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Mathematics Quiz - Class 10 Mathematics Medium Level 59 Quiz

Question 1/50 Medium Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

समीकरण (5x+4y=18) और (10x+8y=k) के अनंत हल होने के लिए (k) का मान क्या होगा?

What is the value of (k) for (5x+4y=18) and (10x+8y=k) to have infinitely many solutions?

Explanation opens after your attempt

Correct Answer

B. (36)

Step 1

Concept

The second equation must be (2) times the first, so (k=36). For infinitely many solutions, keep all three ratios equal.

Step 2

Why this answer is correct

The correct answer is B. (36). The second equation must be (2) times the first, so (k=36). For infinitely many solutions, keep all three ratios equal.

Step 3

Exam Tip

दूसरा समीकरण पहले का (2) गुना होना चाहिए, इसलिए (k=36)। अनंत हल के लिए तीनों अनुपात बराबर रखें।

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Question 2/50 Medium Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

समीकरण (3x+my=24) और (12x+28y=96) के अनंत हल होने के लिए (m) का मान क्या होगा?

What will be the value of (m) for (3x+my=24) and (12x+28y=96) to have infinitely many solutions?

Explanation opens after your attempt

Correct Answer

C. (7)

Step 1

Concept

For infinitely many solutions, (3/12=m/28=24/96) must hold. Therefore, (m=7) is correct.

Step 2

Why this answer is correct

The correct answer is C. (7). For infinitely many solutions, (3/12=m/28=24/96) must hold. Therefore, (m=7) is correct.

Step 3

Exam Tip

अनंत हल के लिए (3/12=m/28=24/96) होना चाहिए। इसलिए (m=7) सही है।

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Question 3/50 Medium Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

समीकरण (3x+ay=21) और (9x+12y=63) के अनंत हल होने के लिए (a) क्या होगा?

What will (a) be for (3x+ay=21) and (9x+12y=63) to have infinitely many solutions?

Explanation opens after your attempt

Correct Answer

C. (4)

Step 1

Concept

For infinitely many solutions, (3/9=a/12=21/63) must hold. Therefore, (a=4).

Step 2

Why this answer is correct

The correct answer is C. (4). For infinitely many solutions, (3/9=a/12=21/63) must hold. Therefore, (a=4).

Step 3

Exam Tip

अनंत हल के लिए (3/9=a/12=21/63) होना चाहिए। इसलिए (a=4) है।

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Question 4/50 Medium Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

समीकरण (11x-4y=26) और (22x-8y=53) के लिए सही हल-स्थिति क्या है?

What is the correct solution status for (11x-4y=26) and (22x-8y=53)?

Explanation opens after your attempt

Correct Answer

C. कोई हल नहींNo solution

Step 1

Concept

Here (11/22=(-4)/(-8)) but (26/53) 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 (11/22=(-4)/(-8)) but (26/53) is different. Therefore, the lines are parallel and distinct.

Step 3

Exam Tip

यहां (11/22=(-4)/(-8)) लेकिन (26/53) अलग है। इसलिए रेखाएं समानांतर और अलग हैं।

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Question 5/50 Medium Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

समीकरण (kx+7y=28) और (8x+14y=60) का कोई हल न होने के लिए (k) का मान क्या होगा?

What value of (k) makes (kx+7y=28) and (8x+14y=60) have no solution?

Explanation opens after your attempt

Correct Answer

C. (4)

Step 1

Concept

For no solution, (k/8=7/14) and (28/60) must be different. This gives (k=4).

Step 2

Why this answer is correct

The correct answer is C. (4). For no solution, (k/8=7/14) and (28/60) must be different. This gives (k=4).

Step 3

Exam Tip

कोई हल नहीं के लिए (k/8=7/14) और (28/60) अलग होना चाहिए। इससे (k=4) मिलता है।

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Question 6/50 Medium Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

समीकरण (5x+7y=32) और (9x+13y=58) में (a) और (b) के अनुपातों की तुलना से क्या निष्कर्ष निकलेगा?

What conclusion follows from comparing the ratios of (a) and (b) in (5x+7y=32) and (9x+13y=58)?

Explanation opens after your attempt

Correct Answer

B. (59 \ne 7 / 13), इसलिए एक अद्वितीय हल / 13), so one unique solution

Step 1

Concept

Here \(5/9 \ne 7/13\), so the lines will intersect at one point. If the first two ratios differ, one unique solution is obtained.

Step 2

Why this answer is correct

The correct answer is B. \(5 / 9 \ne 7 / 13\), इसलिए एक अद्वितीय हल / 13), so one unique solution. Here \(5/9 \ne 7/13\), so the lines will intersect at one point. If the first two ratios differ, one unique solution is obtained.

