{"id":1509,"date":"2025-01-28T04:52:11","date_gmt":"2025-01-27T23:22:11","guid":{"rendered":"https:\/\/samacheerkalvi.guide\/?p=1509"},"modified":"2025-01-29T09:55:55","modified_gmt":"2025-01-29T04:25:55","slug":"samacheer-kalvi-10th-maths-model-question-paper-1-english-medium","status":"publish","type":"post","link":"https:\/\/samacheerkalvi.guide\/samacheer-kalvi-10th-maths-model-question-paper-1-english-medium\/","title":{"rendered":"Samacheer Kalvi 10th Maths Model Question Paper 1 English Medium"},"content":{"rendered":"<p>Students can Download Samacheer Kalvi 10th Maths Model Question Paper 1 English Medium Pdf, <a href=\"https:\/\/samacheerkalvi.guide\/samacheer-kalvi-10th-maths-model-question-papers\/\">Samacheer Kalvi 10th Maths Model Question Papers<\/a> helps you to revise the complete Tamilnadu State Board New Syllabus, helps students complete homework assignments and to score high marks in board exams.<\/p>\n<h2>Tamil Nadu Samacheer Kalvi 10th Maths Model Question Paper 1 English Medium<\/h2>\n<p>Instructions<\/p>\n<ul>\n<li>The question paper comprises of <span style=\"color: #0000ff;\">four<\/span> parts.<\/li>\n<li>You are to attempt all the parts. An internal choice of questions is provided wherever applicable.<\/li>\n<li>All questions of Part I, II, III and IV are to be attempted separately.<\/li>\n<li>Question numbers <span style=\"color: #0000ff;\">1<\/span> to <span style=\"color: #0000ff;\">14<\/span> in <span style=\"color: #0000ff;\">Part I<\/span> are Multiple Choice Qu\u00e8stions of <span style=\"color: #0000ff;\">one-mark<\/span> each. These are to be answered by choosing the most suitable answer from the given four alternatives and.writing the option code and the corresponding answer.<\/li>\n<li>Question numbers <span style=\"color: #0000ff;\">15<\/span> to <span style=\"color: #0000ff;\">28<\/span> in <span style=\"color: #0000ff;\">Part II<\/span> \u00e0re <span style=\"color: #0000ff;\">two-marks<\/span> questions. These are to be answered in about one or two sentences.<\/li>\n<li>Question numbers <span style=\"color: #0000ff;\">29<\/span> to <span style=\"color: #0000ff;\">42<\/span> in <span style=\"color: #0000ff;\">Part III<\/span> are <span style=\"color: #0000ff;\">five-marks<\/span> questions. These are to be answered in about three to five short sentences.<\/li>\n<li>Question numbers <span style=\"color: #0000ff;\">43<\/span> to <span style=\"color: #0000ff;\">44<\/span> in <span style=\"color: #0000ff;\">Part IV<\/span> are <span style=\"color: #0000ff;\">eight-marks<\/span> questions. These are to be answered in detail. Draw diagrams wherever necessary.<\/li>\n<\/ul>\n<p>Time: 3 Hours<br \/>\nMaximum Marks: 100<\/p>\n<p style=\"text-align: center;\"><span style=\"color: #0000ff;\">PART -1<\/span><\/p>\n<p><span style=\"color: #0000ff;\">I. Choose the correct answer. Answer all the questions. [14 \u00d7 1 = 14]<\/span><\/p>\n<p>Question 1.<br \/>\nLet A = {1, 2, 3, 4} and B = {4, 8, 9, 10}. A function f : A \u2192 B given by f = {(1,4),(2, 8),(3,9),(4,10)} is a &#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230; .<br \/>\n(1) Many-one function<br \/>\n(2) Identity function<br \/>\n(3) One-to-one function<br \/>\n(4) Into function<br \/>\nAnswer:<br \/>\n(3) One-to-one function<\/p>\n<p>Question 2.<br \/>\nIf g = {(1,1),(2, 3),(3,5),(4,7)} is a function given by g(x) = \u03b1x + \u03b2 then the values of \u03b1 and \u03b2 are &#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230; .<br \/>\n(1) (-1,2)<br \/>\n(2) (2,-1)<br \/>\n(3) (-1,-2)<br \/>\n(4) (1,2)<br \/>\nAnswer:<br \/>\n(2) (2,-1)<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/i0.wp.com\/samacheerkalvi.guide\/wp-content\/uploads\/2020\/01\/SamacheerKalvi.Guide_.png?resize=197%2C19&#038;ssl=1\" alt=\"Samacheer Kalvi 10th Social Science Model Question Paper 1 English Medium\" width=\"197\" height=\"19\" data-recalc-dims=\"1\" \/><\/p>\n<p>Question 3.