100 results found for "infinite plane sheet" in Class 10.
C. (23) सेमी(23) cm
(x(x+6)=667) से (x=23) मिलता है। क्षेत्रफल की जाँच \(23 \times 29=667\) से करें। / (x(x+6)=667) gives (x=23). Check the area using \(23 \times 29=667\).
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Why does binary fission in Leishmania occur in a definite plane?
A. क्योंकि उसमें एक निश्चित संरचनात्मक दिशा होती हैBecause it has a definite structural direction
लीशमैनिया की कोशिका में कोड़े जैसी संरचना एक निश्चित स्थान पर होती है। / Leishmania has a whip like structure at a definite position.
इससे शरीर में एक दिशा स्पष्ट होती है। / This gives the cell a definite direction.
इसलिए इसमें विभाजन निश्चित तल में देखा जाता है। / Therefore division is seen in a definite plane.
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B. (12 cm)
मूल चौड़ाई (x) हो, तो डिब्बे का आधार ((x-4)(x+4)) और ऊँचाई (2) है। (2(x-4)(x+4)=240) से \(x^2=136\), इसलिए विकल्पों में कोई सही नहीं। / Let original breadth be (x), then the box base is ((x-4)(x+4)) and height is (2). From (2(x-4)(x+4)=240), \(x^2=136\), so none of the options is exact.
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B. (10 cm)
वर्ग की भुजा (x) हो, तो शेष क्षेत्रफल (x(x-3)=70)। इससे \(x^2-3x-70=0\), इसलिए (x=10)। / Let the square side be (x), then the remaining area is (x(x-3)=70). This gives \(x^2-3x-70=0\), so (x=10).
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A square sheet has area (144) square cm. What is its perimeter?
D. (48) सेमी(48) cm
\(x^2=144\) से भुजा (12) सेमी है और परिमाप (4x=48) सेमी है। परिमाप पूछे जाने पर केवल भुजा लिखकर न रुकें। / \(x^2=144\) gives side (12) cm and perimeter (4x=48) cm. If perimeter is asked, do not stop after finding the side.
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How can a small object placed higher on the picture plane appear?
D. दूरFar
चित्र तल पर ऊपर रखी वस्तु दूर का आभास दे सकती है। परीक्षा में placement को depth cue मानें। / An object placed higher on the picture plane can appear far. Exam tip: treat placement as a depth cue.
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Binary fission in Amoeba is not in a fixed plane but it is in Leishmania. What is the reason?
B. लीशमैनिया में निश्चित संरचनात्मक दिशा होती हैLeishmania has a definite structural direction
अमीबा का आकार अनियमित होता है। / Amoeba has an irregular shape.
लीशमैनिया में कोड़े जैसी संरचना एक निश्चित स्थान पर होती है। / Leishmania has a whip like structure at a definite position.
इसलिए लीशमैनिया में विभाजन का तल अधिक निश्चित होता है। / Therefore the plane of division is more definite in Leishmania.
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Why does binary fission in Amoeba not occur in one fixed plane?
A. क्योंकि अमीबा का आकार अनियमित होता हैBecause Amoeba has an irregular shape
अमीबा एककोशिकीय और अनियमित आकार वाला जीव है। / Amoeba is unicellular and irregular in shape.
इसमें शरीर का कोई स्थायी लंबा या चौड़ा तल नहीं होता। / It does not have a fixed long or broad plane.
इसलिए द्विखंडन किसी निश्चित तल में नहीं माना जाता। / Therefore its binary fission is not considered fixed in one plane.
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C. (11)
अनंत हल के लिए (6/18=a/33=42/126) होना चाहिए। इसलिए (a=11) सही है। / For infinitely many solutions, (6/18=a/33=42/126) must hold. Therefore, (a=11) is correct.
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What will (k) be for the equations (12x+ky=132) and (3x+10y=33) to have infinitely many solutions?
C. (40)
पहला समीकरण दूसरे का (4) गुना होना चाहिए। इसलिए (k=40) है। / The first equation must be (4) times the second. Therefore, (k=40).
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C. अनंत हलInfinitely many solutions
दूसरा समीकरण पहले का (3) गुना है। इसलिए दोनों शर्तें एक ही जानकारी देती हैं और अनंत हल होते हैं। / The second equation is (3) times the first. Therefore, both conditions give the same information and have infinitely many solutions.