Step 3

Exam Tip

यहां \(5/9 \ne 7/13\), इसलिए रेखाएं एक बिंदु पर कटेंगी। पहले दो अनुपात अलग हों तो एक अद्वितीय हल मिलता है।

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Question 7/50 Medium Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

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)?

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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Question 8/50 Medium Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

दो वस्तुओं की कीमतों के लिए (4x+3y=125) और (8x+6y=260) समीकरण बने। यह प्रणाली कैसी है?

For prices of two items, the equations (4x+3y=125) and (8x+6y=260) are formed. What type of system is this?

Explanation opens after your attempt

Correct Answer

C. असंगतInconsistent

Step 1

Concept

The first two ratios (4/8=3/6) are equal but (125/260) 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 (4/8=3/6) are equal but (125/260) is different. Therefore, the system is inconsistent.

Step 3

Exam Tip

पहले दो अनुपात (4/8=3/6) बराबर हैं लेकिन (125/260) अलग है। इसलिए प्रणाली असंगत है।

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Question 9/50 Medium Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

समीकरण (7x+2y=19) और (14x+4y=38) के लिए सही निष्कर्ष क्या है?

What is the correct conclusion for (7x+2y=19) and (14x+4y=38)?

Explanation opens after your attempt

Correct Answer

C. अनंत हलInfinitely many solutions

Step 1

Concept

The second equation is (2) times the first, so both lines are coincident. Coincident lines 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 (2) times the first, so both lines are coincident. Coincident lines have infinitely many solutions.

Step 3

Exam Tip

दूसरा समीकरण पहले का (2) गुना है, इसलिए दोनों रेखाएं संपाती हैं। संपाती रेखाओं के अनंत हल होते हैं।

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Question 10/50 Medium Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

समीकरण (6x-5y=14) और (12x-10y=31) के लिए हलों की संख्या क्या होगी?

How many solutions will (6x-5y=14) and (12x-10y=31) have?

Explanation opens after your attempt

Correct Answer

B. कोई हल नहींNo solution

Step 1

Concept

Here (6/12=(-5)/(-10)) but (14/31) is different. Therefore, the lines are parallel and distinct.

Step 2

Why this answer is correct

The correct answer is B. कोई हल नहीं / No solution. Here (6/12=(-5)/(-10)) but (14/31) is different. Therefore, the lines are parallel and distinct.

Step 3

Exam Tip

यहां (6/12=(-5)/(-10)) लेकिन (14/31) अलग है। इसलिए रेखाएं समानांतर और अलग हैं।

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Question 11/50 Medium Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

समीकरण (4x+9y=25) और (8x+17y=49) के लिए सही हल-स्थिति क्या है?

What is the correct solution status for (4x+9y=25) and (8x+17y=49)?

Explanation opens after your attempt

Correct Answer

D. एक अद्वितीय हलOne unique solution

Step 1

Concept

Here \(4/8 \ne 9/17\), so the lines intersect at one point. Different first two ratios give a unique solution.

Step 2

Why this answer is correct

The correct answer is D. एक अद्वितीय हल / One unique solution. Here \(4/8 \ne 9/17\), so the lines intersect at one point. Different first two ratios give a unique solution.

Step 3

Exam Tip

यहां \(4/8 \ne 9/17\), इसलिए रेखाएं एक बिंदु पर कटती हैं। अलग पहले दो अनुपात अद्वितीय हल देते हैं।

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Question 12/50 Medium Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

यदि \(a_1/a_2=b_1/b_2=c_1/c_2\), तो युग्म का वर्गीकरण क्या होगा?

If \(a_1/a_2=b_1/b_2=c_1/c_2\), what will be the classification of the pair?

Explanation opens after your attempt

Correct Answer

C. संगत और आश्रितConsistent and dependent

Step 1

Concept

When all three ratios are equal, both equations form the same line. Therefore, the pair is consistent and dependent.

Step 2

Why this answer is correct

The correct answer is C. संगत और आश्रित / Consistent and dependent. When all three ratios are equal, both equations form the same line. Therefore, the pair is consistent and dependent.

Step 3

Exam Tip

तीनों अनुपात बराबर होने पर दोनों समीकरण एक ही रेखा बनाते हैं। इसलिए युग्म संगत और आश्रित होता है।

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Question 13/50 Medium Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

यदि \(a_1/a_2=b_1/b_2 \ne c_1/c_2\), तो ग्राफ में रेखाएं कैसी होंगी?

If \(a_1/a_2=b_1/b_2 \ne c_1/c_2\), how will the lines appear in the graph?

Explanation opens after your attempt

Correct Answer

C. अलग समानांतरDistinct parallel

Step 1

Concept

Equal first two ratios give the same slope and a different third ratio keeps the lines separate. Hence, they are distinct parallel.