<br \/>\nThe least number that is divisible by all the numbers from 1 to 10 (both inclusive) is &#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230; .<br \/>\n(1) 2025<br \/>\n(2) 5220<br \/>\n(3) 5025<br \/>\n(4) 2520<br \/>\nAnswer:<br \/>\n(4) 2520<\/p>\n<p>Question 4.<br \/>\nIf the sequence t<sub>1<\/sub>, t<sub>2<\/sub>, t<sub>3<\/sub>, are in A.P. then the sequence t<sub>6<\/sub> ,t<sub>12<\/sub>,t<sub>18<\/sub>,&#8230; is &#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230; .<br \/>\n(1) a Geometric progression<br \/>\n(2) an Arithmetic progression<br \/>\n(3) neither an Arithmetic progression nor a Geometric progression<br \/>\n(4) a constant sequence<br \/>\nAnswer:<br \/>\n(2) an Arithmetic progression<\/p>\n<p>Question 5.<br \/>\n\\(\\frac{x}{x^{2}-25}-\\frac{8}{x^{2}+6 x+5}\\) gives &#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230; .<br \/>\n(1) \\(\\frac{x^{2}-7 x+40}{(x-5)(x+5)}\\)<br \/>\n(2) \\(\\frac{x^{2}+7 x+40}{(x-5)(x+5)(x+1)}\\)<br \/>\n(3) \\(\\frac{x^{2}-7 x+40}{\\left(x^{2}-25\\right)(x+1)}\\)<br \/>\n(4) \\(\\frac{x^{2}+10}{\\left(x^{2}-25\\right)(x+1)}\\)<br \/>\nAnswer:<br \/>\n(3) \\(\\frac{x^{2}-7 x+40}{\\left(x^{2}-25\\right)(x+1)}\\)<\/p>\n<p>Question 6.<br \/>\nThe values of a and b if 4x<sup>4<\/sup> &#8211; 24x<sup>3<\/sup> + 76x<sup>2<\/sup> + ax + b is a perfect square are &#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230; .<br \/>\n(1) 100,120<br \/>\n(2) 10,12<br \/>\n(3) -120,100<br \/>\n(4) 12,10<br \/>\nAnswer:<br \/>\n(3) -120,100<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/i0.wp.com\/samacheerkalvi.guide\/wp-content\/uploads\/2020\/01\/SamacheerKalvi.Guide_.png?resize=197%2C19&#038;ssl=1\" alt=\"Samacheer Kalvi 10th Social Science Model Question Paper 1 English Medium\" width=\"197\" height=\"19\" data-recalc-dims=\"1\" \/><\/p>\n<p>Question 7.<br \/>\nIf \u2206ABC is an isosceles triangle with \u2220C = 90\u00b0 and AC = 5 cm, then AB is &#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230; .<br \/>\n(1) 2.5 cm<br \/>\n(2) 5 cm<br \/>\n(3) 10 cm<br \/>\n(4) 5\u221a2 cm<br \/>\nAnswer:<br \/>\n(4) 5\u221a2 cm<\/p>\n<p>Question 8.<br \/>\nThe area of triangle formed by the points (- 5, 0), (0, &#8211; 5) and (5, 0) is &#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230; .<br \/>\n(1) 0 sq.units<br \/>\n(2) 25 sq.units<br \/>\n(3) 5 sq.units<br \/>\n(4) none of these<br \/>\nAnswer:<br \/>\n(2) 25 sq.units<\/p>\n<p>Question 9.<br \/>\nThe value of sin<sup>2<\/sup>\u03b8 + \\(\\frac{1}{1+\\tan ^{2} \\theta}\\) is equal to &#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230; .<br \/>\n(1) tan<sup>2<\/sup>\u03b8<br \/>\n(2) 1<br \/>\n(3) cot<sup>2<\/sup>\u03b8<br \/>\n(4) \u03b8<br \/>\nAnswer:<br \/>\n(2) 1<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/i0.wp.com\/samacheerkalvi.guide\/wp-content\/uploads\/2020\/01\/SamacheerKalvi.Guide_.png?resize=197%2C19&#038;ssl=1\" alt=\"Samacheer Kalvi 10th Social Science Model Question Paper 1 English Medium\" width=\"197\" height=\"19\" data-recalc-dims=\"1\" \/><\/p>\n<p>Question 10.<br \/>\nIf the radius of the base of a right circular cylinder is halved keeping the same height, then the ratio of the volume of the cylinder thus obtained to the volume of original cylinder is &#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230; .<br \/>\n(1) 1 : 2<br \/>\n(2) 1 : 4<br \/>\n(3) 1 : 6<br \/>\n(4) 1 : 8<br \/>\nAnswer:<br \/>\n(2) 1 : 4<\/p>\n<p>Question 11.<br \/>\nIf the mean and coefficient of variation of a data are 4 and 87.5% then the standard deviation is &#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230; .<br \/>\n(1) 3.5<br \/>\n(2) 3<br \/>\n(3) 4.5<br \/>\n(4) 2.5<br \/>\nAnswer:<br \/>\n(1) 3.5<\/p>\n<p>Question 12.<br \/>\nIf \u03b1 and \u03b2 are the roots of the equation x<sup>2<\/sup> + 2x + 8 = 0 then the value of \\(\\frac{\\alpha}{\\beta}+\\frac{\\beta}{\\alpha}\\) is &#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230; .