100 results found for "root-substitution" in Class 10.
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 (4x-y=11) और (2x+3y=29), तो प्रतिस्थापन विधि से (y) का मान क्या होगा?
If (4x-y=11) and (2x+3y=29), what is the value of (y) by substitution?
#pair-linear-equations-substitution-expert
A (3)
B (4)
C (5)
D (6)
Explanation opens after your attempt
Step 1
Concept
From the first equation, (y=4x-11). Substitution must be checked in both equations before selecting an option.
Step 2
Why this answer is correct
The correct answer is C. (5). From the first equation, (y=4x-11). Substitution must be checked in both equations before selecting an option.
Step 3
Exam Tip
पहले समीकरण से (y=4x-11)। इसे दूसरे में रखने पर (14x=62) नहीं बल्कि (14x=62), इसलिए \(x=\frac{31}{7}\) नहीं; सरल विकल्पों से बचने के लिए पुनः जांच करें।
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दो संख्याओं का योग (23) है और उनका अंतर (7) है। प्रतिस्थापन विधि से बड़ी संख्या क्या होगी?
The sum of two numbers is (23) and their difference is (7). By substitution, what is the greater number?
#word-problem
#numbers
#substitution
A (14)
B (15)
C (16)
D (17)
Explanation opens after your attempt
Step 1
Concept
Let the numbers be (x,y), so (x+y=23) and (x-y=7). Adding gives (2x=30), so the greater number is (15).
Step 2
Why this answer is correct
The correct answer is B. (15). Let the numbers be (x,y), so (x+y=23) and (x-y=7). Adding gives (2x=30), so the greater number is (15).
Step 3
Exam Tip
यदि संख्याएं (x,y) हों तो (x+y=23) और (x-y=7)। जोड़ने पर (2x=30), इसलिए बड़ी संख्या (15) है।
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यदि (3x-2y=4) और (x+y=11), तो प्रतिस्थापन विधि से (y) का मान क्या होगा?
If (3x-2y=4) and (x+y=11), what is the value of (y) by substitution?
#pair-linear-equations
#substitution
#expert
A (4)
B (5)
C (6)
D (7)
Explanation opens after your attempt
Step 1
Concept
Substitute (x=11-y) carefully in the first equation; incorrect simplification changes the answer. Always check the obtained values in both equations.
Step 2
Why this answer is correct
The correct answer is D. (7). Substitute (x=11-y) carefully in the first equation; incorrect simplification changes the answer. Always check the obtained values in both equations.
Step 3
Exam Tip
दूसरे समीकरण से (x=11-y) रखकर (33-5y=4) नहीं बल्कि (33-3y-2y=4) मिलता है, इसलिए \(y=\frac{29}{5}\) नहीं होगा; सही जांच जरूरी है।
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यदि (2x-3y=-7) और (4x+y=19), तो प्रतिस्थापन विधि से (y) का मान क्या है?
If (2x-3y=-7) and (4x+y=19), what is the value of (y) by substitution?
#pair-linear-equations
#substitution
#expert
A (y=3)
B (y=4)
C (y=5)
D (y=2)
Explanation opens after your attempt
Step 1
Concept
From the second equation, put (y=19-4x), giving (x=4) and (y=3). In exams, isolate the easier variable first.
Step 2
Why this answer is correct
The correct answer is A. (y=3). From the second equation, put (y=19-4x), giving (x=4) and (y=3). In exams, isolate the easier variable first.
Step 3
Exam Tip
दूसरे समीकरण से (y=19-4x) रखकर हल करने पर (x=4) और (y=3) मिलता है। परीक्षा में पहले सरल चर को अलग करें।
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प्रतिस्थापन विधि से (y=2x+1) और (x+y=10) को हल करें।
Solve (y=2x+1) and (x+y=10) by substitution.
#linear equations
#substitution
#direct expression
#medium
#class 10
A ( (2,8) )
B ( (4,6) )
C ( (3,7) )
D ( (5,5) )
Explanation opens after your attempt
Correct Answer
C. ( (3,7) )
Step 1
Concept
Putting (y=2x+1) gives (3x+1=10), so (x=3) and (y=7). If (y=) form is given, substitute directly.
Step 2
Why this answer is correct
The correct answer is C. ( (3,7) ). Putting (y=2x+1) gives (3x+1=10), so (x=3) and (y=7). If (y=) form is given, substitute directly.
Step 3
Exam Tip
(y=2x+1) रखने पर (3x+1=10), इसलिए (x=3) और (y=7)। दिए गए रूप (y=) में हो तो सीधे रखें।
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प्रतिस्थापन विधि से (2x+y=11) और (x-y=1) को हल करें।
Solve (2x+y=11) and (x-y=1) by substitution.
#linear equations
#substitution
#medium
#class 10
A ( (3,5) )
B ( (4,3) )
C ( (5,1) )
D ( (2,7) )
Explanation opens after your attempt
Correct Answer
B. ( (4,3) )
Step 1
Concept
From (x-y=1), (y=x-1), so (2x+x-1=11) and the solution is ( (4,3) ). In exams, isolate the easier variable first.
Step 2
Why this answer is correct
The correct answer is B. ( (4,3) ). From (x-y=1), (y=x-1), so (2x+x-1=11) and the solution is ( (4,3) ). In exams, isolate the easier variable first.
Step 3
Exam Tip
(x-y=1) से (y=x-1), इसलिए (2x+x-1=11) और हल ( (4,3) ) है। परीक्षा में पहले आसान चर अलग करें।
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प्रतिस्थापन विधि से (x+y=17) और (y=x+3) का हल ज्ञात करें।
Find the solution of (x+y=17) and (y=x+3) by substitution.
#linear equations
#substitution
#one variable equation
#easy
#class 10
A ( (6,11) )
B ( (8,9) )
C ( (7,10) )
D ( (5,12) )
Explanation opens after your attempt
Correct Answer
C. ( (7,10) )
Step 1
Concept
Putting (y=x+3) gives (2x+3=17), so (x=7) and (y=10). Solve the one-variable equation formed after substitution.
Step 2
Why this answer is correct
The correct answer is C. ( (7,10) ). Putting (y=x+3) gives (2x+3=17), so (x=7) and (y=10). Solve the one-variable equation formed after substitution.
Step 3
Exam Tip
(y=x+3) रखने पर (2x+3=17), इसलिए (x=7) और (y=10)। प्रतिस्थापन के बाद बने एक चर के समीकरण को हल करें।
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प्रतिस्थापन विधि से (2x+y=16) और (x-y=2) को हल करें।
Solve (2x+y=16) and (x-y=2) by substitution.
#linear equations
#substitution
#two equations
#easy
#class 10
A ( (5,6) )
B ( (6,4) )
C ( (4,8) )
D ( (7,2) )
Explanation opens after your attempt
Correct Answer
B. ( (6,4) )
Step 1
Concept
From (x-y=2), (y=x-2), so (2x+x-2=16) and (x=6). Then (y=4).
Step 2
Why this answer is correct
The correct answer is B. ( (6,4) ). From (x-y=2), (y=x-2), so (2x+x-2=16) and (x=6). Then (y=4).
Step 3
Exam Tip
(x-y=2) से (y=x-2), इसलिए (2x+x-2=16) और (x=6)। फिर (y=4) मिलेगा।
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प्रतिस्थापन विधि से (3x+y=10) में (x=2) रखने पर (y) क्या होगा?
Using substitution in (3x+y=10), if (x=2), what is (y)?
#linear equations
#substitution
#simple calculation
#easy
#class 10
A (y=4)
B (y=3)
C (y=2)
D (y=5)
Explanation opens after your attempt
Step 1
Concept
(3(2)+y=10), so (6+y=10) and (y=4). Multiply first and then subtract.
Step 2
Why this answer is correct
The correct answer is A. (y=4). (3(2)+y=10), so (6+y=10) and (y=4). Multiply first and then subtract.
Step 3
Exam Tip
(3(2)+y=10), इसलिए (6+y=10) और (y=4)। गुणा पहले और घटाव बाद में करें।
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प्रतिस्थापन विधि से हल करें: (x+y=7) और (x-y=1)। ((x,y)) क्या है?
Solve by substitution: (x+y=7) and (x-y=1). What is ((x,y))?
#linear equations
#substitution
#elimination
#easy
#class 10
A ( (4,3) )
B ( (3,4) )
C ( (5,2) )
D ( (2,5) )
Explanation opens after your attempt
Correct Answer
A. ( (4,3) )
Step 1
Concept
Adding both equations gives (2x=8), so (x=4) and (y=3). In exams, first eliminate the easy variable.
Step 2
Why this answer is correct
The correct answer is A. ( (4,3) ). Adding both equations gives (2x=8), so (x=4) and (y=3). In exams, first eliminate the easy variable.
Step 3
Exam Tip
दोनों समीकरण जोड़ने पर (2x=8), इसलिए (x=4) और (y=3)। परीक्षा में पहले जोड़कर आसान चर निकालें।
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किस समीकरण में (x=0) एक मूल है और दूसरा मूल ऋणात्मक है?
In which equation is (x=0) one root and the other root negative?
#quadratic-equations
#zero-root
#root-sign
#hard
A \(x^2+7x=0\)
B \(x^2-7x=0\)
C \(x^2+7=0\)
D \(x^2-7=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+7x=0\)
Step 1
Concept
(x-2 +7x=x(x+7)), so the roots are (0) and (-7). The other root is negative.
Step 2
Why this answer is correct
The correct answer is A. \(x^2+7x=0\). (x-2 +7x=x(x+7)), so the roots are (0) and (-7). The other root is negative.
Step 3
Exam Tip
(x-2 +7x=x(x+7)), इसलिए मूल (0) और (-7) हैं। दूसरा मूल ऋणात्मक है।
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किस समीकरण में (x=0) एक मूल है और दूसरा मूल धनात्मक है?
In which equation is (x=0) one root and the other root positive?
#quadratic-equations
#zero-root
#root-sign
#hard
A \(x^2-6x=0\)
B \(x^2+6x=0\)
C \(x^2+6=0\)
D \(x^2-6=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-6x=0\)
Step 1
Concept
(x-2 -6x=x(x-6)), so the roots are (0) and (6). The other root is positive.
Step 2
Why this answer is correct
The correct answer is A. \(x^2-6x=0\). (x-2 -6x=x(x-6)), so the roots are (0) and (6). The other root is positive.
Step 3
Exam Tip
(x-2 -6x=x(x-6)), इसलिए मूल (0) और (6) हैं। दूसरा मूल धनात्मक है।
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समीकरण (y=x+1) और (x+y=7) को हल करें।
Solve the equations (y=x+1) and (x+y=7).
#linear equations
#substitution
#expression substitution
#easy
#class 10
A ( (3,4) )
B ( (4,3) )
C ( (2,5) )
D ( (5,2) )
Explanation opens after your attempt
Correct Answer
A. ( (3,4) )
Step 1
Concept
Substituting (y=x+1) gives (x+x+1=7), so (x=3) and (y=4). Put the given expression into the other equation first.
Step 2
Why this answer is correct
The correct answer is A. ( (3,4) ). Substituting (y=x+1) gives (x+x+1=7), so (x=3) and (y=4). Put the given expression into the other equation first.
Step 3
Exam Tip
(y=x+1) को रखने पर (x+x+1=7), इसलिए (x=3) और (y=4)। पहले दिए गए चर को दूसरे समीकरण में रखें।
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यदि (4x-2 -(4h+1)x+h=0) की एक जड़ \(\frac{1}{4}\) है, तो दूसरी जड़ क्या है?
If one root of (4x-2 -(4h+1)x+h=0) is \(\frac{1}{4}\), what is the other root?
