{"id":20387,"date":"2022-01-17T18:07:43","date_gmt":"2022-01-17T12:37:43","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/?p=20387"},"modified":"2022-02-08T17:52:44","modified_gmt":"2022-02-08T12:22:44","slug":"cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2012","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/study-materials\/previous-year-question-papers\/class-10-maths\/sa2-delhi-2012\/","title":{"rendered":"CBSE Previous Year Question Papers Class 10 Maths SA2 Delhi \u2013 2012"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_37 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" style=\"display: none;\"><label for=\"item\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/label><input type=\"checkbox\" id=\"item\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' style='display:block'><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/previous-year-question-papers\/class-10-maths\/sa2-delhi-2012\/#SET_I\" title=\"SET I\">SET I<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/previous-year-question-papers\/class-10-maths\/sa2-delhi-2012\/#SET_II\" title=\"SET II\">SET II<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/previous-year-question-papers\/class-10-maths\/sa2-delhi-2012\/#SET_III\" title=\"SET III\">SET III<\/a><\/li><\/ul><\/nav><\/div>\n<p><strong>Time allowed: 3 hours                                                                                           Maximum marks: 90<\/strong><\/p>\n<p><span style=\"color: #0000ff\"><strong>GENERAL INSTRUCTIONS:<\/strong><\/span><\/p>\n<ol>\n<li><strong>All questions are compulsory.<\/strong><\/li>\n<li><strong>The Question Taper consists of 31 questions divided into four Sections A, B. C. and D.<\/strong><\/li>\n<li><strong>Section A contains 4 questions of 1 mark each. Section B contains 6 questions of 2 marks each, Section C contains 10 questions of 3 marks each and Section D contains 11 questions of 4 marks each.<\/strong><\/li>\n<li><strong> Use of calculators is not permitted.<\/strong><\/li>\n<\/ol>\n<h3 style=\"text-align: center\"><span class=\"ez-toc-section\" id=\"SET_I\"><\/span><span style=\"color: #0000ff\"><strong>SET I<\/strong><\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><span style=\"color: #0000ff\"><strong>SECTION A<\/strong><\/span><br \/>\n<strong> Questions number 1 to 4 carry 1 mark each.<\/strong><br \/>\n<strong> Question.1 If 1 is a root of the equations ay<sup>2<\/sup> + ay + 3 = 0 and y<sup>2<\/sup> + y + b = 0, then find the value of ab.<\/strong><br \/>\n<strong> Solution.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/30338738651_d98241d6ca_o.png\" alt=\"cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2012-1\" width=\"356\" height=\"122\" \/><\/p>\n<p><strong>Question.2 In Fig. 1, the sides AB, BC and CA of a triangle ABC touch a circle at P, Q and R respectively. If PA = 4 cm, BP = 3 cm and AC = 11 cm, find the length of BC (in cm).<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/30389509576_4757259cc4_o.png\" alt=\"cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2012-66\" width=\"169\" height=\"181\" \/><br \/>\n<strong>Solution.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/30338738591_c5310ced76_o.png\" alt=\"cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2012-2\" width=\"358\" height=\"172\" \/><\/p>\n<p><strong>Question.3 In Fig. 2, a circle touches the side DF of \u0394EDF at H and touches ED and EF produced at K and M respectively. If EK = 9 cm, calculate the perimeter of \u0394EDF (in cm).<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/29794795204_1851bf0289_o.png\" alt=\"cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2012-67\" width=\"142\" height=\"204\" \/><br \/>\n<strong>Solution.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/30388888036_f09ecf7fda_o.png\" alt=\"cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2012-3\" width=\"299\" height=\"25\" \/><\/p>\n<p><strong>Question.4 If the area of a circle is equal to sum of the areas of two circles of diameters 10 cm and 24 cm, calculate the diameter of the larger circle (in cm).<\/strong><br \/>\n<strong> Solution.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/30338738441_c5c4efcbb6_o.png\" alt=\"cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2012-4\" width=\"385\" height=\"190\" \/><\/p>\n<p><span style=\"color: #0000ff\"><strong>SECTION B<\/strong><\/span><br \/>\n<strong>Questions number 5 to 10 carry 2 marks each.<\/strong><br \/>\n<strong> Question.5 Find the sum of the first 25 terms of an A.P. whose n<sup>th<\/sup> term is given by <sub> <\/sub>t<sub>n<\/sub>= 2 \u2013 3n.<\/strong><br \/>\n<strong> Solution.