100 results found for "subtraction relation" in Class 10.
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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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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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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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 (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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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 (m) leaves remainder 12 when divided by 53, what is the remainder when (m-118) is divided by 53?
A. 0
(m=53q+12) लिखें। / Write (m=53q+12).
(m-118=53q+12-118=53q-106=53(q-2))। / (m-118=53q+12-118=53q-106=53(q-2)).
यह 53 से पूर्णतः विभाजित है, इसलिए शेषफल 0 है। / It is exactly divisible by 53, so the remainder is 0.
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If (a=67q+52), what is the remainder when (a-119) is divided by 67?
A. 0
(a-119=67q+52-119=67q-67)। / (a-119=67q+52-119=67q-67).
इसे (67(q-1)+0) लिखा जा सकता है। / This can be written as (67(q-1)+0).
संख्या 67 से पूर्णतः विभाजित है, इसलिए शेषफल 0 है। / The number is exactly divisible by 67, so the 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 (m) leaves remainder 9 when divided by 43, what is the remainder when (m-95) is divided by 43?
A. 0
(m=43q+9) लिखें। / Write (m=43q+9).
(m-95=43q+9-95=43q-86=43(q-2))। / (m-95=43q+9-95=43q-86=43(q-2)).
यह 43 से पूर्णतः विभाजित है, इसलिए शेषफल 0 है। / It is exactly divisible by 43, so the remainder is 0.
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If (a=59q+44), what is the remainder when (a-103) is divided by 59?
A. 0
(a-103=59q+44-103=59q-59)। / (a-103=59q+44-103=59q-59).
इसे (59(q-1)+0) लिखा जा सकता है। / This can be written as (59(q-1)+0).
इसलिए संख्या 59 से पूर्णतः विभाजित है और शेषफल 0 है। / Therefore, the number is exactly divisible by 59 and the 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 (m) leaves remainder 6 when divided by 31, what is the remainder when (m-68) is divided by 31?
C. 29
(m=31q+6) लिखें। / Write (m=31q+6).
(m-68=31q-62=31(q-2)), इसलिए शेषफल 0 है। / (m-68=31q-62=31(q-2)), so the remainder is 0.
घटाव में अंतिम रूप को \(भाजक\timesभागफल+शेषफल\) की तरह जांचें। / In subtraction, check the final form as divisor times quotient plus remainder.
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If (a=37q+29), what is the remainder when (a-48) is divided by 37?
C. 18
(a-48=37q+29-48=37q-19)। / (a-48=37q+29-48=37q-19).
इसे (37(q-1)+18) लिखा जा सकता है, इसलिए शेषफल 18 है। / This can be written as (37(q-1)+18), so the remainder is 18.
ऋणात्मक शेषफल को वैध बनाने के लिए एक बार भाजक जोड़ें। / Add the divisor once to make a negative remainder valid.
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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 (m) leaves remainder 4 when divided by 17, what is the remainder when (m-23) is divided by 17?
A. 15
(m=17q+4) लिखें। / Write (m=17q+4).
(m-23=17q-19=17(q-2)+15), इसलिए शेषफल 15 है। / (m-23=17q-19=17(q-2)+15), so the remainder is 15.
घटाव में ऋणात्मक शेषफल आए तो भाजक को जरूरत के अनुसार जोड़ें। / If subtraction gives a negative remainder, add the divisor as needed.
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If (a=29q+20), what is the remainder when (a-35) is divided by 29?
A. 14
(a-35=29q+20-35=29q-15)। / (a-35=29q+20-35=29q-15).
इसे (29(q-1)+14) लिखा जा सकता है, इसलिए शेषफल 14 है। / This can be written as (29(q-1)+14), so the remainder is 14.
ऋणात्मक शेषफल को वैध बनाने के लिए भाजक जोड़ें। / Add the divisor to a negative remainder to make it valid.
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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 (m) leaves remainder 5 when divided by 12, what is the remainder when (m-19) is divided by 12?
A. 10
(m=12q+5) लिखें। / Write (m=12q+5).
(m-19=12q-14=12(q-2)+10), इसलिए शेषफल 10 है। / (m-19=12q-14=12(q-2)+10), so the remainder is 10.
घटाव में ऋणात्मक शेषफल आए तो भाजक को उचित बार जोड़कर वैध शेषफल बनाएं। / If subtraction gives a negative remainder, add the divisor enough times to make it valid.
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