{"id":3787,"date":"2020-07-14T10:41:13","date_gmt":"2020-07-14T05:11:13","guid":{"rendered":"http:\/\/ncertsolutions.guru\/?p=3787"},"modified":"2020-07-15T14:45:59","modified_gmt":"2020-07-15T09:15:59","slug":"cbse-sample-papers-for-class-10-maths-paper-3","status":"publish","type":"post","link":"https:\/\/ncertsolutions.guru\/cbse-sample-papers-for-class-10-maths-paper-3\/","title":{"rendered":"CBSE Sample Papers for Class 10 Maths Paper 3"},"content":{"rendered":"<h2>CBSE Sample Papers for Class 10 Maths Paper 3<\/h2>\n<p>These Sample papers are part of <a href=\"http:\/\/ncertsolutions.guru\/cbse-sample-papers-for-class-10-maths\/\">CBSE Sample Papers for Class 10 Maths<\/a>. Here we have given CBSE Sample Papers for Class 10 Maths Paper 3<\/p>\n<p><strong>Time Allowed : 3 hours<\/strong><br \/>\n<strong>Maximum Marks : 80<\/strong><\/p>\n<p style=\"text-align: center;\"><span style=\"color: #0000ff;\"><strong>General Instructions<\/strong><\/span><\/p>\n<ul>\n<li>All questions are compulsory.<\/li>\n<li>The question paper consists of 30 questions divided into four sections \u2014 A, B, C and D.<\/li>\n<li>Section A contains 6 questions of 1 mark each. Section B contains 6 questions of 2 marks each. Section C contains 10 questions of 3 marks each. Section D contains 8 questions of 4 marks each.<\/li>\n<li>There is no overall choice. However, an internal choice has been provided in 4 questions of 3 marks each and 3 questions of 4 marks each. You have to attempt only one of the alternatives in all such questions.<\/li>\n<li>Use of calculator is not permitted.<\/li>\n<\/ul>\n<p style=\"text-align: center;\"><strong>SECTION-A<\/strong><\/p>\n<p><strong>Question 1.<\/strong><br \/>\nVertices of a triangle are (- 4, 0), (4, 0), (0, 3). What type of triangle is it ? <strong>[1]<\/strong><\/p>\n<p><strong>Question 2.<\/strong><br \/>\nIf two positive integers p and q can be expressed as p = ab<sup>2<\/sup> and q = a<sup>2<\/sup>b; a, b being prime<br \/>\nnumbers, then find LCM (p, q).\u00a0\u00a0<strong>[1]<\/strong><\/p>\n<p><strong>Question 3.<\/strong><br \/>\nD and E are respectively the points on the sides AB and AC of a triangle ABC such that<br \/>\nAD = 2 cm, BD = 4 cm, BC = 9 cm and DE || BC. Then, find the length of DE.\u00a0\u00a0<strong>[1]<\/strong><\/p>\n<p><strong>Question 4.<\/strong><br \/>\nFind a quadratic polynomial, the sum and product of whose zeroes are 3 and &#8211; 2 respectively.\u00a0\u00a0<strong>[1]<\/strong><\/p>\n<p><strong>Question 5.<\/strong><br \/>\nFor what value of p are 2p + 1, 12, 5p &#8211; 3 are three consecutive terms of an A.P. ?\u00a0\u00a0<strong>[1]<\/strong><\/p>\n<p><strong>Question 6.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/i2.wp.com\/farm2.staticflickr.com\/1976\/44260882285_3711942699_o.png?resize=288%2C60&#038;ssl=1\" alt=\"CBSE Sample Papers for Class 10 Maths Paper 3 Q 6.\" width=\"288\" height=\"60\" data-recalc-dims=\"1\" \/><\/p>\n<p style=\"text-align: center;\"><strong>SECTION-B<\/strong><\/p>\n<p><strong>Question 7.<\/strong><br \/>\nThe decimal expansion of the rational number \\(\\frac { 33 }{ { 2 }^{ 2 }.{ 5 }^{ n } } \\) terminates after 3 places of decimal. Then find the value of n.\u00a0\u00a0<strong>[2]<\/strong><\/p>\n<p><strong>Question 8.<\/strong><br \/>\nFind the value of a, if the distance between the points A(- 3, &#8211; 14) and B(a, &#8211; 5) is 9 units\u00a0\u00a0<strong>[2]<\/strong><\/p>\n<p><strong>Question 9.<\/strong><br \/>\n17 cards numbered 1, 2, 3, &#8230;, 17 are put in a box and mixed thoroughly. One person draws a card from the box. Find the probability that the number on the card is :\u00a0\u00a0<strong>[2]<\/strong><\/p>\n<ul>\n<li>Odd<\/li>\n<li>A prime<\/li>\n<li>Divisible by 3<\/li>\n<li>Divisible by 3 and 2 bot<\/li>\n<\/ul>\n<p><strong>Question 10.<\/strong><br \/>\nWhat is the probability that an ordinary year has 53 Sundays.\u00a0\u00a0<strong>[2]<\/strong><\/p>\n<p><strong>Question 11.<\/strong><br \/>\nDetermine the sum of first 100 odd natural number.\u00a0\u00a0<strong>[2]<\/strong><\/p>\n<p><strong>Question 12.\u00a0\u00a0<\/strong><br \/>\nFind the zeroes of the polynomial 2x<sup>2<\/sup> + x &#8211; 6.\u00a0\u00a0<strong>[2]<\/strong><\/p>\n<p style=\"text-align: center;\"><strong>SECTION-C<\/strong><\/p>\n<p><strong>Question 13.<\/strong><br \/>\nFind the largest number that divides 1251, 9377 and 15628 leaving remainders 1, 2 and 3 respectively.\u00a0\u00a0<strong>[3]<\/strong><\/p>\n<p><strong>Question 14.<\/strong><br \/>\nThe points A(2, 9), B(a, 5) and C(5, 5) are the vertices of a triangle ABC right angled at B. Find the values of a and hence the area of \u2206ABC.\u00a0\u00a0<strong>[3]<\/strong><br \/>\n<strong>OR<\/strong><br \/>\nA(6,1), B(8, 2) and C(9, 4) are three vertices of a parallelogram \u2206BCD. If E is the mid-point of DC, find the area of \u2206ADE.<\/p>\n<p><strong>Question 15.<\/strong><br \/>\nProve that the sum of the squares of the sides of a rhombus is equal to the sum of the squares of its diagonals.\u00a0<strong>[3]<\/strong><br \/>\n<strong>OR<\/strong><br \/>\nIf BL and CM are median of a triangle ABC right angled at A then prove that:<br \/>\n4(BL<sup>2<\/sup> + CM<sup>2<\/sup>) = 5BC<sup>2<\/sup>.<\/p>\n<p><strong>Question 16.<\/strong><br \/>\nProve that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line segment joining the points of contact at the centre.\u00a0\u00a0<strong>[3]<\/strong><\/p>\n<p><strong>Question 17.