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What is the most suitable conclusion by observing the equations (8x+15y=73) and (24x+45y=219)?
C. अनंत हल हैंThere are infinitely many solutions
दूसरा समीकरण पहले का (3) गुना है। इसलिए दोनों रेखाएं संपाती हैं। / The second equation is (3) times the first. Therefore, both lines are coincident.
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If (11x+7y=59) and (33x+21y=n) have infinitely many solutions, what is (n)?
C. (177)
दूसरा समीकरण पहले का (3) गुना होना चाहिए। इसलिए (n=177) होगा। / The second equation must be (3) times the first. Therefore, (n=177).
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Which ratio relation is correct for the equations (10x+13y-71=0) and (30x+39y-213=0)?
C. (1030=13 / 39=(-71) / (-213))
यहां तीनों अनुपात बराबर हैं। इसलिए दोनों रेखाएं संपाती हैं और अनंत हल हैं। / Here all three ratios are equal. Therefore, both lines are coincident and have infinitely many solutions.
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What will (k) be for the equations (kx+14y=42) and (18x+21y=63) to have infinitely many solutions?
C. (12)
अनंत हल के लिए (k/18=14/21=42/63) होना चाहिए। इसलिए (k=12) सही है। / For infinitely many solutions, (k/18=14/21=42/63) must hold. Therefore, (k=12) is correct.
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C. (7)
अनंत हल के लिए (4/12=a/21=32/96) होना चाहिए। इसलिए (a=7) सही है। / For infinitely many solutions, (4/12=a/21=32/96) must hold. Therefore, (a=7) is correct.
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C. (7)
अनंत हल के लिए (5/20=a/28=45/180) होना चाहिए। इसलिए (a=7) सही है। / For infinitely many solutions, (5/20=a/28=45/180) must hold. Therefore, (a=7) is correct.
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What will (k) be for the equations (10x+ky=110) and (2x+9y=22) to have infinitely many solutions?
C. (45)
पहला समीकरण दूसरे का (5) गुना होना चाहिए। इसलिए (k=45) है। / The first equation must be (5) times the second. Therefore, (k=45).
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C. अनंत हलInfinitely many solutions
दूसरा समीकरण पहले का (3) गुना है। इसलिए दोनों शर्तें एक ही जानकारी देती हैं और अनंत हल होते हैं। / The second equation is (3) times the first. Therefore, both conditions give the same information and have infinitely many solutions.
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What is the most suitable conclusion by observing the equations (9x+14y=71) and (27x+42y=213)?
C. अनंत हल हैंThere are infinitely many solutions
दूसरा समीकरण पहले का (3) गुना है। इसलिए दोनों रेखाएं संपाती हैं। / The second equation is (3) times the first. Therefore, both lines are coincident.
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If (9x+5y=47) and (27x+15y=n) have infinitely many solutions, what is (n)?
C. (141)
दूसरा समीकरण पहले का (3) गुना होना चाहिए। इसलिए (n=141) होगा। / The second equation must be (3) times the first. Therefore, (n=141).
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Which ratio relation is correct for the equations (8x+13y-59=0) and (24x+39y-177=0)?
C. (824=13 / 39=(-59) / (-177))
यहां तीनों अनुपात बराबर हैं। इसलिए दोनों रेखाएं संपाती हैं और अनंत हल हैं। / Here all three ratios are equal. Therefore, both lines are coincident and have infinitely many solutions.
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What will (k) be for the equations (kx+12y=36) and (15x+20y=60) to have infinitely many solutions?
C. (9)
अनंत हल के लिए (k/15=12/20=36/60) होना चाहिए। इसलिए (k=9) सही है। / For infinitely many solutions, (k/15=12/20=36/60) must hold. Therefore, (k=9) is correct.
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C. (6)
अनंत हल के लिए (5/15=2/a=18/54) होना चाहिए। इसलिए (a=6) सही है। / For infinitely many solutions, (5/15=2/a=18/54) must hold. Therefore, (a=6) is correct.
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D. (6)
अनंत हल के लिए (10/20=3/a=44/88) होना चाहिए। इसलिए (a=6) सही है। / For infinitely many solutions, (10/20=3/a=44/88) must hold. Therefore, (a=6) is correct.
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What will (k) be for the equations (9x+ky=81) and (3x+8y=27) to have infinitely many solutions?