Step 2

Why this answer is correct

The correct answer is C. अलग समानांतर / Distinct parallel. Equal first two ratios give the same slope and a different third ratio keeps the lines separate. Hence, they are distinct parallel.

Step 3

Exam Tip

पहले दो अनुपात बराबर होने से ढाल समान होती है और तीसरा अलग होने से रेखाएं अलग रहती हैं। इसलिए वे अलग समानांतर होती हैं।

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Question 14/50 Medium Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

समीकरण (px+3y=15) और (12x+6y=30) के अनंत हल होने के लिए (p) क्या होगा?

What will (p) be for (px+3y=15) and (12x+6y=30) to have infinitely many solutions?

Explanation opens after your attempt

Correct Answer

C. (6)

Step 1

Concept

For infinitely many solutions, (p/12=3/6=15/30) must hold. Therefore, (p=6).

Step 2

Why this answer is correct

The correct answer is C. (6). For infinitely many solutions, (p/12=3/6=15/30) must hold. Therefore, (p=6).

Step 3

Exam Tip

अनंत हल के लिए (p/12=3/6=15/30) होना चाहिए। इसलिए (p=6) है।

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Question 15/50 Medium Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

समीकरण (3x+qy=11) और (7x+14y=26) का अद्वितीय हल होने के लिए कौन-सी शर्त सही है?

Which condition is correct for (3x+qy=11) and (7x+14y=26) to have a unique solution?

Explanation opens after your attempt

Correct Answer

B. \(q \ne 6\)

Step 1

Concept

For a unique solution, \(3/7 \ne q/14\) must hold. Therefore, \(q \ne 6\) is correct.

Step 2

Why this answer is correct

The correct answer is B. \(q \ne 6\). For a unique solution, \(3/7 \ne q/14\) must hold. Therefore, \(q \ne 6\) is correct.

Step 3

Exam Tip

अद्वितीय हल के लिए \(3/7 \ne q/14\) होना चाहिए। इसलिए \(q \ne 6\) सही है।

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Question 16/50 Medium Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

समीकरण (5x+ky=35) और (x+4y=7) के अनंत हल होने के लिए (k) का मान क्या होगा?

What is the value of (k) for (5x+ky=35) and (x+4y=7) to have infinitely many solutions?

Explanation opens after your attempt

Correct Answer

C. (20)

Step 1

Concept

The first equation must be (5) times the second, so (k=20). A common multiplier makes both lines coincident.

Step 2

Why this answer is correct

The correct answer is C. (20). The first equation must be (5) times the second, so (k=20). A common multiplier makes both lines coincident.

Step 3

Exam Tip

पहला समीकरण दूसरे का (5) गुना होना चाहिए, इसलिए (k=20)। समान गुणक से दोनों रेखाएं संपाती होती हैं।

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Question 17/50 Medium Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

समीकरण (8x+ay=40) और (2x+6y=13) का कोई हल न होने के लिए (a) क्या होगा?

What will (a) be for (8x+ay=40) and (2x+6y=13) to have no solution?

Explanation opens after your attempt

Correct Answer

D. (24)

Step 1

Concept

For no solution, (8/2=a/6) and (40/13) must be different. Therefore, (a=24).

Step 2

Why this answer is correct

The correct answer is D. (24). For no solution, (8/2=a/6) and (40/13) must be different. Therefore, (a=24).

Step 3

Exam Tip

कोई हल नहीं के लिए (8/2=a/6) और (40/13) अलग होना चाहिए। इसलिए (a=24) है।

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Question 18/50 Medium Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

समीकरण (10x+15y=35) और (2x+3y=9) के ग्राफ के बारे में सही कथन कौन-सा है?

Which statement is correct about the graph of (10x+15y=35) and (2x+3y=9)?

Explanation opens after your attempt

Correct Answer

C. रेखाएं अलग समानांतर हैंLines are distinct parallel

Step 1

Concept

Here (10/2=15/3) but (35/9) 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 (10/2=15/3) but (35/9) is different. Therefore, the graph will show distinct parallel lines.

Step 3

Exam Tip

यहां (10/2=15/3) लेकिन (35/9) अलग है। इसलिए ग्राफ में अलग समानांतर रेखाएं बनेंगी।

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Question 19/50 Medium Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

समीकरण (12x+8y=44) और (3x+2y=11) के ग्राफ में क्या दिखेगा?

What will be shown in the graph of (12x+8y=44) and (3x+2y=11)?

Explanation opens after your attempt

Correct Answer

A. एक ही रेखाSame line

Step 1

Concept

The first equation is (4) 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 (4) times the second. Therefore, both equations show the same line.

Step 3

Exam Tip

पहला समीकरण दूसरे का (4) गुना है। इसलिए दोनों समीकरण एक ही रेखा दिखाते हैं।

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Question 20/50 Medium Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

समीकरण (3x+8y=20) और (7x+13y=34) के ग्राफ का सही वर्णन क्या है?

