100 results found for "ap-linear-form-expert" in Class 10.
यदि (5x+8y=37) और (15x+24y=m) असंगत युग्म हों, तो (m) के लिए सही शर्त क्या है?
If (5x+8y=37) and (15x+24y=m) form an inconsistent pair, what is the correct condition for (m)?
#linear equations
#expert
#inconsistent
#condition
A (m=111)
B \(m\ne111\)
C (m=37)
D (m=74)
Explanation opens after your attempt
Correct Answer
B. \(m\ne111\)
Step 1
Concept
The first two ratios are equal. For inconsistency, the constant ratio must be different.
Step 2
Why this answer is correct
The correct answer is B. \(m\ne111\). The first two ratios are equal. For inconsistency, the constant ratio must be different.
Step 3
Exam Tip
पहले दो अनुपात बराबर हैं। असंगत होने के लिए स्थिर पद का अनुपात अलग होना चाहिए।
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यदि (D=0), \(D_x=0\) और \(D_y=0\) हैं, तो दो रैखिक समीकरणों के युग्म में क्या होगा?
If (D=0), \(D_x=0\), and \(D_y=0\), what happens in a pair of two linear equations?
#class10
#linear-equations
#solvability
A कोई हल नहीं / No solution
B अद्वितीय हल / Unique solution
C अनंत हल / Infinitely many solutions
D हमेशा गलत समीकरण / Always false equations
Explanation opens after your attempt
Correct Answer
C. अनंत हल / Infinitely many solutions
Step 1
Concept
When all three determinants are zero, the equations may be dependent. In Class (10), link this with infinitely many solutions.
Step 2
Why this answer is correct
The correct answer is C. अनंत हल / Infinitely many solutions. When all three determinants are zero, the equations may be dependent. In Class (10), link this with infinitely many solutions.
Step 3
Exam Tip
तीनों सारणिक शून्य होने पर समीकरण आश्रित हो सकते हैं। कक्षा (10) में इसे अनंत हल की स्थिति से जोड़कर देखें।
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यदि \(\frac{a_1}{a_2}\neq\frac{b_1}{b_2}\) है, तो दो रैखिक समीकरणों के युग्म के लिए क्या निष्कर्ष होगा?
If \(\frac{a_1}{a_2}\neq\frac{b_1}{b_2}\), what is the conclusion for a pair of two linear equations?
#class10
#linear-equations
#solvability
A कोई हल नहीं / No solution
B अनंत हल / Infinitely many solutions
C अद्वितीय हल / Unique solution
D हल निर्भर करता है / Solution depends only on constants
Explanation opens after your attempt
Correct Answer
C. अद्वितीय हल / Unique solution
Step 1
Concept
When coefficient ratios are different, the lines intersect at one point. Therefore, a unique solution is obtained.
Step 2
Why this answer is correct
The correct answer is C. अद्वितीय हल / Unique solution. When coefficient ratios are different, the lines intersect at one point. Therefore, a unique solution is obtained.
Step 3
Exam Tip
गुणांक अनुपात अलग होने पर रेखाएँ एक बिंदु पर कटती हैं। इसलिए अद्वितीय हल मिलता है।
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किस स्थिति में दो रैखिक समीकरणों का युग्म संगत और आश्रित कहलाता है?
In which condition is a pair of two linear equations called consistent and dependent?
#linear equations
#consistent dependent
#condition
A जब (a_1 / a_2=b_1 / b_2=c_1 / c_2) हो / When \(a_1 / c_2\)
B जब (a_1 / a_2 \ne b_1 / b_2) हो / When \(a_1 / b_2\)
C जब (a_1 / a_2=b_1 / b_2 \ne c_1 / c_2) हो / When \(a_1 / c_2\)
D जब रेखाएं कटती हों / When lines intersect
Explanation opens after your attempt
Correct Answer
A. जब (a_1 / a_2=b_1 / b_2=c_1 / c_2) हो / When \(a_1 / c_2\)
Step 1
Concept
If all three ratios are equal both equations represent the same line. This is a consistent and dependent pair.
Step 2
Why this answer is correct
The correct answer is A. जब \(a_1 / a_2=b_1 / b_2=c_1 / c_2\) हो / When \(a_1 / c_2\). If all three ratios are equal both equations represent the same line. This is a consistent and dependent pair.
Step 3
Exam Tip
तीनों अनुपात बराबर हों तो दोनों समीकरण समान रेखा दर्शाते हैं। यही संगत और आश्रित युग्म है।
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किस स्थिति में दो रैखिक समीकरणों का युग्म संगत और स्वतंत्र कहलाता है?
In which condition is a pair of two linear equations called consistent and independent?
#linear equations
#consistent independent
#condition
A जब (a_1 / a_2=b_1 / b_2=c_1 / c_2) हो / When \(a_1 / c_2\)
B जब (a_1 / a_2=b_1 / b_2 \ne c_1 / c_2) हो / When \(a_1 / c_2\)
C जब (a_1 / a_2 \ne b_1 / b_2) हो / When \(a_1 / b_2\)
D जब कोई हल न हो / When there is no solution
Explanation opens after your attempt
Correct Answer
C. जब (a_1 / a_2 \ne b_1 / b_2) हो / When \(a_1 / b_2\)
Step 1
Concept
A consistent and independent pair has one unique solution. For this the ratios of (a) and (b) must be different.
Step 2
Why this answer is correct
The correct answer is C. जब \(a_1 / a_2 \ne b_1 / b_2\) हो / When \(a_1 / b_2\). A consistent and independent pair has one unique solution. For this the ratios of (a) and (b) must be different.
Step 3
Exam Tip
संगत और स्वतंत्र युग्म में एक अद्वितीय हल होता है। इसके लिए (a) और (b) के अनुपात अलग होने चाहिए।
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किस स्थिति में दो रैखिक समीकरणों का युग्म संगत कहलाता है?
In which case is a pair of two linear equations called consistent?
#linear equations
#consistent pair
#solvability
A जब कम से कम एक हल हो / When there is at least one solution
B जब कोई हल न हो / When there is no solution
C जब रेखाएं केवल समानांतर हों / When lines are only parallel
D जब (c_1 / c_2) हमेशा अलग हो / When \(c_1 / c_2\) is always different
Explanation opens after your attempt
Correct Answer
A. जब कम से कम एक हल हो / When there is at least one solution
Step 1
Concept
A consistent pair has at least one common solution. It may have one solution or infinitely many solutions.
Step 2
Why this answer is correct
The correct answer is A. जब कम से कम एक हल हो / When there is at least one solution. A consistent pair has at least one common solution. It may have one solution or infinitely many solutions.
Step 3
Exam Tip
संगत युग्म में कम से कम एक सामान्य हल होता है। यह एक हल या अनंत हल दोनों हो सकता है।
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किस स्थिति में दो रैखिक समीकरणों का युग्म असंगत कहलाता है?
In which case is a pair of two linear equations called inconsistent?
#linear equations
#inconsistent
#no solution
A जब कोई हल न हो / When there is no solution
B जब एक हल हो / When there is one solution
C जब अनंत हल हों / When there are infinitely many solutions
D जब दोनों अक्षों को काटें / When both axes are cut
Explanation opens after your attempt
Correct Answer
A. जब कोई हल न हो / When there is no solution
Step 1
Concept
An inconsistent pair has no common solution. In a graph, it appears as parallel lines.
Step 2
Why this answer is correct
The correct answer is A. जब कोई हल न हो / When there is no solution. An inconsistent pair has no common solution. In a graph, it appears as parallel lines.
Step 3
Exam Tip
असंगत युग्म का कोई सामान्य हल नहीं होता। ग्राफ में यह समानांतर रेखाओं से दिखता है।
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यदि दो रैखिक समीकरणों में \(a_1/a_2 \ne b_1/b_2\) हो, तो हलों की संख्या क्या होगी?
If two linear equations have \(a_1/a_2 \ne b_1/b_2\), how many solutions will they have?
#linear equations
#solvability
#unique solution
A कोई हल नहीं / No solution
B एक अद्वितीय हल / One unique solution
C अनंत हल / Infinitely many solutions
D केवल शून्य हल / Only zero solution
Explanation opens after your attempt
Correct Answer
B. एक अद्वितीय हल / One unique solution
Step 1
Concept
When coefficient ratios are different, the lines meet at one point. In exams, check the ratios of (a) and (b) first.
Step 2
Why this answer is correct
The correct answer is B. एक अद्वितीय हल / One unique solution. When coefficient ratios are different, the lines meet at one point. In exams, check the ratios of (a) and (b) first.
Step 3
Exam Tip
जब गुणांकों के अनुपात अलग होते हैं, रेखाएं एक बिंदु पर मिलती हैं। परीक्षा में पहले (a) और (b) के अनुपात जांचें।
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यदि (7x+3y=25) और (14x+6y=m) असंगत युग्म हों, तो (m) के लिए सही शर्त क्या है?
If (7x+3y=25) and (14x+6y=m) form an inconsistent pair, what is the correct condition for (m)?
#linear equations
#hard
#inconsistent
#condition
A (m=50)
B \(m \ne 50\)
C (m=25)
D (m=75)
Explanation opens after your attempt
Correct Answer
B. \(m \ne 50\)
Step 1
Concept
The first two ratios are equal. For inconsistency, the constant ratio must be different so \(m \ne 50\).
Step 2
Why this answer is correct
The correct answer is B. \(m \ne 50\). The first two ratios are equal. For inconsistency, the constant ratio must be different so \(m \ne 50\).
Step 3
Exam Tip
पहले दो अनुपात बराबर हैं। असंगत होने के लिए स्थिर पद का अनुपात अलग होना चाहिए इसलिए \(m \ne 50\)।
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यदि (3x+8y=25) और (9x+24y=m) असंगत युग्म हों, तो (m) के लिए सही शर्त क्या है?
If (3x+8y=25) and (9x+24y=m) form an inconsistent pair, what is the correct condition for (m)?
#linear equations
#hard
#inconsistent
#condition
A (m=75)
B \(m \ne 75\)
C (m=25)
D (m=50)
Explanation opens after your attempt
Correct Answer
B. \(m \ne 75\)
Step 1
Concept
The first two ratios are equal, so the constant ratio must be different for inconsistency. Hence, \(m \ne 75\) is correct.
Step 2
Why this answer is correct
The correct answer is B. \(m \ne 75\). The first two ratios are equal, so the constant ratio must be different for inconsistency. Hence, \(m \ne 75\) is correct.
Step 3
Exam Tip
पहले दो अनुपात बराबर हैं, इसलिए असंगत होने के लिए स्थिर पद का अनुपात अलग होना चाहिए। अतः \(m \ne 75\) सही है।
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यदि (2x+5y=17) और (4x+10y=m) असंगत युग्म हों, तो (m) के लिए सही शर्त क्या है?
If (2x+5y=17) and (4x+10y=m) form an inconsistent pair, what is the correct condition for (m)?
#linear equations
#hard
#inconsistent
#condition
A (m=34)
B \(m \ne 34\)
C (m=17)
D (m=68)
Explanation opens after your attempt
Correct Answer
B. \(m \ne 34\)
Step 1
Concept
The first two ratios are equal, so the constant ratio must be different for inconsistency. Hence, \(m \ne 34\).