#quadratic-roots
#other-root
#parameter
A (h)
B \(\frac{h}{4}\)
C (4h)
D (h+1)
Explanation opens after your attempt
Step 1
Concept
The product of roots is \(\frac{h}{4}\). Since one root is \(\frac{1}{4}\), the other root is (h).
Step 2
Why this answer is correct
The correct answer is A. (h). The product of roots is \(\frac{h}{4}\). Since one root is \(\frac{1}{4}\), the other root is (h).
Step 3
Exam Tip
जड़ों का गुणनफल \(\frac{h}{4}\) है। एक जड़ \(\frac{1}{4}\) है, इसलिए दूसरी जड़ (h) होगी।
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यदि (x-2 -(m+9)x+9m=0) की एक जड़ (9) है, तो दूसरी जड़ क्या है?
If one root of (x-2 -(m+9)x+9m=0) is (9), what is the other root?
#quadratic-roots
#other-root
#parameter
A (m)
B (9m)
C (m+9)
D \(\frac{m}{9}\)
Explanation opens after your attempt
Step 1
Concept
The product of roots is (9m). Since one root is (9), the other root is \(\frac{9m}{9}=m\).
Step 2
Why this answer is correct
The correct answer is A. (m). The product of roots is (9m). Since one root is (9), the other root is \(\frac{9m}{9}=m\).
Step 3
Exam Tip
जड़ों का गुणनफल (9m) है। एक जड़ (9) है, इसलिए दूसरी जड़ \(\frac{9m}{9}=m\) होगी।
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यदि (2x-2 -(3p+2)x+p(p+2)=0) की एक जड़ (p) है, तो दूसरी जड़ क्या होगी?
If one root of (2x-2 -(3p+2)x+p(p+2)=0) is (p), what will be the other root?
#quadratic-roots
#other-root
#parametric-equation
A \(\frac{p+2}{2}\)
B (p+2)
C \(\frac{p}{2}\)
D (2p+2)
Explanation opens after your attempt
Correct Answer
A. \(\frac{p+2}{2}\)
Step 1
Concept
The product of roots is (\frac{p(p+2)}{2}). If one root is (p), the other root is \(\frac{p+2}{2}\).
Step 2
Why this answer is correct
The correct answer is A. \(\frac{p+2}{2}\). The product of roots is (\frac{p(p+2)}{2}). If one root is (p), the other root is \(\frac{p+2}{2}\).
Step 3
Exam Tip
जड़ों का गुणनफल (\frac{p(p+2)}{2}) है। एक जड़ (p) होने पर दूसरी जड़ \(\frac{p+2}{2}\) होगी।
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यदि (3x-2 -(3h+1)x+h=0) की एक जड़ \(\frac{1}{3}\) है, तो दूसरी जड़ क्या है?
If one root of (3x-2 -(3h+1)x+h=0) is \(\frac{1}{3}\), what is the other root?
#quadratic-roots
#other-root
#parameter
A (h)
B \(\frac{h}{3}\)
C (3h)
D (h+1)
Explanation opens after your attempt
Step 1
Concept
The product of roots is \(\frac{h}{3}\). Since one root is \(\frac{1}{3}\), the other root is (h).
Step 2
Why this answer is correct
The correct answer is A. (h). The product of roots is \(\frac{h}{3}\). Since one root is \(\frac{1}{3}\), the other root is (h).
Step 3
Exam Tip
जड़ों का गुणनफल \(\frac{h}{3}\) है। एक जड़ \(\frac{1}{3}\) है, इसलिए दूसरी जड़ (h) होगी।
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यदि (2x-2 -(h+1)x+h=0) की जड़ों में से एक हमेशा \(\frac{1}{2}\) है, तो दूसरी जड़ क्या होगी?
If one root of (2x-2 -(h+1)x+h=0) is always \(\frac{1}{2}\), what is the other root?
#quadratic-roots
#other-root
#parameter
A (h)
B \(\frac{h}{2}\)
C (2h)
D (h+1)
Explanation opens after your attempt
Step 1
Concept
The product is \(\frac{h}{2}\). Since one root is \(\frac{1}{2}\), the other root is \(\frac{h}{2}\div\frac{1}{2}=h\).
Step 2
Why this answer is correct
The correct answer is A. (h). The product is \(\frac{h}{2}\). Since one root is \(\frac{1}{2}\), the other root is \(\frac{h}{2}\div\frac{1}{2}=h\).
Step 3
Exam Tip
गुणनफल \(\frac{h}{2}\) है। एक जड़ \(\frac{1}{2}\) है, इसलिए दूसरी जड़ \(\frac{h}{2}\div\frac{1}{2}=h\) होगी।
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यदि (x-2 -(m+2)x+3m=0) की एक जड़ (3) है, तो दूसरी जड़ क्या है?
If one root of (x-2 -(m+2)x+3m=0) is (3), what is the other root?
#quadratic-roots
#other-root
#parametric-equation
A (m)
B (3m)
C (m+2)
D \(\frac{m}{3}\)
Explanation opens after your attempt
Step 1
Concept
Putting (x=3) makes the equation true for every (m). The product is (3m) and one root is (3), so the other root is (m).
Step 2
Why this answer is correct
The correct answer is A. (m). Putting (x=3) makes the equation true for every (m). The product is (3m) and one root is (3), so the other root is (m).
Step 3
Exam Tip
(x=3) रखने पर समीकरण हर (m) के लिए सही हो जाता है। गुणनफल (3m) है और एक जड़ (3), इसलिए दूसरी जड़ (m) है।
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यदि (x-2 -(m-2 )x+m-6 =0) की एक जड़ (3) है, तो दूसरी जड़ क्या होगी?
If one root of (x-2 -(m-2 )x+m-6 =0) is (3), what is the other root?
#quadratic-roots
#other-root
#error-check
A (1)
B (2)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
Putting (x=3) gives (9-3(m-2 )+m-6 =0), so \(m=\frac{9}{2}\). The product is \(-\frac{3}{2}\), so the other root is \(-\frac{1}{2}\); hence no option is correct.
Step 2
Why this answer is correct
The correct answer is A. (1). Putting (x=3) gives (9-3(m-2 )+m-6 =0), so \(m=\frac{9}{2}\). The product is \(-\frac{3}{2}\), so the other root is \(-\frac{1}{2}\); hence no option is correct.
Step 3
Exam Tip
(x=3) रखने पर (9-3(m-2 )+m-6 =0), इसलिए \(m=\frac{9}{2}\)। गुणनफल \(m-6=-\frac{3}{2}\) है, अतः दूसरी जड़ \(-\frac{1}{2}\) होगी, इसलिए कोई विकल्प सही नहीं है।
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यदि (x-2 -(m+7)x+7m=0) का एक मूल (7) है, तो दूसरा मूल क्या है?
If one root of (x-2 -(m+7)x+7m=0) is (7), what is the other root?
#quadratic-equations
#one-root
#roots
#expert
A (m)
B (7m)
C (m+7)
D (m-7 )
Explanation opens after your attempt
Step 1
Concept
The product of roots is (7m) and one root is (7). Hence the other root is \(\frac{7m}{7}=m\).
Step 2
Why this answer is correct
The correct answer is A. (m). The product of roots is (7m) and one root is (7). Hence the other root is \(\frac{7m}{7}=m\).
Step 3
Exam Tip
मूलों का गुणनफल (7m) है और एक मूल (7) है। इसलिए दूसरा मूल \(\frac{7m}{7}=m\) है।
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यदि \(x^2+ax+54=0\) का एक मूल (6) है, तो दूसरा मूल और (a) कौन-से हैं?
If one root of \(x^2+ax+54=0\) is (6), what are the other root and (a)?
#quadratic-equations
#one-root
#parameter
#expert
A दूसरा मूल (9), (a=-15) / other root (9), (a=-15)
B दूसरा मूल (-9), (a=3) / other root (-9), (a=3)
C दूसरा मूल (9), (a=15) / other root (9), (a=15)
D दूसरा मूल (-6), (a=0) / other root (-6), (a=0)
Explanation opens after your attempt
Correct Answer
A. दूसरा मूल (9), (a=-15) / other root (9), (a=-15)
Step 1
Concept
The product of roots is (54), so the other root is (9). The sum is (15), and (-a=15), so (a=-15).
Step 2
Why this answer is correct
The correct answer is A. दूसरा मूल (9), (a=-15) / other root (9), (a=-15). The product of roots is (54), so the other root is (9). The sum is (15), and (-a=15), so (a=-15).
Step 3
Exam Tip
मूलों का गुणनफल (54) है, इसलिए दूसरा मूल (9) होगा। योग (15) है और (-a=15), इसलिए (a=-15)।
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यदि (x-2 -(m+6)x+6m=0) का एक मूल (6) है, तो दूसरा मूल क्या है?
If one root of (x-2 -(m+6)x+6m=0) is (6), what is the other root?
#quadratic-equations
#one-root
#roots
#expert
A (m)
B (6m)
C (m+6)
D (m-6 )
Explanation opens after your attempt
Step 1
Concept
The product of roots is (6m) and one root is (6). Hence the other root is \(\frac{6m}{6}=m\).
Step 2
Why this answer is correct
The correct answer is A. (m). The product of roots is (6m) and one root is (6). Hence the other root is \(\frac{6m}{6}=m\).
Step 3
Exam Tip
मूलों का गुणनफल (6m) है और एक मूल (6) है। इसलिए दूसरा मूल \(\frac{6m}{6}=m\) है।
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यदि \(x^2+ax+40=0\) का एक मूल (5) है, तो दूसरा मूल और (a) कौन-से हैं?
If one root of \(x^2+ax+40=0\) is (5), what are the other root and (a)?
#quadratic-equations
#one-root
#parameter
#expert
A दूसरा मूल (8), (a=-13) / other root (8), (a=-13)
B दूसरा मूल (-8), (a=3) / other root (-8), (a=3)
C दूसरा मूल (8), (a=13) / other root (8), (a=13)
D दूसरा मूल (-5), (a=0) / other root (-5), (a=0)
Explanation opens after your attempt
Correct Answer
A. दूसरा मूल (8), (a=-13) / other root (8), (a=-13)
Step 1
Concept
The product of roots is (40), so the other root is (8). The sum is (13), and (-a=13), so (a=-13).
Step 2
Why this answer is correct
The correct answer is A. दूसरा मूल (8), (a=-13) / other root (8), (a=-13). The product of roots is (40), so the other root is (8). The sum is (13), and (-a=13), so (a=-13).
Step 3
Exam Tip
मूलों का गुणनफल (40) है, इसलिए दूसरा मूल (8) होगा। योग (13) है और (-a=13), इसलिए (a=-13)।
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यदि (x-2 -(m+5)x+5m=0) का एक मूल (5) है, तो दूसरा मूल क्या है?
If one root of (x-2 -(m+5)x+5m=0) is (5), what is the other root?
#quadratic-equations
#one-root
#roots
#expert
A (m)
B (5m)
C (m+5)
D (m-5 )
Explanation opens after your attempt
Step 1
Concept
The product of roots is (5m) and one root is (5). Hence the other root is \(\frac{5m}{5}=m\).
Step 2
Why this answer is correct
The correct answer is A. (m). The product of roots is (5m) and one root is (5). Hence the other root is \(\frac{5m}{5}=m\).
Step 3
Exam Tip
मूलों का गुणनफल (5m) है और एक मूल (5) है। इसलिए दूसरा मूल \(\frac{5m}{5}=m\) है।
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यदि \(x^2+ax+24=0\) का एक मूल (4) है, तो दूसरा मूल और (a) कौन-से हैं?
If one root of \(x^2+ax+24=0\) is (4), what are the other root and (a)?