What is the correct description of the graph of (3x+8y=20) and (7x+13y=34)?

Explanation opens after your attempt

Correct Answer

C. एक बिंदु पर कटती रेखाएंLines intersecting at one point

Step 1

Concept

Here \(3/7 \ne 8/13\), 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 \(3/7 \ne 8/13\), so the lines will intersect at one point. This gives one unique solution.

Step 3

Exam Tip

यहां \(3/7 \ne 8/13\), इसलिए रेखाएं एक बिंदु पर कटेंगी। इससे एक अद्वितीय हल मिलेगा।

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Question 21/50 Medium Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

यदि दो रेखाओं की ढाल समान और अवरोध भी समान हो, तो युग्म का प्रकार क्या होगा?

If two lines have the same slope and the same intercept, what will be the type of pair?

Explanation opens after your attempt

Correct Answer

C. संगत और आश्रितConsistent and dependent

Step 1

Concept

Same slope and same intercept mean both lines are identical. Therefore, the pair is consistent and dependent.

Step 2

Why this answer is correct

The correct answer is C. संगत और आश्रित / Consistent and dependent. Same slope and same intercept mean both lines are identical. Therefore, the pair is consistent and dependent.

Step 3

Exam Tip

समान ढाल और समान अवरोध का मतलब दोनों रेखाएं एक ही हैं। इसलिए युग्म संगत और आश्रित होता है।

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Question 22/50 Medium Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

यदि दो रेखाओं की ढाल समान लेकिन अवरोध अलग हो, तो सही निष्कर्ष क्या है?

If two lines have the same slope but different intercepts, what is the correct conclusion?

Explanation opens after your attempt

Correct Answer

B. कोई हल नहींNo solution

Step 1

Concept

Same slope and different intercepts make the lines distinct parallel. Therefore, there is no common solution.

Step 2

Why this answer is correct

The correct answer is B. कोई हल नहीं / No solution. Same slope and different intercepts make the lines distinct parallel. Therefore, there is no common solution.

Step 3

Exam Tip

समान ढाल और अलग अवरोध रेखाओं को अलग समानांतर बनाते हैं। इसलिए कोई सामान्य हल नहीं होता।

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Question 23/50 Medium Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

समीकरण (3x+5y-20=0) और (9x+15y-60=0) के लिए सही अनुपात संबंध कौन-सा है?

Which ratio relation is correct for (3x+5y-20=0) and (9x+15y-60=0)?

Explanation opens after your attempt

Correct Answer

C. (39=5 / 15=(-20) / (-60))

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. (3 / 9=5 / 15=(-20) / (-60)). 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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Question 24/50 Medium Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

समीकरण (6x-7y+9=0) और (12x-14y+25=0) के लिए सही अनुपात संबंध क्या है?

What is the correct ratio relation for (6x-7y+9=0) and (12x-14y+25=0)?

Explanation opens after your attempt

Correct Answer

A. (612=(-7) / (-14) \ne 9 / 25)

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. (6 / 12=(-7) / (-14) \ne 9 / 25). 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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Question 25/50 Medium Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

समीकरण (7x+4y-13=0) और (14x+9y-26=0) के लिए सही निष्कर्ष क्या है?

What is the correct conclusion for (7x+4y-13=0) and (14x+9y-26=0)?

Explanation opens after your attempt

Correct Answer

C. एक अद्वितीय हलOne unique solution

Step 1

Concept

Here \(7/14 \ne 4/9\), 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 \(7/14 \ne 4/9\), so the lines intersect at one point. In this case, one unique solution is obtained.

Step 3

Exam Tip

यहां \(7/14 \ne 4/9\), इसलिए रेखाएं एक बिंदु पर कटती हैं। ऐसी स्थिति में एक अद्वितीय हल मिलता है।

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Question 26/50 Medium Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

यदि (ax+6y=18) और (10x+15y=47) का कोई हल नहीं है, तो (a) क्या होगा?

If (ax+6y=18) and (10x+15y=47) have no solution, what will (a) be?

Explanation opens after your attempt

Correct Answer

C. (4)

Step 1

Concept

For no solution, (a/10=6/15) and (18/47) must be different. Therefore, (a=4).

Step 2

Why this answer is correct

The correct answer is C. (4). For no solution, (a/10=6/15) and (18/47) must be different. Therefore, (a=4).

Step 3

Exam Tip

कोई हल नहीं के लिए (a/10=6/15) और (18/47) अलग होना चाहिए। इसलिए (a=4) है।

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Question 27/50 Medium Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

समीकरण (4x+by=28) और (12x+21y=84) के अनंत हल होने के लिए (b) का मान क्या है?