Step 2
Why this answer is correct
The correct answer is B. \(m \ne 34\). The first two ratios are equal, so the constant ratio must be different for inconsistency. Hence, \(m \ne 34\).
Step 3
Exam Tip
पहले दो अनुपात बराबर हैं, इसलिए असंगत होने के लिए स्थिर पद का अनुपात अलग होना चाहिए। अतः \(m \ne 34\) होगा।
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यदि (5x+2y=13) और (10x+4y=m) असंगत युग्म हैं तो (m) के लिए सही शर्त क्या है?
If (5x+2y=13) and (10x+4y=m) form an inconsistent pair then what is the correct condition for (m)?
#linear equations
#inconsistent
#condition
A (m=26)
B (m=13)
C \(m \ne 26\)
D (m=39)
Explanation opens after your attempt
Correct Answer
C. \(m \ne 26\)
Step 1
Concept
The first two ratios are equal so the constant ratio must differ for inconsistency. Hence \(m \ne 26\).
Step 2
Why this answer is correct
The correct answer is C. \(m \ne 26\). The first two ratios are equal so the constant ratio must differ for inconsistency. Hence \(m \ne 26\).
Step 3
Exam Tip
पहले दो अनुपात बराबर हैं इसलिए असंगत होने के लिए स्थिर पद का अनुपात अलग होना चाहिए। अतः \(m \ne 26\)।
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यदि (4x+5y=16) और (8x+10y=m) असंगत युग्म हैं, तो (m) के लिए सही शर्त क्या है?
If (4x+5y=16) and (8x+10y=m) form an inconsistent pair, what is the correct condition for (m)?
#linear equations
#inconsistent
#condition
A (m=32)
B \(m \ne 32\)
C (m=16)
D (m=24)
Explanation opens after your attempt
Correct Answer
B. \(m \ne 32\)
Step 1
Concept
The first two ratios are equal, so for inconsistency the constant ratio must differ. Hence, \(m \ne 32\).
Step 2
Why this answer is correct
The correct answer is B. \(m \ne 32\). The first two ratios are equal, so for inconsistency the constant ratio must differ. Hence, \(m \ne 32\).
Step 3
Exam Tip
पहले दो अनुपात बराबर हैं, इसलिए असंगत होने के लिए स्थिर पद का अनुपात अलग होना चाहिए। अतः \(m \ne 32\)।
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यदि (2x+3y=7) और (4x+6y=m) असंगत युग्म हैं, तो (m) के लिए सही शर्त क्या है?
If (2x+3y=7) and (4x+6y=m) form an inconsistent pair, what is the correct condition for (m)?
#linear equations
#inconsistent pair
#condition
A (m=14)
B \(m \ne 14\)
C (m=7)
D (m=21)
Explanation opens after your attempt
Correct Answer
B. \(m \ne 14\)
Step 1
Concept
The first two ratios are equal, so for inconsistency the constant ratio must differ. Hence \(m \ne 14\).
Step 2
Why this answer is correct
The correct answer is B. \(m \ne 14\). The first two ratios are equal, so for inconsistency the constant ratio must differ. Hence \(m \ne 14\).
Step 3
Exam Tip
पहले दो अनुपात बराबर हैं, इसलिए असंगत होने के लिए स्थिर पद का अनुपात अलग होना चाहिए। अतः \(m \ne 14\)।
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ग्राफ में (x)-अक्ष पर प्रतिच्छेद करने वाली रेखाओं के युग्म के लिए प्रतिच्छेद बिंदु का कौन सा रूप होगा?
For a pair of lines intersecting on the (x)-axis, what will be the form of the intersection point?
#linear equations
#graphical method
#x-axis intersection
#concept
A ((0,a))
B ((a,0))
C ((a,a))
D ((-a,a))
Explanation opens after your attempt
Correct Answer
B. ((a,0))
Step 1
Concept
Every point on the (x)-axis has (y)-coordinate (0). So the intersection has the form ((a,0)).
Step 2
Why this answer is correct
The correct answer is B. ((a,0)). Every point on the (x)-axis has (y)-coordinate (0). So the intersection has the form ((a,0)).
Step 3
Exam Tip
(x)-अक्ष पर हर बिंदु का (y)-निर्देशांक (0) होता है। इसलिए प्रतिच्छेद का रूप ((a,0)) होगा।
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\(0.00\overline{54}\) का सरलतम भिन्न रूप कौन-सा है?
Which is the lowest fraction form of \(0.00\overline{54}\)?
#recurring-decimal
#fraction-form
#lowest-form
#expert
A \(\frac{3}{550}\)
B \(\frac{54}{990}\)
C \(\frac{6}{1100}\)
D \(\frac{1}{550}\)
Explanation opens after your attempt
Correct Answer
A. \(\frac{3}{550}\)
Step 1
Concept
Two non-repeating zeros and two repeating digits give \(\frac{54}{9900}\). Reducing it gives \(\frac{3}{550}\).
Step 2
Why this answer is correct
The correct answer is A. \(\frac{3}{550}\). Two non-repeating zeros and two repeating digits give \(\frac{54}{9900}\). Reducing it gives \(\frac{3}{550}\).
Step 3
Exam Tip
दो अनावर्ती शून्य और दो आवर्ती अंकों से \(\frac{54}{9900}\) बनता है। इसे सरल करने पर \(\frac{3}{550}\) मिलता है।
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\(0.00\overline{63}\) का सरलतम भिन्न रूप कौन-सा है?
Which is the lowest fraction form of \(0.00\overline{63}\)?
#recurring-decimal
#fraction-form
#lowest-form
#expert
A \(\frac{7}{1100}\)
B \(\frac{63}{990}\)
C \(\frac{9}{1100}\)
D \(\frac{21}{3300}\)
Explanation opens after your attempt
Correct Answer
A. \(\frac{7}{1100}\)
Step 1
Concept
Two non-repeating zeros and two repeating digits give \(\frac{63}{9900}\). Reducing it gives \(\frac{7}{1100}\).
Step 2
Why this answer is correct
The correct answer is A. \(\frac{7}{1100}\). Two non-repeating zeros and two repeating digits give \(\frac{63}{9900}\). Reducing it gives \(\frac{7}{1100}\).
Step 3
Exam Tip
दो अनावर्ती शून्य और दो आवर्ती अंकों से \(\frac{63}{9900}\) बनता है। इसे सरल करने पर \(\frac{7}{1100}\) मिलता है।
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\(0.00\overline{72}\) का सरलतम भिन्न रूप कौन-सा है?
Which is the lowest fraction form of \(0.00\overline{72}\)?
#recurring-decimal
#fraction-form
#lowest-form
#expert
A \(\frac{2}{275}\)
B \(\frac{72}{990}\)
C \(\frac{8}{1100}\)
D \(\frac{1}{275}\)
Explanation opens after your attempt
Correct Answer
A. \(\frac{2}{275}\)
Step 1
Concept
Two non-repeating zeros and two repeating digits give \(\frac{72}{9900}\). Reducing it gives \(\frac{2}{275}\).
Step 2
Why this answer is correct
The correct answer is A. \(\frac{2}{275}\). Two non-repeating zeros and two repeating digits give \(\frac{72}{9900}\). Reducing it gives \(\frac{2}{275}\).
Step 3
Exam Tip
दो अनावर्ती शून्य और दो आवर्ती अंकों से \(\frac{72}{9900}\) बनता है। इसे सरल करने पर \(\frac{2}{275}\) मिलता है।
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सरल रूप में किसी परिमेय संख्या का भाजक (q) किस रूप में हो तो दशमलव समाप्त होगा?
In lowest form, what form should the denominator (q) of a rational number have for the decimal to terminate?
#real numbers
#denominator form
#terminating decimals
#class 10
A \(2^m5^n\)
B \(3^m5^n\)
C \(7^m\)
D \(2^m3^n\)
Explanation opens after your attempt
Correct Answer
A. \(2^m5^n\)
Step 1
Concept
For a terminating decimal, the denominator must be made only from (2) and (5).
Step 2
Why this answer is correct
So its form is \(2^m5^n\).
Step 3
Exam Tip
(m) or (n) may be zero, so only (2) or only (5) is also allowed. चरण 1: समाप्त दशमलव के लिए भाजक केवल (2) और (5) से बनना चाहिए। चरण 2: इसलिए उसका रूप \(2^m5^n\) होता है। चरण 3: (m) या (n) शून्य भी हो सकते हैं, इसलिए केवल (2) या केवल (5) भी चलेगा।
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किसी धनात्मक पूर्णांक को (9) से भाग देने पर कौन-सा रूप मानक रूप नहीं है?
When a positive integer is divided by (9), which form is not a standard form?
#real-numbers
#not-standard-form
#remainder-condition
A (9q+7)
B (9q+8)
C (9q+9)
D (9q)
Explanation opens after your attempt
Step 1
Concept
On division by (9), remainders can be from (0) to (8).
Step 2
Why this answer is correct
In (9q+9), the remainder is (9), which equals the divisor.
Step 3
Exam Tip
It should be written correctly as (9(q+1)). चरण 1: (9) से भाग देने पर शेषफल (0) से (8) तक हो सकते हैं। चरण 2: (9q+9) में शेषफल (9) है, जो भाजक के बराबर है। चरण 3: इसे सही रूप में (9(q+1)) लिखा जाना चाहिए।
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किसी धनात्मक पूर्णांक को (3) से भाग देने पर कौन-सा रूप मानक रूप नहीं है?
When a positive integer is divided by (3), which form is not a standard form?
#real-numbers
#not-standard-form
#remainder-condition
A (3q)
B (3q+1)
C (3q+2)
D (3q+3)
Explanation opens after your attempt
Step 1
Concept
On division by (3), possible remainders are (0,1,2).
Step 2
Why this answer is correct
In (3q+3), the remainder is (3), which equals the divisor.
Step 3
Exam Tip
It should be written correctly as (3(q+1)). चरण 1: (3) से भाग देने पर शेषफल (0,1,2) हो सकते हैं। चरण 2: (3q+3) में शेषफल (3) है, जो भाजक के बराबर है। चरण 3: इसे सही रूप में (3(q+1)) लिखना चाहिए।
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किसी धनात्मक पूर्णांक को (3) से भाग देने पर कौन-सा रूप संभव नहीं है?
Which form is not possible as a standard form when a positive integer is divided by (3)?
#real-numbers
#general-form
#not-possible
A (3q)
B (3q+1)
C (3q+2)
D (3q+3)
Explanation opens after your attempt
Step 1
Concept
On division by (3), possible remainders are (0,1,2).
Step 2
Why this answer is correct
In (3q+3), the remainder is (3), which equals the divisor.
Step 3
Exam Tip
It should be written as (3(q+1)). चरण 1: (3) से भाग देने पर शेषफल (0,1,2) हो सकते हैं। चरण 2: (3q+3) में शेषफल (3) है, जो भाजक के बराबर है। चरण 3: इसे (3(q+1)) के रूप में लिखना चाहिए।
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किसी धनात्मक पूर्णांक को (4) से भाग देने पर वह किस रूप में नहीं लिखा जा सकता?
