100 results found for "linear subtraction" in Class 10.
What is the intersection of (x+4y=18) and (2x+4y=20)?
A. ( (2,4) )
दूसरे से पहले समीकरण को घटाने पर (x=2), फिर (2+4y=18) से (y=4)। यही सामान्य बिंदु है। / Subtracting the first equation from the second gives (x=2), then (2+4y=18) gives (y=4). This is the common point.
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At which point do the lines (4x+y=25) and (x+y=10) meet on the graph?
A. बिंदु (\left\(5,5\right\))Point (\left\(5,5\right\))
दोनों समीकरण घटाने पर (3x=15), इसलिए (x=5) और (y=5)। ग्राफ पर यही दोनों रेखाओं का प्रतिच्छेद बिंदु है। / Subtracting the equations gives (3x=15), so (x=5) and (y=5). On the graph, this is the intersection point of both lines.
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At which point do the lines (3x+2y=22) and (x+2y=10) meet on the graph?
A. बिंदु (\left\(6,2\right\))Point (\left\(6,2\right\))
दोनों समीकरण घटाने पर (2x=12), इसलिए (x=6) और (y=2)। ग्राफ पर यही प्रतिच्छेद बिंदु है। / Subtracting the equations gives (2x=12), so (x=6) and (y=2). This is the intersection point on the graph.
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Where do the lines (4x+y=18) and (x+y=9) meet?
B. बिंदु (\left\(3,6\right\))Point (\left\(3,6\right\))
दोनों समीकरण घटाने पर (3x=9), इसलिए (x=3) और (y=6)। ग्राफ पर यही मिलन बिंदु है। / Subtracting the equations gives (3x=9), so (x=3) and (y=6). This is the meeting point on the graph.
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At which point do the lines (x+5y=13) and (2x+5y=16) meet?
A. ( (3,2) )
दूसरे समीकरण से पहले को घटाने पर (x=3), फिर (3+5y=13) से (y=2)। यही ग्राफीय हल है। / Subtracting the first equation from the second gives (x=3), then (3+5y=13) gives (y=2). This is the graphical solution.
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Where do the lines (x+4y=14) and (2x+4y=16) meet?
A. ( (2,3) )
दोनों समीकरण घटाने पर (x=2), फिर (2+4y=14) से (y=3)। ग्राफ पर यही सामान्य बिंदु है। / Subtracting the equations gives (x=2), then (2+4y=14) gives (y=3). This is the common point on the graph.
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If (D=0), \(D_x=0\), and \(D_y=0\), what happens in a pair of two linear equations?
C. अनंत हलInfinitely many solutions
तीनों सारणिक शून्य होने पर समीकरण आश्रित हो सकते हैं। कक्षा (10) में इसे अनंत हल की स्थिति से जोड़कर देखें। / When all three determinants are zero, the equations may be dependent. In Class (10), link this with infinitely many solutions.
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C. अद्वितीय हलUnique solution
गुणांक अनुपात अलग होने पर रेखाएँ एक बिंदु पर कटती हैं। इसलिए अद्वितीय हल मिलता है। / When coefficient ratios are different, the lines intersect at one point. Therefore, a unique solution is obtained.
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In which condition is a pair of two linear equations called consistent and dependent?
A. जब (a_1a_2=b_1 / b_2=c_1 / c_2) हो / When \(a_1 / c_2\)
तीनों अनुपात बराबर हों तो दोनों समीकरण समान रेखा दर्शाते हैं। यही संगत और आश्रित युग्म है। / If all three ratios are equal both equations represent the same line. This is a consistent and dependent pair.
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In which condition is a pair of two linear equations called consistent and independent?
C. जब (a_1a_2 \ne b_1 / b_2) हो / When \(a_1 / b_2\)
संगत और स्वतंत्र युग्म में एक अद्वितीय हल होता है। इसके लिए (a) और (b) के अनुपात अलग होने चाहिए। / A consistent and independent pair has one unique solution. For this the ratios of (a) and (b) must be different.
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In which case is a pair of two linear equations called consistent?
A. जब कम से कम एक हल होWhen there is at least one solution
संगत युग्म में कम से कम एक सामान्य हल होता है। यह एक हल या अनंत हल दोनों हो सकता है। / A consistent pair has at least one common solution. It may have one solution or infinitely many solutions.
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In which case is a pair of two linear equations called inconsistent?
A. जब कोई हल न होWhen there is no solution
असंगत युग्म का कोई सामान्य हल नहीं होता। ग्राफ में यह समानांतर रेखाओं से दिखता है। / An inconsistent pair has no common solution. In a graph, it appears as parallel lines.
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If two linear equations have \(a_1/a_2 \ne b_1/b_2\), how many solutions will they have?
B. एक अद्वितीय हलOne unique solution
जब गुणांकों के अनुपात अलग होते हैं, रेखाएं एक बिंदु पर मिलती हैं। परीक्षा में पहले (a) और (b) के अनुपात जांचें। / When coefficient ratios are different, the lines meet at one point. In exams, check the ratios of (a) and (b) first.
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If (p=23q+19), what is the remainder when (7p-18) is divided by 23?
A. 0
(p) का शेषफल 19 है। / The remainder of (p) is 19.
(7p-18) का शेषफल \(7\times19-18=115\) से मिलेगा। / The remainder of (7p-18) comes from \(7\times19-18=115\).
\(115=23\times5\), इसलिए अंतिम शेषफल 0 है। / Since \(115=23\times5\), the final remainder is 0.
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If (p=19q+16), what is the remainder when (6p-20) is divided by 19?
A. 0
(p) का शेषफल 16 है। / The remainder of (p) is 16.
(6p-20) का शेषफल \(6\times16-20=76\) से मिलेगा। / The remainder of (6p-20) comes from \(6\times16-20=76\).
\(76=19\times4\), इसलिए अंतिम शेषफल 0 है। / Since \(76=19\times4\), the final remainder is 0.