C. (24)
पहला समीकरण दूसरे का (3) गुना होना चाहिए। इसलिए (k=24) है। / The first equation must be (3) times the second. Therefore, (k=24).
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C. अनंत हलInfinitely many solutions
दूसरा समीकरण पहले का (3) गुना है। इसलिए दोनों शर्तें एक ही जानकारी देती हैं और अनंत हल होते हैं। / The second equation is (3) times the first. Therefore, both conditions give the same information and have infinitely many solutions.
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What is the most suitable conclusion by observing the equations (7x+12y=53) and (21x+36y=159)?
C. अनंत हल हैंThere are infinitely many solutions
दूसरा समीकरण पहले का (3) गुना है। इसलिए दोनों रेखाएं संपाती हैं। / The second equation is (3) times the first. Therefore, both lines are coincident.
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If (8x+5y=43) and (24x+15y=n) have infinitely many solutions, what is (n)?
C. (129)
दूसरा समीकरण पहले का (3) गुना होना चाहिए। इसलिए (n=129) होगा। / The second equation must be (3) times the first. Therefore, (n=129).
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Which ratio relation is correct for the equations (6x+11y-47=0) and (18x+33y-141=0)?
C. (618=11 / 33=(-47) / (-141))
यहां तीनों अनुपात बराबर हैं। इसलिए दोनों रेखाएं संपाती हैं और अनंत हल हैं। / Here all three ratios are equal. Therefore, both lines are coincident and have infinitely many solutions.
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If two lines have the same slope and the same (y)-intercept, what will be the solutions of the pair?
C. अनंत हलInfinitely many solutions
समान ढाल और समान अवरोध का अर्थ है कि दोनों रेखाएं एक ही हैं। इसलिए युग्म के अनंत हल होते हैं। / Same slope and same intercept mean both lines are identical. Therefore, the pair has infinitely many solutions.
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What will (k) be for the equations (kx+10y=30) and (12x+15y=45) to have infinitely many solutions?
B. (8)
अनंत हल के लिए (k/12=10/15=30/45) होना चाहिए। इसलिए (k=8) सही है। / For infinitely many solutions, (k/12=10/15=30/45) must hold. Therefore, (k=8) is correct.
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B. (5)
अनंत हल के लिए (4/12=a/15=28/84) होना चाहिए। इसलिए (a=5) सही है। / For infinitely many solutions, (4/12=a/15=28/84) must hold. Therefore, (a=5) is correct.
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C. (6)
अनंत हल के लिए (m/18=5/15=15/45) होना चाहिए। इसलिए (m=6) सही है। / For infinitely many solutions, (m/18=5/15=15/45) must hold. Therefore, (m=6) is correct.
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What will (k) be for the equations (8x+ky=72) and (2x+7y=18) to have infinitely many solutions?
C. (28)
पहला समीकरण दूसरे का (4) गुना होना चाहिए। इसलिए (k=28) है। / The first equation must be (4) times the second. Therefore, (k=28).
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What is the most suitable conclusion by observing the equations (6x+7y=41) and (18x+21y=123)?
C. अनंत हल हैंThere are infinitely many solutions
दूसरा समीकरण पहले का (3) गुना है। इसलिए दोनों रेखाएं संपाती हैं। / The second equation is (3) times the first. Therefore, both lines are coincident.
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Which ratio relation is correct for the equations (4x+9y-31=0) and (12x+27y-93=0)?
C. (412=9 / 27=(-31) / (-93))
यहां तीनों अनुपात बराबर हैं। इसलिए दोनों रेखाएं संपाती हैं और अनंत हल हैं। / Here all three ratios are equal. Therefore, both lines are coincident and have infinitely many solutions.
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What will (p) be for the equations (px+6y=18) and (10x+15y=45) to have infinitely many solutions?
B. (3)
अनंत हल के लिए (p/10=6/15=18/45) होना चाहिए। इसलिए (p=4) नहीं, (p=4) नहीं बल्कि (p=4) अनुपात बिगाड़ता है और सही (p=4) नहीं है। / For infinitely many solutions, (p/10=6/15=18/45) must hold. Since the common ratio is (2/5), (p=4) would be required.
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C. (5)
अनंत हल के लिए (3/9=k/15=12/36) होना चाहिए। इसलिए (k=5) सही है। / For infinitely many solutions, (3/9=k/15=12/36) must hold. Therefore, (k=5) is correct.