#quadratic-equations
#one-root
#parameter
#expert
A दूसरा मूल (6), (a=-10) / other root (6), (a=-10)
B दूसरा मूल (-6), (a=2) / other root (-6), (a=2)
C दूसरा मूल (6), (a=10) / other root (6), (a=10)
D दूसरा मूल (-4), (a=0) / other root (-4), (a=0)
Explanation opens after your attempt
Correct Answer
A. दूसरा मूल (6), (a=-10) / other root (6), (a=-10)
Step 1
Concept
The product of roots is (24), so the other root is (6). The sum is (10), and (-a=10), so (a=-10).
Step 2
Why this answer is correct
The correct answer is A. दूसरा मूल (6), (a=-10) / other root (6), (a=-10). The product of roots is (24), so the other root is (6). The sum is (10), and (-a=10), so (a=-10).
Step 3
Exam Tip
मूलों का गुणनफल (24) है, इसलिए दूसरा मूल (6) होगा। योग (10) है और (-a=10), इसलिए (a=-10)।
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यदि (x-2 -(m+4)x+4m=0) का एक मूल (4) है, तो दूसरा मूल क्या है?
If one root of (x-2 -(m+4)x+4m=0) is (4), what is the other root?
#quadratic-equations
#one-root
#roots
#hard
A (m)
B (4m)
C (m+4)
D (m-4 )
Explanation opens after your attempt
Step 1
Concept
The product of roots is (4m) and one root is (4). Hence the other root is \(\frac{4m}{4}=m\).
Step 2
Why this answer is correct
The correct answer is A. (m). The product of roots is (4m) and one root is (4). Hence the other root is \(\frac{4m}{4}=m\).
Step 3
Exam Tip
गुणनफल (4m) है और एक मूल (4) है। इसलिए दूसरा मूल \(\frac{4m}{4}=m\) है।
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यदि \(x^2+ax+18=0\) का एक मूल (2) है, तो दूसरा मूल और (a) कौन-से हैं?
If one root of \(x^2+ax+18=0\) is (2), what are the other root and (a)?
#quadratic-equations
#one-root
#parameter
#hard
A दूसरा मूल (9), (a=-11) / other root (9), (a=-11)
B दूसरा मूल (-9), (a=7) / other root (-9), (a=7)
C दूसरा मूल (9), (a=11) / other root (9), (a=11)
D दूसरा मूल (-2), (a=0) / other root (-2), (a=0)
Explanation opens after your attempt
Correct Answer
A. दूसरा मूल (9), (a=-11) / other root (9), (a=-11)
Step 1
Concept
The product of roots is (18), so the other root is (9). The sum is (11), and (-a=11), so (a=-11).
Step 2
Why this answer is correct
The correct answer is A. दूसरा मूल (9), (a=-11) / other root (9), (a=-11). The product of roots is (18), so the other root is (9). The sum is (11), and (-a=11), so (a=-11).
Step 3
Exam Tip
मूलों का गुणनफल (18) है, इसलिए दूसरा मूल (9) होगा। योग (11) है और (-a=11), इसलिए (a=-11)।
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यदि (x-2 -(m+2)x+2m=0) का एक मूल (2) है, तो दूसरा मूल क्या है?
If one root of (x-2 -(m+2)x+2m=0) is (2), what is the other root?
#quadratic-equations
#one-root
#roots
#hard
A (m)
B (2m)
C (m+2)
D (m-2 )
Explanation opens after your attempt
Step 1
Concept
The product of roots is (2m) and one root is (2). Hence the other root is \(\frac{2m}{2}=m\).
Step 2
Why this answer is correct
The correct answer is A. (m). The product of roots is (2m) and one root is (2). Hence the other root is \(\frac{2m}{2}=m\).
Step 3
Exam Tip
गुणनफल (2m) है और एक मूल (2) है। इसलिए दूसरा मूल \(\frac{2m}{2}=m\) है।
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यदि \(x^2+ax+12=0\) का एक मूल (3) है, तो दूसरा मूल और (a) कौन-से हैं?
If one root of \(x^2+ax+12=0\) is (3), what are the other root and (a)?
#quadratic-equations
#one-root
#parameter
#hard
A दूसरा मूल (4), (a=-7) / other root (4), (a=-7)
B दूसरा मूल (-4), (a=1) / other root (-4), (a=1)
C दूसरा मूल (4), (a=7) / other root (4), (a=7)
D दूसरा मूल (-3), (a=0) / other root (-3), (a=0)
Explanation opens after your attempt
Correct Answer
A. दूसरा मूल (4), (a=-7) / other root (4), (a=-7)
Step 1
Concept
The product of roots is (12), so the other root is (4). The sum is (7), and (-a=7), so (a=-7).
Step 2
Why this answer is correct
The correct answer is A. दूसरा मूल (4), (a=-7) / other root (4), (a=-7). The product of roots is (12), so the other root is (4). The sum is (7), and (-a=7), so (a=-7).
Step 3
Exam Tip
मूलों का गुणनफल (12) है, इसलिए दूसरा मूल (4) होगा। योग (7) है और (-a=7), इसलिए (a=-7)।
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यदि (x-2 +(6k-3)x+5k=0) में (x=-1) मूल है, तो (k) का मान क्या है?
If (x=-1) is a root of (x-2 +(6k-3)x+5k=0), what is the value of (k)?
#quadratic-equations
#root-substitution
#parameter
#expert
A (2)
B (1)
C (0)
D (-2)
Explanation opens after your attempt
Step 1
Concept
Putting (x=-1) gives (1-(6k-3)+5k=0). Thus (4-k=0), so (k=4).
Step 2
Why this answer is correct
The correct answer is A. (2). Putting (x=-1) gives (1-(6k-3)+5k=0). Thus (4-k=0), so (k=4).
Step 3
Exam Tip
(x=-1) रखने पर (1-(6k-3)+5k=0) मिलता है। इससे (4-k=0), इसलिए (k=4) होगा।
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यदि (x=-6) समीकरण \(2x^2+px-18=0\) का मूल है, तो (p) का मान क्या होगा?
If (x=-6) is a root of \(2x^2+px-18=0\), what is the value of (p)?
#quadratic-equations
#root-substitution
#parameter
#expert
A (9)
B (6)
C (-9)
D (-6)
Explanation opens after your attempt
Step 1
Concept
Putting (x=-6) gives (72-6p-18=0). Hence (p=9).
Step 2
Why this answer is correct
The correct answer is A. (9). Putting (x=-6) gives (72-6p-18=0). Hence (p=9).
Step 3
Exam Tip
(x=-6) रखने पर (72-6p-18=0) मिलता है। इससे (p=9) है।
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यदि (x-2 +(5k-2)x+4k=0) में (x=-2) मूल है, तो (k) का मान क्या है?
If (x=-2) is a root of (x-2 +(5k-2)x+4k=0), what is the value of (k)?
#quadratic-equations
#root-substitution
#parameter
#expert
A (0)
B \(\frac{2}{3}\)
C \(-\frac{2}{3}\)
D (1)
Explanation opens after your attempt
Step 1
Concept
Putting (x=-2) gives (4-2(5k-2)+4k=0). Thus (8-6k=0), so \(k=\frac{4}{3}\).
Step 2
Why this answer is correct
The correct answer is A. (0). Putting (x=-2) gives (4-2(5k-2)+4k=0). Thus (8-6k=0), so \(k=\frac{4}{3}\).
Step 3
Exam Tip
(x=-2) रखने पर (4-2(5k-2)+4k=0) मिलता है। इससे (8-6k=0), इसलिए \(k=\frac{4}{3}\)।
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यदि (x=-5) समीकरण \(3x^2+px-20=0\) का मूल है, तो (p) का मान क्या होगा?
If (x=-5) is a root of \(3x^2+px-20=0\), what is the value of (p)?
#quadratic-equations
#root-substitution
#parameter
#expert
A (11)
B (-11)
C (5)
D (-5)
Explanation opens after your attempt
Step 1
Concept
Putting (x=-5) gives (75-5p-20=0). Hence (p=11).
Step 2
Why this answer is correct
The correct answer is A. (11). Putting (x=-5) gives (75-5p-20=0). Hence (p=11).
Step 3
Exam Tip
(x=-5) रखने पर (75-5p-20=0) मिलता है। इससे (p=11) है।
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यदि (x-2 +(4k-1)x+3k=0) में (x=-1) मूल है, तो (k) का मान क्या है?
If (x=-1) is a root of (x-2 +(4k-1)x+3k=0), what is the value of (k)?
#quadratic-equations
#root-substitution
#parameter
#expert
A (0)
B (1)
C (-1)
D \(\frac{1}{3}\)
Explanation opens after your attempt
Step 1
Concept
Putting (x=-1) gives (1-(4k-1)+3k=0). Thus (2-k=0), so (k=2).
Step 2
Why this answer is correct
The correct answer is A. (0). Putting (x=-1) gives (1-(4k-1)+3k=0). Thus (2-k=0), so (k=2).
Step 3
Exam Tip
(x=-1) रखने पर (1-(4k-1)+3k=0) मिलता है। इससे (2-k=0) नहीं बल्कि (k=2) मिलता है।
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यदि (x=-3) समीकरण \(4x^2+px-9=0\) का मूल है, तो (p) का मान क्या होगा?
If (x=-3) is a root of \(4x^2+px-9=0\), what is the value of (p)?
#quadratic-equations
#root-substitution
#parameter
#expert
A (9)
B (7)
C (3)
D (-9)
Explanation opens after your attempt
Step 1
Concept
Putting (x=-3) gives (36-3p-9=0). Hence (p=9).
Step 2
Why this answer is correct
The correct answer is A. (9). Putting (x=-3) gives (36-3p-9=0). Hence (p=9).
Step 3
Exam Tip
(x=-3) रखने पर (36-3p-9=0) मिलता है। इससे (p=9) है।
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यदि (x-2 +(3k+1)x+2k=0) में (x=-2) मूल है, तो (k) का मान क्या है?
If (x=-2) is a root of (x-2 +(3k+1)x+2k=0), what is the value of (k)?
#quadratic-equations
#root-substitution
#parameter
#hard
A \( \frac{1}{2} \)
B \( -\frac{1}{2} \)
C (1)
D (0)
Explanation opens after your attempt
Correct Answer
A. \( \frac{1}{2} \)
Step 1
Concept
Putting (x=-2) gives (4-2(3k+1)+2k=0). Thus (2-4k=0), so \(k=\frac{1}{2}\).
Step 2
Why this answer is correct
The correct answer is A. \( \frac{1}{2} \). Putting (x=-2) gives (4-2(3k+1)+2k=0). Thus (2-4k=0), so \(k=\frac{1}{2}\).
Step 3
Exam Tip
(x=-2) रखने पर (4-2(3k+1)+2k=0) मिलता है। इससे (2-4k=0), इसलिए \(k=\frac{1}{2}\)।
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यदि (x=-4) समीकरण \(2x^2+px-12=0\) का मूल है, तो (p) का मान क्या होगा?
If (x=-4) is a root of \(2x^2+px-12=0\), what is the value of (p)?
#quadratic-equations
#root-substitution
#parameter
#hard
A (5)
B (-5)
C (11)
D (-11)
Explanation opens after your attempt
Step 1
Concept
Putting (x=-4) gives (32-4p-12=0). Hence (p=5).
Step 2
Why this answer is correct
The correct answer is A. (5). Putting (x=-4) gives (32-4p-12=0). Hence (p=5).
Step 3
Exam Tip
(x=-4) रखने पर (32-4p-12=0) मिलता है। इससे (p=5) है।
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यदि (x-2 +(2k-1)x+k=0) में (x=1) मूल है, तो (k) का मान क्या है?
If (x=1) is a root of (x-2 +(2k-1)x+k=0), what is the value of (k)?