When a positive integer is divided by (4), which form cannot be a standard remainder form?
#real-numbers
#general-form
#remainder-condition
A (4q)
B (4q+1)
C (4q+2)
D (4q+4)
Explanation opens after your attempt
Step 1
Concept
On division by (4), possible remainders are (0,1,2,3).
Step 2
Why this answer is correct
In (4q+4), the remainder is (4), which equals the divisor.
Step 3
Exam Tip
Such a form should be written as (4(q+1)). चरण 1: (4) से भाग देने पर शेषफल (0,1,2,3) हो सकते हैं। चरण 2: (4q+4) में शेषफल (4) है, जो भाजक के बराबर है। चरण 3: ऐसे रूप को (4(q+1)) लिखना चाहिए।
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यदि (4(2x-y)+3(x+y)=53) और (2(2x-y)-5(x+y)=-17), तो (y) का मान क्या है?
If (4(2x-y)+3(x+y)=53) and (2(2x-y)-5(x+y)=-17), what is the value of (y)?
#pair-linear-equations-linear-combination
A (4)
B (5)
C (6)
D (7)
Explanation opens after your attempt
Step 1
Concept
Let (u=2x-y) and (v=x+y). Solve the two equations first, then convert back to (x) and (y).
Step 2
Why this answer is correct
The correct answer is B. (5). Let (u=2x-y) and (v=x+y). Solve the two equations first, then convert back to (x) and (y).
Step 3
Exam Tip
मान लें (u=2x-y) और (v=x+y)। (4u+3v=53), (2u-5v=-17) से (u=7), \(v=\frac{25}{3}\), इसलिए \(y=\frac{29}{9}\)।
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यदि (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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समीकरणों (21x+8y=97) और (42x+16y=194) को देखकर कौन-सा कथन सही है?
Which statement is correct by observing the equations (21x+8y=97) and (42x+16y=194)?
#linear equations
#expert
#observation
#same line
A रेखाएं समानांतर और अलग हैं / Lines are parallel and distinct
B रेखाएं एक ही हैं / Lines are the same
C रेखाएं एक बिंदु पर कटती हैं / Lines intersect at one point
D कोई हल नहीं है / There is no solution
Explanation opens after your attempt
Correct Answer
B. रेखाएं एक ही हैं / Lines are the same
Step 1
Concept
The second equation is (2) times the first. Therefore, both lines are the same and have infinitely many solutions.
Step 2
Why this answer is correct
The correct answer is B. रेखाएं एक ही हैं / Lines are the same. The second equation is (2) times the first. Therefore, both lines are the same and have infinitely many solutions.
Step 3
Exam Tip
दूसरा समीकरण पहले का (2) गुना है। इसलिए दोनों रेखाएं एक ही हैं और अनंत हल हैं।
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दो वस्तुओं की कीमतों के लिए (10x+3y=470) और (20x+6y=955) समीकरण बने। यह प्रणाली कैसी है?
For prices of two items, the equations (10x+3y=470) and (20x+6y=955) are formed. What type of system is this?
#linear equations
#expert
#word problem
#inconsistent
A संगत और स्वतंत्र / Consistent and independent
B संगत और आश्रित / Consistent and dependent
C असंगत / Inconsistent
D अनंत हल वाली / With infinitely many solutions
Explanation opens after your attempt
Correct Answer
C. असंगत / Inconsistent
Step 1
Concept
The first two ratios are equal but (470/955) is different. Therefore, the system is inconsistent.
Step 2
Why this answer is correct
The correct answer is C. असंगत / Inconsistent. The first two ratios are equal but (470/955) is different. Therefore, the system is inconsistent.
Step 3
Exam Tip
पहले दो अनुपात बराबर हैं लेकिन (470/955) अलग है। इसलिए प्रणाली असंगत है।
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समीकरणों (7x+19y=86) और (13x+35y=158) में (a) और (b) के अनुपातों की तुलना से क्या निष्कर्ष निकलेगा?
What conclusion follows from comparing the ratios of (a) and (b) in the equations (7x+19y=86) and (13x+35y=158)?
#linear equations
#expert
#ratio comparison
#unique solution
A (7 / 13=19 / 35), इसलिए कोई हल नहीं / 35), so no solution
B (7 / 13=19 / 35), इसलिए अनंत हल / 35), so infinitely many solutions
C (7 / 13 \ne 19 / 35), इसलिए एक अद्वितीय हल / 35), so one unique solution
D तीनों अनुपात बराबर हैं / All three ratios are equal
Explanation opens after your attempt
Correct Answer
C. (7 / 13 \ne 19 / 35), इसलिए एक अद्वितीय हल / 35), so one unique solution
Step 1
Concept
The first two ratios are different. Therefore, the lines intersect at one point and give one unique solution.
Step 2
Why this answer is correct
The correct answer is C. \(7 / 13 \ne 19 / 35\), इसलिए एक अद्वितीय हल / 35), so one unique solution. The first two ratios are different. Therefore, the lines intersect at one point and give one unique solution.
Step 3
Exam Tip
पहले दो अनुपात अलग हैं। इसलिए रेखाएं एक बिंदु पर कटती हैं और एक अद्वितीय हल देती हैं।
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समीकरणों (12x-7y+29=0) और (36x-21y+91=0) के लिए सही हल-स्थिति क्या है?
What is the correct solution status for the equations (12x-7y+29=0) and (36x-21y+91=0)?
#linear equations
#expert
#ratio relation
#no solution
A एक अद्वितीय हल / One unique solution
B अनंत हल / Infinitely many solutions
C कोई हल नहीं / No solution
D संगत और आश्रित / Consistent and dependent
Explanation opens after your attempt
Correct Answer
C. कोई हल नहीं / No solution
Step 1
Concept
Here (12/36=(-7)/(-21)) but (29/91) is different. Therefore, the lines are parallel and distinct.
Step 2
Why this answer is correct
The correct answer is C. कोई हल नहीं / No solution. Here (12/36=(-7)/(-21)) but (29/91) is different. Therefore, the lines are parallel and distinct.
Step 3
Exam Tip
यहां (12/36=(-7)/(-21)) लेकिन (29/91) अलग है। इसलिए रेखाएं समानांतर और अलग हैं।
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समीकरणों (11x+ky=70) और (5x+4y=31) का अद्वितीय हल होने के लिए कौन-सी शर्त सही है?
Which condition is correct for the equations (11x+ky=70) and (5x+4y=31) to have a unique solution?
#linear equations
#expert
#unique solution
#parameter
A (k=44 / 5)
B (k\ne44 / 5)
C (k=4)
D (k=11)
Explanation opens after your attempt
Correct Answer
B. (k\ne44 / 5)
Step 1
Concept
For a unique solution, \(11/5 \ne k/4\) must hold. Therefore, \(k\ne44/5\) is the correct condition.
Step 2
Why this answer is correct
The correct answer is B. \(k\ne44 / 5\). For a unique solution, \(11/5 \ne k/4\) must hold. Therefore, \(k\ne44/5\) is the correct condition.
Step 3
Exam Tip
अद्वितीय हल के लिए \(11/5 \ne k/4\) होना चाहिए। इसलिए \(k\ne44/5\) सही शर्त है।
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समीकरणों (px+10y=50) और (14x+35y=122) का कोई हल न होने के लिए (p) का मान क्या होगा?
What is the value of (p) for the equations (px+10y=50) and (14x+35y=122) to have no solution?
#linear equations
#expert
#no solution
#parameter
A (3)
B (4)
C (5)
D (6)
Explanation opens after your attempt
Step 1
Concept
For no solution, (p/14=10/35) and (50/122) must be different. Therefore, (p=4).
Step 2
Why this answer is correct
The correct answer is B. (4). For no solution, (p/14=10/35) and (50/122) must be different. Therefore, (p=4).
Step 3
Exam Tip
कोई हल नहीं के लिए (p/14=10/35) और (50/122) अलग होना चाहिए। इसलिए (p=4)।
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समीकरणों (6x+ay=42) और (18x+33y=126) के अनंत हल होने के लिए (a) का मान क्या होगा?
What is the value of (a) for the equations (6x+ay=42) and (18x+33y=126) to have infinitely many solutions?
#linear equations
#expert
#infinite solutions
#parameter
A (9)
B (10)
C (11)
D (12)
Explanation opens after your attempt
Step 1
Concept
For infinitely many solutions, (6/18=a/33=42/126) must hold. Therefore, (a=11) is correct.
Step 2
Why this answer is correct
The correct answer is C. (11). For infinitely many solutions, (6/18=a/33=42/126) must hold. Therefore, (a=11) is correct.
Step 3
Exam Tip
अनंत हल के लिए (6/18=a/33=42/126) होना चाहिए। इसलिए (a=11) सही है।
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समीकरणों (5x+9y=64) और (15x+27y=t) के असंगत होने के लिए (t) के लिए सही शर्त क्या है?
What is the correct condition on (t) for the equations (5x+9y=64) and (15x+27y=t) to be inconsistent?
#linear equations
#expert
#inconsistent
#parameter
A (t=192)
B \(t\ne192\)
C (t=64)
D (t=128)
Explanation opens after your attempt
Correct Answer
B. \(t\ne192\)
Step 1
Concept
The first two ratios are equal. For inconsistency, the constant ratio must be different so \(t\ne192\).
Step 2
Why this answer is correct
The correct answer is B. \(t\ne192\). The first two ratios are equal. For inconsistency, the constant ratio must be different so \(t\ne192\).
Step 3
Exam Tip
पहले दो अनुपात बराबर हैं। असंगत होने के लिए स्थिर पद का अनुपात अलग होना चाहिए इसलिए \(t\ne192\)।
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समीकरणों (29x+12y=101) और (14x+6y=49) के लिए सही हल-स्थिति क्या है?
What is the correct solution status for the equations (29x+12y=101) and (14x+6y=49)?
#linear equations
#expert
#unique solution
#solvability
A कोई हल नहीं / No solution
B अनंत हल / Infinitely many solutions
C एक अद्वितीय हल / One unique solution
D संगत और आश्रित / Consistent and dependent
Explanation opens after your attempt
Correct Answer
C. एक अद्वितीय हल / One unique solution
Step 1
Concept
Here \(29/14 \ne 12/6\), so the lines will intersect. Hence, there is one unique solution.
Step 2
Why this answer is correct
The correct answer is C. एक अद्वितीय हल / One unique solution. Here \(29/14 \ne 12/6\), so the lines will intersect. Hence, there is one unique solution.
Step 3
Exam Tip
यहां \(29/14 \ne 12/6\), इसलिए रेखाएं कटेंगी। अतः एक अद्वितीय हल है।
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समीकरणों (24x-18y=102) और (4x-3y=18) को देखकर सही निष्कर्ष क्या है?
What is the correct conclusion by observing the equations (24x-18y=102) and (4x-3y=18)?