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What will be the value of (a) for (4x+ay=36) and (12x+21y=108) to have infinitely many solutions?
C. (7)
अनंत हल के लिए (4/12=a/21=36/108) होना चाहिए। इसलिए (a=7) मिलता है। / For infinitely many solutions (4/12=a/21=36/108) must hold. Therefore (a=7).
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What will (k) be for (8x+ky=72) and (2x+7y=18) to have infinitely many solutions?
C. (28)
पहला समीकरण दूसरे का (4) गुना होना चाहिए। इसलिए (k=28) है। / The first equation must be (4) times the second. Therefore (k=28).
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C. अनंत हलInfinitely many solutions
दूसरा समीकरण पहले का (3) गुना है। इसलिए दोनों शर्तें एक ही जानकारी देती हैं और अनंत हल होते हैं। / The second equation is (3) times the first. Therefore both conditions give the same information and have infinitely many solutions.
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What is the most suitable conclusion by observing (6x+7y=41) and (18x+21y=123)?
C. अनंत हल हैंThere are infinitely many solutions
दूसरा समीकरण पहले का (3) गुना है। इसलिए दोनों रेखाएं संपाती हैं। / The second equation is (3) times the first. Therefore both lines are coincident.
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If (7x+4y=37) and (21x+12y=n) have infinitely many solutions then what is (n)?
C. (111)
दूसरा समीकरण पहले का (3) गुना होना चाहिए। इसलिए (n=111) होगा। / The second equation must be (3) times the first. Therefore (n=111).
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Which ratio relation is correct for (4x+9y-31=0) and (12x+27y-93=0)?
C. (412=9 / 27=(-31) / (-93))
यहां तीनों अनुपात बराबर हैं। इसलिए दोनों रेखाएं संपाती हैं और अनंत हल हैं। / Here all three ratios are equal. Therefore both lines are coincident and have infinitely many solutions.
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What is the value of (p) for (px+6y=18) and (10x+15y=45) to have infinitely many solutions?
B. (3)
अनंत हल के लिए (p/10=6/15=18/45) होना चाहिए। इसलिए (p=3)। / For infinitely many solutions (p/10=6/15=18/45) must hold. Therefore (p=3).
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What is the correct conclusion for (8x+3y=21) and (16x+6y=42)?
A. अनंत हलInfinitely many solutions
दूसरा समीकरण पहले का (2) गुना है इसलिए दोनों रेखाएं संपाती हैं। संपाती रेखाओं के अनंत हल होते हैं। / The second equation is (2) times the first so both lines are coincident. Coincident lines have infinitely many solutions.
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What is the value of (k) for (2x+5y=16) and (6x+15y=k) to have infinitely many solutions?
B. (48)
दूसरा समीकरण पहले का (3) गुना होना चाहिए इसलिए (k=48)। अनंत हल के लिए सभी अनुपात बराबर होने चाहिए। / The second equation must be (3) times the first so (k=48). For infinitely many solutions all ratios must be equal.
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What will be the value of (m) for (3x+my=24) and (12x+28y=96) to have infinitely many solutions?
C. (7)
अनंत हल के लिए (3/12=m/28=24/96) होना चाहिए। इसलिए (m=7) सही है। / For infinitely many solutions, (3/12=m/28=24/96) must hold. Therefore, (m=7) is correct.
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What will (k) be for (6x+ky=42) and (2x+5y=14) to have infinitely many solutions?
B. (15)
पहला समीकरण दूसरे का (3) गुना होना चाहिए। इसलिए (k=15) है। / The first equation must be (3) times the second. Therefore, (k=15).
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C. अनंत हलInfinitely many solutions
दूसरा समीकरण पहले का (2) गुना है। इसलिए दोनों शर्तें एक ही जानकारी देती हैं और अनंत हल होते हैं। / The second equation is (2) times the first. Therefore, both conditions give the same information and have infinitely many solutions.
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What is the most suitable conclusion by observing (5x+3y=17) and (15x+9y=51)?
C. अनंत हल हैंThere are infinitely many solutions
दूसरा समीकरण पहले का (3) गुना है। इसलिए दोनों रेखाएं संपाती हैं। / The second equation is (3) times the first. Therefore, both lines are coincident.
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If (6x+5y=31) and (12x+10y=n) have infinitely many solutions, what is (n)?