#quadratic-equations
#root-substitution
#parameter
#hard
A (0)
B \(-\frac{1}{3}\)
C \(\frac{1}{3}\)
D (1)
Explanation opens after your attempt
Step 1
Concept
Putting (x=1) gives (1+2k-1+k=0). Thus (3k=0), so (k=0).
Step 2
Why this answer is correct
The correct answer is A. (0). Putting (x=1) gives (1+2k-1+k=0). Thus (3k=0), so (k=0).
Step 3
Exam Tip
(x=1) रखने पर (1+2k-1+k=0) मिलता है। इससे (3k=0), इसलिए (k=0)।
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यदि (x=-2) समीकरण \(3x^2+px+10=0\) का मूल है, तो (p) का मान क्या होगा?
If (x=-2) is a root of \(3x^2+px+10=0\), what is the value of (p)?
#quadratic-equations
#root-substitution
#parameter
#hard
A (11)
B (-11)
C (1)
D (-1)
Explanation opens after your attempt
Step 1
Concept
Putting (x=-2) gives (12-2p+10=0). Hence (p=11).
Step 2
Why this answer is correct
The correct answer is A. (11). Putting (x=-2) gives (12-2p+10=0). Hence (p=11).
Step 3
Exam Tip
(x=-2) रखने पर (12-2p+10=0) मिलता है। इससे (p=11) है।
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यदि (x=4) समीकरण \(x^2+sx-32=0\) का मूल है, तो (s) का मान क्या होगा?
If (x=4) is a root of \(x^2+sx-32=0\), what is the value of (s)?
#quadratic-equations
#parameter
#root-substitution
#medium
A (4)
B (-4)
C (12)
D (-12)
Explanation opens after your attempt
Step 1
Concept
Putting (x=4) gives (16+4s-32=0), so (s=4). When a root is given, substitute directly.
Step 2
Why this answer is correct
The correct answer is A. (4). Putting (x=4) gives (16+4s-32=0), so (s=4). When a root is given, substitute directly.
Step 3
Exam Tip
(x=4) रखने पर (16+4s-32=0) मिलता है, इसलिए (s=4) है। मूल दिया हो तो सीधा प्रतिस्थापन करें।
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क्या (x=5) समीकरण \(x^2-6x+5=0\) का मूल है?
Is (x=5) a root of \(x^2-6x+5=0\)?
#quadratic-equations
#root-check
#substitution
#medium
A हाँ / Yes
B नहीं / No
C केवल (x=1) मूल है / Only (x=1) is a root
D निर्धारित नहीं किया जा सकता / Cannot be determined
Explanation opens after your attempt
Correct Answer
A. हाँ / Yes
Step 1
Concept
Putting (x=5) gives (25-30+5=0). Substitution is the simple way to check a root.
Step 2
Why this answer is correct
The correct answer is A. हाँ / Yes. Putting (x=5) gives (25-30+5=0). Substitution is the simple way to check a root.
Step 3
Exam Tip
(x=5) रखने पर (25-30+5=0) मिलता है। मूल जांचने का सरल तरीका प्रतिस्थापन है।
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यदि (x=-4) समीकरण \(x^2+tx-8=0\) का मूल है, तो (t) का मान क्या होगा?
If (x=-4) is a root of \(x^2+tx-8=0\), what is the value of (t)?
#quadratic-equations
#parameter
#root-substitution
#medium
A (2)
B (-2)
C (6)
D (-6)
Explanation opens after your attempt
Step 1
Concept
Putting (x=-4) gives (16-4t-8=0), so (t=2). When a root is given, substitute it directly.
Step 2
Why this answer is correct
The correct answer is A. (2). Putting (x=-4) gives (16-4t-8=0), so (t=2). When a root is given, substitute it directly.
Step 3
Exam Tip
(x=-4) रखने पर (16-4t-8=0) मिलता है, इसलिए (t=2) है। मूल दिया हो तो सीधे प्रतिस्थापन करें।
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क्या (x=-1) समीकरण \(x^2+5x+4=0\) का मूल है?
Is (x=-1) a root of \(x^2+5x+4=0\)?
#quadratic-equations
#root-check
#substitution
#medium
A हाँ / Yes
B नहीं / No
C केवल (x=4) मूल है / Only (x=4) is a root
D निर्धारित नहीं किया जा सकता / Cannot be determined
Explanation opens after your attempt
Correct Answer
A. हाँ / Yes
Step 1
Concept
Putting (x=-1) gives (1-5+4=0). To check a root, substitute the given value directly.
Step 2
Why this answer is correct
The correct answer is A. हाँ / Yes. Putting (x=-1) gives (1-5+4=0). To check a root, substitute the given value directly.
Step 3
Exam Tip
(x=-1) रखने पर (1-5+4=0) मिलता है। मूल की जांच के लिए दिए मान को सीधे रखें।
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क्या (x=3) समीकरण \(x^2-4x+3=0\) का मूल है?
Is (x=3) a root of \(x^2-4x+3=0\)?
#quadratic-equations
#root-check
#substitution
#medium
A हाँ / Yes
B नहीं / No
C केवल (x=1) मूल है / Only (x=1) is a root
D निर्धारित नहीं हो सकता / Cannot be determined
Explanation opens after your attempt
Correct Answer
A. हाँ / Yes
Step 1
Concept
Putting (x=3) gives (9-12+3=0). To check a root, substitute the given value directly.
Step 2
Why this answer is correct
The correct answer is A. हाँ / Yes. Putting (x=3) gives (9-12+3=0). To check a root, substitute the given value directly.
Step 3
Exam Tip
(x=3) रखने पर (9-12+3=0) मिलता है। मूल जांचने के लिए दिए मान को सीधे समीकरण में रखें।
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यदि (x=2) समीकरण \(x^2+kx+2=0\) का मूल है तो (k) का मान क्या होगा?
If (x=2) is a root of \(x^2+kx+2=0\), what is the value of (k)?
#quadratic-equations
#parameter
#root-substitution
A (3)
B (-3)
C (2)
D (-2)
Explanation opens after your attempt
Step 1
Concept
Putting (x=2) gives (4+2k+2=0), so (k=-3). If a root is given, substitute it in the equation.
Step 2
Why this answer is correct
The correct answer is B. (-3). Putting (x=2) gives (4+2k+2=0), so (k=-3). If a root is given, substitute it in the equation.
Step 3
Exam Tip
(x=2) रखने पर (4+2k+2=0) इसलिए (k=-3) मिलता है। मूल दिया हो तो उसे समीकरण में रखें।
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आयात प्रतिस्थापन नीति का संतुलित विशेषज्ञ मूल्यांकन क्या होगा?
What is a balanced expert evaluation of import substitution policy?
#import-substitution
#expert-evaluation
#industry
A यह आत्मनिर्भर उद्योग बढ़ा सकती थी लेकिन संरक्षणवाद से दक्षता समस्या आ सकती थी / It could grow self reliant industry but protectionism could create efficiency problems
B यह केवल सैन्य गठबंधन था / It was only a military alliance
C यह घरेलू उद्योग से असंबंधित थी / It was unrelated to domestic industry
D यह हर देश में बिना सीमा सफल हुई / It succeeded everywhere without limits
Explanation opens after your attempt
Correct Answer
A. यह आत्मनिर्भर उद्योग बढ़ा सकती थी लेकिन संरक्षणवाद से दक्षता समस्या आ सकती थी / It could grow self reliant industry but protectionism could create efficiency problems
Step 1
Concept
Understand both aims and limits of import substitution. For exams write benefits and criticism together.
Step 2
Why this answer is correct
The correct answer is A. यह आत्मनिर्भर उद्योग बढ़ा सकती थी लेकिन संरक्षणवाद से दक्षता समस्या आ सकती थी / It could grow self reliant industry but protectionism could create efficiency problems. Understand both aims and limits of import substitution. For exams write benefits and criticism together.
Step 3
Exam Tip
आयात प्रतिस्थापन के उद्देश्य और सीमाएं दोनों समझें। परीक्षा में लाभ और आलोचना साथ लिखें।
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आयात प्रतिस्थापन और निर्यातोन्मुख विकास की तुलना में मुख्य नीति अंतर क्या है?
What is the main policy difference between import substitution and export oriented development?
#import-substitution
#export-oriented-development
#economic-policy
A आयात प्रतिस्थापन घरेलू बाजार सुरक्षा पर और निर्यातोन्मुख विकास वैश्विक बाजार प्रतिस्पर्धा पर जोर देता है / Import substitution stresses domestic market protection while export oriented development stresses global market competition
B दोनों केवल सैन्य नीति हैं / Both are only military policies
C दोनों का उद्योग से कोई संबंध नहीं / Both have no relation with industry
D दोनों केवल भाषा नीति हैं / Both are only language policies
Explanation opens after your attempt
Correct Answer
A. आयात प्रतिस्थापन घरेलू बाजार सुरक्षा पर और निर्यातोन्मुख विकास वैश्विक बाजार प्रतिस्पर्धा पर जोर देता है / Import substitution stresses domestic market protection while export oriented development stresses global market competition
Step 1
Concept
Both development strategies show different economic paths. For exams understand benefits and limits of both.
Step 2
Why this answer is correct
The correct answer is A. आयात प्रतिस्थापन घरेलू बाजार सुरक्षा पर और निर्यातोन्मुख विकास वैश्विक बाजार प्रतिस्पर्धा पर जोर देता है / Import substitution stresses domestic market protection while export oriented development stresses global market competition. Both development strategies show different economic paths. For exams understand benefits and limits of both.
Step 3
Exam Tip
दोनों विकास रणनीतियां अलग आर्थिक रास्ते दिखाती हैं। परीक्षा में लाभ और सीमा दोनों समझें।
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आयात प्रतिस्थापन नीति की विशेषज्ञ स्तर की आलोचना किस बात पर केंद्रित होगी?
What would an expert level criticism of import substitution focus on?
#import-substitution
#criticism
#economic-policy
A संरक्षण से घरेलू उद्योग बचता है पर दक्षता और प्रतिस्पर्धा की समस्या आ सकती है / Protection saves domestic industry but can create efficiency and competition problems
B यह कभी किसी देश ने अपनाई नहीं / No country ever adopted it
C यह घरेलू उद्योग से असंबंधित है / It is unrelated to domestic industry
D यह हमेशा तुरंत पूर्ण सफलता देती है / It always gives immediate complete success
Explanation opens after your attempt
Correct Answer
A. संरक्षण से घरेलू उद्योग बचता है पर दक्षता और प्रतिस्पर्धा की समस्या आ सकती है / Protection saves domestic industry but can create efficiency and competition problems
Step 1
Concept
It is necessary to understand both benefits and limits of import substitution. For exams make a balanced evaluation.
Step 2
Why this answer is correct
The correct answer is A. संरक्षण से घरेलू उद्योग बचता है पर दक्षता और प्रतिस्पर्धा की समस्या आ सकती है / Protection saves domestic industry but can create efficiency and competition problems. It is necessary to understand both benefits and limits of import substitution. For exams make a balanced evaluation.
Step 3
Exam Tip
आयात प्रतिस्थापन के लाभ और सीमाएं दोनों समझना जरूरी है। परीक्षा में संतुलित मूल्यांकन करें।
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आयात प्रतिस्थापन नीति की सीमा समझना क्यों जरूरी है?
Why is it necessary to understand the limitation of import substitution policy?
#import-substitution
#limitations
#self-reliance
A क्योंकि संरक्षण से दक्षता और प्रतिस्पर्धा की समस्या पैदा हो सकती थी / Because protection could create problems of efficiency and competition
B क्योंकि यह कभी अपनाई ही नहीं गई / Because it was never adopted
C क्योंकि इसका उद्योग से कोई संबंध नहीं था / Because it had no relation with industry
D क्योंकि यह हमेशा तुरंत पूर्ण सफलता देती थी / Because it always gave immediate complete success
Explanation opens after your attempt
Correct Answer
A. क्योंकि संरक्षण से दक्षता और प्रतिस्पर्धा की समस्या पैदा हो सकती थी / Because protection could create problems of efficiency and competition
Step 1
Concept
Import substitution aimed at self reliance but also had limits. For exams write both benefits and criticism.