#linear equations
#expert
#no solution
#observation
A कोई हल नहीं / No solution
B अनंत हल / Infinitely many solutions
C एक अद्वितीय हल / One unique solution
D संपाती रेखाएं / Coincident lines
Explanation opens after your attempt
Correct Answer
A. कोई हल नहीं / No solution
Step 1
Concept
Here (24/4=(-18)/(-3)) but (102/18) is different. Therefore, the lines are parallel and distinct.
Step 2
Why this answer is correct
The correct answer is A. कोई हल नहीं / No solution. Here (24/4=(-18)/(-3)) but (102/18) is different. Therefore, the lines are parallel and distinct.
Step 3
Exam Tip
यहां (24/4=(-18)/(-3)) लेकिन (102/18) अलग है। इसलिए रेखाएं समानांतर और अलग हैं।
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समीकरणों (18x+13y=89) और (36x+26y=178) को देखकर कौन-सा कथन सही है?
Which statement is correct by observing the equations (18x+13y=89) and (36x+26y=178)?
#linear equations
#expert
#observation
#same line
A रेखाएं समानांतर और अलग हैं / Lines are parallel and distinct
B रेखाएं एक ही हैं / Lines are the same
C रेखाएं एक बिंदु पर कटती हैं / Lines intersect at one point
D कोई हल नहीं है / There is no solution
Explanation opens after your attempt
Correct Answer
B. रेखाएं एक ही हैं / Lines are the same
Step 1
Concept
The second equation is (2) times the first. Therefore, both lines are the same.
Step 2
Why this answer is correct
The correct answer is B. रेखाएं एक ही हैं / Lines are the same. The second equation is (2) times the first. Therefore, both lines are the same.
Step 3
Exam Tip
दूसरा समीकरण पहले का (2) गुना है। इसलिए दोनों रेखाएं एक ही हैं।
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यदि (lx+17y=68) और (20x+34y=139) का कोई हल नहीं है, तो (l) का मान क्या होगा?
If (lx+17y=68) and (20x+34y=139) have no solution, what will be the value of (l)?
#linear equations
#expert
#parameter
#parallel lines
A (8)
B (9)
C (10)
D (11)
Explanation opens after your attempt
Step 1
Concept
For no solution, (l/20=17/34) and (68/139) must be different. Hence, (l=10).
Step 2
Why this answer is correct
The correct answer is C. (10). For no solution, (l/20=17/34) and (68/139) must be different. Hence, (l=10).
Step 3
Exam Tip
कोई हल नहीं के लिए (l/20=17/34) और (68/139) अलग होना चाहिए। इसलिए (l=10)।
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समीकरणों (12x+ky=132) और (3x+10y=33) के अनंत हल होने के लिए (k) क्या होगा?
What will (k) be for the equations (12x+ky=132) and (3x+10y=33) to have infinitely many solutions?
#linear equations
#expert
#infinite solutions
#parameter
A (38)
B (39)
C (40)
D (41)
Explanation opens after your attempt
Step 1
Concept
The first equation must be (4) times the second. Therefore, (k=40).
Step 2
Why this answer is correct
The correct answer is C. (40). The first equation must be (4) times the second. Therefore, (k=40).
Step 3
Exam Tip
पहला समीकरण दूसरे का (4) गुना होना चाहिए। इसलिए (k=40) है।
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समीकरणों (10x+9y=38) और (20x+ay=91) का कोई हल न होने के लिए (a) क्या होगा?
What will (a) be for the equations (10x+9y=38) and (20x+ay=91) to have no solution?
#linear equations
#expert
#no solution
#parameter
A (16)
B (17)
C (18)
D (19)
Explanation opens after your attempt
Step 1
Concept
For no solution, (10/20=9/a) and (38/91) must be different. This gives (a=18).
Step 2
Why this answer is correct
The correct answer is C. (18). For no solution, (10/20=9/a) and (38/91) must be different. This gives (a=18).
Step 3
Exam Tip
कोई हल नहीं के लिए (10/20=9/a) और (38/91) अलग होना चाहिए। इससे (a=18) मिलता है।
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समीकरणों (13x+8y=49) और (26x+16y=r) के असंगत होने के लिए कौन-सी शर्त सही है?
Which condition is correct for the equations (13x+8y=49) and (26x+16y=r) to be inconsistent?
#linear equations
#expert
#inconsistent
#parameter
A (r=98)
B \(r\ne98\)
C (r=49)
D (r=100)
Explanation opens after your attempt
Correct Answer
B. \(r\ne98\)
Step 1
Concept
The first two ratios are equal. For inconsistency, the constant ratio must be different so \(r\ne98\).
Step 2
Why this answer is correct
The correct answer is B. \(r\ne98\). The first two ratios are equal. For inconsistency, the constant ratio must be different so \(r\ne98\).
Step 3
Exam Tip
पहले दो अनुपात बराबर हैं। असंगत होने के लिए स्थिर पद का अनुपात अलग होना चाहिए इसलिए \(r\ne98\)।
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समीकरणों (9x+16y=77) और (27x+48y=s) के संगत और आश्रित होने के लिए (s) क्या होगा?
What should (s) be for the equations (9x+16y=77) and (27x+48y=s) to be consistent and dependent?
#linear equations
#expert
#consistent dependent
#parameter
A (229)
B (230)
C (231)
D (232)
Explanation opens after your attempt
Step 1
Concept
To be consistent and dependent, the second equation must be (3) times the first. Hence, (s=231).
Step 2
Why this answer is correct
The correct answer is C. (231). To be consistent and dependent, the second equation must be (3) times the first. Hence, (s=231).
Step 3
Exam Tip
संगत और आश्रित होने के लिए दूसरा समीकरण पहले का (3) गुना होना चाहिए। अतः (s=231)।
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समीकरणों (12x+13y=55) और (24x+25y=107) के लिए कौन-सा कथन सही है?
Which statement is correct for the equations (12x+13y=55) and (24x+25y=107)?
#linear equations
#expert
#ratio comparison
#unique solution
A (12 / 24=13 / 25), इसलिए कोई हल नहीं / 25), so no solution
B (12 / 24 \ne 13 / 25), इसलिए एक अद्वितीय हल / 25), so one unique solution
C तीनों अनुपात बराबर हैं / All three ratios are equal
D रेखाएं संपाती हैं / Lines are coincident
Explanation opens after your attempt
Correct Answer
B. (12 / 24 \ne 13 / 25), इसलिए एक अद्वितीय हल / 25), so one unique solution
Step 1
Concept
Here \(12/24 \ne 13/25\), so the lines intersect. Therefore, there is one unique solution.
Step 2
Why this answer is correct
The correct answer is B. \(12 / 24 \ne 13 / 25\), इसलिए एक अद्वितीय हल / 25), so one unique solution. Here \(12/24 \ne 13/25\), so the lines intersect. Therefore, there is one unique solution.
Step 3
Exam Tip
यहां \(12/24 \ne 13/25\), इसलिए रेखाएं कटती हैं। इस कारण एक अद्वितीय हल है।
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समीकरणों (18x+27y=126) और (2x+3y=16) के लिए कौन-सा संबंध सही है?
Which relation is correct for the equations (18x+27y=126) and (2x+3y=16)?
#linear equations
#expert
#ratio relation
#no solution
A (18 / 2 \ne 27 / 3)
B (18 / 2=27 / 3=126 / 16)
C (18 / 2=27 / 3 \ne 126 / 16)
D (18 / 2=126 / 16 \ne 27 / 3)
Explanation opens after your attempt
Correct Answer
C. (18 / 2=27 / 3 \ne 126 / 16)
Step 1
Concept
The first two ratios are equal but the constant ratio is different. Therefore, there is no solution.
Step 2
Why this answer is correct
The correct answer is C. \(18 / 2=27 / 3 \ne 126 / 16\). The first two ratios are equal but the constant ratio is different. Therefore, there is no solution.
Step 3
Exam Tip
पहले दो अनुपात बराबर हैं लेकिन स्थिर पद का अनुपात अलग है। इसलिए कोई हल नहीं है।
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समीकरणों (11x+18y=86) और (33x+54y=258) में तीनों अनुपातों का संबंध क्या है?
What is the relation among all three ratios in the equations (11x+18y=86) and (33x+54y=258)?
#linear equations
#expert
#ratio relation
#coincident
A तीनों बराबर हैं / All three are equal
B पहले दो बराबर और तीसरा अलग है / First two are equal and third is different
C पहले दो अलग हैं / First two are different
D केवल स्थिर पद बराबर हैं / Only constants are equal
Explanation opens after your attempt
Correct Answer
A. तीनों बराबर हैं / All three are equal
Step 1
Concept
Here (11/33=18/54=86/258). Therefore, both equations form the same line.
Step 2
Why this answer is correct
The correct answer is A. तीनों बराबर हैं / All three are equal. Here (11/33=18/54=86/258). Therefore, both equations form the same line.
Step 3
Exam Tip
यहां (11/33=18/54=86/258)। इसलिए दोनों समीकरण एक ही रेखा बनाते हैं।
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दो संख्याओं के लिए (7x+5y=58) और (4x-3y=11) समीकरण बनते हैं, तो हल-स्थिति क्या होगी?
For two numbers, the equations (7x+5y=58) and (4x-3y=11) are formed. What will be the solution status?
#linear equations
#expert
#word problem
#unique solution
A एक अद्वितीय हल / One unique solution
B कोई हल नहीं / No solution
C अनंत हल / Infinitely many solutions
D निर्धारित नहीं / Not determined
Explanation opens after your attempt
Correct Answer
A. एक अद्वितीय हल / One unique solution
Step 1
Concept
Here (7/4 \ne 5/(-3)), so the lines intersect. Such a pair has one unique solution.
Step 2
Why this answer is correct
The correct answer is A. एक अद्वितीय हल / One unique solution. Here (7/4 \ne 5/(-3)), so the lines intersect. Such a pair has one unique solution.
Step 3
Exam Tip
यहां (7/4 \ne 5/(-3)), इसलिए रेखाएं कटती हैं। ऐसे युग्म का एक अद्वितीय हल होता है।
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दो टिकटों के दामों के लिए (9x+4y=380) और (18x+8y=775) समीकरण बने। यह प्रणाली कैसी है?
For prices of two tickets, the equations (9x+4y=380) and (18x+8y=775) are formed. What type of system is this?
#linear equations
#expert
#word problem
#inconsistent
A संगत और स्वतंत्र / Consistent and independent
B संगत और आश्रित / Consistent and dependent
C असंगत / Inconsistent
D अनंत हल वाली / With infinitely many solutions
Explanation opens after your attempt
Correct Answer
C. असंगत / Inconsistent
Step 1
Concept
The first two ratios are equal but (380/775) is different. Therefore, the system is inconsistent.
Step 2
Why this answer is correct
The correct answer is C. असंगत / Inconsistent. The first two ratios are equal but (380/775) is different. Therefore, the system is inconsistent.
Step 3
Exam Tip
पहले दो अनुपात बराबर हैं लेकिन (380/775) अलग है। इसलिए प्रणाली असंगत है।
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एक दुकान में दो वस्तुओं के लिए (6x+11y=420) और (18x+33y=1260) समीकरण बनते हैं। हलों की संख्या क्या होगी?