C. (62)
दूसरा समीकरण पहले का (2) गुना होना चाहिए। इसलिए (n=62) होगा। / The second equation must be (2) times the first. Therefore, (n=62).
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Which ratio relation is correct for (3x+5y-20=0) and (9x+15y-60=0)?
C. (39=5 / 15=(-20) / (-60))
यहां तीनों अनुपात बराबर हैं। इसलिए दोनों रेखाएं संपाती हैं और अनंत हल हैं। / Here all three ratios are equal. Therefore, both lines are coincident and have infinitely many solutions.
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What will (p) be for (px+3y=15) and (12x+6y=30) to have infinitely many solutions?
C. (6)
अनंत हल के लिए (p/12=3/6=15/30) होना चाहिए। इसलिए (p=6) है। / For infinitely many solutions, (p/12=3/6=15/30) must hold. Therefore, (p=6).
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What is the correct conclusion for (7x+2y=19) and (14x+4y=38)?
C. अनंत हलInfinitely many solutions
दूसरा समीकरण पहले का (2) गुना है, इसलिए दोनों रेखाएं संपाती हैं। संपाती रेखाओं के अनंत हल होते हैं। / The second equation is (2) times the first, so both lines are coincident. Coincident lines have infinitely many solutions.
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What is the value of (k) for (5x+4y=18) and (10x+8y=k) to have infinitely many solutions?
B. (36)
दूसरा समीकरण पहले का (2) गुना होना चाहिए, इसलिए (k=36)। अनंत हल के लिए तीनों अनुपात बराबर रखें। / The second equation must be (2) times the first, so (k=36). For infinitely many solutions, keep all three ratios equal.
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What will be the value of (m) for (2x+my=14) and (8x+20y=56) to have infinitely many solutions?
A. (5)
अनंत हल के लिए (2/8=m/20=14/56) होना चाहिए। इसलिए (m=5) है। / For infinitely many solutions, (2/8=m/20=14/56) must hold. Therefore, (m=5).
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What will (k) be for (5x+ky=25) and (x+3y=5) to have infinitely many solutions?
B. (15)
पहला समीकरण दूसरे का (5) गुना होना चाहिए। इसलिए (k=15)। / The first equation must be (5) times the second. Therefore, (k=15).
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C. अनंत हलInfinitely many solutions
दूसरा समीकरण पहले का (2) गुना है। इसलिए दोनों शर्तें एक ही जानकारी देती हैं और अनंत हल होते हैं। / The second equation is (2) times the first. Therefore, both conditions give the same information and have infinitely many solutions.
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What is the most suitable conclusion by observing (3x+2y=8) and (9x+6y=24)?
C. अनंत हल हैंThere are infinitely many solutions
दूसरा समीकरण पहले का (3) गुना है। इसलिए दोनों रेखाएं संपाती हैं। / The second equation is (3) times the first. Therefore, both lines are coincident.
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If (5x+2y=16) and (10x+4y=n) have infinitely many solutions, what is (n)?
D. (32)
दूसरा समीकरण पहले का (2) गुना होना चाहिए। इसलिए (n=32) होगा। / The second equation must be (2) times the first. Therefore, (n=32).
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Which ratio relation is correct for (2x+3y-11=0) and (6x+9y-33=0)?
C. (26=3 / 9=(-11) / (-33))
यहां तीनों अनुपात (1/3) के बराबर हैं। इसलिए समीकरणों के अनंत हल होंगे। / Here all three ratios are equal to (1/3). Therefore, the equations will have infinitely many solutions.
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What is the value of (p) for (px+2y=6) and (9x+6y=18) to have infinitely many solutions?
C. (3)
अनंत हल के लिए (p/9=2/6=6/18), इसलिए (p=3)। तीनों अनुपात बराबर होने चाहिए। / For infinitely many solutions, (p/9=2/6=6/18), so (p=3). All three ratios must be equal.
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Which conclusion is correct for (5x+2y=11) and (10x+4y=22)?
C. अनंत हलInfinitely many solutions
दूसरा समीकरण पहले का (2) गुना है, इसलिए दोनों रेखाएं संपाती हैं। संपाती रेखाओं के अनंत हल होते हैं। / The second equation is (2) times the first, so both lines are coincident. Coincident lines have infinitely many solutions.
