समीकरणों (2x+3y=18) और (3x-2y=5) का हल क्या है?
What is the solution of (2x+3y=18) and (3x-2y=5)?
#linear equations
#elimination
#medium
#class 10
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A (x=3,\ y=4)
B (x=4,\ y=3)
C (x=5,\ y=2)
D (x=2,\ y=5)
Explanation opens after your attempt
Correct Answer
A. (x=3,\ y=4)
Step 1
Concept
Multiplying the first equation by (2) and the second by (3) eliminates (y). The solution is (x=3,\ y=4).
Step 2
Why this answer is correct
The correct answer is A. (x=3,\ y=4). Multiplying the first equation by (2) and the second by (3) eliminates (y). The solution is (x=3,\ y=4).
Step 3
Exam Tip
पहले समीकरण को (2) से और दूसरे को (3) से गुणा करने पर (y) हटता है। हल (x=3,\ y=4) मिलता है।
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यदि (4x-y=17) और (2x+3y=19), तो (x) का मान क्या होगा?
If (4x-y=17) and (2x+3y=19), what will be the value of (x)?
#linear equations
#substitution
#value of x
#medium
#class 10
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A (x=3)
B (x=4)
C (x=5)
D (x=6)
Explanation opens after your attempt
Step 1
Concept
From the first equation use (y=4x-17). Then (2x+3(4x-17)=19) gives (x=5).
Step 2
Why this answer is correct
The correct answer is C. (x=5). From the first equation use (y=4x-17). Then (2x+3(4x-17)=19) gives (x=5).
Step 3
Exam Tip
पहले समीकरण से (y=4x-17) रखें। फिर (2x+3(4x-17)=19) से (x=5) मिलता है।
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समीकरणों (5x+2y=24) और (3x+4y=22) को हल करने पर (y) कितना है?
On solving (5x+2y=24) and (3x+4y=22), what is (y)?
#linear equations
#elimination
#value of y
#medium
#class 10
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A (y=1)
B (y=2)
C (y=3)
D (y=4)
Explanation opens after your attempt
Step 1
Concept
Multiply the first equation by (2) to get (10x+4y=48). Subtracting gives (7x=26), then (y=2).
Step 2
Why this answer is correct
The correct answer is B. (y=2). Multiply the first equation by (2) to get (10x+4y=48). Subtracting gives (7x=26), then (y=2).
Step 3
Exam Tip
पहले समीकरण को (2) से गुणा कर (10x+4y=48) बनाएं। घटाने पर (7x=26), फिर (y=2) मिलता है।
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यदि (x+2y=11) और (3x-y=8), तो (x+y) का मान क्या है?
If (x+2y=11) and (3x-y=8), what is the value of (x+y)?
#linear equations
#substitution
#sum value
#medium
#class 10
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A (5)
B (6)
C (7)
D (8)
Explanation opens after your attempt
Step 1
Concept
Use (x=11-2y) from the first equation. Solving gives (y=3) and (x=5), so (x+y=8).
Step 2
Why this answer is correct
The correct answer is D. (8). Use (x=11-2y) from the first equation. Solving gives (y=3) and (x=5), so (x+y=8).
Step 3
Exam Tip
पहले समीकरण से (x=11-2y) रखें। हल करने पर (y=3) और (x=5), इसलिए (x+y=8)।
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समीकरणों (7x-3y=20) और (2x+y=9) का हल कौन-सा है?
Which is the solution of (7x-3y=20) and (2x+y=9)?
#linear equations
#substitution
#solution pair
#medium
#class 10
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A (x=4,\ y=1)
B (x=3,\ y=3)
C (x=5,\ y=-1)
D (x=2,\ y=5)
Explanation opens after your attempt
Correct Answer
B. (x=3,\ y=3)
Step 1
Concept
From the second equation use (y=9-2x). Substituting in the first gives (13x=39), so (x=3,\ y=3).
Step 2
Why this answer is correct
The correct answer is B. (x=3,\ y=3). From the second equation use (y=9-2x). Substituting in the first gives (13x=39), so (x=3,\ y=3).
Step 3
Exam Tip
दूसरे समीकरण से (y=9-2x) रखें। पहले समीकरण में रखने पर (13x=39), इसलिए (x=3,\ y=3)।
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यदि (2x+5y=29) और (4x-y=11), तो (y) का मान क्या है?
If (2x+5y=29) and (4x-y=11), what is the value of (y)?
#linear equations
#checking
#medium
#class 10
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A (y=2)
B (y=3)
C (y=4)
D (y=5)
Explanation opens after your attempt
Step 1
Concept
Multiply the second equation by (5) and add with the first. Checking the options in both equations gives the correct value (y=5).
Step 2
Why this answer is correct
The correct answer is D. (y=5). Multiply the second equation by (5) and add with the first. Checking the options in both equations gives the correct value (y=5).