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/30338738321_5988eb71b9_o.png\" alt=\"cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2012-5\" width=\"390\" height=\"116\" \/><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/30338738261_a677032fa3_o.png\" alt=\"cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2012-6\" width=\"385\" height=\"84\" \/><\/p>\n<p><strong>Question.6 In a simultaneous toss of two coins, find the probability of getting:<\/strong><br \/>\n<strong> (i) exactly one head, (ii) atmost one head.<\/strong><br \/>\n<strong> Solution.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/30338738231_3d075e16fb_o.png\" alt=\"cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2012-7\" width=\"367\" height=\"202\" \/><\/p>\n<p><strong>Question.7 Find the value(s) of k so that the quadratic equation x<sup>2<\/sup> \u2013 4kx + k = 0 has equal roots.<\/strong><br \/>\n<strong> Solution.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/30338738141_c3c944d38b_o.png\" alt=\"cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2012-8\" width=\"390\" height=\"232\" \/><\/p>\n<p><strong>Question.8 Find the sum of all three digit natural numbers, which are multiples of 11.<\/strong><br \/>\n<strong> Solution.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/30338738061_31c2a80953_o.png\" alt=\"cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2012-9\" width=\"388\" height=\"162\" \/><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/30338738001_958212195c_o.png\" alt=\"cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2012-10\" width=\"347\" height=\"172\" \/><\/p>\n<p><strong>Question.9 Tangents PA and PB are drawn from an external point P to two concentric circles with centre O and radii 8 cm and 5 cm respectively, as shown in Fig. 3. If AP = 15 cm, then find the length of BP.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/30308754242_1d2a01df4b_o.png\" alt=\"cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2012-68\" width=\"259\" height=\"171\" \/><br \/>\n<strong>Solution.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/29793375563_727c6c57bc_o.png\" alt=\"cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2012-11\" width=\"389\" height=\"389\" \/><\/p>\n<p><strong>Question.10 In Fig. 4, an isosceles triangle ABC, with AB = AC, circumscribes a circle. Prove that the point of contact P bisects the base BC.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/29794795104_72dcef533e_o.png\" alt=\"cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2012-69\" width=\"168\" height=\"179\" \/><br \/>\n<strong>Or<\/strong><br \/>\n<strong> In Fig. 5, the chord AB of the larger of the two concentric circles, with centre O, touches the smaller circle at C. Prove that AC = CB.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/30425655245_117ddceefa_o.png\" alt=\"cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2012-70\" width=\"138\" height=\"156\" \/><br \/>\n<strong>Solution.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/29794215314_e807aee1ca_o.png\" alt=\"cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2012-12\" width=\"389\" height=\"353\" \/><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/29794215154_a5f35d9fbf_o.png\" alt=\"cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2012-13\" width=\"391\" height=\"174\" \/><\/p>\n<p><span style=\"color: #0000ff\"><strong>SECTION C<\/strong><\/span><br \/>\n<strong>Questions number 11 to 20 carry 3 marks each.<\/strong><br \/>\n<strong> Question.11 A milkman was serving his customers using two types of mugs A and B of inner diameter 5 cm to serve the customers. The height of the mugs is 10 cm.<\/strong><br \/>\n<strong> He decided to serve the customers in \u2018B\u2019 type of mug.<\/strong><br \/>\n<strong> (a) Find the volume of the mugs of both types.<\/strong><br \/>\n<strong> (b) Which mathematical concept is used in the above problem?<\/strong><br \/>\n<strong> (c) By chasing the mug of type \u2018B\u2019, which value is being depicted MUg \u2018A\u2019 bv the milkman?<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/30425655145_16099ddfde_o.png\" alt=\"cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2012-71\" width=\"187\" height=\"104\" \/><br \/>\n<strong>Solution.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/30338737681_8944fa14ee_o.png\" alt=\"cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2012-14\" width=\"371\" height=\"287\" \/><\/p>\n<p><strong>Question.12 In Fig. 6, OABC is a square of side 7 cm. If OAPC is a quadrant of a circle with centre O, then find the area of the shaded region.<\/strong><br \/>\n<strong> [Use \u03c0 = 22\/7 ]<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/29794795404_555a66573b_o.png\" alt=\"cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2012-72\" width=\"173\" height=\"161\" \/><br \/>\n<strong>Solution.