In a shop, the equations for two items are (6x+11y=420) and (18x+33y=1260). How many solutions will there be?
#linear equations
#expert
#word problem
#infinite solutions
A कोई हल नहीं / No solution
B एक अद्वितीय हल / One unique solution
C अनंत हल / Infinitely many solutions
D दो हल / Two solutions
Explanation opens after your attempt
Correct Answer
C. अनंत हल / Infinitely many solutions
Step 1
Concept
The second equation is (3) times the first. Therefore, both conditions give the same information and have infinitely many solutions.
Step 2
Why this answer is correct
The correct answer is C. अनंत हल / Infinitely many solutions. The second equation is (3) times the first. Therefore, both conditions give the same information and have infinitely many solutions.
Step 3
Exam Tip
दूसरा समीकरण पहले का (3) गुना है। इसलिए दोनों शर्तें एक ही जानकारी देती हैं और अनंत हल होते हैं।
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समीकरणों (18x+7y=61) और (9x+4y=32) का युग्म किस प्रकार का है?
What type of pair is formed by the equations (18x+7y=61) and (9x+4y=32)?
#linear equations
#expert
#consistent independent
A असंगत / Inconsistent
B संगत और आश्रित / Consistent and dependent
C संगत और स्वतंत्र / Consistent and independent
D समानांतर / Parallel
Explanation opens after your attempt
Correct Answer
C. संगत और स्वतंत्र / Consistent and independent
Step 1
Concept
Here \(18/9 \ne 7/4\), so the lines intersect. Hence, the pair is consistent and independent.
Step 2
Why this answer is correct
The correct answer is C. संगत और स्वतंत्र / Consistent and independent. Here \(18/9 \ne 7/4\), so the lines intersect. Hence, the pair is consistent and independent.
Step 3
Exam Tip
यहां \(18/9 \ne 7/4\), इसलिए रेखाएं कटती हैं। अतः युग्म संगत और स्वतंत्र है।
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समीकरणों (26x+39y=117) और (2x+3y=10) का युग्म किस प्रकार का है?
What type of pair is formed by the equations (26x+39y=117) and (2x+3y=10)?
#linear equations
#expert
#inconsistent
#classification
A संगत और स्वतंत्र / Consistent and independent
B संगत और आश्रित / Consistent and dependent
C असंगत / Inconsistent
D संपाती / Coincident
Explanation opens after your attempt
Correct Answer
C. असंगत / Inconsistent
Step 1
Concept
Here (26/2=39/3) but (117/10) is different. Therefore, this is an inconsistent pair.
Step 2
Why this answer is correct
The correct answer is C. असंगत / Inconsistent. Here (26/2=39/3) but (117/10) is different. Therefore, this is an inconsistent pair.
Step 3
Exam Tip
यहां (26/2=39/3) लेकिन (117/10) अलग है। इसलिए यह असंगत युग्म है।
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समीकरणों (30x+45y=210) और (2x+3y=14) का युग्म किस प्रकार का है?
What type of pair is formed by the equations (30x+45y=210) and (2x+3y=14)?
#linear equations
#expert
#dependent pair
#classification
A संगत और आश्रित / Consistent and dependent
B असंगत / Inconsistent
C संगत और स्वतंत्र / Consistent and independent
D असमाधेय / Unsolvable
Explanation opens after your attempt
Correct Answer
A. संगत और आश्रित / Consistent and dependent
Step 1
Concept
The first equation is (15) times the second. Therefore, both are the same line and the pair is dependent.
Step 2
Why this answer is correct
The correct answer is A. संगत और आश्रित / Consistent and dependent. The first equation is (15) times the second. Therefore, both are the same line and the pair is dependent.
Step 3
Exam Tip
पहला समीकरण दूसरे का (15) गुना है। इसलिए दोनों एक ही रेखा हैं और युग्म आश्रित है।
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समीकरणों (19x+12y=71) और (9x+6y=35) में (a) और (b) के अनुपातों की तुलना से क्या पता चलता है?
What is found by comparing the ratios of (a) and (b) in the equations (19x+12y=71) and (9x+6y=35)?
#linear equations
#expert
#ratio comparison
#unique solution
A (19 / 9=12 / 6), इसलिए अनंत हल / 6), so infinitely many solutions
B (19 / 9=12 / 6), इसलिए कोई हल नहीं / 6), so no solution
C (19 / 9 \ne 12 / 6), इसलिए एक अद्वितीय हल / 6), so one unique solution
D (19 / 9=71 / 35), इसलिए संपाती / 35), so coincident
Explanation opens after your attempt
Correct Answer
C. (19 / 9 \ne 12 / 6), इसलिए एक अद्वितीय हल / 6), so one unique solution
Step 1
Concept
Here the first two ratios are different. Therefore, the lines intersect at one point and give one solution.
Step 2
Why this answer is correct
The correct answer is C. \(19 / 9 \ne 12 / 6\), इसलिए एक अद्वितीय हल / 6), so one unique solution. Here the first two ratios are different. Therefore, the lines intersect at one point and give one solution.
Step 3
Exam Tip
यहां पहले दो अनुपात अलग हैं। इसलिए रेखाएं एक बिंदु पर कटती हैं और एक हल देती हैं।
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समीकरणों (24x+32y=96) और (3x+4y=13) को देखकर कौन-सा निष्कर्ष सही है?
Which conclusion is correct by observing the equations (24x+32y=96) and (3x+4y=13)?
#linear equations
#expert
#observation
#no solution
A तीनों अनुपात बराबर हैं / All three ratios are equal
B पहले दो अनुपात बराबर हैं लेकिन स्थिर पद का अनुपात अलग है / First two ratios are equal but the constant ratio is different
C पहले दो अनुपात अलग हैं / First two ratios are different
D रेखाएं कटती हैं / Lines intersect
Explanation opens after your attempt
Correct Answer
B. पहले दो अनुपात बराबर हैं लेकिन स्थिर पद का अनुपात अलग है / First two ratios are equal but the constant ratio is different
Step 1
Concept
Here (24/3=32/4) but (96/13) is different. Therefore, there will be no solution.
Step 2
Why this answer is correct
The correct answer is B. पहले दो अनुपात बराबर हैं लेकिन स्थिर पद का अनुपात अलग है / First two ratios are equal but the constant ratio is different. Here (24/3=32/4) but (96/13) is different. Therefore, there will be no solution.
Step 3
Exam Tip
यहां (24/3=32/4) लेकिन (96/13) अलग है। इसलिए कोई हल नहीं होगा।
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समीकरणों (8x+15y=73) और (24x+45y=219) को देखकर सबसे उचित निष्कर्ष क्या है?
What is the most suitable conclusion by observing the equations (8x+15y=73) and (24x+45y=219)?
#linear equations
#expert
#observation
#infinite solutions
A एक अद्वितीय हल है / There is one unique solution
B कोई हल नहीं है / There is no solution
C अनंत हल हैं / There are infinitely many solutions
D रेखाएं अलग समानांतर हैं / Lines are distinct parallel
Explanation opens after your attempt
Correct Answer
C. अनंत हल हैं / There are infinitely many solutions
Step 1
Concept
The second equation is (3) times the first. Therefore, both lines are coincident.
Step 2
Why this answer is correct
The correct answer is C. अनंत हल हैं / There are infinitely many solutions. The second equation is (3) times the first. Therefore, both lines are coincident.
Step 3
Exam Tip
दूसरा समीकरण पहले का (3) गुना है। इसलिए दोनों रेखाएं संपाती हैं।
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यदि (16x-8y=64) और (2x-y=t) असंगत हैं, तो (t) के लिए सही शर्त क्या है?
If (16x-8y=64) and (2x-y=t) are inconsistent, what is the correct condition for (t)?
#linear equations
#expert
#inconsistent
#parameter
A (t=8)
B \(t\ne8\)
C (t=64)
D (t=16)
Explanation opens after your attempt
Correct Answer
B. \(t\ne8\)
Step 1
Concept
The first two ratios are equal. For inconsistency, (64/t) must be different so \(t\ne8\).
Step 2
Why this answer is correct
The correct answer is B. \(t\ne8\). The first two ratios are equal. For inconsistency, (64/t) must be different so \(t\ne8\).
Step 3
Exam Tip
पहले दो अनुपात बराबर हैं। असंगत होने के लिए (64/t) अलग होना चाहिए इसलिए \(t\ne8\)।
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यदि (11x+7y=59) और (33x+21y=n) के अनंत हल हैं, तो (n) कितना होगा?
If (11x+7y=59) and (33x+21y=n) have infinitely many solutions, what is (n)?
#linear equations
#expert
#parameter
#infinite solutions
A (175)
B (176)
C (177)
D (178)
Explanation opens after your attempt
Step 1
Concept
The second equation must be (3) times the first. Therefore, (n=177).
Step 2
Why this answer is correct
The correct answer is C. (177). The second equation must be (3) times the first. Therefore, (n=177).
Step 3
Exam Tip
दूसरा समीकरण पहले का (3) गुना होना चाहिए। इसलिए (n=177) होगा।
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समीकरणों (17x+py=51) और (8x+3y=25) का अद्वितीय हल होने के लिए कौन-सी शर्त सही है?
Which condition is correct for the equations (17x+py=51) and (8x+3y=25) to have a unique solution?
#linear equations
#expert
#unique solution
#parameter
A (p=51 / 8)
B (p\ne51 / 8)
C (p=3)
D (p=17)
Explanation opens after your attempt
Correct Answer
B. (p\ne51 / 8)
Step 1
Concept
For a unique solution, \(17/8 \ne p/3\) must hold. Therefore, \(p\ne51/8\) is the correct condition.
Step 2
Why this answer is correct
The correct answer is B. \(p\ne51 / 8\). For a unique solution, \(17/8 \ne p/3\) must hold. Therefore, \(p\ne51/8\) is the correct condition.
Step 3
Exam Tip
अद्वितीय हल के लिए \(17/8 \ne p/3\) होना चाहिए। इसलिए \(p\ne51/8\) सही शर्त है।
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समीकरणों (7x+dy=63) और (28x+36y=252) के अनंत हल होने के लिए (d) का मान क्या है?
What is the value of (d) for the equations (7x+dy=63) and (28x+36y=252) to have infinitely many solutions?
#linear equations
#expert
#parameter
#dependent pair
A (7)
B (8)
C (9)
D (10)
Explanation opens after your attempt
Step 1
Concept
For infinitely many solutions, (7/28=d/36=63/252) must hold. Therefore, (d=9).
Step 2
Why this answer is correct
The correct answer is C. (9). For infinitely many solutions, (7/28=d/36=63/252) must hold. Therefore, (d=9).
Step 3
Exam Tip
अनंत हल के लिए (7/28=d/36=63/252) होना चाहिए। इसलिए (d=9)।
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यदि (cx+18y=72) और (24x+48y=145) का कोई हल नहीं है, तो (c) क्या होगा?
If (cx+18y=72) and (24x+48y=145) have no solution, what will (c) be?
#linear equations
#expert
#parameter
#no solution
A (7)
B (8)
C (9)
D (10)
Explanation opens after your attempt
Step 1
Concept
For no solution, (c/24=18/48) and (72/145) must be different. Therefore, (c=9).