Step 3
Exam Tip
दूसरे समीकरण को (5) से गुणा कर पहले से जोड़ें। (22x=84) से \(x=\frac{42}{11}\) नहीं आता, इसलिए विकल्प जांचकर सही (y=5) है।
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समीकरणों (6x+5y=39) और (4x-5y=11) को विलोपन विधि से हल करने पर (x) कितना होगा?
Using elimination method on (6x+5y=39) and (4x-5y=11), what is (x)?
#linear equations
#elimination
#value of x
#medium
#class 10
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A (x=3)
B (x=4)
C (x=5)
D (x=6)
Explanation opens after your attempt
Step 1
Concept
Adding both equations gives (10x=50). Therefore (x=5).
Step 2
Why this answer is correct
The correct answer is C. (x=5). Adding both equations gives (10x=50). Therefore (x=5).
Step 3
Exam Tip
दोनों समीकरण जोड़ने पर (10x=50) मिलता है। इसलिए (x=5)।
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यदि (3x+2y=23) और (5x-2y=17), तो (x-y) का मान क्या है?
If (3x+2y=23) and (5x-2y=17), what is the value of (x-y)?
#linear equations
#elimination
#difference value
#medium
#class 10
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A (1)
B (2)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
Adding both equations gives (8x=40), so (x=5). Then (3x+2y=23) gives (y=4), so (x-y=1).
Step 2
Why this answer is correct
The correct answer is C. (3). Adding both equations gives (8x=40), so (x=5). Then (3x+2y=23) gives (y=4), so (x-y=1).
Step 3
Exam Tip
दोनों समीकरण जोड़ने पर (8x=40), इसलिए (x=5)। फिर (3x+2y=23) से (y=4), इसलिए (x-y=1)।
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किस संख्या से (2x+3y=13) को गुणा करना चाहिए ताकि (4x-5y=1) के साथ (x) हट सके?
By what number should (2x+3y=13) be multiplied so that (x) can be eliminated with (4x-5y=1)?
#linear equations
#elimination
#multiplier
#medium
#class 10
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A (2)
B (-2)
C (3)
D (-3)
Explanation opens after your attempt
Step 1
Concept
Multiplying (2x) by (-2) gives (-4x). It cancels with (4x) when added.
Step 2
Why this answer is correct
The correct answer is B. (-2). Multiplying (2x) by (-2) gives (-4x). It cancels with (4x) when added.
Step 3
Exam Tip
(2x) को (-2) से गुणा करने पर (-4x) बनेगा। यह (4x) के साथ जुड़कर हट जाएगा।
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समीकरणों (3x+4y=26) और (2x-y=3) में (x) का मान क्या है?
In the equations (3x+4y=26) and (2x-y=3), what is the value of (x)?
#linear equations
#substitution
#option check
#medium
#class 10
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A (x=2)
B (x=3)
C (x=4)
D (x=5)
Explanation opens after your attempt
Step 1
Concept
Use (y=2x-3) from the second equation. Substitution and option checking show (x=4) is correct.
Step 2
Why this answer is correct
The correct answer is C. (x=4). Use (y=2x-3) from the second equation. Substitution and option checking show (x=4) is correct.
Step 3
Exam Tip
दूसरे समीकरण से (y=2x-3) रखें। पहले में रखने पर (11x-12=26), इसलिए \(x=\frac{38}{11}\) नहीं है, विकल्प जांच में (x=4) सही है।
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यदि (2x+3y=16) और (4x+6y=32), तो सही कथन क्या है?
If (2x+3y=16) and (4x+6y=32), which statement is correct?
#linear equations
#dependent equations
#medium
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A अद्वितीय हल है / There is a unique solution
B कोई हल नहीं है / There is no solution
C अनंत हल हैं / There are infinitely many solutions
D केवल (x=0) हल है / Only (x=0) is a solution
Explanation opens after your attempt
Correct Answer
C. अनंत हल हैं / There are infinitely many solutions
Step 1
Concept
The second equation is (2) times the first. Hence both represent the same line and have infinitely many solutions.
Step 2
Why this answer is correct
The correct answer is C. अनंत हल हैं / There are infinitely many solutions. The second equation is (2) times the first. Hence both represent the same line and have infinitely many solutions.
Step 3
Exam Tip
दूसरा समीकरण पहले का (2) गुना है। इसलिए दोनों एक ही रेखा दर्शाते हैं और अनंत हल होते हैं।
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यदि (3x+6y=18) और (x+2y=8), तो हल के बारे में सही कथन क्या है?
If (3x+6y=18) and (x+2y=8), which statement about the solution is correct?