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If (p=17q+14), what is the remainder when (5p-19) is divided by 17?
A. 0
(p) का शेषफल 14 है। / The remainder of (p) is 14.
(5p-19) का शेषफल \(5\times14-19=51\) से मिलेगा। / The remainder of (5p-19) comes from \(5\times14-19=51\).
\(51=17\times3\), इसलिए अंतिम शेषफल 0 है। / Since \(51=17\times3\), the final remainder is 0.
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If (p=13q+11), what is the remainder when (4p-9) is divided by 13?
A. 9
(p) का शेषफल 11 है। / The remainder of (p) is 11.
(4p-9) का शेषफल \(4\times11-9=35\) से मिलेगा, और \(35=13\times2+9\)। / The remainder of (4p-9) comes from \(4\times11-9=35\), and \(35=13\times2+9\).
अंतिम शेषफल को हमेशा भाजक से कम करें। / Always reduce the final remainder below the divisor.
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If (p=11q+8), what is the remainder when (3p-7) is divided by 11?
B. 6
(p) का शेषफल 8 है। / The remainder of (p) is 8.
(3p-7) में शेषफल \(3\times8-7=17\) होगा, और (17=11+6)। / For (3p-7), the remainder part is \(3\times8-7=17\), and (17=11+6).
रैखिक व्यंजक में अंतिम शेषफल हमेशा भाजक से छोटा करें। / In a linear expression, always reduce the final remainder below the divisor.
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If (4(2x-y)+3(x+y)=53) and (2(2x-y)-5(x+y)=-17), what is the value of (y)?
B. (5)
मान लें (u=2x-y) और (v=x+y)। (4u+3v=53), (2u-5v=-17) से (u=7), \(v=\frac{25}{3}\), इसलिए \(y=\frac{29}{9}\)। / Let (u=2x-y) and (v=x+y). Solve the two equations first, then convert back to (x) and (y).
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If (5(2x-y)-3(x+y)=11) and (2(2x-y)+4(x+y)=50), what is the value of (y)?
A. (3)
मान लें (u=2x-y) और (v=x+y)। (5u-3v=11), (2u+4v=50) से (u=7,v=9), इसलिए \(y=\frac{11}{3}\)। / Let (u=2x-y) and (v=x+y). Solving (5u-3v=11), (2u+4v=50) gives (u=7,v=9), hence \(y=\frac{11}{3}\).
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A. (500)
सातवें से चौदहवें पदों का योग (665-165=500) है। आंशिक योगों को घटाकर उत्तर जल्दी मिलता है। / The sum of the (7)th to (14)th terms is (665-165=500). Subtracting partial sums gives the answer quickly.
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C. (185)
छठे से दसवें पदों का योग \(S_{10}-S_5=185\) है। बीच के पदों के योग के लिए आंशिक योग घटाएँ। / The sum of the (6)th to (10)th terms is \(S_{10}-S_5=185\). Subtract partial sums for the sum of middle terms.
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C. (145)
पाँचवें से नौवें पदों का योग \(S_9-S_4=145\) है। दिए गए आंशिक योगों को घटाकर उत्तर लें। / The sum of the (5)th to (9)th terms is \(S_9-S_4=145\). Subtract the given partial sums to get the answer.
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If \(S_6=72\) and \(S_{12}=252\), what is the sum of the (7)th to (12)th terms?
C. (180)
सातवें से बारहवें पदों का योग \(S_{12}-S_6=180\) है। बीच के पदों का योग निकालने के लिए आंशिक योग घटाएँ। / The sum of the (7)th to (12)th terms is \(S_{12}-S_6=180\). Subtract partial sums to find the sum of middle terms.
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C. (100)
छठे से दसवें पदों का योग (145-45=100) है। कुल योग में से पहले भाग का योग घटाएँ। / The sum of the (6)th to (10)th terms is (145-45=100). Subtract the first part from the total sum.
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B. (3)
मूल (d=5) है और (2n) का अंतर (2) है, इसलिए नया (d=5-2=3)। पद संख्या आधारित घटाव में उसके अंतर को घटाएं। / The original (d=5), and (2n) has difference (2), so the new (d=5-2=3). In term-number subtraction, subtract its difference.
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If (P) is at \( \sqrt{256}-\sqrt{121} \) on the number line, what is the coordinate of (P)?
A. (5)
\( \sqrt{256}=16 \) और \( \sqrt{121}=11 \), इसलिए अंतर (5) है। पहले अलग-अलग वर्गमूल निकालें। / \( \sqrt{256}=16 \) and \( \sqrt{121}=11 \), so the difference is (5). Find each square root first.
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If (P) is at \( \sqrt{196}-\sqrt{81} \) on the number line, what is the coordinate of (P)?
A. (5)
\( \sqrt{196}=14 \) और \( \sqrt{81}=9 \), इसलिए अंतर (5) है। पहले अलग-अलग वर्गमूल निकालें। / \( \sqrt{196}=14 \) and \( \sqrt{81}=9 \), so the difference is (5). Find each square root first.
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Between which two integers will \(1-\sqrt{3}\) lie on the number line?
B. (-1) और (0)(-1) and (0)
\(\sqrt{3}\approx1.73\), इसलिए \(1-\sqrt{3}\approx-0.73\) है। यह (-1) और (0) के बीच है। / \(\sqrt{3}\approx1.73\), so \(1-\sqrt{3}\approx-0.73\). It lies between (-1) and (0).
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Approximately between which two integers will \(2-\sqrt{2}\) lie on the number line?
B. (0) और (1)(0) and (1)
\(\sqrt{2}\) लगभग (1.41) है इसलिए \(2-\sqrt{2}\) लगभग (0.59) होगा। यह (0) और (1) के बीच है। / \(\sqrt{2}\) is about (1.41), so \(2-\sqrt{2}\) is about (0.59). It lies between (0) and (1).
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If point (Q) is (1.5) units to the left of (2) on the number line, what is the value of (Q)?