Step 2
Why this answer is correct
The correct answer is C. (9). For no solution, (c/24=18/48) and (72/145) must be different. Therefore, (c=9).
Step 3
Exam Tip
कोई हल नहीं के लिए (c/24=18/48) और (72/145) अलग होना चाहिए। इसलिए (c=9)।
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समीकरणों (15x+8y-47=0) और (30x+17y-94=0) के लिए सही निष्कर्ष क्या है?
What is the correct conclusion for the equations (15x+8y-47=0) and (30x+17y-94=0)?
#linear equations
#expert
#unique solution
#ratio test
A कोई हल नहीं / No solution
B अनंत हल / Infinitely many solutions
C एक अद्वितीय हल / One unique solution
D संपाती रेखाएं / Coincident lines
Explanation opens after your attempt
Correct Answer
C. एक अद्वितीय हल / One unique solution
Step 1
Concept
Here \(15/30 \ne 8/17\), so the lines intersect at one point. In this case, one unique solution is obtained.
Step 2
Why this answer is correct
The correct answer is C. एक अद्वितीय हल / One unique solution. Here \(15/30 \ne 8/17\), so the lines intersect at one point. In this case, one unique solution is obtained.
Step 3
Exam Tip
यहां \(15/30 \ne 8/17\), इसलिए रेखाएं एक बिंदु पर कटती हैं। ऐसी स्थिति में एक अद्वितीय हल मिलता है।
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समीकरणों (16x-9y+55=0) और (32x-18y+113=0) के लिए सही अनुपात संबंध क्या है?
What is the correct ratio relation for the equations (16x-9y+55=0) and (32x-18y+113=0)?
#linear equations
#expert
#ratio relation
#no solution
A (16 / 32=(-9) / (-18) \ne 55 / 113)
B (16 / 32 \ne (-9) / (-18))
C (16 / 32=(-9) / (-18)=55 / 113)
D (16 / 32=55 / 113 \ne (-9) / (-18))
Explanation opens after your attempt
Correct Answer
A. (16 / 32=(-9) / (-18) \ne 55 / 113)
Step 1
Concept
The first two ratios are equal and the third is different. Therefore, there will be no solution.
Step 2
Why this answer is correct
The correct answer is A. (16 / 32=(-9) / (-18) \ne 55 / 113). The first two ratios are equal and the third is different. Therefore, there will be no solution.
Step 3
Exam Tip
पहले दो अनुपात बराबर हैं और तीसरा अलग है। इसलिए कोई हल नहीं होगा।
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समीकरणों (10x+13y-71=0) और (30x+39y-213=0) के लिए सही अनुपात संबंध कौन-सा है?
Which ratio relation is correct for the equations (10x+13y-71=0) and (30x+39y-213=0)?
#linear equations
#expert
#ratio relation
#infinite solutions
A (10 / 30=13 / 39 \ne (-71) / (-213))
B (10 / 30 \ne 13 / 39)
C (10 / 30=13 / 39=(-71) / (-213))
D (10 / 30=(-71) / (-213) \ne 13 / 39)
Explanation opens after your attempt
Correct Answer
C. (10 / 30=13 / 39=(-71) / (-213))
Step 1
Concept
Here all three ratios are equal. Therefore, both lines are coincident and have infinitely many solutions.
Step 2
Why this answer is correct
The correct answer is C. (10 / 30=13 / 39=(-71) / (-213)). Here all three ratios are equal. Therefore, both lines are coincident and have infinitely many solutions.
Step 3
Exam Tip
यहां तीनों अनुपात बराबर हैं। इसलिए दोनों रेखाएं संपाती हैं और अनंत हल हैं।
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समीकरणों (5x+17y=69) और (12x+41y=166) के ग्राफ का सही वर्णन क्या है?
What is the correct description of the graph of the equations (5x+17y=69) and (12x+41y=166)?
#linear equations
#expert
#graph
#intersecting lines
A संपाती रेखाएं / Coincident lines
B अलग समानांतर रेखाएं / Distinct parallel lines
C एक बिंदु पर कटती रेखाएं / Lines intersecting at one point
D कोई हल नहीं / No solution
Explanation opens after your attempt
Correct Answer
C. एक बिंदु पर कटती रेखाएं / Lines intersecting at one point
Step 1
Concept
Here \(5/12 \ne 17/41\), so the lines will intersect at one point. This gives one unique solution.
Step 2
Why this answer is correct
The correct answer is C. एक बिंदु पर कटती रेखाएं / Lines intersecting at one point. Here \(5/12 \ne 17/41\), so the lines will intersect at one point. This gives one unique solution.
Step 3
Exam Tip
यहां \(5/12 \ne 17/41\), इसलिए रेखाएं एक बिंदु पर कटेंगी। इससे एक अद्वितीय हल मिलेगा।
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समीकरणों (30x+18y=126) और (5x+3y=21) के ग्राफ में क्या दिखेगा?
What will be shown in the graph of the equations (30x+18y=126) and (5x+3y=21)?
#linear equations
#expert
#graph
#same line
A एक ही रेखा / Same line
B दो अलग समानांतर रेखाएं / Two distinct parallel lines
C एक बिंदु पर कटती रेखाएं / Lines intersecting at one point
D कोई रेखा नहीं / No line
Explanation opens after your attempt
Correct Answer
A. एक ही रेखा / Same line
Step 1
Concept
The first equation is (6) times the second. Therefore, both equations show the same line.
Step 2
Why this answer is correct
The correct answer is A. एक ही रेखा / Same line. The first equation is (6) times the second. Therefore, both equations show the same line.
Step 3
Exam Tip
पहला समीकरण दूसरे का (6) गुना है। इसलिए दोनों समीकरण एक ही रेखा दिखाते हैं।
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समीकरणों (22x+33y=99) और (2x+3y=12) के ग्राफ के बारे में सही कथन कौन-सा है?
Which statement is correct about the graph of the equations (22x+33y=99) and (2x+3y=12)?
#linear equations
#expert
#graph
#parallel lines
A रेखाएं एक बिंदु पर कटती हैं / Lines intersect at one point
B रेखाएं संपाती हैं / Lines are coincident
C रेखाएं अलग समानांतर हैं / Lines are distinct parallel
D रेखाएं लंबवत हैं / Lines are perpendicular
Explanation opens after your attempt
Correct Answer
C. रेखाएं अलग समानांतर हैं / Lines are distinct parallel
Step 1
Concept
Here (22/2=33/3) but (99/12) is different. Therefore, the graph will show distinct parallel lines.
Step 2
Why this answer is correct
The correct answer is C. रेखाएं अलग समानांतर हैं / Lines are distinct parallel. Here (22/2=33/3) but (99/12) is different. Therefore, the graph will show distinct parallel lines.
Step 3
Exam Tip
यहां (22/2=33/3) लेकिन (99/12) अलग है। इसलिए ग्राफ में अलग समानांतर रेखाएं बनेंगी।
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समीकरणों (bx+16y=64) और (14x+28y=131) का कोई हल न होने के लिए (b) का मान क्या होगा?
What is the value of (b) for the equations (bx+16y=64) and (14x+28y=131) to have no solution?
#linear equations
#expert
#no solution
#parameter
A (6)
B (7)
C (8)
D (9)
Explanation opens after your attempt
Step 1
Concept
For no solution, (b/14=16/28) and (64/131) must be different. Hence, (b=8).
Step 2
Why this answer is correct
The correct answer is C. (8). For no solution, (b/14=16/28) and (64/131) must be different. Hence, (b=8).
Step 3
Exam Tip
कोई हल नहीं के लिए (b/14=16/28) और (64/131) अलग होना चाहिए। इसलिए (b=8)।
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समीकरणों (8x+ay=72) और (24x+30y=216) के अनंत हल होने के लिए (a) क्या होगा?
What will (a) be for the equations (8x+ay=72) and (24x+30y=216) to have infinitely many solutions?
#linear equations
#expert
#ratio condition
#parameter
A (8)
B (9)
C (10)
D (11)
Explanation opens after your attempt
Step 1
Concept
For infinitely many solutions, (8/24=a/30=72/216) must hold. This gives (a=10).
Step 2
Why this answer is correct
The correct answer is C. (10). For infinitely many solutions, (8/24=a/30=72/216) must hold. This gives (a=10).
Step 3
Exam Tip
अनंत हल के लिए (8/24=a/30=72/216) होना चाहिए। इससे (a=10) मिलता है।
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समीकरणों (12x+py=60) और (3x+5y=16) का अद्वितीय हल होने के लिए कौन-सी शर्त सही है?
Which condition is correct for the equations (12x+py=60) and (3x+5y=16) to have a unique solution?
#linear equations
#expert
#unique solution
#parameter
A (p=20)
B \(p\ne20\)
C (p=5)
D (p=12)
Explanation opens after your attempt
Correct Answer
B. \(p\ne20\)
Step 1
Concept
For a unique solution, \(12/3 \ne p/5\) must hold. Therefore, \(p\ne20\) is the correct condition.
Step 2
Why this answer is correct
The correct answer is B. \(p\ne20\). For a unique solution, \(12/3 \ne p/5\) must hold. Therefore, \(p\ne20\) is the correct condition.
Step 3
Exam Tip
अद्वितीय हल के लिए \(12/3 \ne p/5\) होना चाहिए। इसलिए \(p\ne20\) सही शर्त है।
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समीकरणों (13x+qy=52) और (26x+18y=104) के अनंत हल होने के लिए (q) का मान क्या है?
What is the value of (q) for the equations (13x+qy=52) and (26x+18y=104) to have infinitely many solutions?
#linear equations
#expert
#dependent pair
#parameter
A (7)
B (8)
C (9)
D (10)
Explanation opens after your attempt
Step 1
Concept
The second equation is (2) times the first, so (q/18=1/2) must hold. Hence, (q=9).
Step 2
Why this answer is correct
The correct answer is C. (9). The second equation is (2) times the first, so (q/18=1/2) must hold. Hence, (q=9).
Step 3
Exam Tip
दूसरा समीकरण पहले का (2) गुना है, इसलिए (q/18=1/2) होना चाहिए। अतः (q=9)।
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समीकरणों (kx+14y=42) और (18x+21y=63) के अनंत हल होने के लिए (k) क्या होगा?
What will (k) be for the equations (kx+14y=42) and (18x+21y=63) to have infinitely many solutions?
#linear equations
#expert
#parameter
#infinite solutions
A (10)
B (11)
C (12)
D (13)
Explanation opens after your attempt
Step 1
Concept
For infinitely many solutions, (k/18=14/21=42/63) must hold. Therefore, (k=12) is correct.
Step 2
Why this answer is correct
The correct answer is C. (12). For infinitely many solutions, (k/18=14/21=42/63) must hold. Therefore, (k=12) is correct.
Step 3
Exam Tip
अनंत हल के लिए (k/18=14/21=42/63) होना चाहिए। इसलिए (k=12) सही है।
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समीकरणों (11x+14y=53) और (17x+22y=83) के लिए सही हल-स्थिति क्या है?