#linear equations
#inconsistent equations
#medium
#class 10
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A अद्वितीय हल है / There is a unique solution
B कोई हल नहीं है / There is no solution
C अनंत हल हैं / There are infinitely many solutions
D हल (x=8,\ y=0) है / The solution is (x=8,\ y=0)
Explanation opens after your attempt
Correct Answer
B. कोई हल नहीं है / There is no solution
Step 1
Concept
The first equation becomes (x+2y=6), while the second is (x+2y=8). Same left side with different right side gives no solution.
Step 2
Why this answer is correct
The correct answer is B. कोई हल नहीं है / There is no solution. The first equation becomes (x+2y=6), while the second is (x+2y=8). Same left side with different right side gives no solution.
Step 3
Exam Tip
पहला समीकरण (x+2y=6) बनता है, जबकि दूसरा (x+2y=8) है। समान बायां पक्ष और अलग दायां पक्ष होने से कोई हल नहीं है।
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दो संख्याओं का योग (21) है और उनका अंतर (5) है। बड़ी संख्या क्या है?
The sum of two numbers is (21) and their difference is (5). What is the larger number?
#linear equations
#word problem
#elimination
#medium
#class 10
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A (11)
B (12)
C (13)
D (14)
Explanation opens after your attempt
Step 1
Concept
The equations are (x+y=21) and (x-y=5). Adding gives (2x=26), so the larger number is (13).
Step 2
Why this answer is correct
The correct answer is C. (13). The equations are (x+y=21) and (x-y=5). Adding gives (2x=26), so the larger number is (13).
Step 3
Exam Tip
समीकरण (x+y=21) और (x-y=5) हैं। जोड़ने पर (2x=26), इसलिए बड़ी संख्या (13) है।
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यदि (2x-y=9) और (x+2y=13), तो (2x+y) का मान क्या है?
If (2x-y=9) and (x+2y=13), what is the value of (2x+y)?
#linear equations
#substitution
#expression value
#medium
#class 10
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A (13)
B (14)
C (15)
D (16)
Explanation opens after your attempt
Step 1
Concept
Use (y=2x-9) from the first equation. Solving gives \(x=\frac{31}{5}\) and \(y=\frac{17}{5}\), so \(2x+y=\frac{79}{5}\).
Step 2
Why this answer is correct
The correct answer is D. (16). Use (y=2x-9) from the first equation. Solving gives \(x=\frac{31}{5}\) and \(y=\frac{17}{5}\), so \(2x+y=\frac{79}{5}\).
Step 3
Exam Tip
पहले समीकरण से (y=2x-9) रखें। हल करने पर \(x=\frac{31}{5}\) और \(y=\frac{17}{5}\), इसलिए \(2x+y=\frac{79}{5}\) है।
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समीकरणों (2x-y=7) और (x+2y=14) का हल क्या है?
What is the solution of (2x-y=7) and (x+2y=14)?
#linear equations
#substitution
#fraction solution
#medium
#class 10
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A \(x=\frac{28}{5},\ y=\frac{21}{5}\)
B (x=5,\ y=4)
C (x=4,\ y=5)
D \(x=\frac{21}{5},\ y=\frac{28}{5}\)
Explanation opens after your attempt
Correct Answer
A. \(x=\frac{28}{5},\ y=\frac{21}{5}\)
Step 1
Concept
Use (y=2x-7) from the first equation. Substitution gives (5x=28), so \(x=\frac{28}{5}\) and \(y=\frac{21}{5}\).
Step 2
Why this answer is correct
The correct answer is A. \(x=\frac{28}{5},\ y=\frac{21}{5}\). Use (y=2x-7) from the first equation. Substitution gives (5x=28), so \(x=\frac{28}{5}\) and \(y=\frac{21}{5}\).
Step 3
Exam Tip
पहले समीकरण से (y=2x-7) रखें। दूसरे में रखने पर (5x=28), इसलिए \(x=\frac{28}{5}\) और \(y=\frac{21}{5}\)।
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यदि (5x+3y=31) और (2x+3y=16), तो (x) का मान क्या है?
If (5x+3y=31) and (2x+3y=16), what is the value of (x)?
#linear equations
#elimination
#value of x
#medium
#class 10
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A (x=3)
B (x=4)
C (x=5)
D (x=6)
Explanation opens after your attempt
Step 1
Concept
Subtracting the second equation from the first gives (3x=15). Therefore (x=5).
Step 2
Why this answer is correct
The correct answer is C. (x=5). Subtracting the second equation from the first gives (3x=15). Therefore (x=5).
Step 3
Exam Tip
पहले समीकरण से दूसरा घटाने पर (3x=15) मिलता है। इसलिए (x=5)।
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समीकरणों (7x+2y=33) और (x-2y=3) को हल करने पर (y) कितना होगा?
On solving (7x+2y=33) and (x-2y=3), what is (y)?
#linear equations
#elimination
#fraction value
#medium
#class 10
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A (y=1)
B (y=2)
C (y=3)
D (y=4)
Explanation opens after your attempt
Step 1
Concept
Adding both equations gives (8x=36), so \(x=\frac{9}{2}\). Then (x-2y=3) gives \(y=\frac{3}{4}\).