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/30338737591_57f49cfff6_o.png\" alt=\"cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2012-15\" width=\"334\" height=\"168\" \/><\/p>\n<p><strong>Question.13 If a point A(0, 2) is equidistant from the points B(3, p) and C(p, 5), then find the value of p,<\/strong><br \/>\n<strong> Solution.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/30338737551_93e953ff18_o.png\" alt=\"cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2012-16\" width=\"346\" height=\"266\" \/><\/p>\n<p><strong>Question.14 A number is selected at random from first 50 natural numbers. Find the probability that it is a multiple of 3 and 4.<\/strong><br \/>\n<strong> Solution.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/30338737471_396420a6ba_o.png\" alt=\"cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2012-17\" width=\"386\" height=\"88\" \/><\/p>\n<p><strong>Question.15 Solve for x: 4\u00d72 \u2013 4ax + (a<sup>2<\/sup> \u2013 b<sup>2<\/sup>) = 0<\/strong><br \/>\n<strong> Or<\/strong><br \/>\n<strong> Solve for x: 3x<sup>2<\/sup> \u2013 2\u221a6x + 2 = 0<\/strong><br \/>\n<strong> Solution.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/30338737391_ecc331537b_o.png\" alt=\"cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2012-18\" width=\"338\" height=\"258\" \/><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/29793374423_96a19f2df6_o.png\" alt=\"cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2012-19\" width=\"371\" height=\"226\" \/><\/p>\n<p><strong>Question.16 Prove that the parallelogram circumscribing a circle is a rhombus.<\/strong><br \/>\n<strong> Or<\/strong><br \/>\n<strong> Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle.<\/strong><br \/>\n<strong> Solution.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/29794214584_927e27e723_o.png\" alt=\"cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2012-20\" width=\"378\" height=\"394\" \/><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/29793374203_70598e7e28_o.png\" alt=\"cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2012-21\" width=\"374\" height=\"412\" \/><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/29794214374_a7fdd52524_o.png\" alt=\"cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2012-22\" width=\"389\" height=\"439\" \/><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/30425008435_5f6bde8c9d_o.png\" alt=\"cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2012-23\" width=\"378\" height=\"315\" \/><\/p>\n<p><strong>Question.17 Construct a right triangle in which the sides, (other than the hypotenuse) are of length 6 cm<\/strong><br \/>\n<strong> and 8 cm. Then construct another triangle, whose sides are 3\/5 times the corresponding sides of the given triangle.<\/strong><br \/>\n<strong> Solution.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/30425008355_0586d9e6bd_o.png\" alt=\"cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2012-24\" width=\"315\" height=\"312\" \/><\/p>\n<p><strong>Question.18 In Fig. 7, PQ and AB are respectively the arcs of two concentric circles of radii 7 cm and 3.5 cm and centre O. If \u2220POQ = 30\u00b0<\/strong><br \/>\n<strong> then find the area of the shaded region. [Use \u03c0= 22\/7 ]<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/30308754372_68df5995dc_o.png\" alt=\"cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2012-73\" width=\"216\" height=\"177\" \/><br \/>\n<strong>Solution.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/29793373723_9009cebf5c_o.png\" alt=\"cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2012-25\" width=\"369\" height=\"274\" \/><\/p>\n<p><strong>Question.19 From a solid cylinder of height 7 cm and base diameter 12 cm, a conical cavity of same height and same base diameter is hollowed out. Find the total surface area of the remaining<\/strong><br \/>\n<strong> solid. [Use \u03c0 = 22\/7 ]<\/strong><br \/>\n<strong> Or<\/strong><br \/>\n<strong> A cylindrical bucket, 32 cm high and with radius of base 18 cm, is filled with sand. This bucket is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap is 24 cm, then find the radius and slant height of the heap.<\/strong><br \/>\n<strong> Solution.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/29794213954_3dfabd7a64_o.png\" alt=\"cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2012-26\" width=\"384\" height=\"358\" \/><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/29794213484_b1aaa5c508_o.png\" alt=\"cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2012-27\" width=\"373\" height=\"394\" \/><\/p>\n<p><strong>Question.20 The angles of depression* of two ships from the top of a light house and on the same side of it are found to be 45\u00b0 and 30\u00b0. If the ships are 200 m apart, find the height of the light house.<\/strong><br \/>\n<strong> Solution.