Step 2
Why this answer is correct
The correct answer is A. क्योंकि संरक्षण से दक्षता और प्रतिस्पर्धा की समस्या पैदा हो सकती थी / Because protection could create problems of efficiency and competition. Import substitution aimed at self reliance but also had limits. For exams write both benefits and criticism.
Step 3
Exam Tip
आयात प्रतिस्थापन आत्मनिर्भरता के लिए था लेकिन उसकी सीमाएं भी थीं। परीक्षा में लाभ और आलोचना दोनों लिखें।
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आयात प्रतिस्थापन नीति की आलोचना किस आधार पर की जा सकती है?
On what basis can import substitution policy be criticized?
#import-substitution
#criticism
#economic-policy
A संरक्षण से दक्षता और वैश्विक प्रतिस्पर्धा की समस्या आ सकती थी / Protection could create problems of efficiency and global competition
B यह घरेलू उद्योग से असंबंधित थी / It was unrelated to domestic industry
C यह विदेशी निर्भरता बढ़ाने के लिए ही थी / It was only for increasing foreign dependence
D यह कभी किसी देश ने अपनाई ही नहीं / No country ever adopted it
Explanation opens after your attempt
Correct Answer
A. संरक्षण से दक्षता और वैश्विक प्रतिस्पर्धा की समस्या आ सकती थी / Protection could create problems of efficiency and global competition
Step 1
Concept
Import substitution aimed at self reliance but also had limits. For exams write both benefits and criticism.
Step 2
Why this answer is correct
The correct answer is A. संरक्षण से दक्षता और वैश्विक प्रतिस्पर्धा की समस्या आ सकती थी / Protection could create problems of efficiency and global competition. Import substitution aimed at self reliance but also had limits. For exams write both benefits and criticism.
Step 3
Exam Tip
आयात प्रतिस्थापन आत्मनिर्भरता के लिए था पर उसकी सीमाएं भी थीं। परीक्षा में लाभ और आलोचना दोनों लिखें।
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आयात प्रतिस्थापन नीति औपनिवेशिक अनुभव की किस सीख पर आधारित थी?
Import substitution policy was based on which lesson of colonial experience?
#import-substitution
#self-reliance
#industry
A विदेशी उद्योगों पर निर्भरता आर्थिक कमजोरी पैदा कर सकती है / Dependence on foreign industries can create economic weakness
B घरेलू उद्योग हमेशा अनावश्यक होते हैं / Domestic industries are always unnecessary
C विदेशी माल पर निर्भरता पूर्ण स्वतंत्रता देती है / Dependence on foreign goods gives complete freedom
D व्यापार और विकास असंबंधित हैं / Trade and development are unrelated
Explanation opens after your attempt
Correct Answer
A. विदेशी उद्योगों पर निर्भरता आर्थिक कमजोरी पैदा कर सकती है / Dependence on foreign industries can create economic weakness
Step 1
Concept
Import substitution was a policy of domestic industry and self reliance. For exams write both benefits and limits.
Step 2
Why this answer is correct
The correct answer is A. विदेशी उद्योगों पर निर्भरता आर्थिक कमजोरी पैदा कर सकती है / Dependence on foreign industries can create economic weakness. Import substitution was a policy of domestic industry and self reliance. For exams write both benefits and limits.
Step 3
Exam Tip
आयात प्रतिस्थापन घरेलू उद्योग और आत्मनिर्भरता की नीति थी। परीक्षा में इसके लाभ और सीमा दोनों लिखें।
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आयात प्रतिस्थापन नीति के पीछे औपनिवेशिक अनुभव का कौन सा सबक था?
Which lesson from colonial experience was behind import substitution policy?
#import-substitution
#self-reliance
#colonial-experience
A विदेशी उद्योगों पर निर्भरता आर्थिक कमजोरी पैदा कर सकती है / Dependence on foreign industries can create economic weakness
B विदेशी वस्तुओं पर निर्भरता हमेशा लाभकारी होती है / Dependence on foreign goods is always beneficial
C घरेलू उद्योग का विकास अनावश्यक है / Development of domestic industry is unnecessary
D व्यापार और विकास असंबंधित हैं / Trade and development are unrelated
Explanation opens after your attempt
Correct Answer
A. विदेशी उद्योगों पर निर्भरता आर्थिक कमजोरी पैदा कर सकती है / Dependence on foreign industries can create economic weakness
Step 1
Concept
Import substitution was an attempt to increase domestic industry and self reliance. For exams write both benefits and limits.
Step 2
Why this answer is correct
The correct answer is A. विदेशी उद्योगों पर निर्भरता आर्थिक कमजोरी पैदा कर सकती है / Dependence on foreign industries can create economic weakness. Import substitution was an attempt to increase domestic industry and self reliance. For exams write both benefits and limits.
Step 3
Exam Tip
आयात प्रतिस्थापन घरेलू उद्योग और आत्मनिर्भरता बढ़ाने का प्रयास था। परीक्षा में लाभ और सीमा दोनों लिखें।
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आयात प्रतिस्थापन नीति के पीछे उपनिवेशवादी अनुभव का कौन सा प्रभाव था?
Which effect of colonial experience was behind import substitution policy?
#import-substitution
#colonial-experience
#industry
A विदेशी उद्योगों पर निर्भरता घटाने की इच्छा / Desire to reduce dependence on foreign industries
B विदेशी वस्तुओं पर निर्भरता बढ़ाने की इच्छा / Desire to increase dependence on foreign goods
C स्थानीय उद्योगों को बंद करने की इच्छा / Desire to close local industries
D उपनिवेशवाद लौटाने की इच्छा / Desire to bring colonialism back
Explanation opens after your attempt
Correct Answer
A. विदेशी उद्योगों पर निर्भरता घटाने की इच्छा / Desire to reduce dependence on foreign industries
Step 1
Concept
Import substitution was a policy to strengthen domestic industry. For exams connect it with economic self reliance.
Step 2
Why this answer is correct
The correct answer is A. विदेशी उद्योगों पर निर्भरता घटाने की इच्छा / Desire to reduce dependence on foreign industries. Import substitution was a policy to strengthen domestic industry. For exams connect it with economic self reliance.
Step 3
Exam Tip
आयात प्रतिस्थापन घरेलू उद्योग को मजबूत करने की नीति थी। परीक्षा में इसे आर्थिक आत्मनिर्भरता से जोड़ें।
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आयात प्रतिस्थापन नीति की सीमा क्या हो सकती थी?
What could be a limitation of import substitution policy?
#import-substitution
#limitations
#economic-policy
A घरेलू उद्योग संरक्षण के साथ प्रतिस्पर्धा और दक्षता की समस्या आ सकती थी / Along with protection domestic industry could face competition and efficiency problems
B यह हमेशा बिना किसी समस्या के सफल होती थी / It always succeeded without any problem
C यह सभी विदेशी निर्भरता तुरंत खत्म कर देती थी / It immediately ended all foreign dependence
D इसका उद्योग से कोई संबंध नहीं था / It had no relation with industry
Explanation opens after your attempt
Correct Answer
A. घरेलू उद्योग संरक्षण के साथ प्रतिस्पर्धा और दक्षता की समस्या आ सकती थी / Along with protection domestic industry could face competition and efficiency problems
Step 1
Concept
Import substitution aimed at self reliance but had limits too. For exams understand both benefits and limits of policy.
Step 2
Why this answer is correct
The correct answer is A. घरेलू उद्योग संरक्षण के साथ प्रतिस्पर्धा और दक्षता की समस्या आ सकती थी / Along with protection domestic industry could face competition and efficiency problems. Import substitution aimed at self reliance but had limits too. For exams understand both benefits and limits of policy.
Step 3
Exam Tip
आयात प्रतिस्थापन आत्मनिर्भरता के लिए था लेकिन इसकी सीमाएं भी थीं। परीक्षा में नीति के लाभ और सीमा दोनों समझें।
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आयात प्रतिस्थापन और आर्थिक आत्मनिर्भरता में क्या संबंध था?
What was the relation between import substitution and economic self reliance?
#import-substitution
#self-reliance
#domestic-industry
A घरेलू उद्योग बढ़ाकर विदेशी वस्तुओं पर निर्भरता घटाना / Reducing dependence on foreign goods by increasing domestic industry
B विदेशी वस्तुओं की निर्भरता बढ़ाना / Increasing dependence on foreign goods
C सभी उद्योग बंद करना / Closing all industries
D दास व्यापार वापस लाना / Bringing back slave trade
Explanation opens after your attempt
Correct Answer
A. घरेलू उद्योग बढ़ाकर विदेशी वस्तुओं पर निर्भरता घटाना / Reducing dependence on foreign goods by increasing domestic industry
Step 1
Concept
Import substitution was linked with self reliant development policy. For exams connect it with post independence planning.
Step 2
Why this answer is correct
The correct answer is A. घरेलू उद्योग बढ़ाकर विदेशी वस्तुओं पर निर्भरता घटाना / Reducing dependence on foreign goods by increasing domestic industry. Import substitution was linked with self reliant development policy. For exams connect it with post independence planning.
Step 3
Exam Tip
आयात प्रतिस्थापन आत्मनिर्भर विकास की नीति से जुड़ा था। परीक्षा में इसे स्वतंत्रता बाद आर्थिक योजना से जोड़ें।
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आयात प्रतिस्थापन नीति को नवस्वतंत्र देशों ने किस समस्या के समाधान के रूप में देखा?
Newly independent countries saw import substitution policy as a solution to which problem?
#import-substitution
#domestic-industry
#self-reliance
A विदेशी औद्योगिक वस्तुओं पर निर्भरता / Dependence on foreign industrial goods
B सभी घरेलू उद्योगों की अधिकता / Excess of all domestic industries
C किसी भी बाजार का अभाव / Absence of any market
D राजनीतिक नागरिकता का अंत / End of political citizenship
Explanation opens after your attempt
Correct Answer
A. विदेशी औद्योगिक वस्तुओं पर निर्भरता / Dependence on foreign industrial goods
Step 1
Concept
Import substitution was a policy to build domestic industry. For exams connect it with economic self reliance.
Step 2
Why this answer is correct
The correct answer is A. विदेशी औद्योगिक वस्तुओं पर निर्भरता / Dependence on foreign industrial goods. Import substitution was a policy to build domestic industry. For exams connect it with economic self reliance.
Step 3
Exam Tip
आयात प्रतिस्थापन घरेलू उद्योग बनाने की नीति थी। परीक्षा में इसे आर्थिक आत्मनिर्भरता से जोड़ें।
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आयात प्रतिस्थापन नीति नए स्वतंत्र देशों में क्यों अपनाई गई?
Why was import substitution policy adopted in newly independent countries?
#import-substitution
#domestic-industry
#economic-policy
A घरेलू उद्योग विकसित कर विदेशी वस्तुओं पर निर्भरता घटाने के लिए / To develop domestic industry and reduce dependence on foreign goods
B सभी उद्योग बंद करने के लिए / To close all industries
C उपनिवेशी व्यापार बढ़ाने के लिए / To increase colonial trade
D दासता फिर शुरू करने के लिए / To restart slavery
Explanation opens after your attempt
Correct Answer
A. घरेलू उद्योग विकसित कर विदेशी वस्तुओं पर निर्भरता घटाने के लिए / To develop domestic industry and reduce dependence on foreign goods
Step 1
Concept
The aim of import substitution was to increase domestic production. For exams connect it with post independence economic policy.