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What is the value of (a) for (3x+ay=12) and (6x+8y=24) to have infinitely many solutions?
B. (4)
अनंत हल के लिए (3/6=a/8=12/24), इसलिए (a=4)। पहले गुणांकों और स्थिर पदों के अनुपात मिलाएं। / For infinitely many solutions, (3/6=a/8=12/24), so (a=4). Match the ratios of coefficients and constants first.
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What is the correct conclusion for (18x+6y=12) and (3x+y=2)?
C. अनंत हलInfinitely many solutions
पहला समीकरण दूसरे का (6) गुना है इसलिए दोनों रेखाएं संपाती हैं। संपाती रेखाओं में अनंत हल होते हैं। / The first equation is (6) times the second so both lines are coincident. Coincident lines have infinitely many solutions.
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If (2) equations have \(a_1/a_2=b_1/b_2\) and \(c_1/c_2\) is also the same then what happens?
C. अनंत हलInfinitely many solutions
तीनों अनुपात बराबर होने पर समीकरण समान रेखा बनाते हैं। इसलिए हल अनंत होते हैं। / When all three ratios are equal the equations make the same line. Therefore the solutions are infinite.
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Choose the correct statement for (15x+10y=5) and (3x+2y=1).
C. अनंत हल हैंThere are infinitely many solutions
पहला समीकरण दूसरे का (5) गुना है। इसलिए दोनों समीकरण एक ही रेखा दर्शाते हैं। / The first equation is (5) times the second. Therefore both equations represent the same line.
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What is the quickest conclusion by observing (2x+3y=5) and (4x+6y=10)?
C. दूसरा पहले का (2) गुना है इसलिए अनंत हल हैंThe second is (2) times the first so infinitely many solutions
सभी पद (2) गुना हो गए हैं इसलिए समीकरण समान रेखा देते हैं। ऐसे सवाल में गुणक पहचानना सबसे तेज तरीका है। / All terms are multiplied by (2) so the equations give the same line. In such questions identifying the multiplier is the fastest method.
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What will (m) be for infinitely many solutions of (7x+my=28) and (x+2y=4)?
C. (14)
पहला समीकरण दूसरे का (7) गुना होना चाहिए। इसलिए (m=14) होगा। / The first equation must be (7) times the second. Therefore (m=14).
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What is the value of (a) for (2x+ay=5) and (6x+9y=15) to have infinitely many solutions?
B. (3)
अनंत हल के लिए (2/6=a/9=5/15) होना चाहिए। इसलिए (a=3) है। / For infinitely many solutions (2/6=a/9=5/15) must hold. Therefore (a=3).
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Which option is correct for (3x-2y=6) and (12x-8y=24)?
C. संपाती रेखाएं और अनंत हलCoincident lines and infinitely many solutions
दूसरा समीकरण पहले का (4) गुना है। इसलिए दोनों समीकरण एक ही रेखा को दर्शाते हैं। / The second equation is (4) times the first. Therefore both equations represent the same line.
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Choose the correct statement for (7x+4y=20) and (14x+8y=40).
C. अनंत हल हैंThere are infinitely many solutions
दूसरा समीकरण पहले का (2) गुना है इसलिए दोनों रेखाएं एक ही हैं। समान रेखा अनंत हल देती है। / The second equation is (2) times the first so both lines are the same. The same line gives infinitely many solutions.
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If both equations give the same line in a graph then how many solutions will the pair have?
D. अनंत हलInfinitely many solutions
एक ही रेखा के हर बिंदु से दोनों समीकरण संतुष्ट होते हैं। इसलिए ऐसे युग्म में अनंत हल होते हैं। / Every point on the same line satisfies both equations. Therefore such a pair has infinitely many solutions.
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What is the number of solutions for (3x+2y=7) and (6x+4y=14)?
C. अनंत हलInfinitely many solutions
दूसरा समीकरण पहले का (2) गुना है इसलिए रेखाएं संपाती हैं। संपाती रेखाओं में अनंत हल होते हैं। / The second equation is (2) times the first so the lines are coincident. Coincident lines have infinitely many solutions.
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Choose the correct statement for (15x+9y=6) and (5x+3y=2).
C. अनंत हल हैंThere are infinitely many solutions
पहला समीकरण दूसरे का (3) गुना है। इसलिए दोनों रेखाएं संपाती हैं और अनंत हल हैं। / The first equation is (3) times the second. Therefore both lines are coincident and have infinitely many solutions.