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/29794213314_a813e08021_o.png\" alt=\"cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2012-28\" width=\"336\" height=\"48\" \/><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/30338736071_d85c34b5cc_o.png\" alt=\"cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2012-29\" width=\"378\" height=\"476\" \/><\/p>\n<p><span style=\"color: #0000ff\"><strong>SECTION D<\/strong><\/span><br \/>\n<strong> Questions number 21 to 31 carry 4 marks each.<\/strong><br \/>\n<strong> Question.21 A point P divides the line segment joining the points A(3, -5) and B(-4, 8) such that AP K<\/strong><br \/>\n<strong> pg = Y . If P lies on the line x + y = 0, then find the value of K.<\/strong><br \/>\n<strong> Solution.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/30338735901_5c5b355cc8_o.png\" alt=\"cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2012-30\" width=\"368\" height=\"284\" \/><\/p>\n<p><strong>Question.22 If the vertices of a triangle are (1, -3), (4, p) and (-9, 7) and its area is 15 sq. units, find the value(s) of p.<\/strong><br \/>\n<strong> Solution.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/30425007745_ac4e11a2b2_o.png\" alt=\"cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2012-31\" width=\"367\" height=\"249\" \/><\/p>\n<p><strong>Question.23 A box contains 100 red cards, 200 yellow cards and 50 blue cards. If a card is drawn at random from the box, then find the probability that it will be<\/strong><br \/>\n<strong> (i) a blue card<\/strong><br \/>\n<strong> (ii) not a yellow card<\/strong><br \/>\n<strong> (iii) neither yellow nor a blue card.<\/strong><br \/>\n<strong> Solution.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/30425007645_e8ea1ac81c_o.png\" alt=\"cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2012-32\" width=\"223\" height=\"47\" \/><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/30425007615_3268011b68_o.png\" alt=\"cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2012-33\" width=\"366\" height=\"208\" \/><\/p>\n<p><strong>Question.24 The 17th term of an AP is 5 more than twice its 8th term. If the 11th term of the AP is 43, then find its nth term.<\/strong><br \/>\n<strong> Solution.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/29794212714_ac647e91a4_o.png\" alt=\"cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2012-34\" width=\"378\" height=\"210\" \/><\/p>\n<p><strong>Question. 25 A shopkeeper buys some books for Rs80. If he had bought 4 more books for the same amount, each book would have cost Rs 1 less. Find the number of books he bought.<\/strong><br \/>\n<strong> Or<\/strong><br \/>\n<strong> The sum of two numbers is 9 and the sum of their reciprocals is 1\/2. Find the numbers.<\/strong><br \/>\n<strong> Solution.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/30338735571_fa60f732a6_o.png\" alt=\"cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2012-35\" width=\"375\" height=\"343\" \/><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/30425007425_043c1fe805_o.png\" alt=\"cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2012-36\" width=\"372\" height=\"297\" \/><\/p>\n<p><strong>Question.26 Sum of the first 14 terms of an AP is 1505 and its first term is 10. Find its 25<sup>th<\/sup> term.<\/strong><br \/>\n<strong> Solution.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/29794212354_2e5ace7826_o.png\" alt=\"cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2012-37\" width=\"375\" height=\"223\" \/><\/p>\n<p><strong>Question.27 Prove that the tangent at any point of a circle is perpendicular to the radius through the point of contact.<\/strong><br \/>\n<strong> Or<\/strong><br \/>\n<strong> A quadrilateral ABCD is drawn to circumscribe a circle. Prove that AB + CD = AD + BC.<\/strong><br \/>\n<strong> Solution.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/30338735331_9ac98735a3_o.png\" alt=\"cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2012-38\" width=\"411\" height=\"345\" \/><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/30388877196_80b6d9caf0_o.png\" alt=\"cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2012-39\" width=\"393\" height=\"221\" \/><\/p>\n<p><strong>Question.28 A solid is in the shape of a cone surmounted on a hemisphere, the radius of each of them being 3.5 cm and the total height of solid is 9.5 cm. Find the volume of the solid.<\/strong><br \/>\n<strong> [Use \u03c0 = 22\/7 ]<\/strong><br \/>\n<strong> Solution.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/29794205584_5d1bf530e6_o.png\" alt=\"cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2012-40\" width=\"384\" height=\"322\" \/><\/p>\n<p><strong>Question.29 A bucket is in the form of a frustum of a cone and it can hold 28.49 litres of water. If the radii of its circular ends are 28 cm and 21 cm, find the height of the bucket.