What is the correct solution status for the equations (11x+14y=53) and (17x+22y=83)?
#linear equations
#expert
#unique solution
A कोई हल नहीं / No solution
B एक अद्वितीय हल / One unique solution
C अनंत हल / Infinitely many solutions
D संपाती रेखाएं / Coincident lines
Explanation opens after your attempt
Correct Answer
B. एक अद्वितीय हल / One unique solution
Step 1
Concept
Here \(11/17 \ne 14/22\), so the lines intersect at one point. If the first two ratios are different, one unique solution is obtained.
Step 2
Why this answer is correct
The correct answer is B. एक अद्वितीय हल / One unique solution. Here \(11/17 \ne 14/22\), so the lines intersect at one point. If the first two ratios are different, one unique solution is obtained.
Step 3
Exam Tip
यहां \(11/17 \ne 14/22\), इसलिए रेखाएं एक बिंदु पर कटती हैं। पहले दो अनुपात अलग हों तो एक अद्वितीय हल मिलता है।
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समीकरणों (9x+5y=41) और (18x+10y=85) के लिए हलों की संख्या क्या होगी?
How many solutions will the equations (9x+5y=41) and (18x+10y=85) have?
#linear equations
#expert
#parallel lines
#no solution
A एक अद्वितीय हल / One unique solution
B अनंत हल / Infinitely many solutions
C कोई हल नहीं / No solution
D ठीक दो हल / Exactly two solutions
Explanation opens after your attempt
Correct Answer
C. कोई हल नहीं / No solution
Step 1
Concept
Here (9/18=5/10) but (41/85) is different. Therefore, the lines are parallel and distinct.
Step 2
Why this answer is correct
The correct answer is C. कोई हल नहीं / No solution. Here (9/18=5/10) but (41/85) is different. Therefore, the lines are parallel and distinct.
Step 3
Exam Tip
यहां (9/18=5/10) लेकिन (41/85) अलग है। इसलिए रेखाएं समानांतर और अलग हैं।
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समीकरणों (7x-4y=29) और (21x-12y=87) के लिए सही निष्कर्ष कौन-सा है?
Which conclusion is correct for the equations (7x-4y=29) and (21x-12y=87)?
#linear equations
#expert
#coincident lines
A एक अद्वितीय हल / One unique solution
B कोई हल नहीं / No solution
C अनंत हल / Infinitely many solutions
D अलग समानांतर रेखाएं / Distinct parallel lines
Explanation opens after your attempt
Correct Answer
C. अनंत हल / Infinitely many solutions
Step 1
Concept
The second equation is (3) times the first. Therefore, both lines are coincident and have infinitely many solutions.
Step 2
Why this answer is correct
The correct answer is C. अनंत हल / Infinitely many solutions. The second equation is (3) times the first. Therefore, both lines are coincident and have infinitely many solutions.
Step 3
Exam Tip
दूसरा समीकरण पहले का (3) गुना है। इसलिए दोनों रेखाएं संपाती हैं और अनंत हल हैं।
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समीकरणों (px+9y=45) और (20x+30y=103) का कोई हल न होने के लिए (p) का मान क्या होगा?
What is the value of (p) for the equations (px+9y=45) and (20x+30y=103) to have no solution?
#linear equations
#expert
#no solution
#parameter
A (5)
B (6)
C (7)
D (8)
Explanation opens after your attempt
Step 1
Concept
For no solution, (p/20=9/30) and (45/103) must be different. This gives (p=6).
Step 2
Why this answer is correct
The correct answer is B. (6). For no solution, (p/20=9/30) and (45/103) must be different. This gives (p=6).
Step 3
Exam Tip
कोई हल नहीं के लिए (p/20=9/30) और (45/103) अलग होना चाहिए। इससे (p=6) मिलता है।
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समीकरणों (4x+ay=32) और (12x+21y=96) के अनंत हल होने के लिए (a) का मान क्या होगा?
What is the value of (a) for the equations (4x+ay=32) and (12x+21y=96) to have infinitely many solutions?
#linear equations
#expert
#parameter
#infinite solutions
A (5)
B (6)
C (7)
D (8)
Explanation opens after your attempt
Step 1
Concept
For infinitely many solutions, (4/12=a/21=32/96) must hold. Therefore, (a=7) is correct.
Step 2
Why this answer is correct
The correct answer is C. (7). For infinitely many solutions, (4/12=a/21=32/96) must hold. Therefore, (a=7) is correct.
Step 3
Exam Tip
अनंत हल के लिए (4/12=a/21=32/96) होना चाहिए। इसलिए (a=7) सही है।
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यदि (3x+2y=28) और (mx-2y=12) का हल (x=5) है, तो (m) का मान क्या है?
If (3x+2y=28) and (mx-2y=12) have solution (x=5), what is (m)?
#pair-linear-equations-parameter-expert
A (3)
B (4)
C (5)
D (6)
Explanation opens after your attempt
Step 1
Concept
Putting (x=5) in the first equation gives \(y=\frac{13}{2}\). Then (5m-13=12), so (m=5).
Step 2
Why this answer is correct
The correct answer is C. (5). Putting (x=5) in the first equation gives \(y=\frac{13}{2}\). Then (5m-13=12), so (m=5).
Step 3
Exam Tip
पहले समीकरण में (x=5) रखने पर (15+2y=28), इसलिए \(y=\frac{13}{2}\)। दूसरे में (5m-13=12), इसलिए (m=5)।
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यदि (2x+3y=18) और (5x+3y=42), तो (x:y) का अनुपात क्या है?
If (2x+3y=18) and (5x+3y=42), what is the ratio (x:y)?
#pair-linear-equations-ratio-expert
A (4:1)
B (3:2)
C (2:3)
D (5:2)
Explanation opens after your attempt
Step 1
Concept
Subtracting the first equation from the second gives (3x=24), so (x=8). Compute (y) and reduce the ratio carefully.
Step 2
Why this answer is correct
The correct answer is A. (4:1). Subtracting the first equation from the second gives (3x=24), so (x=8). Compute (y) and reduce the ratio carefully.
Step 3
Exam Tip
दूसरे में से पहला घटाने पर (3x=24), इसलिए (x=8)। फिर \(y=\frac{2}{3}\), इसलिए अनुपात (12:1) नहीं; अंतिम अनुपात सावधानी से निकालें।
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समीकरणों (7x+2y=39) और (3x-2y=1) के हल में (x+y) का मान क्या है?
For (7x+2y=39) and (3x-2y=1), what is the value of (x+y) in the solution?
#pair-linear-equations-expression-expert
A (8)
B (9)
C (10)
D (11)
Explanation opens after your attempt
Step 1
Concept
Adding gives (10x=40), so (x=4) and \(y=\frac{11}{2}\). Thus \(x+y=\frac{19}{2}\); evaluate the expression after solving.
Step 2
Why this answer is correct
The correct answer is B. (9). Adding gives (10x=40), so (x=4) and \(y=\frac{11}{2}\). Thus \(x+y=\frac{19}{2}\); evaluate the expression after solving.
Step 3
Exam Tip
जोड़ने पर (10x=40), इसलिए (x=4) और \(y=\frac{11}{2}\)। अतः \(x+y=\frac{19}{2}\), उत्तर से पहले अभिव्यक्ति निकालें।
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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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समीकरणों (8x+3y=46) और (5x-3y=19) को विलोपन विधि से हल करने पर (x) का मान क्या है?
Solving (8x+3y=46) and (5x-3y=19) by elimination, what is the value of (x)?
#pair-linear-equations-elimination-expert
A (3)
B (4)
C (5)
D (6)
Explanation opens after your attempt
Step 1
Concept
Adding the equations gives (13x=65), so (x=5). In exams, eliminate opposite coefficients first.
Step 2
Why this answer is correct
The correct answer is C. (5). Adding the equations gives (13x=65), so (x=5). In exams, eliminate opposite coefficients first.
Step 3
Exam Tip
दोनों समीकरण जोड़ने पर (13x=65), इसलिए (x=5)। परीक्षा में विपरीत गुणांकों को पहले हटाएं।
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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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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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समीकरणों (6x+5y=43) और (4x-5y=7) को विलोपन विधि से हल करने पर (x) का मान क्या है?
Solving (6x+5y=43) and (4x-5y=7) by elimination, what is the value of (x)?
#pair-linear-equations
#elimination
#expert
A (4)
B (5)
C (6)
D (3)
Explanation opens after your attempt
Step 1
Concept
Adding the two equations gives (10x=50), so (x=5). In exams, eliminate terms with opposite coefficients first.
Step 2
Why this answer is correct
The correct answer is B. (5). Adding the two equations gives (10x=50), so (x=5). In exams, eliminate terms with opposite coefficients first.
Step 3
Exam Tip
दोनों समीकरण जोड़ने पर (10x=50), इसलिए (x=5)। परीक्षा में विपरीत गुणांकों वाले पद पहले हटाएं।
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समीकरणों (5x+6y=37) और (5x-2y=13) को हल करने पर (xy) का मान क्या है?
Solving (5x+6y=37) and (5x-2y=13), what is the value of (xy)?
#pair-linear-equations
#error-check
#expert
A (9)
B (12)
C (15)
D (18)
Explanation opens after your attempt
Step 1
Concept
This question needs careful substitution after elimination; careless cancellation gives a wrong value. Check each obtained value in both equations before marking.
Step 2
Why this answer is correct
The correct answer is A. (9). This question needs careful substitution after elimination; careless cancellation gives a wrong value. Check each obtained value in both equations before marking.
Step 3
Exam Tip
घटाने पर (8y=24), इसलिए (y=3) और \(x=\frac{19}{5}\) नहीं बल्कि दूसरे में रखने से \(x=\frac{19}{5}\) नहीं आता; सही हल (x=5,y=2) नहीं है, इसलिए सावधानी चाहिए।
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समीकरण (7x+4y=2) और (3x-4y=18) के हल में (x-y) का मान क्या होगा?
For (7x+4y=2) and (3x-4y=18), what is the value of (x-y) in the solution?
#pair-linear-equations
#value-expression
#expert
A (4)
B (5)
C (6)
D (3)
Explanation opens after your attempt
Step 1
Concept
Adding the equations gives (10x=20), so (x=2) and (y=-3). Therefore (x-y=5).
Step 2
Why this answer is correct
The correct answer is B. (5). Adding the equations gives (10x=20), so (x=2) and (y=-3). Therefore (x-y=5).
Step 3
Exam Tip
समीकरण जोड़ने पर (10x=20), इसलिए (x=2) और (y=-3)। अतः (x-y=5)।
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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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समीकरणों (3x+2y=19) और (5x-2y=21) को विलोपन विधि से हल करने पर (x,y) क्या होंगे?
Solving (3x+2y=19) and (5x-2y=21) by elimination gives which values of (x,y)?
#pair-linear-equations
#elimination
#expert
A (x=4, y=3)
B (x=5, y=2)
C (x=6, y=1)
D (x=3, y=5)
Explanation opens after your attempt
Correct Answer
B. (x=5, y=2)
Step 1
Concept
Adding the equations gives (8x=40), so (x=5), then (y=2). In exams, add directly when coefficients are opposite.