<\/strong><br \/>\nFrom a circular piece of cardboard of radius 3 cm, two sectors of 90\u00b0 have been cut off. Find the perimeter of the remaining portion to nearest hundredth centimetres. (Take \u03c0 = \\(\\frac { 22 }{ 7 } \\))\u00a0\u00a0<strong>[3]<\/strong><br \/>\n<strong>OR<\/strong><br \/>\nFind the area of the segment of a circle of radius 12 cm whose corresponding sector has a central angle of 60\u00b0.<br \/>\n(Use \u03c0 = 3.14)<\/p>\n<p><strong>Question 18.<\/strong><br \/>\nWater is flowing at the rate of 15 km\/h through a pipe of diameter 14 cm into a cuboidal pond which is 50 m long and 44m wide. In what time will the level of water in pond<br \/>\nrise by 21 cm ?\u00a0\u00a0<strong>[3]<\/strong><br \/>\n<strong>OR<\/strong><br \/>\nHow many spherical lead shots each of diameter 4.2 cm can be obtained from a solid rectangular lead piece with dimensions 66 cm, 42 cm and 21 cm.<\/p>\n<p><strong>Question 19.<\/strong><br \/>\nFind the zeroes of the polynomial 4x<sup>2<\/sup> &#8211; x &#8211; 3 and verify the relationship between the zeroes and the coefficients.\u00a0\u00a0<strong>[3]<\/strong><\/p>\n<p><strong>Question 20.<\/strong><br \/>\nSolve graphically : 4x + 6y = 9; 7x + 5y = 2.\u00a0\u00a0<strong>[3]<\/strong><br \/>\n<strong>OR<\/strong><br \/>\nSum of a two-digit number and the number formed by reversing the order of digits is 88. If difference of digits is 2 and the unit digit is greater, determine the number.<\/p>\n<p><strong>Question 21.<\/strong><br \/>\nIf sec \u03b8 = x + \\(\\frac { 1 }{ 4x } \\), prove that : sec \u03b8 + tan \u03b8 = 2x or \\(\\frac { 1 }{ 2x } \\)\u00a0<strong>[3]<\/strong><\/p>\n<p><strong>Question 22.<\/strong><br \/>\nFind the mean of the following data :\u00a0\u00a0<strong>[3]<\/strong><\/p>\n<table border=\"2\">\n<tbody>\n<tr>\n<td style=\"text-align: center;\" width=\"112\"><strong>Age<\/strong><\/td>\n<td style=\"text-align: center;\" width=\"117\"><strong>No. of females<\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" width=\"112\">Less than 10<\/td>\n<td style=\"text-align: center;\" width=\"117\">7<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" width=\"112\">Less than 20<\/td>\n<td style=\"text-align: center;\" width=\"117\">20<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" width=\"112\">Less than 30<\/td>\n<td style=\"text-align: center;\" width=\"117\">45<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" width=\"112\">Less than 40<\/td>\n<td style=\"text-align: center;\" width=\"117\">58<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" width=\"112\">Less than 50<\/td>\n<td style=\"text-align: center;\" width=\"117\">71<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: center;\"><strong>SECTION-D<\/strong><\/p>\n<p><strong>Question 23.<\/strong><br \/>\nIf the angle of elevation of a cloud from a point h metre above a lake is \u03b1 and the angle of depression of its reflection in the lake is \u03b2, prove that the distance of the cloud from the point of observation is\u00a0 \u00a0<strong>[4]<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/i0.wp.com\/farm2.staticflickr.com\/1958\/45171933801_8389a645a6_o.png?resize=127%2C66&#038;ssl=1\" alt=\"CBSE Sample Papers for Class 10 Maths Paper 3 Q 23.\" width=\"127\" height=\"66\" data-recalc-dims=\"1\" \/><br \/>\n<strong>OR<\/strong><br \/>\nA man is standing on the deck of a ship, which is 8 m above water level. He observes the angle of elevation of the top of a hill as 60\u00b0 and the angle of depression of the base of the hill as 30\u00b0. Calculate the distance of the hill from the ship and the height of the hill.<\/p>\n<p><strong>Question 24.<\/strong><br \/>\nDraw a line segment AB of length 8 cm. Taking A as centre, draw a circle of radius 4 cm and taking B as centre, draw another circle of radius 3 cm. Construct tangents of each circle from the centre of the other circle.\u00a0\u00a0<strong>[4]<\/strong><\/p>\n<p><strong>Question 25.<\/strong><br \/>\nShow that the tangent at any point of a circle is perpendicular to the radius through the point of contact. In the given figure, AT is a tangent to the circle with centre O such that OT = 4 cm and \u2220OTA = 30\u00b0. Find the length of AT.\u00a0<strong>[4]<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/i2.wp.com\/farm2.staticflickr.com\/1937\/44260882155_1b89e0609a_o.png?resize=217%2C157&#038;ssl=1\" alt=\"CBSE Sample Papers for Class 10 Maths Paper 3 Q 25.\" width=\"217\" height=\"157\" data-recalc-dims=\"1\" \/><\/p>\n<p><strong>Question 26.<\/strong><br \/>\nA solid right circular cone of height 120 cm and radius 60 cm is placed in a right circular cylinder full of water of height 180 cm such that it touches the bottom. Find the volume of water left in the cylinder, if the radius of the cylinder is equal to the radius of the cone.\u00a0\u00a0<strong>[4]<\/strong><br \/>\n<strong>OR<\/strong><br \/>\nA well of diameter 3 m is dug 14 m deep. The earth taken out of it has been spread evenly all around it in the shape of a circular ring of width 4 m to form an embankment. Find the height of the embankment.<\/p>\n<p><strong>Question 27.<\/strong><br \/>\nA boat can go 24 km downstream and return in 5 hours. If the speed of the stream is 2 km\/hr, find the speed of the boat in still water.\u00a0\u00a0<strong>[4]<\/strong><br \/>\n<strong>OR<\/strong><br \/>\nProduct of digits of a two-digit number is 14. When 45 is added to the number then the digits interchanged their places. Find the number.