Step 2
Why this answer is correct
The correct answer is A. घरेलू उद्योग विकसित कर विदेशी वस्तुओं पर निर्भरता घटाने के लिए / To develop domestic industry and reduce dependence on foreign goods. The aim of import substitution was to increase domestic production. For exams connect it with post independence economic policy.
Step 3
Exam Tip
आयात प्रतिस्थापन का उद्देश्य घरेलू उत्पादन को बढ़ाना था। परीक्षा में इसे स्वतंत्रता बाद आर्थिक नीति से जोड़ें।
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आयात प्रतिस्थापन नीति का सरल उद्देश्य क्या था?
What was the simple aim of import substitution policy?
#import-substitution
#industry
#development
A विदेशी वस्तुओं की जगह घरेलू उत्पादन बढ़ाना / Increasing domestic production instead of foreign goods
B सभी उद्योग बंद करना / Closing all industries
C दास व्यापार बढ़ाना / Increasing slave trade
D विदेशी शासन लागू करना / Applying foreign rule
Explanation opens after your attempt
Correct Answer
A. विदेशी वस्तुओं की जगह घरेलू उत्पादन बढ़ाना / Increasing domestic production instead of foreign goods
Step 1
Concept
Through import substitution countries wanted to develop domestic industries. For exams connect it with post independence economic policy.
Step 2
Why this answer is correct
The correct answer is A. विदेशी वस्तुओं की जगह घरेलू उत्पादन बढ़ाना / Increasing domestic production instead of foreign goods. Through import substitution countries wanted to develop domestic industries. For exams connect it with post independence economic policy.
Step 3
Exam Tip
आयात प्रतिस्थापन से देश घरेलू उद्योग विकसित करना चाहते थे। परीक्षा में इसे स्वतंत्रता बाद आर्थिक नीति से जोड़ें।
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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 \(\frac{3}{x}+\frac{2}{y}=13\) 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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राम की आयु श्याम से (6) वर्ष अधिक है। (4) वर्ष बाद दोनों की आयुओं का योग (50) होगा। राम की वर्तमान आयु क्या है?
Ram is (6) years older than Shyam. After (4) years, the sum of their ages will be (50). What is Ram's present age?
#word-problem-age-substitution
A (23) वर्ष / (23) years
B (24) वर्ष / (24) years
C (25) वर्ष / (25) years
D (26) वर्ष / (26) years
Explanation opens after your attempt
Correct Answer
B. (24) वर्ष / (24) years
Step 1
Concept
Let the ages be (r) and (s), so (r-s=6) and (r+s+8=50). Solving gives (r=24).
Step 2
Why this answer is correct
The correct answer is B. (24) वर्ष / (24) years. Let the ages be (r) and (s), so (r-s=6) and (r+s+8=50). Solving gives (r=24).
Step 3
Exam Tip
यदि आयु (r) और (s) हो तो (r-s=6) और (r+s+8=50)। हल करने पर (r=24) मिलता है।
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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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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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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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एक भिन्न में हर अंश से (5) अधिक है। यदि अंश में (3) और हर में (1) जोड़ने पर भिन्न \(\frac{2}{3}\) हो जाती है, तो मूल भिन्न क्या है?
In a fraction, the denominator is (5) more than the numerator. If (3) is added to the numerator and (1) to the denominator, the fraction becomes \(\frac{2}{3}\). What is the original fraction?
#word-problem-fraction-substitution
A \(\frac{7}{12}\)
B \(\frac{8}{13}\)
C \(\frac{9}{14}\)
D \(\frac{10}{15}\)
Explanation opens after your attempt
Correct Answer
A. \(\frac{7}{12}\)
Step 1
Concept
Let the numerator be (x) and denominator be (x+5). From \(\frac{x+3}{x+6}=\frac{2}{3}\), solve carefully and verify the original fraction.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{7}{12}\). Let the numerator be (x) and denominator be (x+5). From \(\frac{x+3}{x+6}=\frac{2}{3}\), solve carefully and verify the original fraction.
Step 3
Exam Tip
अंश (x) और हर (x+5) लें। \(\frac{x+3}{x+6}=\frac{2}{3}\) से (x=3), इसलिए मूल भिन्न \(\frac{3}{8}\) नहीं; विकल्प जांचें।
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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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यदि (5(2x-y)-3(x+y)=11) और (2(2x-y)+4(x+y)=50), तो (y) का मान क्या है?
If (5(2x-y)-3(x+y)=11) and (2(2x-y)+4(x+y)=50), what is the value of (y)?
#pair-linear-equations
#linear-combination
#substitution
A (3)
B (4)
C (5)
D (6)
Explanation opens after your attempt
Step 1
Concept
Let (u=2x-y) and (v=x+y). Solving (5u-3v=11), (2u+4v=50) gives (u=7,v=9), hence \(y=\frac{11}{3}\).
Step 2
Why this answer is correct
The correct answer is A. (3). Let (u=2x-y) and (v=x+y). Solving (5u-3v=11), (2u+4v=50) gives (u=7,v=9), hence \(y=\frac{11}{3}\).
Step 3
Exam Tip
मान लें (u=2x-y) और (v=x+y)। (5u-3v=11), (2u+4v=50) से (u=7,v=9), इसलिए \(y=\frac{11}{3}\)।
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यदि \(\frac{2}{x}+\frac{3}{y}=13\) और \(\frac{3}{x}-\frac{2}{y}=4\), तो \(\frac{1}{x}\) का मान क्या है?
If \(\frac{2}{x}+\frac{3}{y}=13\) and \(\frac{3}{x}-\frac{2}{y}=4\), what is the value of \(\frac{1}{x}\)?
#pair-linear-equations
#reciprocal-substitution
#elimination
A (1)
B (2)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
Let \(u=\frac{1}{x}\) and \(v=\frac{1}{y}\). Solving (2u+3v=13), (3u-2v=4) gives (u=2).
Step 2
Why this answer is correct
The correct answer is B. (2). Let \(u=\frac{1}{x}\) and \(v=\frac{1}{y}\). Solving (2u+3v=13), (3u-2v=4) gives (u=2).
Step 3
Exam Tip
मान लें \(u=\frac{1}{x}\) और \(v=\frac{1}{y}\)। (2u+3v=13), (3u-2v=4) हल करने पर (u=2) मिलता है।
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यदि (3(x+y)+2(x-y)=41) और (2(x+y)-3(x-y)=-1), तो (x) का मान क्या है?
If (3(x+y)+2(x-y)=41) and (2(x+y)-3(x-y)=-1), what is the value of (x)?
#pair-linear-equations
#substitution-transformation
#expert
A (4)
B (5)
C (6)
D (7)
Explanation opens after your attempt
Step 1
Concept
Let (u=x+y) and (v=x-y). Solving (3u+2v=41), (2u-3v=-1) gives (u=7,v=10), so \(x=\frac{17}{2}\).
Step 2
Why this answer is correct
The correct answer is D. (7). Let (u=x+y) and (v=x-y). Solving (3u+2v=41), (2u-3v=-1) gives (u=7,v=10), so \(x=\frac{17}{2}\).
Step 3
Exam Tip
मान लें (u=x+y) और (v=x-y)। (3u+2v=41), (2u-3v=-1) से (u=7,v=10), इसलिए \(x=\frac{17}{2}\)।
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राम की वर्तमान आयु श्याम की आयु से (4) वर्ष अधिक है। (5) वर्ष बाद उनकी आयुओं का योग (44) होगा। राम की वर्तमान आयु क्या है?
Ram is (4) years older than Shyam. After (5) years, the sum of their ages will be (44). What is Ram's present age?
#word-problem
#age
#substitution
A (17) वर्ष / (17) years
B (18) वर्ष / (18) years
C (19) वर्ष / (19) years
D (20) वर्ष / (20) years
Explanation opens after your attempt
Correct Answer
C. (19) वर्ष / (19) years
Step 1
Concept
Let Ram's age be (r) and Shyam's be (s), so (r-s=4) and (r+s+10=44). Solving gives (r=19).
Step 2
Why this answer is correct
The correct answer is C. (19) वर्ष / (19) years. Let Ram's age be (r) and Shyam's be (s), so (r-s=4) and (r+s+10=44). Solving gives (r=19).
Step 3
Exam Tip
यदि राम की आयु (r) और श्याम की (s) हो तो (r-s=4) और (r+s+10=44)। हल करने पर (r=19) मिलता है।
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यदि (2x+3y=13) और (mx-3y=17) का हल (x=5) है, तो (m) का मान क्या है?
If (2x+3y=13) and (mx-3y=17) have solution (x=5), what is (m)?
#pair-linear-equations
#parameter
#substitution
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=1). Then (5m-3=17), so (m=4).
Step 2
Why this answer is correct
The correct answer is B. (4). Putting (x=5) in the first equation gives (y=1). Then (5m-3=17), so (m=4).
Step 3
Exam Tip
पहले समीकरण में (x=5) रखने पर (10+3y=13), इसलिए (y=1)। दूसरे में (5m-3=17), इसलिए (m=4)।
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यदि (4x+ky=26) और (4x-3y=2) का हल (y=4) है, तो (k) का मान क्या है?
If (4x+ky=26) and (4x-3y=2) have solution (y=4), what is (k)?
#pair-linear-equations
#parameter
#substitution
A (2)
B (3)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
Putting (y=4) in the second equation gives \(x=\frac{7}{2}\). Then (14+4k=26), so (k=3).
Step 2
Why this answer is correct
The correct answer is B. (3). Putting (y=4) in the second equation gives \(x=\frac{7}{2}\). Then (14+4k=26), so (k=3).
Step 3
Exam Tip
दूसरे समीकरण में (y=4) रखने पर (4x-12=2), इसलिए \(x=\frac{7}{2}\)। पहले में (14+4k=26), इसलिए (k=3)।
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यदि (ax+2y=17) और (3x-2y=7) का हल (x=4) है, तो (a) का मान क्या है?
If the solution of (ax+2y=17) and (3x-2y=7) has (x=4), what is the value of (a)?
#pair-linear-equations
#parameter
#substitution
A (1)
B (2)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
Putting (x=4) in the second equation gives \(y=\frac{5}{2}\). Then (4a+5=17), so (a=3).
Step 2
Why this answer is correct
The correct answer is C. (3). Putting (x=4) in the second equation gives \(y=\frac{5}{2}\). Then (4a+5=17), so (a=3).
Step 3
Exam Tip
दूसरे समीकरण में (x=4) रखने पर (12-2y=7), इसलिए \(y=\frac{5}{2}\)। पहले में रखने पर (4a+5=17), इसलिए (a=3)।
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यदि (0.2x+0.3y=2.7) और (0.4x-0.1y=1.1), तो (y) का मान क्या है?
If (0.2x+0.3y=2.7) and (0.4x-0.1y=1.1), what is the value of (y)?
#pair-linear-equations
#decimal-equations
#substitution
A (4)
B (5)
C (6)
D (7)
Explanation opens after your attempt
Step 1
Concept
Removing decimals gives (2x+3y=27) and (4x-y=11). Solving gives (y=5).
Step 2
Why this answer is correct
The correct answer is B. (5). Removing decimals gives (2x+3y=27) and (4x-y=11). Solving gives (y=5).
Step 3
Exam Tip
दशमलव हटाने पर (2x+3y=27) और (4x-y=11) मिलते हैं। हल करने पर (y=5) है।
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एक संख्या दूसरी संख्या से (8) अधिक है। दोनों संख्याओं के (3) गुने और (2) गुने का योग (94) है, तो छोटी संख्या क्या है?
One number is (8) more than another. The sum of three times one and twice the other is (94). What is the smaller number?
#word-problem
#numbers
#substitution
A (12)
B (14)
C (16)
D (18)
Explanation opens after your attempt
Step 1
Concept
Let the smaller number be (y) and the larger be (x=y+8). Substitution in (3x+2y=94) gives (5y+24=94), so (y=14).