<br \/>\n(1) \\(\\frac { 1 }{ 2 }\\)<br \/>\n(2) 6<br \/>\n(3) \\(\\frac { 3 }{ 2 }\\)<br \/>\n(4) \\(\\frac { -3 }{ 2 }\\)<br \/>\nAnswer:<br \/>\n(4) \\(\\frac{-3}{2}\\)<\/p>\n<p>Question 13.<br \/>\nIf the points (k, 2k) (3k, 3k) and (3, 1) are collinear, then k is &#8230;&#8230;&#8230;&#8230;.. .<br \/>\n(1) \\(\\frac { 1 }{ 3 }\\)<br \/>\n(2) \\(\\frac { -1 }{ 3 }\\)<br \/>\n(3) \\(\\frac { 2 }{ 3 }\\)<br \/>\n(4) \\(\\frac { -2 }{ 3 }\\)<br \/>\nAnswer:<br \/>\n(2) \\(\\frac{-1}{3}\\)<\/p>\n<p>Question 14.<br \/>\nIf the variance of 14, 18, 22, 26, 30 is 32 then the variance is 28, 36, 44, 52, 60 is &#8230;&#8230;&#8230;&#8230;&#8230;&#8230;&#8230; .<br \/>\n(a) 64<br \/>\n(b) 128<br \/>\n(c) 32\u221a2<br \/>\n(d) 32<br \/>\nAnswer:<br \/>\n(b) 128<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/i0.wp.com\/samacheerkalvi.guide\/wp-content\/uploads\/2020\/01\/SamacheerKalvi.Guide_.png?resize=197%2C19&#038;ssl=1\" alt=\"Samacheer Kalvi 10th Social Science Model Question Paper 1 English Medium\" width=\"197\" height=\"19\" data-recalc-dims=\"1\" \/><\/p>\n<p style=\"text-align: center;\"><span style=\"color: #0000ff;\">PART &#8211; II<\/span><\/p>\n<p><span style=\"color: #0000ff;\">II. Answer any ten questions. Question No. 28 is compulsory. [10 \u00d7 2 = 20]<\/span><\/p>\n<p>Question 15.<br \/>\nRepresent the given relation {(x, y) |y = x + 3 are natural numbers &lt; 10} by<br \/>\n(i) an arrow diagram (ii) a set in roster form, wherever possible<br \/>\nAnswer:<br \/>\n(i)<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-15726\" src=\"https:\/\/i0.wp.com\/samacheerkalvi.guide\/wp-content\/uploads\/2020\/03\/Samacheer-Kalvi-10th-Maths-Model-Question-Paper-1-English-Medium-2.png?resize=296%2C292&#038;ssl=1\" alt=\"Samacheer Kalvi 10th Maths Model Question Paper 1 English Medium - 2\" width=\"296\" height=\"292\" data-recalc-dims=\"1\" \/><\/p>\n<p>(ii) R = {(1, 4) (2, 5) (3, 6) (4, 7) (5, 8) (6, 9)}<\/p>\n<p>Question 16.<br \/>\nIf f: R \u2192 R and g : R \u2192 R are defined by f(x) = x<sup>5<\/sup> and g(x) = x<sup>4<\/sup> then check if f, g are one &#8211; one and fog is one &#8211; one?<br \/>\nAnswer:<br \/>\nf(x) = x<sup>5<\/sup> &#8211; It is one &#8211; one function<br \/>\ng(x) = x<sup>4<\/sup> &#8211; It is one &#8211; one function<br \/>\nfag = f[g{x)] = f(x<sup>4<\/sup>) = (x<sup>4<\/sup>)<sup>5<\/sup><br \/>\nfog = x<sup>20<\/sup><br \/>\nIt is also one-one function.<\/p>\n<p>Question 17.<br \/>\nFind the first five terms of the following sequence.<br \/>\na<sub>1<\/sub> = 1, a<sub>2<\/sub>, a<sub>n<\/sub> = \\(\\frac{a_{n-1}}{a_{n-2}+3}\\) ; n \u2265 3 ; n \u2208 N<br \/>\nAnswer:<br \/>\nThe first two terms of this sequence are given by a<sub>1<\/sub> = 1, a<sub>2<\/sub> = 1. The third term a<sub>3<\/sub> depends on the first and second terms.<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-15725\" src=\"https:\/\/i0.wp.com\/samacheerkalvi.guide\/wp-content\/uploads\/2020\/03\/Samacheer-Kalvi-10th-Maths-Model-Question-Paper-1-English-Medium-3.png?resize=250%2C52&#038;ssl=1\" alt=\"Samacheer Kalvi 10th Maths Model Question Paper 1 English Medium - 3\" width=\"250\" height=\"52\" data-recalc-dims=\"1\" \/><br \/>\nSimilarly the fourth term a<sub>4<\/sub> depends upon a<sub>2<\/sub> and a<sub>3<\/sub>.<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-15724\" src=\"https:\/\/i0.wp.com\/samacheerkalvi.guide\/wp-content\/uploads\/2020\/03\/Samacheer-Kalvi-10th-Maths-Model-Question-Paper-1-English-Medium-4.png?resize=354%2C74&#038;ssl=1\" alt=\"Samacheer Kalvi 10th Maths Model Question Paper 1 English Medium - 4\" width=\"354\" height=\"74\" srcset=\"https:\/\/i0.wp.com\/samacheerkalvi.guide\/wp-content\/uploads\/2020\/03\/Samacheer-Kalvi-10th-Maths-Model-Question-Paper-1-English-Medium-4.png?w=354&amp;ssl=1 354w, https:\/\/i0.wp.com\/samacheerkalvi.guide\/wp-content\/uploads\/2020\/03\/Samacheer-Kalvi-10th-Maths-Model-Question-Paper-1-English-Medium-4.png?resize=300%2C63&amp;ssl=1 300w\" sizes=\"(max-width: 354px) 100vw, 354px\" data-recalc-dims=\"1\" \/><br \/>\nIn the same way, the fifth term a<sub>5<\/sub> can be calculated as<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-15723\" src=\"https:\/\/i0.wp.com\/samacheerkalvi.guide\/wp-content\/uploads\/2020\/03\/Samacheer-Kalvi-10th-Maths-Model-Question-Paper-1-English-Medium-5.png?resize=343%2C88&#038;ssl=1\" alt=\"Samacheer Kalvi 10th Maths Model Question Paper 1 English Medium - 5\" width=\"343\" height=\"88\" srcset=\"https:\/\/i0.wp.com\/samacheerkalvi.guide\/wp-content\/uploads\/2020\/03\/Samacheer-Kalvi-10th-Maths-Model-Question-Paper-1-English-Medium-5.png?w=343&amp;ssl=1 343w, https:\/\/i0.wp.com\/samacheerkalvi.guide\/wp-content\/uploads\/2020\/03\/Samacheer-Kalvi-10th-Maths-Model-Question-Paper-1-English-Medium-5.png?resize=300%2C77&amp;ssl=1 300w\" sizes=\"(max-width: 343px) 100vw, 343px\" data-recalc-dims=\"1\" \/><br \/>\nTherefore, the first fie terms of the sequence are 1,1, \\(\\frac{1}{4}, \\frac{1}{16}, \\frac{1}{52}\\)<\/p>\n<p>Question 18.<br \/>\nIf 1<sup>3<\/sup> + 2<sup>3<\/sup> + 3<sup>3<\/sup> +. . . .+ k<sup>3<\/sup> = 44100 then find 1+ 2 + 3 + &#8230;. + k<br \/>\nAnswer:<br \/>\n1<sup>3<\/sup> + 2<sup>3<\/sup> + 3<sup>3<\/sup> + &#8230;&#8230;&#8230;. + K<sup>3<\/sup> = 44100<br \/>\n\\(\\left[\\frac{k(k+1)}{2}\\right]^{2}\\) = 44100<br \/>\n\\(\\frac{k(k+1)}{2}\\) = \\(\\sqrt{44100}\\) = 210<br \/>\n1 + 2 + 3 + &#8230;&#8230;.. + k = \\(\\frac{k(k+1)}{2}\\)<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/i0.wp.com\/samacheerkalvi.guide\/wp-content\/uploads\/2020\/01\/SamacheerKalvi.Guide_.png?resize=197%2C19&#038;ssl=1\" alt=\"Samacheer Kalvi 10th Social Science Model Question Paper 1 English Medium\" width=\"197\" height=\"19\" data-recalc-dims=\"1\" \/><\/p>\n<p>Question 19.<br \/>\nFind the LCM of the polynomials a<sup>2<\/sup> + 4a &#8211; 12, a<sup>2<\/sup> &#8211; 5a + 6 whose GCD is a &#8211; 2<br \/>\nAnswer:<br \/>\np(x) = a<sup>2<\/sup> + 4a &#8211; 12<br \/>\n= a<sup>2<\/sup> + 6a &#8211; 2a &#8211; 12<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-15722\" src=\"https:\/\/i0.wp.com\/samacheerkalvi.guide\/wp-content\/uploads\/2020\/03\/Samacheer-Kalvi-10th-Maths-Model-Question-Paper-1-English-Medium-6.png?resize=139%2C81&#038;ssl=1\" alt=\"Samacheer Kalvi 10th Maths Model Question Paper 1 English Medium - 6\" width=\"139\" height=\"81\" data-recalc-dims=\"1\" \/><br \/>\n= a (a + 6) &#8211; 2(a + 6)<br \/>\n= (a + 6) (a &#8211; 2)<br \/>\ng(x) = a<sup>2<\/sup> &#8211; 5a + 6<br \/>\n= a<sup>2<\/sup> &#8211; 3a &#8211; 2a + 6<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-15721\" src=\"https:\/\/i0.wp.com\/samacheerkalvi.guide\/wp-content\/uploads\/2020\/03\/Samacheer-Kalvi-10th-Maths-Model-Question-Paper-1-English-Medium-7.png?resize=128%2C66&#038;ssl=1\" alt=\"Samacheer Kalvi 10th Maths Model Question Paper 1 English Medium - 7\" width=\"128\" height=\"66\" data-recalc-dims=\"1\" \/><br \/>\n= a(a &#8211; 3) &#8211; 2 (a &#8211; 3)<br \/>\n= (a &#8211; 3) (a &#8211; 2)<br \/>\nL.C.M. = \\(\\frac{p(x) \\times g(x)}{\\text { G.C.D. }}\\)<br \/>\n= \\(\\frac{(a+6)(a-2) \\times(a-3)(a-2)}{(a-2)}\\)<br \/>\n= (a + 6) (a &#8211; 3) (a &#8211; 2)<\/p>\n<p>Question 20.<br \/>\nFind the value of \u2018k\u2019 whose roots of the equation kx<sup>2<\/sup> + (6k + 2)x + 16 = 0 are real and equal.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-15720\" src=\"https:\/\/i0.wp.com\/samacheerkalvi.guide\/wp-content\/uploads\/2020\/03\/Samacheer-Kalvi-10th-Maths-Model-Question-Paper-1-English-Medium-8.png?resize=133%2C83&#038;ssl=1\" alt=\"Samacheer Kalvi 10th Maths Model Question Paper 1 English Medium - 8\" width=\"133\" height=\"83\" data-recalc-dims=\"1\" \/><br \/>\nHere a = k, b = 6k+ 2 ; c = 16<br \/>\nSince the equation has real and equal roots .