<\/p>\n<p><strong>Question 28.<\/strong><br \/>\nShalini gets pocket money from her father every day. Out of the pocket money, she saves \u20b930 on the first day and on each succeeding day, she increases her savings by 500 paise.\u00a0\u00a0<strong>[4]<\/strong><\/p>\n<ol>\n<li>Find the amount saved by Shalini on 10th day.<\/li>\n<li>Find the total amount saved by Shalini in 30 days.<\/li>\n<\/ol>\n<p><strong>Question 29.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/i1.wp.com\/farm2.staticflickr.com\/1913\/45171933241_b1bc37653b_o.png?resize=463%2C62&#038;ssl=1\" alt=\"CBSE Sample Papers for Class 10 Maths Paper 3 Q 29.\" width=\"463\" height=\"62\" data-recalc-dims=\"1\" \/><\/p>\n<p><strong>Question 30.<\/strong><br \/>\nDraw &#8220;more than ogive&#8221; for the following data :\u00a0\u00a0<strong>[4]<\/strong><\/p>\n<table border=\"2\">\n<tbody>\n<tr>\n<td style=\"text-align: center;\" width=\"94\"><strong>Classes<\/strong><\/td>\n<td style=\"text-align: center;\" width=\"93\"><strong>Frequency<\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" width=\"94\">1-10<\/td>\n<td style=\"text-align: center;\" width=\"93\">2<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" width=\"94\">11-20<\/td>\n<td style=\"text-align: center;\" width=\"93\">12<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" width=\"94\">21-30<\/td>\n<td style=\"text-align: center;\" width=\"93\">38<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" width=\"94\">31-40<\/td>\n<td style=\"text-align: center;\" width=\"93\">24<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\" width=\"94\">41-50<\/td>\n<td style=\"text-align: center;\" width=\"93\">10<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: center;\"><span style=\"color: #0000ff;\"><strong>SOLUTIONS<\/strong><\/span><br \/>\n<strong>SECTION-A<\/strong><\/p>\n<p><strong>Answer 1.<\/strong><br \/>\nGiven vertices of triangle are A(- 4, 0), B(4, 0) and C(0, 3).<br \/>\nWe know that distance formula is,<br \/>\n<img loading=\"lazy\" src=\"https:\/\/i1.wp.com\/farm2.staticflickr.com\/1950\/45123200022_990b517094_o.png?resize=846%2C449&#038;ssl=1\" alt=\"CBSE Sample Papers for Class 10 Maths Paper 3 Ans 1.1.\" width=\"846\" height=\"449\" data-recalc-dims=\"1\" \/><br \/>\n<img loading=\"lazy\" src=\"https:\/\/i0.wp.com\/farm2.staticflickr.com\/1980\/44260983595_202e99c087_o.png?resize=569%2C257&#038;ssl=1\" alt=\"CBSE Sample Papers for Class 10 Maths Paper 3 Ans 1.2.\" width=\"569\" height=\"257\" data-recalc-dims=\"1\" \/><\/p>\n<p><strong>Answer 2.<\/strong><br \/>\nWe have, p = ab<sup>2<\/sup> and q = a<sup>2<\/sup>b<br \/>\nNow, p = a \u00d7 b \u00d7 b<br \/>\nand q = a \u00d7 a \u00d7 b<br \/>\n\u2234 H.C.F. (p,q) = ab<br \/>\nWe know,<br \/>\nProduct of two numbers = H.C.F \u00d7 L.C.M<br \/>\n<img loading=\"lazy\" src=\"https:\/\/i0.wp.com\/farm2.staticflickr.com\/1958\/44260983445_d4522dce9f_o.png?resize=591%2C177&#038;ssl=1\" alt=\"CBSE Sample Papers for Class 10 Maths Paper 3 Ans 2.\" width=\"591\" height=\"177\" data-recalc-dims=\"1\" \/><\/p>\n<p><strong>Answer 3.<\/strong><br \/>\nGiven : AD = 2 cm, BD = 4 cm, BC = 9 cm<br \/>\nand DE || BC<br \/>\nIn \u0394ABC and \u0394ADE,<br \/>\nDE || BC<br \/>\n\u2234 \u2220B = \u2220D [Corresponding angles]<br \/>\nand \u2220C = \u2220E [Corresponding angles]<br \/>\n\u2234 By AA similarly axiom<br \/>\n<img loading=\"lazy\" src=\"https:\/\/i1.wp.com\/farm2.staticflickr.com\/1919\/45123199352_d7d8168dec_o.png?resize=841%2C424&#038;ssl=1\" alt=\"CBSE Sample Papers for Class 10 Maths Paper 3 Ans 3.\" width=\"841\" height=\"424\" data-recalc-dims=\"1\" \/><\/p>\n<p><strong>Answer 4.<\/strong><br \/>\nGiven : Sum of zeroes = 3 and Product of zeroes = &#8211; 2<br \/>\nWe know that, equation of quadratic polyomial is given as<br \/>\n= k[x<sup>2<\/sup> &#8211; (Sum of zeroes)x + Product of zeroes]<br \/>\n= k[x<sup>2<\/sup> &#8211; 3x &#8211; 2] where k \u2260 0.<\/p>\n<p><strong>Answer 5.<\/strong><br \/>\nGiven : 2p + 1, 12, 5p &#8211; 3 are three consecutive terms of A.P.<br \/>\n12 &#8211; (2p + 1) = (5p &#8211; 3) &#8211; 12<br \/>\n12 &#8211; 2p &#8211; 1 = 5p &#8211; 3 &#8211; 12<br \/>\n11 &#8211; 2p = 5 p &#8211; 15<br \/>\n-2p &#8211; 5p = -15 &#8211; 11<br \/>\n&#8211; 7p = &#8211; 26<br \/>\np = \\(\\frac { 26 }{ 7 } \\).<\/p>\n<p><strong>Answer 6.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/i1.wp.com\/farm2.staticflickr.com\/1980\/44260983245_7ddaf06ce4_o.png?resize=843%2C457&#038;ssl=1\" alt=\"CBSE Sample Papers for Class 10 Maths Paper 3 Ans 6.1.\" width=\"843\" height=\"457\" data-recalc-dims=\"1\" \/><br \/>\n<img loading=\"lazy\" src=\"https:\/\/i0.wp.com\/farm2.staticflickr.com\/1903\/44449776984_b21a55d924_o.png?resize=277%2C276&#038;ssl=1\" alt=\"CBSE Sample Papers for Class 10 Maths Paper 3 Ans 6.2.\" width=\"277\" height=\"276\" data-recalc-dims=\"1\" \/><\/p>\n<p style=\"text-align: center;\"><strong>SECTION-B<\/strong><\/p>\n<p><strong>Answer 7.<\/strong><br \/>\nGiven : Decimal expansion of rational number \\frac { 33 }{ { 2 }^{ 2 }.{ 5 }^{ n } } terminate after 3 decimals.<br \/>\n\u2234 Denominator of decimal number will be in the form = (2 x 5)n and n = 3 to terminate after 3 decimals.<\/p>\n<p><strong>Answer 8.<\/strong><br \/>\nGiven : A(- 3, &#8211; 14), B(a, &#8211; 5) and AB = 9 units<br \/>\nBy distance formula,<br \/>\n<img loading=\"lazy\" src=\"https:\/\/i1.wp.com\/farm2.staticflickr.com\/1921\/45173289821_ba5d18bb1d_o.png?resize=278%2C106&#038;ssl=1\" alt=\"CBSE Sample Papers for Class 10 Maths Paper 3 Ans 8.