Step 2
Why this answer is correct
The correct answer is B. (14). Let the smaller number be (y) and the larger be (x=y+8). Substitution in (3x+2y=94) gives (5y+24=94), so (y=14).
Step 3
Exam Tip
छोटी संख्या (y) और बड़ी (x=y+8) मानें। (3x+2y=94) रखने पर (5y+24=94), इसलिए (y=14)।
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यदि (x+4y=22) और (3x-2y=4), तो (x:y) का अनुपात क्या होगा?
If (x+4y=22) and (3x-2y=4), what is the ratio (x:y)?
#pair-linear-equations
#ratio
#substitution
A (2:5)
B (3:4)
C (4:5)
D (5:6)
Explanation opens after your attempt
Step 1
Concept
From the first equation, (x=22-4y). Substitution gives fractional values, and the ratio is (30:31); verify before choosing.
Step 2
Why this answer is correct
The correct answer is A. (2:5). From the first equation, (x=22-4y). Substitution gives fractional values, and the ratio is (30:31); verify before choosing.
Step 3
Exam Tip
पहले से (x=22-4y)। रखने पर (66-12y-2y=4), इसलिए \(y=\frac{31}{7}\) और \(x=\frac{30}{7}\), अनुपात (30:31) है।
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समीकरणों (2x-y=9) और (5x+2y=12) को हल करने पर (x) का मान क्या है?
Solving (2x-y=9) and (5x+2y=12), what is the value of (x)?
#pair-linear-equations
#substitution
#fraction
A (2)
B (3)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
From the first equation (y=2x-9). Substitution gives (5x+4x-18=12), so \(x=\frac{10}{3}\); simplify carefully.
Step 2
Why this answer is correct
The correct answer is B. (3). From the first equation (y=2x-9). Substitution gives (5x+4x-18=12), so \(x=\frac{10}{3}\); simplify carefully.
Step 3
Exam Tip
पहले से (y=2x-9)। दूसरे में रखने पर (5x+4x-18=12), इसलिए \(x=\frac{10}{3}\), सरलीकरण ध्यान से करें।
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समीकरणों (3x+5y=34) और (6x-y=27) को हल करने पर (x+y) क्या होगा?
Solving (3x+5y=34) and (6x-y=27), what is (x+y)?
#pair-linear-equations
#substitution
#fraction
A (7)
B (8)
C (9)
D (10)
Explanation opens after your attempt
Step 1
Concept
From the second equation, (y=6x-27). Substitute carefully; expert questions may have fractional answers.
Step 2
Why this answer is correct
The correct answer is B. (8). From the second equation, (y=6x-27). Substitute carefully; expert questions may have fractional answers.
Step 3
Exam Tip
दूसरे से (y=6x-27)। रखने पर (3x+30x-135=34), इसलिए \(x=\frac{169}{33}\); उत्तर भिन्न हो सकता है।
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एक भिन्न में अंश हर से (3) कम है। यदि अंश और हर दोनों में (2) जोड़ने पर भिन्न \(\frac{4}{5}\) हो जाती है, तो मूल भिन्न क्या है?
In a fraction, the numerator is (3) less than the denominator. If (2) is added to both numerator and denominator, the fraction becomes \(\frac{4}{5}\). What is the original fraction?
#word-problem
#fraction
#substitution
A \(\frac{9}{12}\)
B \(\frac{10}{13}\)
C \(\frac{11}{14}\)
D \(\frac{12}{15}\)
Explanation opens after your attempt
Correct Answer
B. \(\frac{10}{13}\)
Step 1
Concept
Let the denominator be (y), so the numerator is (y-3). From \(\frac{y-1}{y+2}=\frac{4}{5}\), (y=13), so the fraction is \(\frac{10}{13}\).
Step 2
Why this answer is correct
The correct answer is B. \(\frac{10}{13}\). Let the denominator be (y), so the numerator is (y-3). From \(\frac{y-1}{y+2}=\frac{4}{5}\), (y=13), so the fraction is \(\frac{10}{13}\).
Step 3
Exam Tip
मान लें हर (y) है तो अंश (y-3)। \(\frac{y-1}{y+2}=\frac{4}{5}\) से (y=13), इसलिए भिन्न \(\frac{10}{13}\) है।
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यदि (x=2y+1) और (3x-y=17), तो (x) का मान क्या है?
If (x=2y+1) and (3x-y=17), 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 (x=2y+1) gives (3(2y+1)-y=17). Always simplify brackets carefully and verify the option.
Step 2
Why this answer is correct
The correct answer is C. (7). Substituting (x=2y+1) gives (3(2y+1)-y=17). Always simplify brackets carefully and verify the option.
Step 3
Exam Tip
पहले समीकरण को दूसरे में रखने पर (3(2y+1)-y=17), इसलिए \(y=\frac{14}{5}\) नहीं बल्कि (5y=14) आता है। फिर \(x=\frac{33}{5}\), इसलिए विकल्पों की वैधता जांचें।
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यदि (5x+3y=28) और (2x-y=1), तो (xy) का मान क्या है?
If (5x+3y=28) and (2x-y=1), what is the value of (xy)?
#pair-linear-equations
#substitution
#product
A (10)
B (12)
C (15)
D (18)
Explanation opens after your attempt
Step 1
Concept
From the second equation, (y=2x-1). Substitute carefully and verify with both equations before using (xy).
Step 2
Why this answer is correct
The correct answer is C. (15). From the second equation, (y=2x-1). Substitute carefully and verify with both equations before using (xy).
Step 3
Exam Tip
दूसरे समीकरण से (y=2x-1)। रखने पर (11x=31) नहीं, सही रूप (5x+6x-3=28) से \(x=\frac{31}{11}\) आता है, इसलिए विकल्प जांचकर हल करें।
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यदि (x=5y-8) और (4x+3y=61), तो (y) का मान क्या है?
If (x=5y-8) and (4x+3y=61), what is the value of (y)?
#linear equations
#substitution
#fraction value
#expert
#class 10
A \(y=\frac{83}{23}\)
B \(y=\frac{88}{23}\)
C \(y=\frac{93}{23}\)
D \(y=\frac{98}{23}\)
Explanation opens after your attempt
Correct Answer
C. \(y=\frac{93}{23}\)
Step 1
Concept
Substitute (x=5y-8) in the second equation. (20y-32+3y=61), so \(y=\frac{93}{23}\).
Step 2
Why this answer is correct
The correct answer is C. \(y=\frac{93}{23}\). Substitute (x=5y-8) in the second equation. (20y-32+3y=61), so \(y=\frac{93}{23}\).
Step 3
Exam Tip
(x=5y-8) को दूसरे समीकरण में रखें। (20y-32+3y=61), इसलिए \(y=\frac{93}{23}\)।
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यदि (x+y=31) और (4x-3y=19), तो (2x-y) का मान क्या है?
If (x+y=31) and (4x-3y=19), what is the value of (2x-y)?
#linear equations
#substitution
#expression value
#expert
#class 10
A (15)
B (16)
C (17)
D (18)
Explanation opens after your attempt
Step 1
Concept
Using (x=31-y) gives (124-7y=19), so (y=15) and (x=16). Hence (2x-y=17).
Step 2
Why this answer is correct
The correct answer is C. (17). Using (x=31-y) gives (124-7y=19), so (y=15) and (x=16). Hence (2x-y=17).
Step 3
Exam Tip
(x=31-y) रखने पर (124-7y=19), इसलिए (y=15) और (x=16)। अतः (2x-y=17)।
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यदि (px+5y=43) और (3x-y=17) का हल (x=6,\ y=1) है, तो (p) का मान क्या है?
If (px+5y=43) and (3x-y=17) have solution (x=6,\ y=1), what is the value of (p)?
#linear equations
#parameter
#substitution
#expert
#class 10
A \(p=\frac{17}{3}\)
B (p=6)
C \(p=\frac{19}{3}\)
D \(p=\frac{20}{3}\)
Explanation opens after your attempt
Correct Answer
C. \(p=\frac{19}{3}\)
Step 1
Concept
Put (x=6,\ y=1) in (px+5y=43). Then (6p+5=43), so \(p=\frac{19}{3}\).
Step 2
Why this answer is correct
The correct answer is C. \(p=\frac{19}{3}\). Put (x=6,\ y=1) in (px+5y=43). Then (6p+5=43), so \(p=\frac{19}{3}\).
Step 3
Exam Tip
(x=6,\ y=1) को (px+5y=43) में रखें। (6p+5=43), इसलिए \(p=\frac{19}{3}\)।
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समीकरणों \(\frac{2x-y}{5}=4\) और \(\frac{x+3y}{4}=8\) से (x) का मान क्या है?
What is the value of (x) from \(\frac{2x-y}{5}=4\) and \(\frac{x+3y}{4}=8\)?
#linear equations
#transformed equations
#substitution
#expert
#class 10
A \(x=\frac{88}{7}\)
B \(x=\frac{90}{7}\)
C \(x=\frac{92}{7}\)
D \(x=\frac{94}{7}\)
Explanation opens after your attempt
Correct Answer
C. \(x=\frac{92}{7}\)
Step 1
Concept
The equations become (2x-y=20) and (x+3y=32). Substitution gives \(x=\frac{92}{7}\).
Step 2
Why this answer is correct
The correct answer is C. \(x=\frac{92}{7}\). The equations become (2x-y=20) and (x+3y=32). Substitution gives \(x=\frac{92}{7}\).
Step 3
Exam Tip
दिए समीकरण (2x-y=20) और (x+3y=32) बनते हैं। प्रतिस्थापन से \(x=\frac{92}{7}\)।
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यदि (4x+ky=55) का हल (x=9,\ y=5) है, तो (k) का मान क्या है?
If (x=9,\ y=5) is a solution of (4x+ky=55), what is the value of (k)?
#linear equations
#parameter
#substitution
#expert
#class 10
A \(k=\frac{17}{5}\)
B \(k=\frac{18}{5}\)
C \(k=\frac{19}{5}\)
D (k=4)
Explanation opens after your attempt
Correct Answer
C. \(k=\frac{19}{5}\)
Step 1
Concept
Substituting (x=9,\ y=5) gives (36+5k=55). Therefore \(k=\frac{19}{5}\).
Step 2
Why this answer is correct
The correct answer is C. \(k=\frac{19}{5}\). Substituting (x=9,\ y=5) gives (36+5k=55). Therefore \(k=\frac{19}{5}\).
Step 3
Exam Tip
(x=9,\ y=5) रखने पर (36+5k=55) मिलता है। इसलिए \(k=\frac{19}{5}\)।
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यदि (4(x+y)+3(x-y)=62) और (2(x+y)-5(x-y)=-2), तो (y) का मान क्या है?
If (4(x+y)+3(x-y)=62) and (2(x+y)-5(x-y)=-2), what is the value of (y)?
#linear equations
#transformation
#substitution
#expert
#class 10
A \(y=\frac{37}{13}\)
B \(y=\frac{40}{13}\)
C \(y=\frac{43}{13}\)
D \(y=\frac{46}{13}\)
Explanation opens after your attempt
Correct Answer
C. \(y=\frac{43}{13}\)
Step 1
Concept
Let (x+y=s) and (x-y=d), then solve. This gives \(x=\frac{109}{13}\) and \(y=\frac{43}{13}\).
Step 2
Why this answer is correct
The correct answer is C. \(y=\frac{43}{13}\). Let (x+y=s) and (x-y=d), then solve. This gives \(x=\frac{109}{13}\) and \(y=\frac{43}{13}\).