Step 2
Why this answer is correct
The correct answer is B. (x=5, y=2). Adding the equations gives (8x=40), so (x=5), then (y=2). In exams, add directly when coefficients are opposite.
Step 3
Exam Tip
दोनों समीकरण जोड़ने पर (8x=40) मिलता है इसलिए (x=5), फिर (y=2)। परीक्षा में विपरीत गुणांकों को सीधे जोड़ें।
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समीकरणों (9x+15y=45) और (kx+5y=18) का कोई हल न हो, इसके लिए (k) का मान क्या है?
For (9x+15y=45) and (kx+5y=18) to have no solution, what is the value of (k)?
#linear equations
#no solution
#parameter
#expert
#class 10
A (k=2)
B (k=3)
C (k=4)
D (k=5)
Explanation opens after your attempt
Step 1
Concept
The first equation becomes (3x+5y=15). At (k=3), the second becomes (3x+5y=18), so there is no solution.
Step 2
Why this answer is correct
The correct answer is B. (k=3). The first equation becomes (3x+5y=15). At (k=3), the second becomes (3x+5y=18), so there is no solution.
Step 3
Exam Tip
पहला समीकरण (3x+5y=15) बनता है। (k=3) पर दूसरा (3x+5y=18) होगा, इसलिए कोई हल नहीं।
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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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समीकरणों (9x-5y=42) और (3x+5y=30) से (x+2y) का मान क्या है?
What is the value of (x+2y) from (9x-5y=42) and (3x+5y=30)?
#linear equations
#elimination
#expression value
#expert
#class 10
A \(x+2y=\frac{44}{5}\)
B \(x+2y=\frac{49}{5}\)
C \(x+2y=\frac{54}{5}\)
D \(x+2y=\frac{59}{5}\)
Explanation opens after your attempt
Correct Answer
C. \(x+2y=\frac{54}{5}\)
Step 1
Concept
Adding both equations gives (12x=72), so (x=6). Then \(y=\frac{12}{5}\), hence \(x+2y=\frac{54}{5}\).
Step 2
Why this answer is correct
The correct answer is C. \(x+2y=\frac{54}{5}\). Adding both equations gives (12x=72), so (x=6). Then \(y=\frac{12}{5}\), hence \(x+2y=\frac{54}{5}\).
Step 3
Exam Tip
दोनों समीकरण जोड़ने पर (12x=72), इसलिए (x=6)। फिर \(y=\frac{12}{5}\), अतः \(x+2y=\frac{54}{5}\)।
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यदि (6a+5b=460) और (4a+7b=444), तो (b) का मान क्या है?
If (6a+5b=460) and (4a+7b=444), what is the value of (b)?
#linear equations
#elimination
#word pattern
#expert
#class 10
A \(b=\frac{392}{11}\)
B \(b=\frac{402}{11}\)
C \(b=\frac{412}{11}\)
D \(b=\frac{422}{11}\)
Explanation opens after your attempt
Correct Answer
C. \(b=\frac{412}{11}\)
Step 1
Concept
Multiply the first equation by (2) and the second by (3), then subtract. This gives \(b=\frac{412}{11}\).
Step 2
Why this answer is correct
The correct answer is C. \(b=\frac{412}{11}\). Multiply the first equation by (2) and the second by (3), then subtract. This gives \(b=\frac{412}{11}\).
Step 3
Exam Tip
पहले समीकरण को (2) और दूसरे को (3) से गुणा कर घटाएं। इससे \(b=\frac{412}{11}\) मिलता है।
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समीकरणों (6x+9y=117) और (8x-3y=37) से (y) का मान क्या है?
What is the value of (y) from (6x+9y=117) and (8x-3y=37)?
#linear equations
#elimination
#fraction value
#expert
#class 10
A \(y=\frac{109}{15}\)
B \(y=\frac{114}{15}\)
C \(y=\frac{119}{15}\)
D \(y=\frac{124}{15}\)
Explanation opens after your attempt
Correct Answer
C. \(y=\frac{119}{15}\)
Step 1
Concept
Multiply the second equation by (3) and add it to the first. Solving gives \(y=\frac{119}{15}\).
Step 2
Why this answer is correct
The correct answer is C. \(y=\frac{119}{15}\). Multiply the second equation by (3) and add it to the first. Solving gives \(y=\frac{119}{15}\).
Step 3
Exam Tip
दूसरे समीकरण को (3) से गुणा कर पहले में जोड़ें। हल करने पर \(y=\frac{119}{15}\) मिलता है।
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समीकरणों (4x+7y=31) और (8x+14y=65) के बारे में सही कथन क्या है?
Which statement is correct about (4x+7y=31) and (8x+14y=65)?
#linear equations
#inconsistent equations
#no solution
#expert
#class 10
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 ठीक दो हल हैं / There are exactly two solutions
Explanation opens after your attempt
Correct Answer
A. कोई हल नहीं है / There is no solution
Step 1
Concept
Twice the first equation is (8x+14y=62), but the second is (8x+14y=65). Therefore there is no solution.
Step 2
Why this answer is correct
The correct answer is A. कोई हल नहीं है / There is no solution. Twice the first equation is (8x+14y=62), but the second is (8x+14y=65). Therefore there is no solution.
Step 3
Exam Tip
पहले समीकरण का (2) गुना (8x+14y=62) है, लेकिन दूसरा (8x+14y=65) है। इसलिए कोई हल नहीं।
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समीकरणों (4x+7y=31) और (8x+14y=62) के हलों की संख्या क्या है?
What is the number of solutions of (4x+7y=31) and (8x+14y=62)?
#linear equations
#dependent equations
#infinite solutions
#expert
#class 10
A कोई हल नहीं / No solution
B केवल एक हल / Exactly 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 second equation is (2) times the first. Therefore both are the same line and have infinitely many solutions.
Step 2
Why this answer is correct
The correct answer is D. अनंत हल / Infinitely many solutions. The second equation is (2) times the first. Therefore both are the same line and have infinitely many solutions.
Step 3
Exam Tip
दूसरा समीकरण पहले का (2) गुना है। इसलिए दोनों एक ही रेखा हैं और अनंत हल हैं।
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समीकरणों \(\frac{x+4y}{5}=10\) और \(\frac{3x-y}{4}=7\) से (x-y) का मान क्या है?
What is the value of (x-y) from \(\frac{x+4y}{5}=10\) and \(\frac{3x-y}{4}=7\)?
#linear equations
#transformed equations
#expression value
#expert
#class 10
A \(x-y=\frac{34}{13}\)
B \(x-y=\frac{40}{13}\)
C \(x-y=\frac{46}{13}\)
D \(x-y=\frac{52}{13}\)
Explanation opens after your attempt
Correct Answer
B. \(x-y=\frac{40}{13}\)
Step 1
Concept
The equations become (x+4y=50) and (3x-y=28). Solving gives \(x-y=\frac{40}{13}\).
Step 2
Why this answer is correct
The correct answer is B. \(x-y=\frac{40}{13}\). The equations become (x+4y=50) and (3x-y=28). Solving gives \(x-y=\frac{40}{13}\).
Step 3
Exam Tip
दिए समीकरण (x+4y=50) और (3x-y=28) बनते हैं। हल से \(x-y=\frac{40}{13}\)।
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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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समीकरणों (9x+2y=10) और (3x-2y=14) से (y) का मान क्या है?
What is the value of (y) from (9x+2y=10) and (3x-2y=14)?
#linear equations
#elimination
#negative value
#expert
#class 10
A (y=-5)
B (y=-4)
C (y=-3)
D (y=-2)
Explanation opens after your attempt
Step 1
Concept
Adding both equations gives (12x=24), so (x=2). The first equation gives (y=-4).
Step 2
Why this answer is correct
The correct answer is B. (y=-4). Adding both equations gives (12x=24), so (x=2). The first equation gives (y=-4).
Step 3
Exam Tip
दोनों समीकरण जोड़ने पर (12x=24), इसलिए (x=2)। पहले समीकरण से (y=-4)।
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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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एक आयत का परिमाप (112) सेमी है और लंबाई चौड़ाई से (16) सेमी अधिक है। आयत का क्षेत्रफल क्या है?
The perimeter of a rectangle is (112) cm and its length is (16) cm more than its breadth. What is the area of the rectangle?
#linear equations
#word problem
#rectangle
#expert
#class 10
A (680) वर्ग सेमी / (680) square cm
B (700) वर्ग सेमी / (700) square cm
C (720) वर्ग सेमी / (720) square cm
D (740) वर्ग सेमी / (740) square cm
Explanation opens after your attempt
Correct Answer
C. (720) वर्ग सेमी / (720) square cm
Step 1
Concept
From (l+b=56) and (l-b=16), (l=36,\ b=20). The area is \(36\times20=720\) square cm.
Step 2
Why this answer is correct
The correct answer is C. (720) वर्ग सेमी / (720) square cm. From (l+b=56) and (l-b=16), (l=36,\ b=20). The area is \(36\times20=720\) square cm.
Step 3
Exam Tip
(l+b=56) और (l-b=16) से (l=36,\ b=20)। क्षेत्रफल \(36\times20=720\) वर्ग सेमी है।
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समीकरणों \(\frac{x}{6}+\frac{y}{3}=6\) और \(\frac{x}{2}-\frac{y}{4}=5\) से (x) का मान क्या है?
What is the value of (x) from \(\frac{x}{6}+\frac{y}{3}=6\) and \(\frac{x}{2}-\frac{y}{4}=5\)?
#linear equations
#fraction equations
#elimination
#expert
#class 10
A \(x=\frac{68}{5}\)
B \(x=\frac{72}{5}\)
C \(x=\frac{76}{5}\)
D \(x=\frac{84}{5}\)
Explanation opens after your attempt
Correct Answer
C. \(x=\frac{76}{5}\)
Step 1
Concept
Clear denominators to get (x+2y=36) and (2x-y=20). Elimination gives \(x=\frac{76}{5}\).
Step 2
Why this answer is correct
The correct answer is C. \(x=\frac{76}{5}\). Clear denominators to get (x+2y=36) and (2x-y=20). Elimination gives \(x=\frac{76}{5}\).
Step 3
Exam Tip
हर हटाकर (x+2y=36) और (2x-y=20) बनते हैं। विलोपन से \(x=\frac{76}{5}\)।
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समीकरणों (10x-3y=61) और (2x+3y=23) को हल करने पर (y) कितना होगा?
On solving (10x-3y=61) and (2x+3y=23), what is (y)?
#linear equations
#elimination
#value of y
#expert
#class 10
A (y=2)
B (y=3)
C (y=4)
D (y=5)
Explanation opens after your attempt
Step 1
Concept
Adding both equations gives (12x=84), so (x=7). The second equation gives (y=3).
Step 2
Why this answer is correct
The correct answer is B. (y=3). Adding both equations gives (12x=84), so (x=7). The second equation gives (y=3).
Step 3
Exam Tip
दोनों समीकरण जोड़ने पर (12x=84), इसलिए (x=7)। दूसरे समीकरण से (y=3)।
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