\" width=\"278\" height=\"106\" data-recalc-dims=\"1\" \/><br \/>\nOn squaring both sides, we get<br \/>\n81 = (a + 3)<sup>2<\/sup> + (9)<sup>2<\/sup><br \/>\n81 &#8211; 81 = (a + 3)<sup>2<\/sup><br \/>\n\u21d2 (a + 3)<sup>2<\/sup> = 0<br \/>\nOn taking square root both side, we get<br \/>\na + 3 = 0<br \/>\na = &#8211; 3.<\/p>\n<p><strong>Answer 9.<\/strong><br \/>\nTotal number of cards = 1, 2, 3, &#8230;, 17.<br \/>\nn(S) = 17<br \/>\n<strong>(i)<\/strong> Probability that the number is odd.<br \/>\nNumber of odd number cards = 1, 3, 5, 7, 9, 11, 13, 15, 17.<br \/>\n\u2234 n(E) = 9<br \/>\nProbability that number on the card is odd,<br \/>\nP(E) = \\(\\frac { n(E) }{ n(S) } \\)<br \/>\nP(E) = \\(\\frac { 9 }{ 17 } \\).<\/p>\n<p><strong>(ii)<\/strong> Probability that the number is a prime.<br \/>\nNumber of prime number cards = 2, 3, 5, 7, 11, 13, 17<br \/>\n\u2234 n(E) =7<br \/>\nProbability that a card is prime number,<br \/>\nn(E) = \\(\\frac { n(E) }{ n(S) } \\) = \\(\\frac { 7 }{ 17 } \\)<\/p>\n<p><strong>(iii)<\/strong> Probability that the number is divisible by 3.<br \/>\nNumber of cards divisible by 3 = 3, 6, 9, 12, 15<br \/>\n\u2234 n(E) = 5<br \/>\nProbability that the number is divisible by 3,<br \/>\nP(E) = \\(\\frac { n(E) }{ n(S) } \\) = \\(\\frac { 5 }{ 17 } \\)<\/p>\n<p><strong>(iv)<\/strong> Probability the number is divisible by 3 and 2 both.<br \/>\nNumber of cards are divisible by 3 and 2 both = Number of cards are divisible by 6 = 6,12<br \/>\n\u2234 n(E) = 2<br \/>\nProbability that the number is divisible by 3 and 2 both,<br \/>\nP(E) = \\(\\frac { n(E) }{ n(S) } \\) = \\(\\frac { 2 }{ 17 } \\)<\/p>\n<p><strong>Answer 10.<\/strong><br \/>\n1 year has 365 days = (52 x 7 + 1) days<br \/>\nOrdinary year has 52 Sunday + 1 day<br \/>\n1 day may be {Sun, Mon, Tue, Wed, Thu, Fri, Sat}<br \/>\nn(S) = 7<br \/>\nThat 1 day may be Sun = {Sun}<br \/>\n\u2234 n(E) = 1<br \/>\nProbability of 53 Sundays in ordinary year<br \/>\nP(E) = \\(\\frac { n(E) }{ n(S) } =\\frac { 1 }{ 7 } \\)<\/p>\n<p><strong>Answer 11.<\/strong><br \/>\nSum of first 100 odd natural numbers i.e.,<br \/>\n1 + 3 + 5 + 7 + 9+ &#8230;<br \/>\nThese are in arithmetic progression, with<br \/>\na = 1, d = 3 &#8211; 1 = 2, n = 100<br \/>\nWe know that<br \/>\n<img loading=\"lazy\" src=\"https:\/\/i2.wp.com\/farm2.staticflickr.com\/1944\/30234886017_09c67eb842_o.png?resize=606%2C190&#038;ssl=1\" alt=\"CBSE Sample Papers for Class 10 Maths Paper 3 Ans 11.\" width=\"606\" height=\"190\" data-recalc-dims=\"1\" \/><\/p>\n<p><strong>Answer 12.<\/strong><br \/>\nGiven polynomial is,<br \/>\n2x<sup>2<\/sup> + x &#8211; 6 = 0<br \/>\n2x<sup>2<\/sup> + 3x &#8211; 3x &#8211; 6 = 0<br \/>\n2x(x + 2) &#8211; 3(x + 2) = 0<br \/>\n(x + 2) (2x &#8211; 3) = 0<br \/>\nEither x + 2 = 0 \u21d2 x = -2 or 2x &#8211; 3 = 0 \u21d2 x = \\(\\frac { 3 }{ 2 }\\)<br \/>\n\u2234 Zeroes of the polynomial are &#8211; 2 and \\(\\frac { 3 }{ 2 }\\)<\/p>\n<p style=\"text-align: center;\"><strong>SECTION-C<\/strong><\/p>\n<p><strong>Answer 13.<\/strong><br \/>\nGiven : 1251, 9377 and 15628 leave remainders 1, 2 and 3 respectively.<br \/>\nRequired number = H.C.F. of (1251 &#8211; 1), (9377 &#8211; 2) and (15628 &#8211; 3)<br \/>\n= H.C.F. of 1250, 9375 and 15625<br \/>\nBy Euclid&#8217;s lemma,<br \/>\n15625 = 1 x 9375 + 6250<br \/>\n9375 = 1 x 6250 + 3125<br \/>\n6250 = 2 x 3125 + 0<br \/>\n\u2234 H.C.F. of 15625 and 9375 = 3125.<br \/>\nand H.C.F. of 3125 and 1250 = 625.<br \/>\nAgain by Euclid&#8217;s lemma<br \/>\n3125 = 2 x 1250 + 625<br \/>\n1250 = 2 x 625 + 0<br \/>\n\u2234 H.C.F. of 1250, 9375 and 15625 = 625<br \/>\nHence, 625 is largest number that divides 1251, 9377 and 15628 leaving remainders 1, 2 and 3 respectively.<\/p>\n<p><strong>Answer 14.<\/strong><br \/>\nGiven : Vertices of triangle are A(2, 9), B(a, 5) and C(5, 5).<br \/>\nBy distance formula,<br \/>\n<img loading=\"lazy\" src=\"https:\/\/i0.wp.com\/farm2.staticflickr.com\/1960\/45124509252_4e06e85ce9_o.png?resize=791%2C464&#038;ssl=1\" alt=\"CBSE Sample Papers for Class 10 Maths Paper 3 Ans 14.1.\" width=\"791\" height=\"464\" data-recalc-dims=\"1\" \/><br \/>\n<img loading=\"lazy\" src=\"https:\/\/i2.wp.com\/farm2.staticflickr.com\/1940\/30234885847_9c4ca80e2f_o.png?resize=772%2C274&#038;ssl=1\" alt=\"CBSE Sample Papers for Class 10 Maths Paper 3 Ans 14.2.\" width=\"772\" height=\"274\" data-recalc-dims=\"1\" \/><br \/>\n<img loading=\"lazy\" src=\"https:\/\/i2.wp.com\/farm2.staticflickr.com\/1939\/45124509082_d52eea4bdc_o.png?resize=657%2C403&#038;ssl=1\" alt=\"CBSE Sample Papers for Class 10 Maths Paper 3 Ans 14.3.\" width=\"657\" height=\"403\" data-recalc-dims=\"1\" \/><br \/>\n<img loading=\"lazy\" src=\"https:\/\/i1.wp.com\/farm2.staticflickr.com\/1926\/43359150270_e4c7c8fe7f_o.png?resize=758%2C435&#038;ssl=1\" alt=\"CBSE Sample Papers for Class 10 Maths Paper 3 Ans 14.4.\" width=\"758\" height=\"435\" data-recalc-dims=\"1\" \/><br \/>\n<img loading=\"lazy\" src=\"https:\/\/i2.wp.com\/farm2.staticflickr.com\/1931\/43359149870_e1c1790f03_o.png?resize=700%2C349&#038;ssl=1\" alt=\"CBSE Sample Papers for Class 10 Maths Paper 3 Ans 14.5.\" width=\"700\" height=\"349\" data-recalc-dims=\"1\" \/><br \/>\n<img loading=\"lazy\" src=\"https:\/\/i0.wp.com\/farm2.staticflickr.com\/1957\/45124508552_da8e21a6fe_o.png?resize=644%2C239&#038;ssl=1\" alt=\"CBSE Sample Papers for Class 10 Maths Paper 3 Ans 14.6.