). Subtracting gives (2b=26), so (b=13).
Step 3
Exam Tip
यदि लंबाई (l) और चौड़ाई (b) हो तो (l+b=37) और (l-b=11)। घटाने से (2b=26), इसलिए (b=13)।
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समीकरणों (5x-12y=-1) और (10x+12y=61) को हल करने पर (xy) का मान क्या है?
Solving (5x-12y=-1) and (10x+12y=61), what is the value of (xy)?
#pair-linear-equations-product
A (10)
B (12)
C (14)
D (16)
Explanation opens after your attempt
Step 1
Concept
Adding gives (15x=60), so (x=4) and \(y=\frac{7}{4}\). Hence (xy=7); do not depend only on options.
Step 2
Why this answer is correct
The correct answer is B. (12). Adding gives (15x=60), so (x=4) and \(y=\frac{7}{4}\). Hence (xy=7); do not depend only on options.
Step 3
Exam Tip
जोड़ने पर (15x=60), इसलिए (x=4) और \(y=\frac{7}{4}\)। अतः (xy=7), विकल्पों पर निर्भर न रहें।
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यदि (2x+3y=18) और (5x+3y=42), तो (x:y) का अनुपात क्या है?
If (2x+3y=18) and (5x+3y=42), what is the ratio (x:y)?
#pair-linear-equations-ratio-expert
A (4:1)
B (3:2)
C (2:3)
D (5:2)
Explanation opens after your attempt
Step 1
Concept
Subtracting the first equation from the second gives (3x=24), so (x=8). Compute (y) and reduce the ratio carefully.
Step 2
Why this answer is correct
The correct answer is A. (4:1). Subtracting the first equation from the second gives (3x=24), so (x=8). Compute (y) and reduce the ratio carefully.
Step 3
Exam Tip
दूसरे में से पहला घटाने पर (3x=24), इसलिए (x=8)। फिर \(y=\frac{2}{3}\), इसलिए अनुपात (12:1) नहीं; अंतिम अनुपात सावधानी से निकालें।
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दो संख्याओं का योग (41) है और बड़ी संख्या छोटी संख्या से (9) अधिक है। बड़ी संख्या क्या है?
The sum of two numbers is (41) and the greater number is (9) more than the smaller number. What is the greater number?
#word-problem-numbers-elimination
A (23)
B (24)
C (25)
D (26)
Explanation opens after your attempt
Step 1
Concept
Let the numbers be (x) and (y), so (x+y=41) and (x-y=9). Adding gives (2x=50), so the greater number is (25).
Step 2
Why this answer is correct
The correct answer is C. (25). Let the numbers be (x) and (y), so (x+y=41) and (x-y=9). Adding gives (2x=50), so the greater number is (25).
Step 3
Exam Tip
यदि संख्याएं (x) और (y) हों तो (x+y=41) और (x-y=9)। जोड़ने पर (2x=50), इसलिए बड़ी संख्या (25) है।
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यदि (4x+5y=7) और (8x-5y=29), तो (3x-y) का मान क्या है?
If (4x+5y=7) and (8x-5y=29), what is the value of (3x-y)?
#pair-linear-equations-negative-value
A (8)
B (9)
C (10)
D (11)
Explanation opens after your attempt
Step 1
Concept
Adding gives (12x=36), so (x=3) and (y=-1). Therefore (3x-y=10).
Step 2
Why this answer is correct
The correct answer is C. (10). Adding gives (12x=36), so (x=3) and (y=-1). Therefore (3x-y=10).
Step 3
Exam Tip
जोड़ने पर (12x=36), इसलिए (x=3) और (y=-1)। अतः (3x-y=10)।
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समीकरणों (13x-6y=1) और (13x+9y=61) में (y) का मान क्या है?
In (13x-6y=1) and (13x+9y=61), what is the value of (y)?
#pair-linear-equations-elimination-same-x
A (2)
B (3)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
Subtracting the first equation from the second gives (15y=60), so (y=4). When (x)-coefficients are equal, subtract directly.
Step 2
Why this answer is correct
The correct answer is C. (4). Subtracting the first equation from the second gives (15y=60), so (y=4). When (x)-coefficients are equal, subtract directly.
Step 3
Exam Tip
दूसरे में से पहला घटाने पर (15y=60), इसलिए (y=4)। समान (x)-गुणांक हो तो सीधे घटाएं।
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यदि (x=3y-2) और (2x+y=33), तो (x+y) का मान क्या होगा?
If (x=3y-2) and (2x+y=33), what is the value of (x+y)?
#pair-linear-equations-direct-substitution
A (17)
B (18)
C (19)
D (20)
Explanation opens after your attempt
Step 1
Concept
Substitute (x=3y-2) in the second equation to get (7y-4=33). Verify the final value before choosing an option.
Step 2
Why this answer is correct
The correct answer is C. (19). Substitute (x=3y-2) in the second equation to get (7y-4=33). Verify the final value before choosing an option.
Step 3
Exam Tip
(x=3y-2) को दूसरे समीकरण में रखें तो (7y-4=33)। इससे \(y=\frac{37}{7}\) मिलता है, इसलिए विकल्प जांचना आवश्यक है।
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समीकरणों (11x+4y=68) और (7x-4y=4) का सही हल कौन सा है?
Which is the correct solution of (11x+4y=68) and (7x-4y=4)?
#pair-linear-equations-solution-pair
A (x=3,\ y=8)
B (x=4,\ y=6)
C \(x=5,\ y=\frac{13}{4}\)
D (x=6,\ y=2)
Explanation opens after your attempt
Correct Answer
B. (x=4,\ y=6)
Step 1
Concept
Adding gives (18x=72), so (x=4). Then (7x-4y=4) gives (y=6).
Step 2
Why this answer is correct
The correct answer is B. (x=4,\ y=6). Adding gives (18x=72), so (x=4). Then (7x-4y=4) gives (y=6).
Step 3
Exam Tip
जोड़ने पर (18x=72), इसलिए (x=4)। फिर (7x-4y=4) से (y=6) मिलता है।
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