What is the value of (b) for (4x+by=28) and (12x+21y=84) to have infinitely many solutions?

Explanation opens after your attempt

Correct Answer

C. (7)

Step 1

Concept

For infinitely many solutions, (4/12=b/21=28/84) must hold. Therefore, (b=7).

Step 2

Why this answer is correct

The correct answer is C. (7). For infinitely many solutions, (4/12=b/21=28/84) must hold. Therefore, (b=7).

Step 3

Exam Tip

अनंत हल के लिए (4/12=b/21=28/84) होना चाहिए। इसलिए (b=7) होगा।

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Question 28/50 Medium Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

समीकरण (9x+py=27) और (3x+5y=11) का अद्वितीय हल होने के लिए कौन-सी शर्त सही है?

Which condition is correct for (9x+py=27) and (3x+5y=11) to have a unique solution?

Explanation opens after your attempt

Correct Answer

B. \(p \ne 15\)

Step 1

Concept

For a unique solution, \(9/3 \ne p/5\) must hold. Therefore, \(p \ne 15\) is the correct condition.

Step 2

Why this answer is correct

The correct answer is B. \(p \ne 15\). For a unique solution, \(9/3 \ne p/5\) must hold. Therefore, \(p \ne 15\) is the correct condition.

Step 3

Exam Tip

अद्वितीय हल के लिए \(9/3 \ne p/5\) होना चाहिए। इसलिए \(p \ne 15\) सही शर्त है।

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Question 29/50 Medium Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

यदि (6x+5y=31) और (12x+10y=n) के अनंत हल हैं, तो (n) कितना होगा?

If (6x+5y=31) and (12x+10y=n) have infinitely many solutions, what is (n)?

Explanation opens after your attempt

Correct Answer

C. (62)

Step 1

Concept

The second equation must be (2) times the first. Therefore, (n=62).

Step 2

Why this answer is correct

The correct answer is C. (62). The second equation must be (2) times the first. Therefore, (n=62).

Step 3

Exam Tip

दूसरा समीकरण पहले का (2) गुना होना चाहिए। इसलिए (n=62) होगा।

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Question 30/50 Medium Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

यदि (8x-4y=24) और (2x-y=t) असंगत हैं, तो (t) के लिए सही शर्त क्या है?

If (8x-4y=24) and (2x-y=t) are inconsistent, what is the correct condition for (t)?

Explanation opens after your attempt

Correct Answer

B. \(t \ne 6\)

Step 1

Concept

The first two ratios are equal, so for inconsistency (24/t) must be different. Hence, \(t \ne 6\).

Step 2

Why this answer is correct

The correct answer is B. \(t \ne 6\). The first two ratios are equal, so for inconsistency (24/t) must be different. Hence, \(t \ne 6\).

Step 3

Exam Tip

पहले दो अनुपात बराबर हैं, इसलिए असंगत होने के लिए (24/t) अलग होना चाहिए। अतः \(t \ne 6\)।

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Question 31/50 Medium Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

समीकरण (5x+3y=17) और (15x+9y=51) को देखकर सबसे उचित निष्कर्ष क्या है?

What is the most suitable conclusion by observing (5x+3y=17) and (15x+9y=51)?

Explanation opens after your attempt

Correct Answer

C. अनंत हल हैंThere 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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Question 32/50 Medium Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

समीकरण (6x+12y=18) और (x+2y=4) को देखकर कौन-सा निष्कर्ष सही है?

Which conclusion is correct by observing (6x+12y=18) and (x+2y=4)?

Explanation opens after your attempt

Correct Answer

B. पहले दो अनुपात बराबर हैं लेकिन स्थिर पद का अनुपात अलग हैFirst two ratios are equal but the constant ratio is different

Step 1

Concept

Here (6/1=12/2) but (18/4) 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 (6/1=12/2) but (18/4) is different. Therefore, there will be no solution.

Step 3

Exam Tip

यहां (6/1=12/2) लेकिन (18/4) अलग है। इसलिए कोई हल नहीं होगा।

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Question 33/50 Medium Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

समीकरण (9x+4y=21) और (4x+2y=10) में (a) और (b) के अनुपातों की तुलना से क्या पता चलता है?

What is found by comparing the ratios of (a) and (b) in (9x+4y=21) and (4x+2y=10)?

Explanation opens after your attempt

Correct Answer

C. (94 \ne 4 / 2), इसलिए एक अद्वितीय हल / 2), so one unique solution

Step 1

Concept

Here the first two ratios are different. Therefore, the lines intersect at one point and give one solution.

Step 2

Why this answer is correct

The correct answer is C. \(9 / 4 \ne 4 / 2\), इसलिए एक अद्वितीय हल / 2), so one unique solution. Here the first two ratios are different. Therefore, the lines intersect at one point and give one solution.