\" width=\"644\" height=\"239\" data-recalc-dims=\"1\" \/><\/p>\n<p><strong>Answer 15.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/i0.wp.com\/farm2.staticflickr.com\/1978\/44262266025_8bfdd39e25_o.png?resize=765%2C447&#038;ssl=1\" alt=\"CBSE Sample Papers for Class 10 Maths Paper 3 Ans 15.1.\" width=\"765\" height=\"447\" data-recalc-dims=\"1\" \/><br \/>\n<img loading=\"lazy\" src=\"https:\/\/i0.wp.com\/farm2.staticflickr.com\/1971\/45124508392_41d307bf11_o.png?resize=774%2C486&#038;ssl=1\" alt=\"CBSE Sample Papers for Class 10 Maths Paper 3 Ans 15.2.\" width=\"774\" height=\"486\" data-recalc-dims=\"1\" \/><br \/>\n<img loading=\"lazy\" src=\"https:\/\/i0.wp.com\/farm2.staticflickr.com\/1941\/44262265715_c40102517b_o.png?resize=777%2C444&#038;ssl=1\" alt=\"CBSE Sample Papers for Class 10 Maths Paper 3 Ans 15.3.\" width=\"777\" height=\"444\" data-recalc-dims=\"1\" \/><\/p>\n<p><strong>Answer 16.<\/strong><br \/>\nGiven : PA and PB are tangents to a circle having centre O.<br \/>\nTo prove : \u2220AOB + \u2220APB = 180\u00b0.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/i0.wp.com\/farm2.staticflickr.com\/1967\/30235054867_39003ae04a_o.png?resize=214%2C120&#038;ssl=1\" alt=\"CBSE Sample Papers for Class 10 Maths Paper 3 Ans 16\" width=\"214\" height=\"120\" data-recalc-dims=\"1\" \/><br \/>\nProof : OA is the radius of circle and PA is the tangent to the circle.<br \/>\n\u2234 \u2220OAP = 90\u00b0 &#8230;(i)<br \/>\nSimilarly, OB is the radius of circle and PB is the tangent to the circle.<br \/>\n\u2234 \u2220OBP = 90\u00b0<br \/>\nIn quadrilateral APBO,<br \/>\n\u2220OAP + \u2220APB + \u2220PBO + \u2220BOA = 360\u00b0<br \/>\n90\u00b0 + \u2220APB + 90\u00b0 + \u2220BOA = 360\u00b0<br \/>\n\u2220APB + \u2220BOA = 360\u00b0 &#8211; 180\u00b0<br \/>\n\u2220APB + \u2220BOA = 180\u00b0.<\/p>\n<p><strong>Answer 17.<\/strong><br \/>\nWe have, radius of cardboard, r = 3 cm.<br \/>\nTwo sectors AOB and COD have been cut off in the circular cardboard.<br \/>\n\u2234 Perimeter of remaining cardboard = OA + length of arc APD + OD + OB + Length of arc BQC + OC<br \/>\n= r + Length of arc APD + r + r + Length of arc BQC + r<br \/>\n= 4 x r + length of arc APD + length of arc BQC<br \/>\n<img loading=\"lazy\" src=\"https:\/\/i1.wp.com\/farm2.staticflickr.com\/1932\/43359149190_74e8693066_o.png?resize=468%2C260&#038;ssl=1\" alt=\"CBSE Sample Papers for Class 10 Maths Paper 3 Ans 17.1\" width=\"468\" height=\"260\" data-recalc-dims=\"1\" \/>|<br \/>\n<strong>OR<br \/>\n<\/strong>Given : Radius of circle, r =12 cm<br \/>\nCentral angle of segment = 60\u00b0<br \/>\nArea of segment = Area of sector OACD &#8211; Area of \u2206AOB<br \/>\n<img loading=\"lazy\" src=\"https:\/\/i1.wp.com\/farm2.staticflickr.com\/1906\/45124508072_37dee41868_o.png?resize=177%2C183&#038;ssl=1\" alt=\"CBSE Sample Papers for Class 10 Maths Paper 3 Ans 17.2\" width=\"177\" height=\"183\" data-recalc-dims=\"1\" \/><br \/>\n<img loading=\"lazy\" src=\"https:\/\/i1.wp.com\/farm2.staticflickr.com\/1939\/44262265295_55c12d99d1_o.png?resize=377%2C289&#038;ssl=1\" alt=\"CBSE Sample Papers for Class 10 Maths Paper 3 Ans 17.3\" width=\"377\" height=\"289\" data-recalc-dims=\"1\" \/><\/p>\n<p><strong>Answer 18.<\/strong><br \/>\nGiven : Diameter of cylindrical pipe = 14 cm<br \/>\n<img loading=\"lazy\" src=\"https:\/\/i2.wp.com\/farm2.staticflickr.com\/1935\/44262264945_712f8e1371_o.png?resize=710%2C321&#038;ssl=1\" alt=\"CBSE Sample Papers for Class 10 Maths Paper 3 Ans 18.1\" width=\"710\" height=\"321\" data-recalc-dims=\"1\" \/><br \/>\n<img loading=\"lazy\" src=\"https:\/\/i1.wp.com\/farm2.staticflickr.com\/1906\/43359148520_050d56fdb7_o.png?resize=687%2C414&#038;ssl=1\" alt=\"CBSE Sample Papers for Class 10 Maths Paper 3 Ans 18.2\" width=\"687\" height=\"414\" data-recalc-dims=\"1\" \/><br \/>\n<strong>OR<\/strong><br \/>\nGiven : Diameter of lead ball = 4.2 cm<br \/>\n\u2234 Radius, r = \\(\\frac { 4.2 }{ 2 }\\) = 2.1 cm<br \/>\nDimensions of lead piece = 66 cm \u00d7 42 cm \u00d7 21 cm<br \/>\nVolume of rectangular lead piece = l \u00d7 b \u00d7 h = 66 \u00d7 42 \u00d7 21 cm<sup>3<\/sup><br \/>\n<img loading=\"lazy\" src=\"https:\/\/i0.wp.com\/farm2.staticflickr.com\/1979\/44262264725_f41d91bfd3_o.png?resize=642%2C309&#038;ssl=1\" alt=\"CBSE Sample Papers for Class 10 Maths Paper 3 Ans 18.3\" width=\"642\" height=\"309\" data-recalc-dims=\"1\" \/><\/p>\n<p><strong>Answer 19.<\/strong><br \/>\nGiven polynomial is<br \/>\n4x<sup>2<\/sup> &#8211; x &#8211; 3 = 0<br \/>\n\u21d2 4x<sup>2<\/sup> &#8211; 4x + 3x &#8211; 3 =0<br \/>\n\u21d2 4x(x &#8211; 1) + 3(x &#8211; 1) =0<br \/>\n\u21d2 (x &#8211; 1) (4x + 3) = 0<br \/>\nEither x &#8211; 1 = 0 \u21d2 x = 1 or x + 3 = 0\u00a0\u21d2 x = &#8211; \\(\\frac { 1 }{ 4 }\\)<br \/>\n\u2234 Zeroes of the polynomial are 1 and &#8211; \\(\\frac { 3 }{ 4 }\\)<br \/>\nNow,<br \/>\n<img loading=\"lazy\" src=\"https:\/\/i1.wp.com\/farm2.staticflickr.com\/1928\/43359148130_bb19093624_o.png?resize=602%2C147&#038;ssl=1\" alt=\"CBSE Sample Papers for Class 10 Maths Paper 3 Ans 19\" width=\"602\" height=\"147\" data-recalc-dims=\"1\" \/><\/p>\n<p><strong>Answer 20.