<br \/>\nA = 0<br \/>\nb<sup>2<\/sup> &#8211; 4ac = 0<br \/>\n(6k + 2)<sup>2<\/sup> &#8211; 4(k)(16) = 0<br \/>\n36k<sup>2<\/sup> + 4 + 24k &#8211; 4(k) (16) = 0<br \/>\n36k<sup>2<\/sup> &#8211; 40k + 4 = 0<br \/>\n(\u00f7 by 4) \u21d2 9k<sup>2<\/sup> &#8211; 10k + 1 = 0<br \/>\n9k<sup>2<\/sup> &#8211; 9k &#8211; k + 1 = 0<br \/>\n9k(k &#8211; 1) &#8211; 1(k &#8211; 1) = 0<br \/>\n(k &#8211; 1) (9k &#8211; 1) = 0<br \/>\nk &#8211; 1 = 0 or 9k &#8211; 1 = 0 \u21d2 k = 1 or k = \\(\\frac { 1 }{ 9 }\\)<br \/>\nThe value of k = 1 or \\(\\frac { 1 }{ 9 }\\)<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/i0.wp.com\/samacheerkalvi.guide\/wp-content\/uploads\/2020\/01\/SamacheerKalvi.Guide_.png?resize=197%2C19&#038;ssl=1\" alt=\"Samacheer Kalvi 10th Social Science Model Question Paper 1 English Medium\" width=\"197\" height=\"19\" data-recalc-dims=\"1\" \/><\/p>\n<p>Question 21.<br \/>\nFind the value of a, b, c, d, x, y from the following matrix equation.<br \/>\n\\(\\left( \\begin{matrix} d &amp; 8 \\\\ 3b &amp; a \\end{matrix} \\right) +\\left( \\begin{matrix} 3 &amp; a \\\\ -2 &amp; -4 \\end{matrix} \\right) =\\left( \\begin{matrix} 2 &amp; 2a \\\\ b &amp; 4c \\end{matrix} \\right) +\\left( \\begin{matrix} 0 &amp; 1 \\\\ -5 &amp; 0 \\end{matrix} \\right) \\)<br \/>\nAnswer:<br \/>\nFirst, we add the two matrices on both left, right hand sides to get<br \/>\n\\(\\left( \\begin{matrix} d+3 &amp; 8+a \\\\ 3b-2 &amp; a-4 \\end{matrix} \\right) =\\left( \\begin{matrix} 2 &amp; 2a+1 \\\\ b-5 &amp; 4c \\end{matrix} \\right) \\)<br \/>\nEquating the corresponding elements of the two matrices, we have<br \/>\nd + 3 = 2 gives d = -1<br \/>\n8 + a = 2a + 1 gives a = 7<br \/>\n3b &#8211; 2 = b &#8211; 5 gives b = \\(\\frac { -3 }{ 2 }\\)<br \/>\nSubstituting a = 7 in a &#8211; 4 = 4c gives c = \\(\\frac { 3 }{ 4 }\\)<br \/>\nTherefore, a = 7, b = \\(\\frac { -3 }{ 2 }\\) ,c = \\(\\frac { 3 }{ 4 }\\) , d = -1.<\/p>\n<p>Question 22.<br \/>\nTo get from point A to point B you must avoid walking through a pond. You must walk 34 m south and 41m east. To the nearest meter, how many meters would be saved if it were possible to make a way through the pond?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-15719\" src=\"https:\/\/i0.wp.com\/samacheerkalvi.guide\/wp-content\/uploads\/2020\/03\/Samacheer-Kalvi-10th-Maths-Model-Question-Paper-1-English-Medium-9.png?resize=270%2C218&#038;ssl=1\" alt=\"Samacheer Kalvi 10th Maths Model Question Paper 1 English Medium - 9\" width=\"270\" height=\"218\" data-recalc-dims=\"1\" \/><br \/>\nIn the right \u2206ABC,<br \/>\nBy Pythagoras theorem<br \/>\nAC<sup>2<\/sup> = AB<sup>2<\/sup> + BC<sup>2<\/sup> = 34<sup>2<\/sup> + 41<sup>2<\/sup><br \/>\n= 1156 + 1681 = 2837<br \/>\nAC = \u221a2837<br \/>\n= 53.26 m<br \/>\nThrough A one must walk (34m + 41m) 75 m to reach C.<br \/>\nThe difference in Distance = 75 &#8211; 53.26<br \/>\n= 21.74 m<\/p>\n<p>Question 23.<br \/>\nIf the points A(-3, 9), B(a, b) and C(4, -5) are collinear and if a + b = 1, then find a and b.<br \/>\nAnswer:<br \/>\nSince the three points are collinear<br \/>\nArea of a \u2206 = 0<br \/>\n\\(\\frac { 1 }{ 2 }\\)[(x<sub>1<\/sub>y<sub>2<\/sub> + x<sub>2<\/sub>y<sub>3<\/sub> + x<sub>3<\/sub>y<sub>1<\/sub>) &#8211; (x<sub>2<\/sub>y<sub>1<\/sub> + x<sub>3<\/sub>y<sub>2<\/sub> + x<sub>1<\/sub>y<sub>3<\/sub>)]<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-15718\" src=\"https:\/\/i0.wp.com\/samacheerkalvi.guide\/wp-content\/uploads\/2020\/03\/Samacheer-Kalvi-10th-Maths-Model-Question-Paper-1-English-Medium-10.png?resize=241%2C56&#038;ssl=1\" alt=\"Samacheer Kalvi 10th Maths Model Question Paper 1 English Medium - 10\" width=\"241\" height=\"56\" data-recalc-dims=\"1\" \/><br \/>\n\\(\\frac { 1 }{ 2 }\\)[(-36 &#8211; 5a 4- 36) &#8211; (9a + 46 + 15)] = 0<br \/>\n-36 &#8211; 5a + 36 &#8211; 9a -4b &#8211; 15 = 0<br \/>\n-7b &#8211; 14a + 21=0<br \/>\n(\u00f7 by 7) &#8211; b &#8211; 2a + 3 = 0<br \/>\n2a + b &#8211; 3 = 0<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-15717\" src=\"https:\/\/i0.wp.com\/samacheerkalvi.guide\/wp-content\/uploads\/2020\/03\/Samacheer-Kalvi-10th-Maths-Model-Question-Paper-1-English-Medium-11.png?resize=259%2C72&#038;ssl=1\" alt=\"Samacheer