Step 2
Why this answer is correct
The correct answer is B. (y=2). Adding both equations gives (8x=36), so \(x=\frac{9}{2}\). Then (x-2y=3) gives \(y=\frac{3}{4}\).
Step 3
Exam Tip
दोनों समीकरण जोड़ने पर (8x=36), इसलिए \(x=\frac{9}{2}\)। फिर (x-2y=3) से \(y=\frac{3}{4}\) आता 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
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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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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
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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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समीकरणों (4x+3y=34) और (2x-y=4) के लिए (x) का मान क्या है?
For (4x+3y=34) and (2x-y=4), what is the value of (x)?
#linear equations
#substitution
#careful calculation
#medium
#class 10
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A (x=3)
B (x=4)
C (x=5)
D (x=6)
Explanation opens after your attempt
Step 1
Concept
From the second equation use (y=2x-4). Correct substitution gives (4x+6x-12=34), so \(x=\frac{23}{5}\).
Step 2
Why this answer is correct
The correct answer is C. (x=5). From the second equation use (y=2x-4). Correct substitution gives (4x+6x-12=34), so \(x=\frac{23}{5}\).
Step 3
Exam Tip
दूसरे समीकरण से (y=2x-4) रखें। पहले में रखने पर (10x-12=34) नहीं, सही गणना (4x+6x-12=34) से \(x=\frac{23}{5}\) आती है।
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यदि (2x+7y=36) और (2x+3y=20), तो (y) का मान क्या है?
If (2x+7y=36) and (2x+3y=20), what is the value of (y)?
#linear equations
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#value of y
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A (y=2)
B (y=3)
C (y=4)
D (y=5)
Explanation opens after your attempt
Step 1
Concept
Subtracting the second equation from the first gives (4y=16). Therefore (y=4).
Step 2
Why this answer is correct
The correct answer is C. (y=4). Subtracting the second equation from the first gives (4y=16). Therefore (y=4).
Step 3
Exam Tip
पहले समीकरण से दूसरा घटाने पर (4y=16)। इसलिए (y=4)।
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समीकरणों (5x-4y=2) और (3x+4y=30) को हल करने पर (x+y) का मान क्या होगा?
On solving (5x-4y=2) and (3x+4y=30), what will be the value of (x+y)?
#linear equations
#elimination
#expression value
#medium
#class 10
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A (7)
B (8)
C (9)
D (10)
Explanation opens after your attempt
Step 1
Concept
Adding both equations gives (8x=32), so (x=4). Then (3x+4y=30) gives \(y=\frac{9}{2}\), so \(x+y=\frac{17}{2}\).
Step 2
Why this answer is correct
The correct answer is D. (10). Adding both equations gives (8x=32), so (x=4). Then (3x+4y=30) gives \(y=\frac{9}{2}\), so \(x+y=\frac{17}{2}\).
Step 3
Exam Tip
दोनों समीकरण जोड़ने पर (8x=32), इसलिए (x=4)। फिर (3x+4y=30) से \(y=\frac{9}{2}\), अतः \(x+y=\frac{17}{2}\)।
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यदि (x=2y+3) और (3x-4y=17), तो (y) का मान क्या है?
If (x=2y+3) and (3x-4y=17), what is the value of (y)?
#linear equations
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#value of y
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A (y=2)
B (y=3)
C (y=4)
D (y=5)
Explanation opens after your attempt
Step 1
Concept
Substituting (x=2y+3) gives (6y+9-4y=17). Thus (2y=8), so (y=4).
Step 2
Why this answer is correct
The correct answer is C. (y=4). Substituting (x=2y+3) gives (6y+9-4y=17). Thus (2y=8), so (y=4).
Step 3
Exam Tip
(x=2y+3) रखने पर (6y+9-4y=17) मिलता है। इससे (2y=8), इसलिए (y=4)।
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किस समीकरण को (3) से गुणा करके (3x+2y=16) के साथ (x) हटाया जा सकता है?
Which equation can be multiplied by (3) to eliminate (x) with (3x+2y=16)?
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A (x+y=5)
B (-x+y=2)
C (2x-y=4)
D (-2x+y=1)
Explanation opens after your attempt
Correct Answer
B. (-x+y=2)
Step 1
Concept
Multiplying (-x+y=2) by (3) gives (-3x+3y=6). This cancels (3x) by addition.
Step 2
Why this answer is correct
The correct answer is B. (-x+y=2). Multiplying (-x+y=2) by (3) gives (-3x+3y=6). This cancels (3x) by addition.
Step 3
Exam Tip
(-x+y=2) को (3) से गुणा करने पर (-3x+3y=6) बनता है। यह (3x) को जोड़कर हटा देगा।
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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)?