Step 3

Exam Tip

यहां पहले दो अनुपात अलग हैं। इसलिए रेखाएं एक बिंदु पर कटती हैं और एक हल देती हैं।

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Question 34/50 Medium Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

समीकरण (14x+21y=70) और (2x+3y=10) का युग्म किस प्रकार का है?

What type of pair is (14x+21y=70) and (2x+3y=10)?

Explanation opens after your attempt

Correct Answer

A. संगत और आश्रितConsistent and dependent

Step 1

Concept

The first equation is (7) 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 (7) times the second. Therefore, both are the same line and the pair is dependent.

Step 3

Exam Tip

पहला समीकरण दूसरे का (7) गुना है। इसलिए दोनों एक ही रेखा हैं और युग्म आश्रित है।

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Question 35/50 Medium Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

समीकरण (12x+18y=42) और (2x+3y=8) का युग्म किस प्रकार का है?

What type of pair is (12x+18y=42) and (2x+3y=8)?

Explanation opens after your attempt

Correct Answer

C. असंगतInconsistent

Step 1

Concept

Here (12/2=18/3) but (42/8) is different. Therefore, this is an inconsistent pair.

Step 2

Why this answer is correct

The correct answer is C. असंगत / Inconsistent. Here (12/2=18/3) but (42/8) is different. Therefore, this is an inconsistent pair.

Step 3

Exam Tip

यहां (12/2=18/3) लेकिन (42/8) अलग है। इसलिए यह असंगत युग्म है।

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Question 36/50 Medium Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

समीकरण (10x+3y=28) और (5x+2y=13) का युग्म किस प्रकार का है?

What type of pair is (10x+3y=28) and (5x+2y=13)?

Explanation opens after your attempt

Correct Answer

C. संगत और स्वतंत्रConsistent and independent

Step 1

Concept

Here \(10/5 \ne 3/2\), 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 \(10/5 \ne 3/2\), so the lines intersect. Hence, the pair is consistent and independent.

Step 3

Exam Tip

यहां \(10/5 \ne 3/2\), इसलिए रेखाएं कटती हैं। अतः युग्म संगत और स्वतंत्र है।

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Question 37/50 Medium Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

एक दुकान में दो वस्तुओं के लिए (2x+3y=90) और (4x+6y=180) समीकरण बनते हैं। हलों की संख्या क्या होगी?

In a shop, the equations for two items are (2x+3y=90) and (4x+6y=180). How many solutions will there be?

Explanation opens after your attempt

Correct Answer

C. अनंत हलInfinitely many solutions

Step 1

Concept

The second equation is (2) 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 (2) times the first. Therefore, both conditions give the same information and have infinitely many solutions.

Step 3

Exam Tip

दूसरा समीकरण पहले का (2) गुना है। इसलिए दोनों शर्तें एक ही जानकारी देती हैं और अनंत हल होते हैं।

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Question 38/50 Medium Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

दो टिकटों के दामों के लिए (4x+3y=120) और (8x+6y=250) समीकरण बने। यह प्रणाली कैसी है?

For prices of two tickets, the equations (4x+3y=120) and (8x+6y=250) are formed. What type of system is this?

Explanation opens after your attempt

Correct Answer

C. असंगतInconsistent

Step 1

Concept

The first two ratios are equal but (120/250) 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 (120/250) is different. Therefore, the system is inconsistent.

Step 3

Exam Tip

पहले दो अनुपात बराबर हैं लेकिन (120/250) अलग है। इसलिए प्रणाली असंगत है।

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Question 39/50 Medium Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

दो संख्याओं के लिए (3x+y=14) और (x-2y=1) समीकरण बनते हैं, तो हल-स्थिति क्या होगी?

For two numbers, the equations (3x+y=14) and (x-2y=1) are formed. What will be the solution status?

Explanation opens after your attempt

Correct Answer

A. एक अद्वितीय हलOne unique solution

Step 1

Concept

Here (3/1 \ne 1/(-2)), 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 (3/1 \ne 1/(-2)), so the lines intersect. Such a pair has one unique solution.

Step 3

Exam Tip

यहां (3/1 \ne 1/(-2)), इसलिए रेखाएं कटती हैं। ऐसे युग्म का एक अद्वितीय हल होता है।

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Question 40/50 Medium Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

समीकरण (3x+4y=22) और (6x+8y=44) में तीनों अनुपातों का संबंध क्या है?

What is the relation among all three ratios in (3x+4y=22) and (6x+8y=44)?

Explanation opens after your attempt

Correct Answer

A. तीनों बराबर हैंAll three are equal

Step 1

Concept

Here (3/6=4/8=22/44). 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 (3/6=4/8=22/44). Therefore, both equations form the same line.