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What is the correct conclusion for (x-5y=1) and (2x-10y=2)?
C. अनंत हलInfinitely many solutions
दूसरा समीकरण पहले का (2) गुना है। इसलिए दोनों समीकरण समान रेखा दर्शाते हैं। / The second equation is (2) times the first. Therefore both equations represent the same line.
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How many solutions are there in a consistent and dependent pair?
D. अनंत हलInfinitely many solutions
संगत और आश्रित युग्म में दोनों समीकरण एक ही रेखा दर्शाते हैं। इसलिए हर सामान्य बिंदु हल होता है। / In a consistent and dependent pair both equations represent the same line. Therefore every common point is a solution.
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Which of the following pairs gives infinitely many solutions?
A. (x+y=5) और (2x+2y=10)(x+y=5) and (2x+2y=10)
पहले विकल्प में दूसरा समीकरण पहले का (2) गुना है। इसलिए दोनों रेखाएं संपाती हैं और अनंत हल हैं। / In the first option the second equation is (2) times the first. Therefore the lines are coincident and have infinitely many solutions.
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What will (a) be for infinitely many solutions of (7x+ay=21) and (x+2y=3)?
C. (14)
पहला समीकरण दूसरे का (7) गुना होना चाहिए इसलिए (a=14)। इससे दोनों समीकरण एक ही रेखा दर्शाते हैं। / The first equation must be (7) times the second so (a=14). Then both equations represent the same line.
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What will (k) be for infinitely many solutions of (3x+ky=12) and (6x+8y=24)?
B. (4)
अनंत हल के लिए (3/6=k/8=12/24) होना चाहिए। इसलिए (k=4) है। / For infinitely many solutions (3/6=k/8=12/24) must hold. Therefore (k=4).
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What is the value of (a) for (2x+ay=7) and (4x+10y=14) to have infinitely many solutions?
C. (5)
अनंत हल के लिए (2/4=a/10=7/14) होना चाहिए इसलिए (a=5)। तीनों अनुपात बराबर करना जरूरी है। / For infinitely many solutions (2/4=a/10=7/14) must hold so (a=5). Making all three ratios equal is necessary.
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If two equations have infinitely many common solutions then how will their graph be?
B. एक ही रेखाSame line
अनंत सामान्य हल तभी मिलते हैं जब दोनों समीकरण एक ही रेखा दर्शाते हैं। परीक्षा में इसे coincident lines लिख सकते हैं। / Infinitely many common solutions occur only when both equations represent the same line. In exams this can be written as coincident lines.
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Choose the correct option for (x-4y=10) and (3x-12y=30).
D. अनंत हलInfinitely many solutions
दूसरा समीकरण पहले का (3) गुना है इसलिए दोनों रेखाएं संपाती हैं। संपाती रेखाएं अनंत हल देती हैं। / The second equation is (3) times the first so both lines are coincident. Coincident lines give infinitely many solutions.
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What is the correct statement for (6x+3y=12) and (2x+y=4)?
C. अनंत हल हैंThere are infinitely many solutions
पहला समीकरण दूसरे का (3) गुना है इसलिए दोनों एक ही रेखा हैं। ऐसे प्रश्नों में समान गुणक पहचानना तेज तरीका है। / The first equation is (3) times the second so both are the same line. In such questions spotting the common multiplier is the fastest method.
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What is the solution type of (5x-2y=8) and (10x-4y=16)?
B. अनंत हलInfinitely many solutions
दूसरा समीकरण पहले का (2) गुना है इसलिए दोनों रेखाएं एक ही हैं। एक ही रेखा के सभी बिंदु हल होते हैं। / The second equation is (2) times the first so both lines are the same. All points on the same line are solutions.
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What will be the number of solutions for (2x+5y=9) and (4x+10y=18)?
C. अनंत हलInfinitely many solutions
दूसरा समीकरण पहले का (2) गुना है इसलिए दोनों रेखाएं संपाती हैं। संपाती रेखाओं में अनंत हल होते हैं। / The second equation is (2) times the first so both lines are coincident. Coincident lines have infinitely many solutions.
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State the number of solutions of (6x-2y=4) and (3x-y=2).