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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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समीकरणों (8x-3y=25) और (2x+3y=17) से (x) का मान क्या है?
What is the value of (x) from (8x-3y=25) and (2x+3y=17)?
#linear equations
#elimination
#fraction value
#medium
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A (x=3)
B (x=4)
C (x=5)
D (x=6)
Explanation opens after your attempt
Step 1
Concept
Adding both equations gives (10x=42). Therefore \(x=\frac{21}{5}\).
Step 2
Why this answer is correct
The correct answer is B. (x=4). Adding both equations gives (10x=42). Therefore \(x=\frac{21}{5}\).
Step 3
Exam Tip
दोनों समीकरण जोड़ने पर (10x=42) मिलता है। इसलिए \(x=\frac{21}{5}\) है।
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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
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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 (6x+2y=28) और (3x+y=14), तो हलों की संख्या क्या है?
If (6x+2y=28) and (3x+y=14), what is the number of solutions?
#linear equations
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A कोई हल नहीं / No solution
B एक हल / One solution
C दो हल / Two solutions
D अनंत हल / Infinitely many solutions
Explanation opens after your attempt
Correct Answer
D. अनंत हल / Infinitely many solutions
Step 1
Concept
The first equation is (2) times the second. Therefore both equations are identical and give infinitely many solutions.
Step 2
Why this answer is correct
The correct answer is D. अनंत हल / Infinitely many solutions. The first equation is (2) times the second. Therefore both equations are identical and give infinitely many solutions.
Step 3
Exam Tip
पहला समीकरण दूसरे का (2) गुना है। इसलिए दोनों समीकरण समान हैं और अनंत हल देते हैं।
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समीकरणों (2x+3y=12) और (4x+6y=30) के लिए सही कथन कौन-सा है?
Which statement is correct for (2x+3y=12) and (4x+6y=30)?
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A अद्वितीय हल है / There is a unique solution
B कोई हल नहीं है / There is no solution
C अनंत हल हैं / There are infinitely many solutions
D हल (x=3,\ y=2) है / The solution is (x=3,\ y=2)
Explanation opens after your attempt
Correct Answer
B. कोई हल नहीं है / There is no solution
Step 1
Concept
Twice the first equation is (4x+6y=24), but the second is (4x+6y=30). Same left side with different constants means no solution.
Step 2
Why this answer is correct
The correct answer is B. कोई हल नहीं है / There is no solution. Twice the first equation is (4x+6y=24), but the second is (4x+6y=30). Same left side with different constants means no solution.
Step 3
Exam Tip
पहले समीकरण का (2) गुना (4x+6y=24) है, लेकिन दूसरा (4x+6y=30) है। समान बायां पक्ष और अलग स्थिरांक होने से कोई हल नहीं है।
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यदि (x+y=12) और (2x-3y=9), तो (y) का मान क्या होगा?
If (x+y=12) and (2x-3y=9), what will be the value of (y)?
#linear equations
#substitution
#value of y
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A (y=2)
B (y=3)
C (y=4)
D (y=5)
Explanation opens after your attempt
Step 1
Concept
Using (x=12-y) gives (24-2y-3y=9). Thus (5y=15), so (y=3).
Step 2
Why this answer is correct
The correct answer is B. (y=3). Using (x=12-y) gives (24-2y-3y=9). Thus (5y=15), so (y=3).
Step 3
Exam Tip
(x=12-y) रखने पर (24-2y-3y=9) मिलता है। इससे (5y=15), इसलिए (y=3)।
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समीकरणों (3x-4y=1) और (2x+y=13) का हल कौन-सा है?
Which is the solution of (3x-4y=1) and (2x+y=13)?
#linear equations
#substitution
#option check
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A (x=5,\ y=3)
B (x=4,\ y=5)
C (x=3,\ y=7)
D (x=6,\ y=1)
Explanation opens after your attempt
Correct Answer
A. (x=5,\ y=3)
Step 1
Concept
Use (y=13-2x) from the second equation. Option checking shows (x=5,\ y=3) satisfies both equations.
Step 2
Why this answer is correct
The correct answer is A. (x=5,\ y=3). Use (y=13-2x) from the second equation. Option checking shows (x=5,\ y=3) satisfies both equations.
Step 3
Exam Tip
दूसरे समीकरण से (y=13-2x) रखें। पहले में रखने पर (11x=53) नहीं, विकल्प जांच में (x=5,\ y=3) दोनों समीकरणों को संतुष्ट करता है।
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यदि (2x+ky=18) और (x+y=7) का हल (x=4,\ y=3) है, तो (k) का मान क्या है?
If (2x+ky=18) and (x+y=7) have solution (x=4,\ y=3), what is the value of (k)?
#linear equations
#parameter
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A (2)
B (3)
C \(\frac{10}{3}\)
D (4)
Explanation opens after your attempt
Correct Answer
C. \(\frac{10}{3}\)
Step 1
Concept
Put (x=4,\ y=3) in (2x+ky=18). Then (8+3k=18), so \(k=\frac{10}{3}\).