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/i0.wp.com\/farm2.staticflickr.com\/1926\/44262264485_a255119dfb_o.png?resize=774%2C286&#038;ssl=1\" alt=\"CBSE Sample Papers for Class 10 Maths Paper 3 Ans 20.1\" width=\"774\" height=\"286\" data-recalc-dims=\"1\" \/><br \/>\n<img loading=\"lazy\" src=\"https:\/\/i2.wp.com\/farm2.staticflickr.com\/1967\/44262264205_4c38204a69_o.png?resize=664%2C478&#038;ssl=1\" alt=\"CBSE Sample Papers for Class 10 Maths Paper 3 Ans 20.2\" width=\"664\" height=\"478\" data-recalc-dims=\"1\" \/><br \/>\n<img loading=\"lazy\" src=\"https:\/\/i2.wp.com\/farm2.staticflickr.com\/1940\/31299846208_ba7a8587ff_o.png?resize=533%2C526&#038;ssl=1\" alt=\"CBSE Sample Papers for Class 10 Maths Paper 3 Ans 20.3\" width=\"533\" height=\"526\" data-recalc-dims=\"1\" \/><br \/>\nThe point of intersection of these lines is (- 1.5, 2.5).<br \/>\n\u2234 x = -1.5 and y = 2.5<br \/>\n<strong>OR<\/strong><br \/>\nLet the ten&#8217;s place of digit be x.<br \/>\nTherefore, unit place of digit will be (x + 2)<br \/>\nTwo-digit number = 10 \u00d7 x + (x + 2) = 11x + 2<br \/>\nReverse of the number = 10(x + 2) + x = 11x + 20<br \/>\nAccording to the question,<br \/>\n11x + 2 + 11x + 20 = 88<br \/>\n22x = 88 &#8211; 22<br \/>\nx = \\(\\frac { 66 }{ 22 }\\) = 3<br \/>\n\u2234 Two-digit number = 11x + 2 = 11 \u00d7 3 + 2 = 35.<\/p>\n<p><strong>Answer 21.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/i1.wp.com\/farm2.staticflickr.com\/1905\/44262263595_58cc35d3f4_o.png?resize=477%2C486&#038;ssl=1\" alt=\"CBSE Sample Papers for Class 10 Maths Paper 3 Ans 21.1\" width=\"477\" height=\"486\" data-recalc-dims=\"1\" \/><br \/>\n<img loading=\"lazy\" src=\"https:\/\/i2.wp.com\/farm2.staticflickr.com\/1909\/31299845638_3052d981b5_o.png?resize=585%2C387&#038;ssl=1\" alt=\"CBSE Sample Papers for Class 10 Maths Paper 3 Ans 21.2\" width=\"585\" height=\"387\" data-recalc-dims=\"1\" \/><\/p>\n<p><strong>Answer 22.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/i1.wp.com\/farm2.staticflickr.com\/1942\/44262263345_af737093be_o.png?resize=534%2C315&#038;ssl=1\" alt=\"CBSE Sample Papers for Class 10 Maths Paper 3 Ans 22\" width=\"534\" height=\"315\" data-recalc-dims=\"1\" \/><\/p>\n<p style=\"text-align: center;\"><strong>SECTION-D<\/strong><\/p>\n<p><strong>Answer 23.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/i0.wp.com\/farm2.staticflickr.com\/1912\/44264161425_bac2cd17d8_o.png?resize=764%2C468&#038;ssl=1\" alt=\"CBSE Sample Papers for Class 10 Maths Paper 3 Ans 23.1\" width=\"764\" height=\"468\" data-recalc-dims=\"1\" \/><br \/>\n<img loading=\"lazy\" src=\"https:\/\/i0.wp.com\/farm2.staticflickr.com\/1912\/44264161265_0061b3c50f_o.png?resize=764%2C336&#038;ssl=1\" alt=\"CBSE Sample Papers for Class 10 Maths Paper 3 Ans 23.2\" width=\"764\" height=\"336\" data-recalc-dims=\"1\" \/><br \/>\n<img loading=\"lazy\" src=\"https:\/\/i0.wp.com\/farm2.staticflickr.com\/1938\/44264161075_7ae6bc77b3_o.png?resize=765%2C488&#038;ssl=1\" alt=\"CBSE Sample Papers for Class 10 Maths Paper 3 Ans 23.3\" width=\"765\" height=\"488\" data-recalc-dims=\"1\" \/><br \/>\n<img loading=\"lazy\" src=\"https:\/\/i1.wp.com\/farm2.staticflickr.com\/1933\/44264160855_8b7e32862b_o.png?resize=766%2C454&#038;ssl=1\" alt=\"CBSE Sample Papers for Class 10 Maths Paper 3 Ans 23.4\" width=\"766\" height=\"454\" data-recalc-dims=\"1\" \/><br \/>\nPutting the value of x in equation (i), we get<br \/>\nh = 8 + \u221a3 . 8\u221a3<br \/>\nh = 8 + 24 = 32 m<br \/>\nand x = 8 \u00d7 1.732 = 13.856 m<br \/>\nThus, height of the hill = 32 m<br \/>\nand distance between hill and ship = 13.856 m.<\/p>\n<p><strong>Answer 24.<\/strong><br \/>\nSteps of construction :<\/p>\n<ul>\n<li>Draw a line segment AB = 8 cm.<\/li>\n<li>With A as centre and radius 4 cm, draw a circle.<\/li>\n<li>With B as centre and radius 3 cm, draw another circle.<\/li>\n<li>Draw perpendicular bisector of AB which meets AB at M.<\/li>\n<li>With M as centre and MA as radius, draw a circle intersecting the circle with centre A at P and Q and the circle with centre B at R and S.<\/li>\n<li>Join AR, AS, BP, BQ which are the required tangents.<\/li>\n<\/ul>\n<p><img loading=\"lazy\" src=\"https:\/\/i2.wp.com\/farm2.staticflickr.com\/1910\/44264160575_1e0527e517_o.png?resize=262%2C200&#038;ssl=1\" alt=\"CBSE Sample Papers for Class 10 Maths Paper 3 Ans 24\" width=\"262\" height=\"200\" data-recalc-dims=\"1\" \/><\/p>\n<p><strong>Answer 25.<\/strong><br \/>\nGiven : A circle C(0, r) and a tangent l at point A.<br \/>\nTo prove : OA \u22a5 l.<br \/>\nConstruction : Take a point B, other than A, on the tangent l. Join OB. Suppose OB meets the circle at C.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/i0.wp.com\/farm2.staticflickr.com\/1968\/44264160365_8347ac1882_o.png?resize=199%2C130&#038;ssl=1\" alt=\"CBSE Sample Papers for Class 10 Maths Paper 3 Ans 25.1\" width=\"199\" height=\"130\" data-recalc-dims=\"1\" \/><br \/>\nProof : We know that, among all line segment joining the point O to a point on l, the perpendicular is shortest to l.<br \/>\nClearly, OA = OC<br \/>\nNow, OB = OC + BC<br \/>\n\u2234 OB &gt; OC<br \/>\n\u21d2 OB &gt; OA<br \/>\n\u21d2 OA &lt; OB<br \/>\nThus, OA is shortest than any other line segment joining O to any point on l.<br \/>\nThus, OA \u22a5 l.<br \/>\nGiven : OT = 4 cm<br \/>\n\u2220OTA = 30\u00b0<br \/>\nConstruction : Join OA.<br \/>\nNow, OA is the radius of circle and AT is the tangent to the circle.