<\/strong><br \/>\n<strong> [Use \u03c0 = 22\/7 ]<\/strong><br \/>\n<strong> Solution.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/30388877096_5edfaf76b5_o.png\" alt=\"cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2012-41\" width=\"395\" height=\"301\" \/><\/p>\n<p><strong>Question.30 The angle of elevation of the top of a hill at the foot of a tower is 60\u00b0 and the angle of depression from the top of the tower of the foot of the hill is 30\u00b0. If the tower is 50 m high, find the height of the hill.<\/strong><br \/>\n<strong> Solution.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/29794205404_7e271d8685_o.png\" alt=\"cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2012-42\" width=\"392\" height=\"315\" \/><\/p>\n<p><strong>Question.31 From the top of a hill, the angles of depression of two consecutive kilometre stones due east are found to be 30\u00b0 and 45\u00b0. Find the height of the hill.<\/strong><br \/>\n<strong> Solution.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/29794205224_2f63b1f47e_o.png\" alt=\"cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2012-43\" width=\"416\" height=\"498\" \/><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/29794204984_e5b4b2d703_o.png\" alt=\"cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2012-44\" width=\"385\" height=\"167\" \/><\/p>\n<h3 style=\"text-align: center\"><span class=\"ez-toc-section\" id=\"SET_II\"><\/span><span style=\"color: #0000ff\"><strong>SET II<\/strong><\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>Note: Except for the following questions, all the remaining questions have been asked in Set-I.<\/strong><br \/>\n<strong> Question.13 Find the value(s) of k so that the quadratic equation 2x<sup>2<\/sup> + kx + 3 = 0 has equal roots.<\/strong><br \/>\n<strong> Solution.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/29794204994_7b9cfcfa1c_o.png\" alt=\"cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2012-45\" width=\"388\" height=\"154\" \/><\/p>\n<p><strong>Question.14 Find the sum of all three digit natural numbers, which are multiples of 9.<\/strong><br \/>\n<strong> Solution.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/29794204794_ace8c2861d_o.png\" alt=\"cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2012-46\" width=\"340\" height=\"336\" \/><\/p>\n<p><strong>Question. 21 A box contains 35 blue, 25 white and 40 red marbles. If a marble is drawn at random from the box, find the probability that the drawn marble is<\/strong><br \/>\n<strong> (i) white<\/strong><br \/>\n<strong> (ii) not blue<\/strong><br \/>\n<strong> (iii) neither white nor blue.<\/strong><br \/>\n<strong> Solution.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/30425002535_628935c898_o.png\" alt=\"cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2012-47\" width=\"392\" height=\"254\" \/><\/p>\n<p><strong>Question.22 The 15th term of an AP is 3 more than twice its 7th term. If the 10th term of the AP is 41, then find its n<sup>th <\/sup>term.<\/strong><br \/>\n<strong> Solution.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/30425002385_07ce5c77e0_o.png\" alt=\"cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2012-48\" width=\"353\" height=\"143\" \/><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/30425002295_3d7d298590_o.png\" alt=\"cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2012-49\" width=\"245\" height=\"163\" \/><\/p>\n<p><strong>Question.23 Draw a triangle ABC with side BC = 7 cm, \u2220ABC = 60\u00b0 and AB = 6 cm. Then construct<\/strong><br \/>\n<strong> another triangle whose sides are 3\/4 times the corresponding sides of \u0394ABC.<\/strong><br \/>\n<strong> Solution.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/30127983800_491490fc6a_o.png\" alt=\"cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2012-50\" width=\"385\" height=\"297\" \/><\/p>\n<p><strong>Question.24 The shadow of a tower standing on a level ground is found to be 20 m longer when the Sun\u2019s altitude is 45\u00b0 than when it is 60\u00b0. Find the height of the tower.<\/strong><br \/>\n<strong> Solution.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/29794204314_8d05eb3467_o.png\" alt=\"cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2012-51\" width=\"391\" height=\"343\" \/><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/30425002145_51e618917b_o.png\" alt=\"cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2012-52\" width=\"388\" height=\"240\" \/><\/p>\n<p><strong>Question.29 The sum of the first 15 terms of an AP is 750 and its first term is 15. Find its 20th term.<\/strong><br \/>\n<strong> Solution.