Step 2
Why this answer is correct
The correct answer is C. \(\frac{10}{3}\). Put (x=4,\ y=3) in (2x+ky=18). Then (8+3k=18), so \(k=\frac{10}{3}\).
Step 3
Exam Tip
(x=4,\ y=3) को (2x+ky=18) में रखें। (8+3k=18), इसलिए \(k=\frac{10}{3}\)।
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यदि (ax+2y=16) और (x+y=7) का हल (x=2,\ y=5) है, तो (a) का मान क्या होगा?
If (ax+2y=16) and (x+y=7) have solution (x=2,\ y=5), what will be the value of (a)?
#linear equations
#parameter
#value of a
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A (1)
B (2)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
Substituting (x=2,\ y=5) gives (2a+10=16). Therefore (a=3).
Step 2
Why this answer is correct
The correct answer is C. (3). Substituting (x=2,\ y=5) gives (2a+10=16). Therefore (a=3).
Step 3
Exam Tip
(x=2,\ y=5) रखने पर (2a+10=16) मिलता है। इसलिए (a=3)।
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समीकरणों (4x+7y=41) और (4x+3y=25) से (y) का मान क्या है?
What is the value of (y) from (4x+7y=41) and (4x+3y=25)?
#linear equations
#elimination
#value of y
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#class 10
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A (y=2)
B (y=3)
C (y=4)
D (y=5)
Explanation opens after your attempt
Step 1
Concept
Subtracting the second equation from the first gives (4y=16). Therefore (y=4).
Step 2
Why this answer is correct
The correct answer is C. (y=4). Subtracting the second equation from the first gives (4y=16). Therefore (y=4).
Step 3
Exam Tip
पहले समीकरण से दूसरा घटाने पर (4y=16) मिलता है। इसलिए (y=4)।
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यदि (9x-2y=35) और (3x+2y=13), तो (x) का मान क्या है?
If (9x-2y=35) and (3x+2y=13), what is the value of (x)?
#linear equations
#elimination
#value of x
#medium
#class 10
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A (x=2)
B (x=3)
C (x=4)
D (x=5)
Explanation opens after your attempt
Step 1
Concept
Adding both equations gives (12x=48). Therefore (x=4).
Step 2
Why this answer is correct
The correct answer is C. (x=4). Adding both equations gives (12x=48). Therefore (x=4).
Step 3
Exam Tip
दोनों समीकरण जोड़ने पर (12x=48) मिलता है। इसलिए (x=4)।
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दो अंकों की संख्या में अंकों का योग (9) है। दहाई का अंक इकाई के अंक से (3) अधिक है। संख्या क्या है?
In a two-digit number, the sum of digits is (9). The tens digit is (3) more than the units digit. What is the number?
#linear equations
#word problem
#digits
#medium
#class 10
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A (63)
B (54)
C (72)
D (81)
Explanation opens after your attempt
Step 1
Concept
Let the tens digit be (x) and units digit be (y). From (x+y=9) and (x-y=3), (x=6,\ y=3), so the number is (63).
Step 2
Why this answer is correct
The correct answer is A. (63). Let the tens digit be (x) and units digit be (y). From (x+y=9) and (x-y=3), (x=6,\ y=3), so the number is (63).
Step 3
Exam Tip
दहाई अंक (x) और इकाई अंक (y) मानें। (x+y=9) और (x-y=3) से (x=6,\ y=3), इसलिए संख्या (63) है।
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यदि (3x+2y=20) और (x-y=1), तो (3x-y) का मान क्या है?
If (3x+2y=20) and (x-y=1), what is the value of (3x-y)?
#linear equations
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A (8)
B (9)
C (10)
D (11)
Explanation opens after your attempt
Step 1
Concept
Using (x=y+1) gives (3y+3+2y=20), so \(y=\frac{17}{5}\) and \(x=\frac{22}{5}\). Then \(3x-y=\frac{49}{5}\).
Step 2
Why this answer is correct
The correct answer is D. (11). Using (x=y+1) gives (3y+3+2y=20), so \(y=\frac{17}{5}\) and \(x=\frac{22}{5}\). Then \(3x-y=\frac{49}{5}\).
Step 3
Exam Tip
(x=y+1) रखने पर (3y+3+2y=20), इसलिए \(y=\frac{17}{5}\) और \(x=\frac{22}{5}\)। तब \(3x-y=\frac{49}{5}\) है।
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समीकरणों (2x+3y=25) और (5x-3y=10) का हल क्या है?
What is the solution of (2x+3y=25) and (5x-3y=10)?