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/i1.wp.com\/farm2.staticflickr.com\/1935\/44264160205_01bff3b106_o.png?resize=189%2C135&#038;ssl=1\" alt=\"CBSE Sample Papers for Class 10 Maths Paper 3 Ans 25.2\" width=\"189\" height=\"135\" data-recalc-dims=\"1\" \/><br \/>\n\u2234 OA \u22a5 AT<br \/>\nIn \u0394OAT, \u2220A = 90\u00b0<br \/>\n\u2234 cos T = \\(\\frac { AT }{ OT } \\)<br \/>\ncos 30\u00b0 = \\(\\frac { AT }{ 4 } \\)<br \/>\n\\(\\frac { \\sqrt { 3 } }{ 2 } \\) = \\(\\frac { AT }{ 4 } \\)<br \/>\n\u2234 AT = 2\u221a3 = 2 \u00d7 1.732 = 3.464 cm<\/p>\n<p><strong>Answer 26.<\/strong><br \/>\nGiven :<br \/>\nRadius of cylinder = Radius of cone = r = 60 cm<br \/>\nHeight of cylinder (h) =180 cm<br \/>\nand Height of cone (H) =120 cm<br \/>\n<img loading=\"lazy\" src=\"https:\/\/i1.wp.com\/farm2.staticflickr.com\/1962\/44264160035_ea1c27710d_o.png?resize=128%2C135&#038;ssl=1\" alt=\"CBSE Sample Papers for Class 10 Maths Paper 3 Ans 26.1\" width=\"128\" height=\"135\" data-recalc-dims=\"1\" \/><br \/>\nNow,<br \/>\n<img loading=\"lazy\" src=\"https:\/\/i2.wp.com\/farm2.staticflickr.com\/1940\/43361378790_8a771b2651_o.png?resize=722%2C312&#038;ssl=1\" alt=\"CBSE Sample Papers for Class 10 Maths Paper 3 Ans 26.2\" width=\"722\" height=\"312\" data-recalc-dims=\"1\" \/><br \/>\n<strong>OR<\/strong><br \/>\nGiven :<br \/>\nDiameter of well = 3 m<br \/>\n\u2234 Radius, r = \\(\\frac { 3 }{ 2 } \\)<br \/>\nDepth of well, h = 14 m<br \/>\nand Width of embankment = 4 m<br \/>\nVolume of sand dug out = \u03c0r\u00b2h<br \/>\n<img loading=\"lazy\" src=\"https:\/\/i1.wp.com\/farm2.staticflickr.com\/1909\/43361378530_e0995f2078_o.png?resize=557%2C515&#038;ssl=1\" alt=\"CBSE Sample Papers for Class 10 Maths Paper 3 Ans 26.3\" width=\"557\" height=\"515\" data-recalc-dims=\"1\" \/><\/p>\n<p><strong>Answer 27.<\/strong><br \/>\nGiven : Speed of stream = 2 Km\/h<br \/>\nLet the speed of the boat in still water = x km\/hr<br \/>\n\u2234 Speed of boat in downstream = (x + 2) km\/hr<br \/>\nand speed of boat in upstream = (x &#8211; 2) Km\/hr<br \/>\nWe know<br \/>\nTime = \\(\\frac { Distance }{ Speed } \\)<br \/>\n\u2234 Time taken to go 24 Km Up stream = \\(\\frac { 24 }{ x-2 } \\)<br \/>\nand time taken to go 24 Km downstream = \\(\\frac { 24 }{ x+2 } \\)<br \/>\nAccording to the question,<br \/>\n<img loading=\"lazy\" src=\"https:\/\/i1.wp.com\/farm2.staticflickr.com\/1905\/43361378270_0469f0ce87_o.png?resize=187%2C117&#038;ssl=1\" alt=\"CBSE Sample Papers for Class 10 Maths Paper 3 Ans 27.1\" width=\"187\" height=\"117\" data-recalc-dims=\"1\" \/><br \/>\n<img loading=\"lazy\" src=\"https:\/\/i0.wp.com\/farm2.staticflickr.com\/1925\/43361378090_319ddf9c98_o.png?resize=415%2C423&#038;ssl=1\" alt=\"CBSE Sample Papers for Class 10 Maths Paper 3 Ans 27.2\" width=\"415\" height=\"423\" data-recalc-dims=\"1\" \/><br \/>\n<img loading=\"lazy\" src=\"https:\/\/i0.wp.com\/farm2.staticflickr.com\/1918\/43361378400_17fb467cc8_o.png?resize=769%2C168&#038;ssl=1\" alt=\"CBSE Sample Papers for Class 10 Maths Paper 3 Ans 27..3\" width=\"769\" height=\"168\" data-recalc-dims=\"1\" \/><br \/>\n<strong>OR<\/strong><br \/>\nLet the unit digit be x and tens digit be y<br \/>\nNumber = 10y + x<br \/>\nand, reverse of the number = 10x + y<br \/>\nAccording to the question,<br \/>\nxy = 14<br \/>\nand, 10y + x + 45 = 10x + y<br \/>\n\u21d2 9x &#8211; 9y = 45<br \/>\n\u21d2 x-y =5<br \/>\n\u21d2 x = 5 + y<br \/>\nSubstituting the value of x in equation (i), we get<br \/>\n(5 + y)y = 14<br \/>\ny<sup>2<\/sup> + 5y &#8211; 14 = 0<br \/>\ny<sup>2<\/sup> + 7y &#8211; 2y &#8211; 14 = 0<br \/>\ny(y + 7)-2(y + 7) =0<br \/>\n(y + 7) (y-2) =0<br \/>\ny + 7 = 0 \u21d2 y = &#8211; 7 (digit is not negative)<br \/>\ny &#8211; 2 = 0 \u21d2 y = 2<br \/>\nx =5 + y = 7<br \/>\nWhen y = 2, then<br \/>\n\u2234 Required two-digit number = 10y + x = 10 \u00d7 2 + 7 = 27<\/p>\n<p><strong>Answer 28.<\/strong><br \/>\nMoney saved on 1st day = \u20b9 30<br \/>\nMoney saved on IInd day = \u20b9 30 + 500 p = \u20b9 35<br \/>\nMoney saved on IIIrd day = \u20b9 30 + 500 p + 500 p = \u20b9 35<br \/>\nand so on.<br \/>\nAmount of money saved on successive days is an AP with<br \/>\nFirst term, a = 30 and common difference, d = 5.<br \/>\n<strong>(i)<\/strong> Money saved on 10th day,<br \/>\nWe know that<br \/>\n\u2234 a<sub>n<\/sub> = a + (n &#8211; 1 )d<br \/>\na<sub>10<\/sub> = a + 9d = 30 + 9 x 5 = \u20b9 75<br \/>\n<strong>(ii)<\/strong> Money saved in 30 days<br \/>\n<img loading=\"lazy\" src=\"https:\/\/i2.wp.com\/farm2.staticflickr.com\/1922\/43361377910_14033c2881_o.png?resize=510%2C91&#038;ssl=1\" alt=\"CBSE Sample Papers for Class 10 Maths Paper 3 Ans 28\" width=\"510\" height=\"91\" data-recalc-dims=\"1\" \/><\/p>\n<p><strong>Answer 29.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/i2.wp.com\/farm2.staticflickr.com\/1937\/43361377790_073e15ab9e_o.png?resize=539%2C447&#038;ssl=1\" alt=\"CBSE Sample Papers for Class 10 Maths Paper 3 Ans 29.1\" width=\"539\" height=\"447\" data-recalc-dims=\"1\" \/><br \/>\n<img loading=\"lazy\" src=\"https:\/\/i1.wp.com\/farm2.staticflickr.com\/1915\/43361377600_57a769f90b_o.png?resize=499%2C341&#038;ssl=1\" alt=\"CBSE Sample Papers for Class 10 Maths Paper 3 Ans 29.2\" width=\"499\" height=\"341\" data-recalc-dims=\"1\" \/><\/p>\n<p><strong>Answer 30.