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/30425002095_62ef1f8d0b_o.png\" alt=\"cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2012-53\" width=\"197\" height=\"66\" \/><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/30127983320_f200c7894c_o.png\" alt=\"cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2012-54\" width=\"299\" height=\"278\" \/><\/p>\n<p><strong>Question.30 A container shaped like a right circular cylinder having base radius 6 cm and height 15 cm is full of ice-cream. The ice-cream is to be filled into cones of height 12 cm and radius 3 cm, having a hemispherical shape on the top. Find the number of such cones which can be filled with ice-cream.<\/strong><br \/>\n<strong> Solution.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/30425002055_e0e9f3730d_o.png\" alt=\"cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2012-55\" width=\"394\" height=\"460\" \/><\/p>\n<h3 style=\"text-align: center\"><span class=\"ez-toc-section\" id=\"SET_III\"><\/span><span style=\"color: #0000ff\"><strong>SET III<\/strong><\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>Note: Except for the following questions, all the remaining questions have been asked in Set-I and Set-II.<\/strong><br \/>\n<strong> Question.13 Find the sum of all three digit natural numbers, which are multiples of 7.<\/strong><br \/>\n<strong> Solution.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/29794203694_657d31d29f_o.png\" alt=\"cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2012-56\" width=\"396\" height=\"264\" \/><\/p>\n<p><strong>Question.14 Find the value(s) of k so that the quadratic equation 3x<sup>2<\/sup>\u2013 2kx + 12 = 0 has equal roots.<\/strong><br \/>\n<strong> Solution.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/29794203544_f226141966_o.png\" alt=\"cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2012-57\" width=\"338\" height=\"50\" \/><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/29794203424_a06fa311b5_o.png\" alt=\"cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2012-58\" width=\"388\" height=\"120\" \/><\/p>\n<p><strong>Question.21 A kite is flying at a height of 45 m above the ground. The string attached to the kite is temporarily tied to a point on the ground. The inclination of the string with the ground is 60\u00b0. Find the length of the string assuming that there is no slack in the string.<\/strong><br \/>\n<strong> Solution.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/30425001905_1b0869af7d_o.png\" alt=\"cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2012-59\" width=\"411\" height=\"277\" \/><\/p>\n<p><strong>Question.22 Draw a triangle ABC with side BC = 6 cm, \u2220C = 30\u00b0 and \u2220A = 105\u00b0. Then construct another<\/strong><br \/>\n<strong> triangle whose sides are 2\/3 times the corresponding sides of \u0394ABC.<\/strong><br \/>\n<strong> Solution.<\/strong><\/p>\n<p><strong>Question.23 The 16th term of an AP is 1 more than twice its 8th term. If the 12th term of the AP is 47, then find its nth term.<\/strong><br \/>\n<strong> Solution.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/30127982680_6c9bba70a5_o.png\" alt=\"cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2012-60\" width=\"391\" height=\"415\" \/><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/29794202934_4e1a7d46fa_o.png\" alt=\"cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2012-62\" width=\"297\" height=\"97\" \/><\/p>\n<p><strong>Question.24 A card is drawn from a well shuffled deck of 52 cards. Find the probability of getting<\/strong><br \/>\n<strong> (i) a king of red colour<\/strong><br \/>\n<strong> (ii) a face card<\/strong><br \/>\n<strong> (iii) the queen of diamonds.<\/strong><br \/>\n<strong> Solution.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/29794216724_46eb08d31f_o.png\" alt=\"cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2012-63\" width=\"385\" height=\"272\" \/><\/p>\n<p><strong>Question.29 Sum of the first 20 terms of an AP is -240, and its first term is 7. Find its 24th term.<\/strong><br \/>\n<strong> Solution.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/29794216534_51e6f6172e_o.png\" alt=\"cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2012-64\" width=\"391\" height=\"331\" \/><\/p>\n<p><strong>Question.30 A solid is in the shape of a cone standing on a hemisphere with both their radii being equal to 7 cm and the height of the cone is equal to its diameter. Find the volume of the solid.<\/strong><br \/>\n<strong> [Use \u03c0 = 22\/7]<\/strong><br \/>\n<strong> Solution.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/30338738701_03b5971b15_o.png\" alt=\"cbse-previous-year-question-papers-class-10-maths-sa2-delhi-2012-65\" width=\"388\" height=\"308\" \/><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Time allowed: 3 hours Maximum marks: 90 GENERAL INSTRUCTIONS: All questions are compulsory. 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