Kalvi 10th Maths Model Question Paper 1 English Medium - 11\" width=\"259\" height=\"72\" data-recalc-dims=\"1\" \/><br \/>\nSubtract (1) and (2) \u21d2 a = 2<br \/>\nSubstitute the value of a = 2 in (2) \u21d2 2 + 6 = 1<br \/>\nb = 1 &#8211; 2 = -1<br \/>\nThe value of a = 2 and b = -1<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/i0.wp.com\/samacheerkalvi.guide\/wp-content\/uploads\/2020\/01\/SamacheerKalvi.Guide_.png?resize=197%2C19&#038;ssl=1\" alt=\"Samacheer Kalvi 10th Social Science Model Question Paper 1 English Medium\" width=\"197\" height=\"19\" data-recalc-dims=\"1\" \/><\/p>\n<p>Question 24.<br \/>\nProve that \\(\\frac{\\sin A}{1+\\cos A}+\\frac{\\sin A}{1-\\cos A}\\) = 2 cosec A.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-15716\" src=\"https:\/\/i0.wp.com\/samacheerkalvi.guide\/wp-content\/uploads\/2020\/03\/Samacheer-Kalvi-10th-Maths-Model-Question-Paper-1-English-Medium-12.png?resize=478%2C165&#038;ssl=1\" alt=\"Samacheer Kalvi 10th Maths Model Question Paper 1 English Medium - 12\" width=\"478\" height=\"165\" srcset=\"https:\/\/i0.wp.com\/samacheerkalvi.guide\/wp-content\/uploads\/2020\/03\/Samacheer-Kalvi-10th-Maths-Model-Question-Paper-1-English-Medium-12.png?w=478&amp;ssl=1 478w, https:\/\/i0.wp.com\/samacheerkalvi.guide\/wp-content\/uploads\/2020\/03\/Samacheer-Kalvi-10th-Maths-Model-Question-Paper-1-English-Medium-12.png?resize=300%2C104&amp;ssl=1 300w\" sizes=\"(max-width: 478px) 100vw, 478px\" data-recalc-dims=\"1\" \/><\/p>\n<p>Question 25.<br \/>\nThe probability that atleast one of A and B occur is 0.6. If A and B occur simultaneously with probability 0.2, then find P(A\u0304) + P(B\u0304).<br \/>\nAnswer:<br \/>\nHere p(A \u222a B) = 0.6, p(A \u2229 B) = 0.2<br \/>\np(A \u222a B) = p(A) + p(B) &#8211; p(A \u2229 B)<br \/>\n0.6 = p(A) + P(B) &#8211; 0.2<br \/>\n\u2234 p(A) + p(B) = 0.8<br \/>\nP(A\u0304) + P(B\u0304) = 1 &#8211; p(A) + 1 &#8211; p(B)<br \/>\n= 2 &#8211; [p(A) + p(B)]<br \/>\n= 2 &#8211; 0.8 = 1.2<\/p>\n<p>Question 26.<br \/>\nIf n = 10, X\u0304 = 12 and \u03a3x<sup>2<\/sup> = 1530, then calculate the coefficient of variation.<br \/>\nAnswer:<br \/>\nGiven that n = 10, X\u0304 = \\(\\frac{\\Sigma x}{n}\\) = 12, \u03a3x<sup>2<\/sup> = 1530<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-15715\" src=\"https:\/\/i0.wp.com\/samacheerkalvi.guide\/wp-content\/uploads\/2020\/03\/Samacheer-Kalvi-10th-Maths-Model-Question-Paper-1-English-Medium-13.png?resize=605%2C62&#038;ssl=1\" alt=\"Samacheer Kalvi 10th Maths Model Question Paper 1 English Medium - 13\" width=\"605\" height=\"62\" srcset=\"https:\/\/i0.wp.com\/samacheerkalvi.guide\/wp-content\/uploads\/2020\/03\/Samacheer-Kalvi-10th-Maths-Model-Question-Paper-1-English-Medium-13.png?w=605&amp;ssl=1 605w, https:\/\/i0.wp.com\/samacheerkalvi.guide\/wp-content\/uploads\/2020\/03\/Samacheer-Kalvi-10th-Maths-Model-Question-Paper-1-English-Medium-13.png?resize=300%2C31&amp;ssl=1 300w\" sizes=\"(max-width: 605px) 100vw, 605px\" data-recalc-dims=\"1\" \/><br \/>\n(\u03c3) = 3<br \/>\ncoefficient of variation = \\(\\frac{\\sigma}{\\bar{x}} \\times 100\\) \u21d2 \\(\\frac{3}{12} \\times 100=25\\)<br \/>\n\u2234 coefficient of variation = 25<\/p>\n<p>Question 27.<br \/>\nFind the volume of the largest right circular cone that can be cut out of a cube whose edge is 14 cm.<br \/>\nAnswer:<br \/>\nGiven, Edge of the cube = 14 cm<br \/>\nThe largest circular cone is cut out from the cube.<br \/>\nRadius of the cone (r) = \\(\\frac { 14 }{ 2 }\\) = 7 cm<br \/>\nHeight of the cone (h) = 14 cm<br \/>\nVolume of a cone = \\(\\frac { 1 }{ 3 }\\) \u03c0r<sup>2<\/sup>h cu. units<br \/>\n= \\(\\frac{1}{3} \\times \\frac{22}{7}\\) \u00d7 7 \u00d7 7 \u00d7 14 cm<sup>3<\/sup><br \/>\n= \\(\\frac{22 \\times 7 \\times 14}{3}\\) cm<sup>3<\/sup><br \/>\n\u2234 Volume of a cone = 718.67 cm<sup>3<\/sup><\/p>\n<p>Question 28.<br \/>\nFind the sum of the first 40 terms of the series 1<sup>2<\/sup> &#8211; 2<sup>2<\/sup> + 3<sup>2<\/sup> &#8211; 4<sup>2<\/sup> + &#8230;..