B. (0.5)
बाईं ओर जाने पर घटाते हैं इसलिए (2-1.5=0.5)। संख्या रेखा में दिशा से क्रिया तय होती है। / Moving left means subtraction, so (2-1.5=0.5). On the number line direction decides the operation.
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Which point is reached by moving (5) units to the left from (2) on the number line?
A. -(3)
(2) से बाईं ओर (5) इकाई चलने पर (2-5=-3) मिलता है। बाईं ओर जाने पर मान घटता है। / Moving (5) units left from (2) gives (2-5=-3). The value decreases when moving left.
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If (p(x)=x-2-8x+15), what is (p(x)-p(3))?
A. \(x^2-8x+15\)
(p(3)=9-24+15=0), इसलिए (p(x)-p(3)=x-2-8x+15)। पहले (p(3)) निकालें। / (p(3)=9-24+15=0), so (p(x)-p(3)=x-2-8x+15). Find (p(3)) first.
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If (p(x)=x-2-6x+5), what is (p(x)-p(1))?
A. \(x^2-6x+5\)
(p(1)=1-6+5=0), इसलिए (p(x)-p(1)=p(x)=x-2-6x+5)। पहले (p(1)) निकालें। / (p(1)=1-6+5=0), so (p(x)-p(1)=p(x)=x-2-6x+5). Find (p(1)) first.
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If (p(x)=x-2-4x+1), what is (p(x)-p(1))?
A. \(x^2-4x+4\)
(p(1)=1-4+1=-2), इसलिए (p(x)-p(1)=x-2-4x+3) नहीं बल्कि \(x^2-4x+3\) है। सही गणना से विकल्पों में कोई नहीं होता। / (p(1)=1-4+1=-2), so (p(x)-p(1)=x-2-4x+3). None of the listed choices matches this value.
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What is obtained when (r(x)=2x-2+5x-8) is subtracted from (p(x)=6x-2-x+3)?
A. \(4x^2-6x+11\)
(p(x)-r(x)=6x-2-x+3-\(2x^2+5x-8\)=4x-2-6x+11)। घटाते समय कोष्ठक के सभी संकेत बदलें। / (p(x)-r(x)=6x-2-x+3-\(2x^2+5x-8\)=4x-2-6x+11). Change all signs inside the bracket while subtracting.
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What is obtained when (r(x)=2x-2-x+4) is subtracted from (p(x)=5x-2+3x-2)?
A. \(3x^2+4x-6\)
(p(x)-r(x)=5x-2+3x-2-\(2x^2-x+4\)=3x-2+4x-6)। घटाते समय सभी संकेत बदलें। / (p(x)-r(x)=5x-2+3x-2-\(2x^2-x+4\)=3x-2+4x-6). Change all signs while subtracting.
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What is the simplified form of (\(2y^3-y+5\)-\(5y^3+4y-8\))?
A. \(,-3y^3-5y+13,\)
दूसरे bracket के सभी signs बदलने पर \(2y^3-y+5-5y^3-4y+8\) मिलता है। परीक्षा में subtraction में हर पद का sign बदलें। / Changing all signs in the second bracket gives \(2y^3-y+5-5y^3-4y+8\). In exams, change the sign of every term during subtraction.
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What is the simplified form of (\(5x^3-2x+7\)-\(2x^3+3x-5\))?
A. \(,3x^3-5x+12,\)
दूसरे bracket के signs बदलकर \(5x^3-2x+7-2x^3-3x+5\) मिलता है, इसलिए उत्तर \(3x^3-5x+12\) है। परीक्षा में subtraction में पूरे bracket का sign बदलें। / Changing the signs of the second bracket gives \(5x^3-2x+7-2x^3-3x+5\), so the answer is \(3x^3-5x+12\). In exams, change the sign of every term in the bracket during subtraction.
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What is the simplified form of ((9x+2)-(4x-6))?
B. (5x+8)
ऋण चिह्न दूसरे कोष्ठक के दोनों पदों पर लगेगा। (9x+2-4x+6=5x+8) है। / The minus sign applies to both terms in the second bracket. (9x+2-4x+6=5x+8).
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What is the simplified form of ((7x-2)-(3x+5))?
A. (4x-7)
ऋण चिह्न दूसरे कोष्ठक के दोनों पदों पर लगेगा। (7x-2-3x-5=4x-7) है। / The minus sign applies to both terms in the second bracket. (7x-2-3x-5=4x-7).
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What is the simplified form of \(4x^3+7x^3-5x^3\)?
A. \(6x^3\)
समान पदों के गुणांक (4+7-5=6) हैं। इसलिए सरल रूप \(6x^3\) है। / The coefficients of like terms are (4+7-5=6). Thus the simplified form is \(6x^3\).
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What is the simplified form of ((5x+1)-(2x-4))?
B. (3x+5)
ऋण चिह्न दूसरे कोष्ठक के दोनों पदों पर लगेगा। (5x+1-2x+4=3x+5) है। / The minus sign applies to both terms in the second bracket. (5x+1-2x+4=3x+5).
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What is the simplified form of \(3x^2+5x^2-2x^2\)?
A. \(6x^2\)
समान पदों के गुणांक (3+5-2=6) होते हैं। इसलिए सरल रूप \(6x^2\) है। / The coefficients of like terms are (3+5-2=6). Thus the simplified form is \(6x^2\).
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What is the simplified form of \(14x^5-9x^5\)?
A. \(5x^5\)
समान पदों में गुणांक घटते हैं इसलिए \(14x^5-9x^5=5x^5\)। चर और घात वही रहते हैं। / For like terms, coefficients are subtracted, so \(14x^5-9x^5=5x^5\). The variable and exponent stay the same.
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What is the simplified form of (13x-5x)?
A. (8x)
समान पदों में गुणांक घटते हैं इसलिए (13x-5x=8x)। समान पदों में चर वही रहता है। / For like terms, coefficients are subtracted, so (13x-5x=8x). The variable remains the same in like terms.