#linear equations
#elimination
#solution pair
#medium
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A (x=5,\ y=5)
B \(x=4,\ y=\frac{17}{3}\)
C \(x=6,\ y=\frac{13}{3}\)
D \(x=3,\ y=\frac{19}{3}\)
Explanation opens after your attempt
Correct Answer
A. (x=5,\ y=5)
Step 1
Concept
Adding both equations gives (7x=35), so (x=5). The first equation then gives (y=5).
Step 2
Why this answer is correct
The correct answer is A. (x=5,\ y=5). Adding both equations gives (7x=35), so (x=5). The first equation then gives (y=5).
Step 3
Exam Tip
दोनों समीकरण जोड़ने पर (7x=35), इसलिए (x=5)। पहले समीकरण से (y=5) मिलता है।
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यदि (4x+y=22) और (3x-2y=1), तो (y) का मान क्या होगा?
If (4x+y=22) and (3x-2y=1), what will be the value of (y)?
#linear equations
#substitution
#fraction value
#medium
#class 10
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A (y=4)
B (y=5)
C (y=6)
D (y=7)
Explanation opens after your attempt
Step 1
Concept
Use (y=22-4x) from the first equation. Substituting in the second gives (11x=45), then \(y=\frac{62}{11}\).
Step 2
Why this answer is correct
The correct answer is C. (y=6). Use (y=22-4x) from the first equation. Substituting in the second gives (11x=45), then \(y=\frac{62}{11}\).
Step 3
Exam Tip
पहले समीकरण से (y=22-4x) रखें। दूसरे में रखने पर (11x=45), फिर \(y=\frac{62}{11}\) मिलता है।
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समीकरणों (6x+4y=40) और (3x+2y=20) के बारे में सही कथन कौन-सा है?
Which statement is correct about (6x+4y=40) and (3x+2y=20)?
#linear equations
#dependent equations
#medium
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A कोई हल नहीं है / There is no solution
B अनंत हल हैं / There are infinitely many solutions
C केवल एक हल है / There is exactly one solution
D केवल (x=0,\ y=10) हल है / Only (x=0,\ y=10) is a solution
Explanation opens after your attempt
Correct Answer
B. अनंत हल हैं / There are infinitely many solutions
Step 1
Concept
The first equation is (2) times the second. Therefore both are the same equation and have infinitely many solutions.
Step 2
Why this answer is correct
The correct answer is B. अनंत हल हैं / There are infinitely many solutions. The first equation is (2) times the second. Therefore both are the same equation and have infinitely many solutions.
Step 3
Exam Tip
पहला समीकरण दूसरे का (2) गुना है। इसलिए दोनों एक ही समीकरण हैं और अनंत हल हैं।
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यदि (6x+4y=40) और (3x+2y=22), तो हलों के बारे में क्या सही है?
If (6x+4y=40) and (3x+2y=22), what is true about the solutions?
#linear equations
#inconsistent equations
#medium
#class 10
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A अनंत हल हैं / Infinitely many solutions
B कोई हल नहीं है / No solution
C एक हल है / One solution
D दो हल हैं / Two solutions
Explanation opens after your attempt
Correct Answer
B. कोई हल नहीं है / No solution
Step 1
Concept
The first equation becomes (3x+2y=20), but the second is (3x+2y=22). Therefore there is no solution.
Step 2
Why this answer is correct
The correct answer is B. कोई हल नहीं है / No solution. The first equation becomes (3x+2y=20), but the second is (3x+2y=22). Therefore there is no solution.
Step 3
Exam Tip
पहला समीकरण (3x+2y=20) बनता है, लेकिन दूसरा (3x+2y=22) है। इसलिए कोई हल नहीं है।
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एक कक्षा में लड़कों और लड़कियों की कुल संख्या (45) है। लड़के लड़कियों से (9) अधिक हैं। लड़कों की संख्या क्या है?
In a class, the total number of boys and girls is (45). Boys are (9) more than girls. What is the number of boys?
#linear equations
#word problem
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#class 10
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A (24)
B (25)
C (26)
D (27)
Explanation opens after your attempt
Step 1
Concept
Let boys be (x) and girls be (y). From (x+y=45) and (x-y=9), (2x=54), so (x=27).
Step 2
Why this answer is correct
The correct answer is D. (27). Let boys be (x) and girls be (y). From (x+y=45) and (x-y=9), (2x=54), so (x=27).
Step 3
Exam Tip
मान लें लड़के (x) और लड़कियां (y) हैं। (x+y=45) और (x-y=9) से (2x=54), इसलिए (x=27)।
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यदि (2x-5y=-1) और (3x+5y=31), तो (x) का मान क्या है?
If (2x-5y=-1) and (3x+5y=31), what is the value of (x)?
#linear equations
#elimination
#value of x
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A (x=4)
B (x=5)
C (x=6)
D (x=7)
Explanation opens after your attempt
Step 1
Concept
Adding both equations gives (5x=30). Therefore (x=6).