<br \/>\nAnswer:<br \/>\nThe given series is 1<sup>2<\/sup> &#8211; 2<sup>2<\/sup> + 3<sup>2<\/sup> &#8211; 4<sup>2<\/sup> + &#8230;. 40 terms<br \/>\nGrouping the terms we get,<br \/>\n(1<sup>2<\/sup> &#8211; 2<sup>2<\/sup>) + (3<sup>2<\/sup> &#8211; 4<sup>2<\/sup>) + (5<sup>2<\/sup> &#8211; 6<sup>2<\/sup>) + &#8230;&#8230;&#8230;&#8230; 20 terms<br \/>\n(1 &#8211; 4) + (9 &#8211; 16) + (25 &#8211; 36) + &#8230;&#8230;&#8230;&#8230;. 20 terms<br \/>\n(-3) + (-7) + (-11) + &#8230;&#8230;&#8230;&#8230; 20 term<br \/>\nThis is an A.P<br \/>\nHere a = &#8211; 3, d = &#8211; 7 &#8211; (- 3) = &#8211; 7 + 3 = -4, n = 20<br \/>\nS<sub>n<\/sub> = \\(\\frac { n }{ 2 }\\)[2a + (n &#8211; 1)d]<br \/>\nS<sub>20 <\/sub> = \\(\\frac { 20 }{ 2 }\\)[2(-3) + 19(-4)]<br \/>\n= 10 (- 6 &#8211; 76) = 10 (- 82) = &#8211; 820<br \/>\n\u2234 Sum of 40 terms of the series is = 820.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/i0.wp.com\/samacheerkalvi.guide\/wp-content\/uploads\/2020\/01\/SamacheerKalvi.Guide_.png?resize=197%2C19&#038;ssl=1\" alt=\"Samacheer Kalvi 10th Social Science Model Question Paper 1 English Medium\" width=\"197\" height=\"19\" data-recalc-dims=\"1\" \/><\/p>\n<p style=\"text-align: center;\"><span style=\"color: #0000ff;\">PART &#8211; III<\/span><\/p>\n<p><span style=\"color: #0000ff;\">III. Answer any ten questions. Question No. 42 is compulsory. [10 \u00d7 5 = 50]<\/span><\/p>\n<p>Question 29.<br \/>\nFind x if gff(x) = fgg(x), given f(x) = 3x + 1 and g(x) = x + 3.<\/p>\n<p>Question 30.<br \/>\nIn a G.P the product of three consecutive terms is 27 and the sum of the product of two terms taken at a time is \\(\\frac{57}{2}\\).Find the three terms.<\/p>\n<p>Question 31.<br \/>\nThe 13th term of an A.P. is 3 and the sum of first 13 terms is 234. Find the common difference and the sum of first 21 terms.<\/p>\n<p>Question 32.<br \/>\nIf Sn = (x + y) + (x<sup>2<\/sup> + xy + y<sup>2<\/sup>) + (x<sup>3<\/sup> + x<sup>2<\/sup>y + xy<sup>2<\/sup> + y<sup>3<\/sup>) + &#8230;&#8230;&#8230;&#8230; n terms then prove that (x &#8211; y)S<sub>n<\/sub> = \\(\\left[\\frac{x^{2}\\left(x^{n}-1\\right)}{x-1}-\\frac{y^{2}\\left(y^{n}-1\\right)}{y-1}\\right]\\)<\/p>\n<p>Question 33.<br \/>\nTwo women together took 100 eggs to a market, one had more than the other. Both sold them for the same sum of money. The first then said to the second: \u201cIf I had your eggs, I would have earned \u20b915\u201d, to which the second replied: \u201cIf I had your eggs, I would have earned \u20b96 \\(\\frac { 2 }{ 3 }\\) \u201d. How many eggs did each had in the beginning?<\/p>\n<p>Question 34.<br \/>\nIf the roots of (a &#8211; b)x<sup>2<\/sup> + (b &#8211; c)x + (c &#8211; a) = 0 are real and equal, then prove that b, a, c are in arithmetic progression.<\/p>\n<p>Question 35.<br \/>\nA circle is inscribed in AABC having sides 8 cm, 10 cm and 12 cm as shown in figure, Find AD, BE and CF.<\/p>\n<p>Question 36.<br \/>\nThe line joining the points A(0,5) and B(4,1) is a tangent to a circle whose centre C is at the point (4, 4) find<br \/>\n(i) the equation of the line AB.<br \/>\n(ii) the equation of the line through C which is perpendicular to the line AB.<br \/>\n(iii) the coordinates of the point of contact of tangent line AB with the circle.<\/p>\n<p>Question 37.<br \/>\nIf sin \u03b8 (1 + sin<sup>2<\/sup>\u03b8) = cos<sup>2<\/sup>\u03b8 , then prove that cos<sup>6<\/sup>\u03b8 &#8211; 4 cos<sup>4<\/sup>\u03b8 + 8 cos<sup>2<\/sup>\u03b8 = 4<\/p>\n<p>Question 38.<br \/>\nA toy is in the shape of a cylinder surmounted by a hemisphere. The height of the toy is 25 cm. Find the total surface area of the toy if its common diameter is 12 cm.<\/p>\n<p>Question 39.<br \/>\nFind the coefficient of variation of 24, 26, 33, 37, 29, 31.<\/p>\n<p>Question 40.