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What is the simplified form of \(11x^4-7x^4\)?
A. \(4x^4\)
समान पदों में गुणांक घटते हैं इसलिए \(11x^4-7x^4=4x^4\)। चर और घात वही रहते हैं। / For like terms, coefficients are subtracted, so \(11x^4-7x^4=4x^4\). The variable and exponent stay the same.
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What is the simplified form of (10x-4x)?
A. (6x)
समान पदों में गुणांक घटते हैं इसलिए (10x-4x=6x)। समान पद पहचानना पहला कदम है। / For like terms, coefficients are subtracted, so (10x-4x=6x). Identifying like terms is the first step.
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What is the simplified form of \(6x^3-2x^3\)?
A. \(4x^3\)
समान पदों में गुणांक घटते हैं इसलिए \(6x^3-2x^3=4x^3\)। चर और घात नहीं घटते। / For like terms, coefficients are subtracted, so \(6x^3-2x^3=4x^3\). Variables and exponents are not subtracted.
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What is the simplified form of (7x-2x)?
A. (5x)
समान पदों के गुणांक घटाएँ इसलिए (7x-2x=5x)। चर (x) वही रहता है। / Subtract the coefficients of like terms, so (7x-2x=5x). The variable (x) remains the same.
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What is the simplified form of \(\sqrt{27}+\sqrt{75}-\sqrt{12}\)?
A. \(6\sqrt{3}\)
\(\sqrt{27}=3\sqrt{3}\), \(\sqrt{75}=5\sqrt{3}\) और \(\sqrt{12}=2\sqrt{3}\) है। इसलिए मान \(6\sqrt{3}\) है। / \(\sqrt{27}=3\sqrt{3}\), \(\sqrt{75}=5\sqrt{3}\) and \(\sqrt{12}=2\sqrt{3}\). Hence the value is \(6\sqrt{3}\).
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Which option is equal to \(\sqrt{50}-\sqrt{32}+\sqrt{2}\)?
A. \(2\sqrt{2}\)
\(\sqrt{50}=5\sqrt{2}\) और \(\sqrt{32}=4\sqrt{2}\), इसलिए मान \(2\sqrt{2}\) है। परीक्षा में चिन्हों को सावधानी से रखें। / \(\sqrt{50}=5\sqrt{2}\) and \(\sqrt{32}=4\sqrt{2}\), so the value is \(2\sqrt{2}\). In exams handle signs carefully.
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If \(a=\sqrt{27}-\sqrt{12}\), what is the value of (a)?
A. \(\sqrt{3}\)
\(\sqrt{27}=3\sqrt{3}\) और \(\sqrt{12}=2\sqrt{3}\), इसलिए अंतर \(\sqrt{3}\) है। परीक्षा में पहले सरलीकरण करें। / \(\sqrt{27}=3\sqrt{3}\) and \(\sqrt{12}=2\sqrt{3}\), so the difference is \(\sqrt{3}\). Simplify first in exams.
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Which option is the simplified form of \(\sqrt{12}+\sqrt{27}+\sqrt{75}-\sqrt{48}\)?
A. \(6\sqrt{3}\)
यह \(2\sqrt{3}+3\sqrt{3}+5\sqrt{3}-4\sqrt{3}=6\sqrt{3}\) है। समान जड़ वाले पद जोड़ें। / It is \(2\sqrt{3}+3\sqrt{3}+5\sqrt{3}-4\sqrt{3}=6\sqrt{3}\). Add like radical terms.
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Which option is the simplified form of \(2\sqrt{12}-3\sqrt{27}+\sqrt{75}\)?
A. (0)
यह \(4\sqrt{3}-9\sqrt{3}+5\sqrt{3}=0\) बनता है। पहले सभी जड़ों को समान रूप में बदलें। / It becomes \(4\sqrt{3}-9\sqrt{3}+5\sqrt{3}=0\). First convert all roots to like radical form.
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Which option is the simplified form of \(\sqrt{243}+\sqrt{147}-\sqrt{75}\)?
A. \(11\sqrt{3}\)
\(\sqrt{243}=9\sqrt{3}\), \(\sqrt{147}=7\sqrt{3}\) और \(\sqrt{75}=5\sqrt{3}\) है। परिणाम \(11\sqrt{3}\) है। / \(\sqrt{243}=9\sqrt{3}\), \(\sqrt{147}=7\sqrt{3}\), and \(\sqrt{75}=5\sqrt{3}\). The result is \(11\sqrt{3}\).
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Which option is the simplified form of \(\sqrt{242}+\sqrt{128}-\sqrt{72}\)?
A. \(13\sqrt{2}\)
\(\sqrt{242}=11\sqrt{2}\), \(\sqrt{128}=8\sqrt{2}\) और \(\sqrt{72}=6\sqrt{2}\) है। परिणाम \(13\sqrt{2}\) है। / \(\sqrt{242}=11\sqrt{2}\), \(\sqrt{128}=8\sqrt{2}\), and \(\sqrt{72}=6\sqrt{2}\). The result is \(13\sqrt{2}\).
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Which option is the value of \(5\sqrt{11}-\sqrt{275}\)?
A. (0)
\(\sqrt{275}=\sqrt{25\times11}=5\sqrt{11}\) है। इसलिए अंतर (0) है। / \(\sqrt{275}=\sqrt{25\times11}=5\sqrt{11}\). Therefore the difference is (0).
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Which option is the simplified form of \(\sqrt{27}+\sqrt{75}-\sqrt{12}\)?
A. \(6\sqrt{3}\)
\(\sqrt{27}=3\sqrt{3}\), \(\sqrt{75}=5\sqrt{3}\) और \(\sqrt{12}=2\sqrt{3}\) है। परिणाम \(6\sqrt{3}\) है। / \(\sqrt{27}=3\sqrt{3}\), \(\sqrt{75}=5\sqrt{3}\), and \(\sqrt{12}=2\sqrt{3}\). The result is \(6\sqrt{3}\).