Step 3

Exam Tip

यहां (3/6=4/8=22/44)। इसलिए दोनों समीकरण एक ही रेखा बनाते हैं।

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Question 41/50 Medium Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

समीकरण (8x+12y=40) और (2x+3y=12) के लिए कौन-सा संबंध सही है?

Which relation is correct for (8x+12y=40) and (2x+3y=12)?

Explanation opens after your attempt

Correct Answer

C. (82=12 / 3 \ne 40 / 12)

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. \(8 / 2=12 / 3 \ne 40 / 12\). 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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Question 42/50 Medium Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

समीकरण (6x+7y=23) और (12x+13y=45) के लिए कौन-सा कथन सही है?

Which statement is correct for (6x+7y=23) and (12x+13y=45)?

Explanation opens after your attempt

Correct Answer

B. (612 \ne 7 / 13), इसलिए एक अद्वितीय हल / 13), so one unique solution

Step 1

Concept

Here \(6/12 \ne 7/13\), so the lines intersect. Therefore, there is one unique solution.

Step 2

Why this answer is correct

The correct answer is B. \(6 / 12 \ne 7 / 13\), इसलिए एक अद्वितीय हल / 13), so one unique solution. Here \(6/12 \ne 7/13\), so the lines intersect. Therefore, there is one unique solution.

Step 3

Exam Tip

यहां \(6/12 \ne 7/13\), इसलिए रेखाएं कटती हैं। इस कारण एक अद्वितीय हल है।

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Question 43/50 Medium Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

समीकरण (2x+5y=17) और (4x+10y=s) के संगत और आश्रित होने के लिए (s) क्या होगा?

What should (s) be for (2x+5y=17) and (4x+10y=s) to be consistent and dependent?

Explanation opens after your attempt

Correct Answer

C. (34)

Step 1

Concept

To be consistent and dependent, the second equation must be (2) times the first. Hence, (s=34).

Step 2

Why this answer is correct

The correct answer is C. (34). To be consistent and dependent, the second equation must be (2) times the first. Hence, (s=34).

Step 3

Exam Tip

संगत और आश्रित होने के लिए दूसरा समीकरण पहले का (2) गुना होना चाहिए। अतः (s=34)।

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Question 44/50 Medium Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

समीकरण (5x+6y=29) और (10x+12y=r) के असंगत होने के लिए कौन-सी शर्त सही है?

Which condition is correct for (5x+6y=29) and (10x+12y=r) to be inconsistent?

Explanation opens after your attempt

Correct Answer

B. \(r \ne 58\)

Step 1

Concept

The first two ratios are equal, so for inconsistency the constant ratio must be different. Hence, \(r \ne 58\).

Step 2

Why this answer is correct

The correct answer is B. \(r \ne 58\). The first two ratios are equal, so for inconsistency the constant ratio must be different. Hence, \(r \ne 58\).

Step 3

Exam Tip

पहले दो अनुपात बराबर हैं, इसलिए असंगत होने के लिए स्थिर पद का अनुपात अलग होना चाहिए। अतः \(r \ne 58\)।

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Question 45/50 Medium Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

समीकरण (3x+4y=10) और (6x+ay=25) का कोई हल न होने के लिए (a) क्या होगा?

What will (a) be for (3x+4y=10) and (6x+ay=25) to have no solution?

Explanation opens after your attempt

Correct Answer

C. (8)

Step 1

Concept

For no solution, (3/6=4/a) and (10/25) must be different. This gives (a=8).

Step 2

Why this answer is correct

The correct answer is C. (8). For no solution, (3/6=4/a) and (10/25) must be different. This gives (a=8).

Step 3

Exam Tip

कोई हल नहीं के लिए (3/6=4/a) और (10/25) अलग होना चाहिए। इससे (a=8) मिलता है।

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Question 46/50 Medium Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

समीकरण (6x+ky=42) और (2x+5y=14) के अनंत हल होने के लिए (k) क्या होगा?

What will (k) be for (6x+ky=42) and (2x+5y=14) to have infinitely many solutions?

Explanation opens after your attempt

Correct Answer

B. (15)

Step 1

Concept

The first equation must be (3) times the second. Therefore, (k=15).

Step 2

Why this answer is correct

The correct answer is B. (15). The first equation must be (3) times the second. Therefore, (k=15).

Step 3

Exam Tip

पहला समीकरण दूसरे का (3) गुना होना चाहिए। इसलिए (k=15) है।

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Question 47/50 Medium Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

यदि (lx+9y=27) और (8x+18y=55) का कोई हल नहीं है, तो (l) का मान क्या होगा?

If (lx+9y=27) and (8x+18y=55) have no solution, what will be the value of (l)?

Explanation opens after your attempt

Correct Answer

C. (4)

Step 1

Concept

For no solution, (l/8=9/18) and (27/55) must be different. Hence, (l=4).