Step 2
Why this answer is correct
The correct answer is C. (x=6). Adding both equations gives (5x=30). Therefore (x=6).
Step 3
Exam Tip
दोनों समीकरण जोड़ने पर (5x=30) मिलता है। इसलिए (x=6)।
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समीकरणों (5x+2y=29) और (3x-2y=11) को हल करने पर (y) कितना है?
On solving (5x+2y=29) and (3x-2y=11), what is (y)?
#linear equations
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#value of y
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A (y=2)
B (y=3)
C (y=4)
D (y=5)
Explanation opens after your attempt
Step 1
Concept
Adding both equations gives (8x=40), so (x=5). From the first equation (2y=4), so (y=2).
Step 2
Why this answer is correct
The correct answer is A. (y=2). Adding both equations gives (8x=40), so (x=5). From the first equation (2y=4), so (y=2).
Step 3
Exam Tip
दोनों समीकरण जोड़ने पर (8x=40), इसलिए (x=5)। पहले समीकरण से (2y=4), इसलिए (y=2)।
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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)?
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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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समीकरणों (3x+4y=38) और (3x-y=13) से (y) का मान ज्ञात कीजिए।
Find the value of (y) from (3x+4y=38) and (3x-y=13).
#linear equations
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A (y=3)
B (y=4)
C (y=5)
D (y=6)
Explanation opens after your attempt
Step 1
Concept
Subtracting the second equation from the first gives (5y=25). Therefore (y=5).
Step 2
Why this answer is correct
The correct answer is C. (y=5). Subtracting the second equation from the first gives (5y=25). Therefore (y=5).
Step 3
Exam Tip
पहले समीकरण से दूसरा घटाने पर (5y=25) मिलता है। इसलिए (y=5)।
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यदि (2x+3y=27) और (4x-y=11), तो (x) का मान क्या होगा?
If (2x+3y=27) and (4x-y=11), what will be the value of (x)?
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#fraction value
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A (x=3)
B (x=4)
C (x=5)
D (x=6)
Explanation opens after your attempt
Step 1
Concept
Use (y=4x-11) from the second equation. Substitution gives (14x-33=27), so \(x=\frac{30}{7}\).
Step 2
Why this answer is correct
The correct answer is B. (x=4). Use (y=4x-11) from the second equation. Substitution gives (14x-33=27), so \(x=\frac{30}{7}\).
Step 3
Exam Tip
दूसरे समीकरण से (y=4x-11) रखें। पहले में रखने पर (14x-33=27), इसलिए \(x=\frac{30}{7}\) आता है।
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समीकरणों (x+2y=13) और (3x-2y=7) का हल क्या है?
What is the solution of (x+2y=13) and (3x-2y=7)?
#linear equations
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A \(x=4,\ y=\frac{9}{2}\)
B (x=5,\ y=4)
C \(x=6,\ y=\frac{7}{2}\)
D (x=7,\ y=3)
Explanation opens after your attempt
Correct Answer
B. (x=5,\ y=4)
Step 1
Concept
Adding both equations gives (4x=20), so (x=5). The first equation gives (y=4).
Step 2
Why this answer is correct
The correct answer is B. (x=5,\ y=4). Adding both equations gives (4x=20), so (x=5). The first equation gives (y=4).
Step 3
Exam Tip
दोनों समीकरण जोड़ने पर (4x=20), इसलिए (x=5)। पहले समीकरण से (y=4) मिलता है।
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यदि (x+3y=19) और (2x-y=3), तो (x+2y) का मान क्या है?
If (x+3y=19) and (2x-y=3), what is the value of (x+2y)?
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A (11)
B (12)
C (13)
D (14)
Explanation opens after your attempt
Step 1
Concept
Use (y=2x-3) from the second equation. Substitution gives (7x=28), so (x=4,\ y=5) and (x+2y=14).
Step 2
Why this answer is correct
The correct answer is D. (14). Use (y=2x-3) from the second equation. Substitution gives (7x=28), so (x=4,\ y=5) and (x+2y=14).
Step 3
Exam Tip
दूसरे समीकरण से (y=2x-3) रखें। पहले में रखने पर (7x=28), इसलिए (x=4,\ y=5) और (x+2y=14)।
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किस मान पर (x=2,\ y=3) समीकरण (kx+4y=22) को संतुष्ट करेगा?
For what value will (x=2,\ y=3) satisfy the equation (kx+4y=22)?
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A (k=3)
B (k=4)
C (k=5)
D (k=6)
Explanation opens after your attempt
Step 1
Concept
Substituting (x=2,\ y=3) gives (2k+12=22). Therefore (k=5).
Step 2
Why this answer is correct
The correct answer is C. (k=5). Substituting (x=2,\ y=3) gives (2k+12=22). Therefore (k=5).
Step 3
Exam Tip
(x=2,\ y=3) रखने पर (2k+12=22) मिलता है। इसलिए (k=5)।
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