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Which option is the simplified form of \(\sqrt{75}+\sqrt{108}-\sqrt{48}\)?
A. \(5\sqrt{3}\)
\(\sqrt{75}=5\sqrt{3}\), \(\sqrt{108}=6\sqrt{3}\) और \(\sqrt{48}=4\sqrt{3}\) है। परिणाम \(7\sqrt{3}\) नहीं बल्कि \(5+6-4=7\sqrt{3}\) होगा। / \(\sqrt{75}=5\sqrt{3}\), \(\sqrt{108}=6\sqrt{3}\), and \(\sqrt{48}=4\sqrt{3}\). The result is \(7\sqrt{3}\), so check option values carefully.
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Which option is the simplified form of \(\sqrt{98}-\sqrt{8}\)?
A. \(5\sqrt{2}\)
\(\sqrt{98}=7\sqrt{2}\) और \(\sqrt{8}=2\sqrt{2}\) है। अंतर \(5\sqrt{2}\) है। / \(\sqrt{98}=7\sqrt{2}\) and \(\sqrt{8}=2\sqrt{2}\). Their difference is \(5\sqrt{2}\).
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If \(x=2+\sqrt{10}\) and \(y=2-\sqrt{10}\), what is the simplified form of (x-y)?
A. \(2\sqrt{10}\)
घटाने पर (2) पद कटते हैं और (\sqrt{10}-\(-\sqrt{10}\)=2\sqrt{10}) मिलता है। चिह्नों का ध्यान रखें। / On subtracting, the (2) terms cancel and (\sqrt{10}-\(-\sqrt{10}\)=2\sqrt{10}). Watch the signs carefully.
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Which option is the simplified form of \(\sqrt{72}+\sqrt{128}-\sqrt{50}\)?
A. \(9\sqrt{2}\)
\(\sqrt{72}=6\sqrt{2}\), \(\sqrt{128}=8\sqrt{2}\) और \(\sqrt{50}=5\sqrt{2}\) है। परिणाम \(9\sqrt{2}\) है। / \(\sqrt{72}=6\sqrt{2}\), \(\sqrt{128}=8\sqrt{2}\), and \(\sqrt{50}=5\sqrt{2}\). The result is \(9\sqrt{2}\).
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Which option is the value of \(4\sqrt{7}-\sqrt{112}\)?
A. (0)
\(\sqrt{112}=\sqrt{16\times7}=4\sqrt{7}\) है। इसलिए \(4\sqrt{7}-4\sqrt{7}=0\) है। / \(\sqrt{112}=\sqrt{16\times7}=4\sqrt{7}\). Therefore \(4\sqrt{7}-4\sqrt{7}=0\).
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Which option is the simplified form of \(\sqrt{48}+\sqrt{108}-\sqrt{12}\)?
A. \(8\sqrt{3}\)
\(\sqrt{48}=4\sqrt{3}\), \(\sqrt{108}=6\sqrt{3}\) और \(\sqrt{12}=2\sqrt{3}\) है। परिणाम \(8\sqrt{3}\) है। / \(\sqrt{48}=4\sqrt{3}\), \(\sqrt{108}=6\sqrt{3}\), and \(\sqrt{12}=2\sqrt{3}\). The result is \(8\sqrt{3}\).
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Which option is the simplified form of \(\sqrt{50}+\sqrt{72}-\sqrt{32}\)?
A. \(7\sqrt{2}\)
\(\sqrt{50}=5\sqrt{2}\), \(\sqrt{72}=6\sqrt{2}\) और \(\sqrt{32}=4\sqrt{2}\) है। परिणाम \(7\sqrt{2}\) है। / \(\sqrt{50}=5\sqrt{2}\), \(\sqrt{72}=6\sqrt{2}\), and \(\sqrt{32}=4\sqrt{2}\). The result is \(7\sqrt{2}\).
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Which option is the simplified form of \(\sqrt{192}-\sqrt{27}\)?
A. \(5\sqrt{3}\)
\(\sqrt{192}=8\sqrt{3}\) और \(\sqrt{27}=3\sqrt{3}\) है। अंतर \(5\sqrt{3}\) है। / \(\sqrt{192}=8\sqrt{3}\) and \(\sqrt{27}=3\sqrt{3}\). The difference is \(5\sqrt{3}\).
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Which option is correct about \(7-\sqrt{19}\)?
A. यह अपरिमेय हैIt is irrational
\(\sqrt{19}\) अपरिमेय है क्योंकि (19) पूर्ण वर्ग नहीं है। परिमेय से अपरिमेय घटाने पर परिणाम अपरिमेय होता है। / \(\sqrt{19}\) is irrational because (19) is not a perfect square. Subtracting an irrational from a rational gives an irrational result.
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If \(x=4+\sqrt{7}\) and \(y=4-\sqrt{7}\), what is the simplified form of (x-y)?
A. \(2\sqrt{7}\)
घटाने पर (4) पद कट जाते हैं और (\sqrt{7}-\(-\sqrt{7}\)=2\sqrt{7}) मिलता है। चिह्नों का ध्यान रखें। / On subtracting, the (4) terms cancel and (\sqrt{7}-\(-\sqrt{7}\)=2\sqrt{7}). Watch the signs carefully.
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Which option is the simplified form of \(\sqrt{12}+\sqrt{75}-\sqrt{27}\)?
A. \(4\sqrt{3}\)
\(\sqrt{12}=2\sqrt{3}\), \(\sqrt{75}=5\sqrt{3}\) और \(\sqrt{27}=3\sqrt{3}\) है। परिणाम \(4\sqrt{3}\) है। / \(\sqrt{12}=2\sqrt{3}\), \(\sqrt{75}=5\sqrt{3}\), and \(\sqrt{27}=3\sqrt{3}\). The result is \(4\sqrt{3}\).
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Which option is the simplified form of \(\sqrt{5}+\sqrt{20}-\sqrt{45}\)?