<br \/>\nThe probability that A, B and C can solve a problem are \\(\\frac { 4 }{ 5 }\\), \\(\\frac { 2 }{ 3 }\\) and \\(\\frac { 3 }{ 7 }\\) respectively. The probability of the problem being solved by A and B is \\(\\frac { 8 }{ 15}\\),B and C is \\(\\frac { 2 }{ 7 }\\) , A and C is \\(\\frac { 12 }{ 13 }\\) . The probability of the problem being solved by all the three is \\(\\frac { 8 }{ 35 }\\). Find the probability that the problem can be solved by atleast one of them.<\/p>\n<p>Question 41.<br \/>\nVerify that (AB)<sub>T<\/sub> = B<sub>T<\/sub>A<sub>T<\/sub> if A = \\(\\left( \\begin{matrix} 2 &amp; 3 &amp; -1 \\\\ 4 &amp; 1 &amp; 5 \\end{matrix} \\right) \\) and B = \\(\\left( \\begin{matrix} 1 &amp; -2 \\\\ 3 &amp; -3 \\\\ 2 &amp; 6 \\end{matrix} \\right) \\)<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/i0.wp.com\/samacheerkalvi.guide\/wp-content\/uploads\/2020\/01\/SamacheerKalvi.Guide_.png?resize=197%2C19&#038;ssl=1\" alt=\"Samacheer Kalvi 10th Social Science Model Question Paper 1 English Medium\" width=\"197\" height=\"19\" data-recalc-dims=\"1\" \/><\/p>\n<p>Question 42.<br \/>\nA function f(-3, 7) \u2192 R is defined as follows<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-15743\" src=\"https:\/\/i0.wp.com\/samacheerkalvi.guide\/wp-content\/uploads\/2020\/03\/Samacheer-Kalvi-10th-Social-Science-Model-Question-Paper-1-Maths-Medium-1-1.png?resize=390%2C117&#038;ssl=1\" alt=\"Samacheer Kalvi 10th Maths Model Question Paper 1 English Medium - 1\" width=\"390\" height=\"117\" srcset=\"https:\/\/i0.wp.com\/samacheerkalvi.guide\/wp-content\/uploads\/2020\/03\/Samacheer-Kalvi-10th-Social-Science-Model-Question-Paper-1-Maths-Medium-1-1.png?w=390&amp;ssl=1 390w, https:\/\/i0.wp.com\/samacheerkalvi.guide\/wp-content\/uploads\/2020\/03\/Samacheer-Kalvi-10th-Social-Science-Model-Question-Paper-1-Maths-Medium-1-1.png?resize=300%2C90&amp;ssl=1 300w\" sizes=\"(max-width: 390px) 100vw, 390px\" data-recalc-dims=\"1\" \/><br \/>\nFind (i) 5f(1) -3f(-2) (ii) 3f(-3) + 4 f(4) (iii) \\(\\frac{7 f(3)-f(-1)}{2 f(6)-f(1)}\\)<\/p>\n<p style=\"text-align: center;\"><span style=\"color: #0000ff;\">PART &#8211; IV<\/span><\/p>\n<p><span style=\"color: #0000ff;\">IV. Answer all the questions. [2 \u00d7 8 = 16]<\/span><\/p>\n<p>Question 43.<br \/>\n(a) Construct a \u2206PQR such that QR = 6.5 cm, \u2220P = 60\u00b0 and the altitude from P to QR is of length 4.5 cm.<\/p>\n<p>[OR]<\/p>\n<p>(b) Draw a tangent to the circle from the point P having radius 3.6 cm, and centre at O. Point P is at a distance 7.2 cm from the centre.<\/p>\n<p>Question 44.<br \/>\n(a) Draw the graph of y = x<sup>2<\/sup> + x and hence solve x<sup>2<\/sup> + 1 = 0<\/p>\n<p>[OR]<\/p>\n<p>(b) Solve graphically (x + 2) (x + 4) = 0<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Students can Download Samacheer Kalvi 10th Maths Model Question Paper 1 English Medium Pdf, Samacheer Kalvi 10th Maths Model Question Papers helps you to revise the complete Tamilnadu State Board New Syllabus, helps students complete homework assignments and to score high marks in board exams. Tamil Nadu Samacheer Kalvi 10th Maths Model Question Paper 1 &hellip;<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","enabled":false},"version":2}},"categories":[2],"tags":[],"class_list":["post-1509","post","type-post","status-publish","format-standard","hentry","category-class-10"],"jetpack_publicize_connections":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/posts\/1509"}],"collection":[{"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/comments?post=1509"}],"version-history":[{"count":1,"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/posts\/1509\/revisions"}],"predecessor-version":[{"id":39988,"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/posts\/1509\/revisions\/39988"}],"wp:attachment":[{"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/media?parent=1509"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/categories?post=1509"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/samacheerkalvi.guide\/wp-json\/wp\/v2\/tags?post=1509"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}