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/i1.wp.com\/farm2.staticflickr.com\/1920\/43361377500_4904398f8a_o.png?resize=512%2C168&#038;ssl=1\" alt=\"CBSE Sample Papers for Class 10 Maths Paper 3 Ans 30.1\" width=\"512\" height=\"168\" data-recalc-dims=\"1\" \/><br \/>\n<img loading=\"lazy\" src=\"https:\/\/i1.wp.com\/farm2.staticflickr.com\/1927\/43361377350_243cff8b74_o.png?resize=598%2C446&#038;ssl=1\" alt=\"CBSE Sample Papers for Class 10 Maths Paper 3 Ans 30.2\" width=\"598\" height=\"446\" data-recalc-dims=\"1\" \/><\/p>\n<p>We hope the CBSE Sample Papers for Class 10 Maths Paper 3 help you. If you have any query regarding CBSE Sample Papers for Class 10 Maths Paper 3, drop a comment below and we will get back to you at the earliest.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>CBSE Sample Papers for Class 10 Maths Paper 3 These Sample papers are part of CBSE Sample Papers for Class 10 Maths. Here we have given CBSE Sample Papers for Class 10 Maths Paper 3 Time Allowed : 3 hours Maximum Marks : 80 General Instructions All questions are compulsory. The question paper consists of &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/ncertsolutions.guru\/cbse-sample-papers-for-class-10-maths-paper-3\/\"> <span class=\"screen-reader-text\">CBSE Sample Papers for Class 10 Maths Paper 3<\/span> Read More &raquo;<\/a><\/p>\n","protected":false},"author":5,"featured_media":7754,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[2],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v16.7 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>CBSE Sample Papers for Class 10 Maths Paper 3 - NCERT Solutions<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/ncertsolutions.guru\/cbse-sample-papers-for-class-10-maths-paper-3\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"CBSE Sample Papers for Class 10 Maths Paper 3 - NCERT Solutions\" \/>\n<meta property=\"og:description\" content=\"CBSE Sample Papers for Class 10 Maths Paper 3 These Sample papers are part of CBSE Sample Papers for Class 10 Maths. 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NCERT Solutions","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/ncertsolutions.guru\/cbse-sample-papers-for-class-10-maths-paper-3\/","og_locale":"en_US","og_type":"article","og_title":"CBSE Sample Papers for Class 10 Maths Paper 3 - NCERT Solutions","og_description":"CBSE Sample Papers for Class 10 Maths Paper 3 These Sample papers are part of CBSE Sample Papers for Class 10 Maths. Here we have given CBSE Sample Papers for Class 10 Maths Paper 3 Time Allowed : 3 hours Maximum Marks : 80 General Instructions All questions are compulsory. The question paper consists of &hellip; CBSE Sample Papers for Class 10 Maths Paper 3 Read More &raquo;","og_url":"https:\/\/ncertsolutions.guru\/cbse-sample-papers-for-class-10-maths-paper-3\/","og_site_name":"NCERT Solutions","article_publisher":"https:\/\/www.facebook.com\/NCERTSolutionsGuru\/","article_published_time":"2020-07-14T05:11:13+00:00","article_modified_time":"2020-07-15T09:15:59+00:00","og_image":[{"width":1280,"height":720,"url":"https:\/\/ncertsolutions.guru\/wp-content\/uploads\/2018\/10\/CBSE-Sample-Papers-for-Class-10-Maths-Paper-3.png","path":"\/home\/412375.cloudwaysapps.com\/bmvvpkvjjm\/public_html\/wp-content\/uploads\/2018\/10\/CBSE-Sample-Papers-for-Class-10-Maths-Paper-3.png","size":"full","id":7754,"alt":"CBSE Sample Papers for Class 10 Maths Paper 3","pixels":921600,"type":"image\/png"}],"twitter_card":"summary_large_image","twitter_creator":"@ncertsolguru","twitter_site":"@ncertsolguru","twitter_misc":{"Written by":"Raju","Est. reading time":"13 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Organization","@id":"https:\/\/ncertsolutions.guru\/#organization","name":"NCERT Solutions","url":"https:\/\/ncertsolutions.guru\/","sameAs":["https:\/\/www.facebook.com\/NCERTSolutionsGuru\/","https:\/\/www.instagram.com\/ncertsolutionsguru\/","https:\/\/www.linkedin.com\/in\/ncertsolutionsguru\/","https:\/\/in.pinterest.com\/ncertsolutionsguru\/","https:\/\/en.wikipedia.org\/wiki\/National_Council_of_Educational_Research_and_Training","https:\/\/twitter.com\/ncertsolguru"],"logo":{"@type":"ImageObject","@id":"https:\/\/ncertsolutions.guru\/#logo","inLanguage":"en-US","url":"https:\/\/i1.wp.com\/ncertsolutions.guru\/wp-content\/uploads\/2020\/05\/NCERT-Solutions.png?fit=460%2C45&ssl=1","contentUrl":"https:\/\/i1.wp.com\/ncertsolutions.guru\/wp-content\/uploads\/2020\/05\/NCERT-Solutions.png?fit=460%2C45&ssl=1","width":460,"height":45,"caption":"NCERT Solutions"},"image":{"@id":"https:\/\/ncertsolutions.guru\/#logo"}},{"@type":"WebSite","@id":"https:\/\/ncertsolutions.guru\/#website","url":"https:\/\/ncertsolutions.guru\/","name":"NCERT Solutions","description":"NCERT Solutions for Class 1 to 12","publisher":{"@id":"https:\/\/ncertsolutions.guru\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/ncertsolutions.guru\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"ImageObject","@id":"https:\/\/ncertsolutions.guru\/cbse-sample-papers-for-class-10-maths-paper-3\/#primaryimage","inLanguage":"en-US","url":"https:\/\/i2.wp.com\/ncertsolutions.guru\/wp-content\/uploads\/2018\/10\/CBSE-Sample-Papers-for-Class-10-Maths-Paper-3.png?fit=1280%2C720&ssl=1","contentUrl":"https:\/\/i2.wp.com\/ncertsolutions.guru\/wp-content\/uploads\/2018\/10\/CBSE-Sample-Papers-for-Class-10-Maths-Paper-3.png?fit=1280%2C720&ssl=1","width":1280,"height":720,"caption":"CBSE Sample Papers for Class 10 Maths Paper 3"},{"@type":"WebPage","@id":"https:\/\/ncertsolutions.guru\/cbse-sample-papers-for-class-10-maths-paper-3\/#webpage","url":"https:\/\/ncertsolutions.guru\/cbse-sample-papers-for-class-10-maths-paper-3\/","name":"CBSE Sample Papers for Class 10 Maths Paper 3 - 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