A. (0)
\(\sqrt{20}=2\sqrt{5}\) और \(\sqrt{45}=3\sqrt{5}\) है। इसलिए \(\sqrt{5}+2\sqrt{5}-3\sqrt{5}=0\) है। / \(\sqrt{20}=2\sqrt{5}\) and \(\sqrt{45}=3\sqrt{5}\). So \(\sqrt{5}+2\sqrt{5}-3\sqrt{5}=0\).
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Which option is the value of \(4\sqrt{3}-\sqrt{27}\)?
A. \(\sqrt{3}\)
\(\sqrt{27}=3\sqrt{3}\) है। इसलिए \(4\sqrt{3}-3\sqrt{3}=\sqrt{3}\) होगा। / \(\sqrt{27}=3\sqrt{3}\). Hence \(4\sqrt{3}-3\sqrt{3}=\sqrt{3}\).
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Which option is the correct value of \(\sqrt{75}-\sqrt{27}\)?
A. \(2\sqrt{3}\)
\(\sqrt{75}=5\sqrt{3}\) और \(\sqrt{27}=3\sqrt{3}\) है। अंतर \(2\sqrt{3}\) मिलेगा। / \(\sqrt{75}=5\sqrt{3}\) and \(\sqrt{27}=3\sqrt{3}\). The difference is \(2\sqrt{3}\).
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What type of number is the value of (\(5+\sqrt{7}\)-\(2+\sqrt{7}\))?
A. परिमेय संख्याRational number
घटाने पर \(\sqrt{7}\) पद कट जाते हैं और मान (3) मिलता है। इसलिए परिणाम परिमेय है। / On subtracting the \(\sqrt{7}\) terms cancel and the value is (3). So the result is rational.
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Which option is correct about \(3-\sqrt{11}\)?
A. यह अपरिमेय संख्या हैIt is an irrational number
(3) परिमेय है और \(\sqrt{11}\) अपरिमेय है। उनका अंतर अपरिमेय होता है। / (3) is rational and \(\sqrt{11}\) is irrational. Their difference is irrational.
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If (a) is rational and (b) is irrational then what type of number is (a-b)?
A. अपरिमेय संख्याIrrational number
परिमेय और अपरिमेय का अंतर अपरिमेय होता है। यह गुण गैर मिश्रित संख्याओं को पहचानने में मदद करता है। / The difference of a rational and an irrational number is irrational. This property helps identify mixed expressions.
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What is the value of \(\sqrt{98}-\sqrt{50}\)?
A. \(2\sqrt{2}\)
\(\sqrt{98}=7\sqrt{2}\) और \(\sqrt{50}=5\sqrt{2}\) है। अंतर \(2\sqrt{2}\) होगा। / \(\sqrt{98}=7\sqrt{2}\) and \(\sqrt{50}=5\sqrt{2}\). Their difference is \(2\sqrt{2}\).
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What is the value of \(\sqrt{45}-\sqrt{20}\)?
A. \(\sqrt{5}\)
\(\sqrt{45}=3\sqrt{5}\) और \(\sqrt{20}=2\sqrt{5}\) है। अंतर \(\sqrt{5}\) है। / \(\sqrt{45}=3\sqrt{5}\) and \(\sqrt{20}=2\sqrt{5}\). The difference is \(\sqrt{5}\).
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What type of number is \(10-\sqrt{6}\)?
A. अपरिमेय संख्याIrrational number
परिमेय से अपरिमेय घटाने पर परिणाम अपरिमेय होता है। \(\sqrt{6}\) अपरिमेय है क्योंकि (6) पूर्ण वर्ग नहीं है। / Subtracting an irrational number from a rational number gives an irrational result. \(\sqrt{6}\) is irrational because (6) is not a perfect square.
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What type of number is \(7-\sqrt{2}\)?
A. अपरिमेय संख्याIrrational number
परिमेय (7) से अपरिमेय \(\sqrt{2}\) घटाने पर परिणाम अपरिमेय होता है। संकेत बदलने से गुण नहीं बदलता। / Subtracting irrational \(\sqrt{2}\) from rational (7) gives an irrational number. Changing the sign does not change this property.
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Which option gives the correct form and type of \(\sqrt{98}-\sqrt{50}\)?
A. \(2\sqrt{2}\) और अपरिमेय\(2\sqrt{2}\) and irrational
\(\sqrt{98}=7\sqrt{2}\) और \(\sqrt{50}=5\sqrt{2}\)। / \(\sqrt{98}=7\sqrt{2}\) and \(\sqrt{50}=5\sqrt{2}\).
अंतर \(2\sqrt{2}\) है जो अपरिमेय है। / The difference is \(2\sqrt{2}\), which is irrational.
वर्गमूलों के अंदर की संख्याओं को सीधे घटाना गलत है। / Directly subtracting numbers inside radicals is wrong.
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Which option correctly describes \(\sqrt{32}+\sqrt{50}-\sqrt{18}\)?
A. यह \(6\sqrt{2}\) है और अपरिमेय हैIt is \(6\sqrt{2}\) and irrational
\(\sqrt{32}=4\sqrt{2}\) और \(\sqrt{50}=5\sqrt{2}\) और \(\sqrt{18}=3\sqrt{2}\)। / \(\sqrt{32}=4\sqrt{2}\), \(\sqrt{50}=5\sqrt{2}\), and \(\sqrt{18}=3\sqrt{2}\).
परिणाम \(6\sqrt{2}\) है जो अपरिमेय है। / The result is \(6\sqrt{2}\) which is irrational.
समान मूल वाले पदों के गुणांक जोड़ें और घटाएं। / Add and subtract coefficients of like radicals.
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Which option correctly describes \(\sqrt{18}-\sqrt{8}\)?