C. अनंत हलInfinitely many solutions
पहला समीकरण दूसरे का (2) गुना है, इसलिए दोनों रेखाएं संपाती हैं। संपाती रेखाओं के अनंत हल होते हैं। / The first equation is (2) times the second, so both lines are coincident. Coincident lines have infinitely many solutions.
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What value of (a) gives infinitely many solutions for (5x+ay=15) and (10x+6y=30)?
B. (3)
अनंत हल के लिए (5/10=a/6=15/30), इसलिए (a=3)। तीनों अनुपात बराबर होने जरूरी हैं। / For infinitely many solutions, (5/10=a/6=15/30), so (a=3). All three ratios must be equal.
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What is the value of (k) for (x+ky=2) and (2x+6y=4) to have infinitely many solutions?
B. (3)
अनंत हल के लिए (1/2=k/6=2/4), इसलिए (k=3)। अनुपात बराबर रखने से equations dependent बनती हैं। / For infinitely many solutions, (1/2=k/6=2/4), so (k=3). Keeping ratios equal makes the equations dependent.
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Which of the following conditions gives infinitely many solutions?
C. (a_1a_2=b_1 / b_2=c_1 / c_2)
अनंत हल के लिए तीनों अनुपात बराबर होने चाहिए। इससे दोनों समीकरण एक ही रेखा बनाते हैं। / For infinitely many solutions, all three ratios must be equal. Then both equations form the same line.
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What value of (k) gives infinitely many solutions for (2x+ky=4) and (6x+9y=12)?
C. (3)
अनंत हल के लिए (2/6=k/9=4/12), इसलिए (k=3)। तीनों अनुपात बराबर करना मुख्य तरीका है। / For infinitely many solutions, (2/6=k/9=4/12), so (k=3). Making all three ratios equal is the key method.
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Choose the correct conclusion for (3x-4y=8) and (6x-8y=16).
C. अनंत हलInfinitely many solutions
दूसरा समीकरण पहले का (2) गुना है, इसलिए दोनों एक ही रेखा हैं। समान रेखा पर अनंत हल मिलते हैं। / The second equation is (2) times the first, so both are the same line. The same line gives infinitely many solutions.
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Choose the correct statement for (9x-3y+6=0) and (3x-y+2=0).
C. अनंत हल हैंHas infinitely many solutions
यहां (9/3=(-3)/(-1)=6/2), इसलिए दोनों समीकरण एक ही रेखा हैं। इसलिए अनंत हल हैं। / Here (9/3=(-3)/(-1)=6/2), so both equations are the same line. Therefore, there are infinitely many solutions.
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Which option is correct for (x-2y+6=0) and (3x-6y+18=0)?
C. अनंत हलInfinitely many solutions
यहां (1/3=(-2)/(-6)=6/18), इसलिए रेखाएं संपाती हैं। संपाती रेखाओं के अनंत सामान्य बिंदु होते हैं। / Here (1/3=(-2)/(-6)=6/18), so the lines are coincident. Coincident lines have infinitely many common points.
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If both lines become the same line in a graph, how many solutions will there be?
C. अनंत हलInfinitely many solutions
एक ही रेखा के हर बिंदु से दोनों समीकरण संतुष्ट होते हैं। इसलिए ऐसे युग्म के अनंत हल होते हैं। / Every point on the same line satisfies both equations. Therefore, such a pair has infinitely many solutions.
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If \(a_1/a_2=b_1/b_2=c_1/c_2\), how many solutions will the equations have?
C. अनंत हलInfinitely many solutions
तीनों अनुपात बराबर हों तो दोनों रेखाएं संपाती होती हैं। ऐसी स्थिति में अनंत हल होते हैं। / If all three ratios are equal, the two lines are coincident. Such a pair has infinitely many solutions.
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What is the number of solutions of (4x+7y=31) and (8x+14y=62)?
D. अनंत हलInfinitely many solutions
दूसरा समीकरण पहले का (2) गुना है। इसलिए दोनों एक ही रेखा हैं और अनंत हल हैं। / The second equation is (2) times the first. Therefore both are the same line and have infinitely many solutions.
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What is the value of (a) for (ax+9y=27) and (2x+3y=9) to have infinitely many solutions?
C. (a=6)
अनंत हल के लिए पहला समीकरण दूसरे का (3) गुना होना चाहिए। इसलिए (a=6)। / For infinitely many solutions, the first equation must be (3) times the second. Therefore (a=6).
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