Step 2

Why this answer is correct

The correct answer is C. (4). For no solution, (l/8=9/18) and (27/55) must be different. Hence, (l=4).

Step 3

Exam Tip

कोई हल नहीं के लिए (l/8=9/18) और (27/55) अलग होना चाहिए। इसलिए (l=4)।

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Question 48/50 Medium Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

समीकरण (9x+2y=31) और (18x+4y=62) को देखकर कौन-सा कथन सही है?

Which statement is correct by observing (9x+2y=31) and (18x+4y=62)?

Explanation opens after your attempt

Correct Answer

B. रेखाएं एक ही हैंLines 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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Question 49/50 Medium Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

समीकरण (12x-8y=20) और (3x-2y=6) को देखकर सही निष्कर्ष क्या है?

What is the correct conclusion by observing (12x-8y=20) and (3x-2y=6)?

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Correct Answer

A. कोई हल नहींNo solution

Step 1

Concept

Here (12/3=(-8)/(-2)) but (20/6) 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 (12/3=(-8)/(-2)) but (20/6) is different. Therefore, the lines are parallel and distinct.

Step 3

Exam Tip

यहां (12/3=(-8)/(-2)) लेकिन (20/6) अलग है। इसलिए रेखाएं समानांतर और अलग हैं।

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Question 50/50 Medium Mathematics Pair of Linear Equations in Two Variables Conditions for solvability Class 10 Level 59

समीकरण (15x+4y=37) और (7x+2y=18) के लिए सही हल-स्थिति क्या है?

What is the correct solution status for (15x+4y=37) and (7x+2y=18)?

Explanation opens after your attempt

Correct Answer

C. एक अद्वितीय हलOne unique solution

Step 1

Concept

Here \(15/7 \ne 4/2\), 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 \(15/7 \ne 4/2\), so the lines will intersect. Hence, there is one unique solution.

Step 3

Exam Tip

यहां \(15/7 \ne 4/2\), इसलिए रेखाएं कटेंगी। अतः एक अद्वितीय हल है।

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Class 10 Mathematics Medium Quiz

समीकरण (5x+4y=18) और (10x+8y=k) के अनंत हल होने के लिए (k) का मान क्या होगा?

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समीकरण (3x+my=24) और (12x+28y=96) के अनंत हल होने के लिए (m) का मान क्या होगा?

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समीकरण (3x+ay=21) और (9x+12y=63) के अनंत हल होने के लिए (a) क्या होगा?

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समीकरण (11x-4y=26) और (22x-8y=53) के लिए सही हल-स्थिति क्या है?

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समीकरण (kx+7y=28) और (8x+14y=60) का कोई हल न होने के लिए (k) का मान क्या होगा?

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समीकरण (5x+7y=32) और (9x+13y=58) में (a) और (b) के अनुपातों की तुलना से क्या निष्कर्ष निकलेगा?

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Exam Tip

यदि (4x+5y=16) और (8x+10y=m) असंगत युग्म हैं, तो (m) के लिए सही शर्त क्या है?

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दो वस्तुओं की कीमतों के लिए (4x+3y=125) और (8x+6y=260) समीकरण बने। यह प्रणाली कैसी है?

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समीकरण (7x+2y=19) और (14x+4y=38) के लिए सही निष्कर्ष क्या है?

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समीकरण (6x-5y=14) और (12x-10y=31) के लिए हलों की संख्या क्या होगी?

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समीकरण (4x+9y=25) और (8x+17y=49) के लिए सही हल-स्थिति क्या है?

Concept

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Exam Tip

यदि \(a_1/a_2=b_1/b_2=c_1/c_2\), तो युग्म का वर्गीकरण क्या होगा?

Concept

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Exam Tip

यदि \(a_1/a_2=b_1/b_2 \ne c_1/c_2\), तो ग्राफ में रेखाएं कैसी होंगी?

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समीकरण (px+3y=15) और (12x+6y=30) के अनंत हल होने के लिए (p) क्या होगा?

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समीकरण (3x+qy=11) और (7x+14y=26) का अद्वितीय हल होने के लिए कौन-सी शर्त सही है?

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समीकरण (5x+ky=35) और (x+4y=7) के अनंत हल होने के लिए (k) का मान क्या होगा?

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समीकरण (8x+ay=40) और (2x+6y=13) का कोई हल न होने के लिए (a) क्या होगा?

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समीकरण (10x+15y=35) और (2x+3y=9) के ग्राफ के बारे में सही कथन कौन-सा है?

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समीकरण (12x+8y=44) और (3x+2y=11) के ग्राफ में क्या दिखेगा?

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समीकरण (3x+8y=20) और (7x+13y=34) के ग्राफ का सही वर्णन क्या है?

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