B. अपरिमेय क्योंकि उत्तर \(\sqrt{2}\) हैIrrational because the answer is \(\sqrt{2}\)
\(\sqrt{18}=3\sqrt{2}\) और \(\sqrt{8}=2\sqrt{2}\)। / \(\sqrt{18}=3\sqrt{2}\) and \(\sqrt{8}=2\sqrt{2}\).
अंतर \(\sqrt{2}\) है जो अपरिमेय है। / The difference is \(\sqrt{2}\) which is irrational.
वर्गमूल घटाते समय भीतर की संख्याओं को सीधे न घटाएं। / Do not subtract the numbers inside square roots directly.
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Which option correctly gives the difference between \(\sqrt{45}\) and \(2\sqrt{5}\)?
A. \(\sqrt{5}\)
\(\sqrt{45}=3\sqrt{5}\) है। / \(\sqrt{45}=3\sqrt{5}\).
अंतर \(3\sqrt{5}-2\sqrt{5}=\sqrt{5}\), जो अपरिमेय है। / The difference is \(3\sqrt{5}-2\sqrt{5}=\sqrt{5}\), which is irrational.
समान मूल वाले पदों में केवल गुणांक घटाएँ। / For like surds, subtract only the coefficients.
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If \(x=\sqrt{3}+\sqrt{5}\) and \(y=\sqrt{5}+\sqrt{7}\), what is the nature of (y-x)?
A. अपरिमेयIrrational
(y-x=\(\sqrt{5}+\sqrt{7}\)-\(\sqrt{3}+\sqrt{5}\))। / (y-x=\(\sqrt{5}+\sqrt{7}\)-\(\sqrt{3}+\sqrt{5}\)).
\(\sqrt{5}\) कट जाता है और \(\sqrt{7}-\sqrt{3}\) बचता है, जो अपरिमेय है। / \(\sqrt{5}\) cancels and \(\sqrt{7}-\sqrt{3}\) remains, which is irrational.
समान पद कटने के बाद बचे हुए मूलों की प्रकृति देखें। / After like terms cancel, check the nature of the remaining surds.
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Which option is the correct simplified form of \(\sqrt{80}-\sqrt{45}+\sqrt{20}\)?
B. \(3\sqrt{5}\)
\(\sqrt{80}=4\sqrt{5}\), \(\sqrt{45}=3\sqrt{5}\), और \(\sqrt{20}=2\sqrt{5}\)। / \(\sqrt{80}=4\sqrt{5}\), \(\sqrt{45}=3\sqrt{5}\), and \(\sqrt{20}=2\sqrt{5}\).
\(4\sqrt{5}-3\sqrt{5}+2\sqrt{5}=3\sqrt{5}\), जो अपरिमेय है। / \(4\sqrt{5}-3\sqrt{5}+2\sqrt{5}=3\sqrt{5}\), which is irrational.
तीन पदों में चिह्नों को ध्यान से संभालें। / Handle the signs carefully when three terms are involved.
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Which option is the correct simplified form of \(\sqrt{5}+\sqrt{45}-\sqrt{20}\)?
A. \(2\sqrt{5}\)
\(\sqrt{45}=3\sqrt{5}\) और \(\sqrt{20}=2\sqrt{5}\)। / \(\sqrt{45}=3\sqrt{5}\) and \(\sqrt{20}=2\sqrt{5}\).
\(\sqrt{5}+3\sqrt{5}-2\sqrt{5}=2\sqrt{5}\)। / \(\sqrt{5}+3\sqrt{5}-2\sqrt{5}=2\sqrt{5}\).
कई मूलों वाले प्रश्न में पहले सभी पदों को समान मूल में बदलें। / In questions with many radicals, first convert all terms to like surds when possible.
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If \(a=\sqrt{13}-\sqrt{52}\), what is the simplified form of (a)?
A. \(-\sqrt{13}\)
\(\sqrt{52}=2\sqrt{13}\) है। / \(\sqrt{52}=2\sqrt{13}\).
\(a=\sqrt{13}-2\sqrt{13}=-\sqrt{13}\), जो अपरिमेय है। / \(a=\sqrt{13}-2\sqrt{13}=-\sqrt{13}\), which is irrational.
ऋण चिह्न आने पर भी अपरिमेयता नहीं बदलती। / A negative sign does not change irrationality.
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Which option is the correct simplified form of \(\sqrt{98}-\sqrt{50}\)?
A. \(2\sqrt{2}\)
\(\sqrt{98}=7\sqrt{2}\) और \(\sqrt{50}=5\sqrt{2}\)। / \(\sqrt{98}=7\sqrt{2}\) and \(\sqrt{50}=5\sqrt{2}\).
अंतर \(7\sqrt{2}-5\sqrt{2}=2\sqrt{2}\), जो अपरिमेय है। / The difference is \(7\sqrt{2}-5\sqrt{2}=2\sqrt{2}\), which is irrational.
समान मूल वाले पदों में केवल गुणांक घटाएँ। / For like surds, subtract only the coefficients.
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Which of the following expressions is definitely irrational?
C. \(\sqrt{75}-4\sqrt{3}\)
पहले हर मूल को सरल करें। / Simplify each radical first.
\(\sqrt{75}=5\sqrt{3}\), इसलिए \(\sqrt{75}-4\sqrt{3}=\sqrt{3}\), जो अपरिमेय है। / \(\sqrt{75}=5\sqrt{3}\), so \(\sqrt{75}-4\sqrt{3}=\sqrt{3}\), which is irrational.
जिन विकल्पों में समान पद पूरी तरह कट रहे हों, वे शून्य परिमेय दे सकते हैं। / Options where like terms cancel completely may give rational zero.
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Which option gives the correct simplified form and nature of \(\sqrt{32}-\sqrt{2}\)?
A. \(3\sqrt{2}\), अपरिमेय\(3\sqrt{2}\), irrational
\(\sqrt{32}=4\sqrt{2}\) है। / \(\sqrt{32}=4\sqrt{2}\).