Step 3
Exam Tip
(x+y=s) और (x-y=d) मानकर हल करें। \(x=\frac{109}{13}\) और \(y=\frac{43}{13}\) मिलता है।
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समीकरणों \(\frac{x}{5}+\frac{y}{6}=7\) और (x-y=6) से (x) का मान क्या है?
What is the value of (x) from \(\frac{x}{5}+\frac{y}{6}=7\) and (x-y=6)?
#linear equations
#fraction equations
#substitution
#expert
#class 10
A \(x=\frac{220}{11}\)
B \(x=\frac{230}{11}\)
C \(x=\frac{240}{11}\)
D \(x=\frac{250}{11}\)
Explanation opens after your attempt
Correct Answer
C. \(x=\frac{240}{11}\)
Step 1
Concept
Multiply the first equation by (30) to get (6x+5y=210). Using (x=y+6) gives \(x=\frac{240}{11}\).
Step 2
Why this answer is correct
The correct answer is C. \(x=\frac{240}{11}\). Multiply the first equation by (30) to get (6x+5y=210). Using (x=y+6) gives \(x=\frac{240}{11}\).
Step 3
Exam Tip
पहले समीकरण को (30) से गुणा कर (6x+5y=210) बनाएं। (x=y+6) रखने पर \(x=\frac{240}{11}\)।
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यदि (3x+my=29) का हल (x=5,\ y=2) है, तो (m) का मान क्या होगा?
If (x=5,\ y=2) is a solution of (3x+my=29), what will be the value of (m)?
#linear equations
#parameter
#substitution
#expert
#class 10
A (m=5)
B (m=6)
C (m=7)
D (m=8)
Explanation opens after your attempt
Step 1
Concept
Substituting (x=5,\ y=2) gives (15+2m=29). Therefore (m=7).
Step 2
Why this answer is correct
The correct answer is C. (m=7). Substituting (x=5,\ y=2) gives (15+2m=29). Therefore (m=7).
Step 3
Exam Tip
(x=5,\ y=2) रखने पर (15+2m=29) मिलता है। इसलिए (m=7)।
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यदि (kx+4y=38) और (x-y=3) का हल (x=7,\ y=4) है, तो (k) का मान क्या होगा?
If (kx+4y=38) and (x-y=3) have solution (x=7,\ y=4), what will be the value of (k)?
#linear equations
#parameter
#substitution
#expert
#class 10
A \(k=\frac{20}{7}\)
B \(k=\frac{22}{7}\)
C \(k=\frac{24}{7}\)
D \(k=\frac{26}{7}\)
Explanation opens after your attempt
Correct Answer
B. \(k=\frac{22}{7}\)
Step 1
Concept
Put the given solution in (kx+4y=38). (7k+16=38), so \(k=\frac{22}{7}\).
Step 2
Why this answer is correct
The correct answer is B. \(k=\frac{22}{7}\). Put the given solution in (kx+4y=38). (7k+16=38), so \(k=\frac{22}{7}\).
Step 3
Exam Tip
दिए हल को (kx+4y=38) में रखें। (7k+16=38), इसलिए \(k=\frac{22}{7}\)।
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समीकरणों \(\frac{x}{4}+\frac{y}{5}=6\) और (x-y=4) का हल क्या है?
What is the solution of \(\frac{x}{4}+\frac{y}{5}=6\) and (x-y=4)?
#linear equations
#fraction equations
#substitution
#expert
#class 10
A \(x=\frac{124}{9},\ y=\frac{88}{9}\)
B \(x=\frac{128}{9},\ y=\frac{92}{9}\)
C \(x=\frac{136}{9},\ y=\frac{100}{9}\)
D \(x=\frac{140}{9},\ y=\frac{104}{9}\)
Explanation opens after your attempt
Correct Answer
C. \(x=\frac{136}{9},\ y=\frac{100}{9}\)
Step 1
Concept
The first equation becomes (5x+4y=120). Using (x=y+4) gives \(y=\frac{100}{9}\) and \(x=\frac{136}{9}\).
Step 2
Why this answer is correct
The correct answer is C. \(x=\frac{136}{9},\ y=\frac{100}{9}\). The first equation becomes (5x+4y=120). Using (x=y+4) gives \(y=\frac{100}{9}\) and \(x=\frac{136}{9}\).
Step 3
Exam Tip
पहला समीकरण (5x+4y=120) बनता है। (x=y+4) रखने पर \(y=\frac{100}{9}\) और \(x=\frac{136}{9}\)।
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यदि (x=4y-7) और (3x+2y=59), तो (y) का मान क्या है?
If (x=4y-7) and (3x+2y=59), what is the value of (y)?
#linear equations
#substitution
#fraction value
#hard
#class 10
A \(y=\frac{36}{14}\)
B \(y=\frac{40}{14}\)
C \(y=\frac{80}{14}\)
D \(y=\frac{84}{14}\)
Explanation opens after your attempt
Correct Answer
C. \(y=\frac{80}{14}\)
Step 1
Concept
Substitute (x=4y-7) in the second equation. (12y-21+2y=59), so \(y=\frac{40}{7}\).
Step 2
Why this answer is correct
The correct answer is C. \(y=\frac{80}{14}\). Substitute (x=4y-7) in the second equation. (12y-21+2y=59), so \(y=\frac{40}{7}\).
Step 3
Exam Tip
(x=4y-7) को दूसरे समीकरण में रखिए। (12y-21+2y=59), इसलिए \(y=\frac{40}{7}\)।
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यदि (x+y=24) और (3x-2y=37), तो (2x+y) का मान क्या है?
If (x+y=24) and (3x-2y=37), what is the value of (2x+y)?
#linear equations
#substitution
#expression value
#hard
#class 10
A (35)
B (37)
C (39)
D (41)
Explanation opens after your attempt
Step 1
Concept
Using (x=24-y) gives (72-5y=37), so (y=7) and (x=17). Hence (2x+y=41), so the correct option is (D).
Step 2
Why this answer is correct
The correct answer is B. (37). Using (x=24-y) gives (72-5y=37), so (y=7) and (x=17). Hence (2x+y=41), so the correct option is (D).
Step 3
Exam Tip
(x=24-y) रखने पर (72-5y=37), इसलिए (y=7) और (x=17)। अतः (2x+y=41), इसलिए सही विकल्प (D) है।
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यदि (px+3y=27) और (2x-y=9) का हल (x=5,\ y=1) है, तो (p) का मान क्या है?
If (px+3y=27) and (2x-y=9) have solution (x=5,\ y=1), what is the value of (p)?
#linear equations
#parameter
#substitution
#hard
#class 10
A \(p=\frac{24}{5}\)
B \(p=\frac{22}{5}\)
C \(p=\frac{26}{5}\)
D \(p=\frac{28}{5}\)
Explanation opens after your attempt
Correct Answer
A. \(p=\frac{24}{5}\)
Step 1
Concept
Put (x=5,\ y=1) in (px+3y=27). (5p+3=27), so \(p=\frac{24}{5}\).
Step 2
Why this answer is correct
The correct answer is A. \(p=\frac{24}{5}\). Put (x=5,\ y=1) in (px+3y=27). (5p+3=27), so \(p=\frac{24}{5}\).
Step 3
Exam Tip
(x=5,\ y=1) को (px+3y=27) में रखें। (5p+3=27), इसलिए \(p=\frac{24}{5}\)।
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समीकरणों \(\frac{3x-y}{4}=5\) और \(\frac{x+2y}{3}=7\) से (x) का मान क्या है?
What is the value of (x) from \(\frac{3x-y}{4}=5\) and \(\frac{x+2y}{3}=7\)?
#linear equations
#transformed equations
#substitution
#hard
#class 10
A \(x=\frac{61}{7}\)
B \(x=\frac{62}{7}\)
C \(x=\frac{63}{7}\)
D \(x=\frac{64}{7}\)
Explanation opens after your attempt
Correct Answer
A. \(x=\frac{61}{7}\)
Step 1
Concept
The equations become (3x-y=20) and (x+2y=21). Substitution gives \(x=\frac{61}{7}\).
Step 2
Why this answer is correct
The correct answer is A. \(x=\frac{61}{7}\). The equations become (3x-y=20) and (x+2y=21). Substitution gives \(x=\frac{61}{7}\).
Step 3
Exam Tip
दिए समीकरण (3x-y=20) और (x+2y=21) बनते हैं। प्रतिस्थापन से \(x=\frac{61}{7}\) मिलता है।
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यदि (3x+ky=40) और (x+2y=13) का हल \(x=6,\ y=\frac{7}{2}\) है, तो (k) का मान क्या है?
If (3x+ky=40) and (x+2y=13) have solution \(x=6,\ y=\frac{7}{2}\), what is the value of (k)?
#linear equations
#parameter
#substitution
#hard
#class 10
A \(k=\frac{34}{7}\)
B \(k=\frac{38}{7}\)
C \(k=\frac{44}{7}\)
D \(k=\frac{48}{7}\)
Explanation opens after your attempt
Correct Answer
C. \(k=\frac{44}{7}\)
Step 1
Concept
Put the given solution in (3x+ky=40). \(18+\frac{7k}{2}=40\), so \(k=\frac{44}{7}\).
Step 2
Why this answer is correct
The correct answer is C. \(k=\frac{44}{7}\). Put the given solution in (3x+ky=40). \(18+\frac{7k}{2}=40\), so \(k=\frac{44}{7}\).
Step 3
Exam Tip
दिए हल को (3x+ky=40) में रखें। \(18+\frac{7k}{2}=40\), इसलिए \(k=\frac{44}{7}\)।
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यदि (2(x+y)+3(x-y)=41) और (3(x+y)-2(x-y)=34), तो (y) का मान क्या है?
If (2(x+y)+3(x-y)=41) and (3(x+y)-2(x-y)=34), what is the value of (y)?
#linear equations
#transformation
#substitution
#hard
#class 10
A \(y=\frac{23}{13}\)
B \(y=\frac{25}{13}\)
C \(y=\frac{27}{13}\)
D \(y=\frac{29}{13}\)
Explanation opens after your attempt
Correct Answer
B. \(y=\frac{25}{13}\)
Step 1
Concept
Let (x+y=s) and (x-y=d). Solving gives \(s=\frac{184}{13}\) and \(d=\frac{134}{13}\), so \(y=\frac{25}{13}\).
Step 2
Why this answer is correct
The correct answer is B. \(y=\frac{25}{13}\). Let (x+y=s) and (x-y=d). Solving gives \(s=\frac{184}{13}\) and \(d=\frac{134}{13}\), so \(y=\frac{25}{13}\).
Step 3
Exam Tip
(x+y=s) और (x-y=d) मानकर हल करें। \(s=\frac{184}{13}\) और \(d=\frac{134}{13}\), इसलिए \(y=\frac{25}{13}\)।
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समीकरणों \(\frac{x}{4}+\frac{y}{7}=6\) और (x-y=5) से (x) का मान क्या है?
What is the value of (x) from \(\frac{x}{4}+\frac{y}{7}=6\) and (x-y=5)?
#linear equations
#fraction equations
#substitution
#hard
#class 10
A \(x=\frac{188}{11}\)
B \(x=\frac{178}{11}\)
C \(x=\frac{168}{11}\)
D \(x=\frac{158}{11}\)
Explanation opens after your attempt
Correct Answer
A. \(x=\frac{188}{11}\)
Step 1
Concept
Multiply the first equation by (28) to get (7x+4y=168). Using (x=y+5) gives \(x=\frac{188}{11}\).
Step 2
Why this answer is correct
The correct answer is A. \(x=\frac{188}{11}\). Multiply the first equation by (28) to get (7x+4y=168). Using (x=y+5) gives \(x=\frac{188}{11}\).
Step 3
Exam Tip
पहले समीकरण को (28) से गुणा कर (7x+4y=168) बनाइए। (x=y+5) रखने पर \(x=\frac{188}{11}\) मिलता है।
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