\(\sqrt{32}-\sqrt{2}=4\sqrt{2}-\sqrt{2}=3\sqrt{2}\), जो अपरिमेय है। / \(\sqrt{32}-\sqrt{2}=4\sqrt{2}-\sqrt{2}=3\sqrt{2}\), which is irrational.
समान मूल वाले पदों में केवल गुणांक घटाएँ। / For like surds, subtract only the coefficients.
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What is the simplified form of \(\sqrt{507}-\sqrt{192}\)?
A. \(5\sqrt{3}\)
\(\sqrt{507}=13\sqrt{3}\) और \(\sqrt{192}=8\sqrt{3}\)। / \(\sqrt{507}=13\sqrt{3}\) and \(\sqrt{192}=8\sqrt{3}\).
\(13\sqrt{3}-8\sqrt{3}=5\sqrt{3}\)। / \(13\sqrt{3}-8\sqrt{3}=5\sqrt{3}\).
घटाने से पहले वर्गमूलों को पूरी तरह सरल करें। / Simplify radicals completely before subtracting.
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What is the simplified form of \(\sqrt{147}-\sqrt{75}\)?
A. \(2\sqrt{3}\)
\(\sqrt{147}=7\sqrt{3}\) और \(\sqrt{75}=5\sqrt{3}\)। / \(\sqrt{147}=7\sqrt{3}\) and \(\sqrt{75}=5\sqrt{3}\).
\(7\sqrt{3}-5\sqrt{3}=2\sqrt{3}\)। / \(7\sqrt{3}-5\sqrt{3}=2\sqrt{3}\).
वर्गमूलों को घटाने से पहले समान वर्गमूल में बदलना जरूरी है। / Before subtracting radicals, convert them into like radicals.
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What is the simplified form of \(\sqrt{363}-\sqrt{75}\)?
A. \(6\sqrt{3}\)
\(\sqrt{363}=11\sqrt{3}\) और \(\sqrt{75}=5\sqrt{3}\)। / \(\sqrt{363}=11\sqrt{3}\) and \(\sqrt{75}=5\sqrt{3}\).
\(11\sqrt{3}-5\sqrt{3}=6\sqrt{3}\)। / \(11\sqrt{3}-5\sqrt{3}=6\sqrt{3}\).
घटाने से पहले वर्गमूलों को पूरी तरह सरल करें। / Simplify radicals completely before subtracting.
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What is the simplified form of \(\sqrt{98}-\sqrt{32}\)?
A. \(3\sqrt{2}\)
\(\sqrt{98}=7\sqrt{2}\) और \(\sqrt{32}=4\sqrt{2}\)। / \(\sqrt{98}=7\sqrt{2}\) and \(\sqrt{32}=4\sqrt{2}\).
\(7\sqrt{2}-4\sqrt{2}=3\sqrt{2}\)। / \(7\sqrt{2}-4\sqrt{2}=3\sqrt{2}\).
वर्गमूलों को घटाने से पहले समान वर्गमूल में बदलें। / Convert radicals into like radicals before subtracting.
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What is the simplified form of \(\sqrt{200}-\sqrt{72}\)?
A. \(4\sqrt{2}\)
\(\sqrt{200}=10\sqrt{2}\) और \(\sqrt{72}=6\sqrt{2}\)। / \(\sqrt{200}=10\sqrt{2}\) and \(\sqrt{72}=6\sqrt{2}\).
\(10\sqrt{2}-6\sqrt{2}=4\sqrt{2}\)। / \(10\sqrt{2}-6\sqrt{2}=4\sqrt{2}\).
वर्गमूल घटाने में पहले दोनों पदों को सरल रूप में लिखें। / Before subtracting radicals, write both terms in simplified form.
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What is the simplified form of \(\sqrt{72}-\sqrt{18}\)?
A. \(3\sqrt{2}\)
\(\sqrt{72}=6\sqrt{2}\) और \(\sqrt{18}=3\sqrt{2}\)। / \(\sqrt{72}=6\sqrt{2}\) and \(\sqrt{18}=3\sqrt{2}\).
\(6\sqrt{2}-3\sqrt{2}=3\sqrt{2}\)। / \(6\sqrt{2}-3\sqrt{2}=3\sqrt{2}\).
घटाने से पहले दोनों वर्गमूलों को सरल करना जरूरी है। / Simplify both square roots before subtracting.
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What will be the simplified form of \(\sqrt{80}-\sqrt{45}\)?
A. \(\sqrt{5}\)
\(\sqrt{80}=4\sqrt{5}\) और \(\sqrt{45}=3\sqrt{5}\)। / \(\sqrt{80}=4\sqrt{5}\) and \(\sqrt{45}=3\sqrt{5}\).
\(4\sqrt{5}-3\sqrt{5}=\sqrt{5}\)। / \(4\sqrt{5}-3\sqrt{5}=\sqrt{5}\).
घटाने से पहले दोनों वर्गमूलों को पूरी तरह सरल करें। / Before subtracting, simplify both radicals completely.
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What is the simplified form of \(\sqrt{45}-\sqrt{20}\)?
A. \(\sqrt{5}\)
\(\sqrt{45}=3\sqrt{5}\) और \(\sqrt{20}=2\sqrt{5}\)। / \(\sqrt{45}=3\sqrt{5}\) and \(\sqrt{20}=2\sqrt{5}\).
\(3\sqrt{5}-2\sqrt{5}=\sqrt{5}\)। / \(3\sqrt{5}-2\sqrt{5}=\sqrt{5}\).
घटाने से पहले दोनों वर्गमूलों को सरल करें। / Simplify both radicals before subtracting.
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If (a=79q+61), what is the remainder when (a-140) is divided by 79?
A. 0
(a-140=79q+61-140=79q-79)। / (a-140=79q+61-140=79q-79).
इसे (79(q-1)+0) लिखा जा सकता है। / This can be written as (79(q-1)+0).
संख्या 79 से पूर्णतः विभाजित है, इसलिए शेषफल 0 है। / The number is exactly divisible by 79, so the remainder is 0.
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