DESIGN OF THE QUESTION PAPER Mathematics …

1 Weightage and the distribution of marks over different dimensions of the questionshall be as follows:(A) Weightage to Content/ Subject Units and Probability10 Total : 80(B) Weightage to Forms of Questions ofMarks for eachNumber ofTotal OF THE QUESTION PAPERM athematicsClass XTime : 3 HoursMaximum Marks : 80 060530 Total 30 80 SET-I03/05/18204 EXEMPLAR PROBLEMS(C) Scheme of OptionsAll questions are compulsory, , there is no overall choice. However, internal choicesare provided in one QUESTION of 2 marks, three questions of 3 marks each and twoquestions of 6 marks each.

2 (D) Weightage to Difficulty Level of Questions DifficultyPercentage of MarksLevel of Questions : A QUESTION may vary in difficulty level from individual to individual. As such, theassessment in respect of each will be made by the PAPER setter/ teacher on the basis ofgeneral anticipation from the groups as whole taking the examination. This provision isonly to make the PAPER balanced in its weight, rather to determine the pattern of markingat any OF THE QUESTION PAPER , SET-I205 BLUE PRINTMATHEMATICSCLASS XForm of QuestionUnits Number Systems2(2)2(1)--4(3)Algebra3(3)2(1)9(3) 6(1)20(8)Polynomials, Pair ofLinear Equations inTwo Variables,Quadratic Equations,Arithmatic ProgressionsTrigonometry1(1)2(1)3(1)6(1) 12(4)Introduction to Trigonometry,Some Applications ofTrigonometryCoordinate Geometry1(1)4(2)3(1)-8(4)Geometry1(1)-9( 3)6(1)16(5)Triangles, Circles,ConstructionsMensuration1(1)-3(1 )

3 6(1)10(3)Areas related to Circles,Surface Areas and VolumesStatistics & Probability1(1)-3(1)6(1)10(3)Total10(10) 10(5)30(10)30(5)80(30) 03/05/18206 EXEMPLAR PROBLEMSM athematicsClass XMaximum Marks : 80 Time : 3 HoursGeneral questions are QUESTION PAPER consists of 30 questions divided into four sections A, B, C, A contains 10 questions of 1 mark each, Section B contains 5 questionsof 2 marks each, Section C contains 10 questions of 3 marks each and Section Dcontains 5 questions of 6 marks is no overall choice. However, an internal choice has been provided inone QUESTION of 2 marks, three questions of 3 marks and two questions of 6marks questions on construction, the drawing should be neat and exactly as per of calculators is not how many decimal places will the decimal expansion of the number324725 terminate?

4 (A) 5(B) 2(C) 3(D) s division lemma states that for two positive integers a and b, there existunique integers q and r such that a = bq + r, where(A) 0 r a(B) 0 < r < b(C) 0 r b(D) 0 r < number of zeroes, the polynomial p (x) = (x 2)2 + 4 can have, is(A) 1(B) 2(C) 0(D) pair of linear equations a1x + b1y + c1 = 0; a2x + b2y + c2 = 0 is said to beinconsistent, if(A) 1122 abab(B) 111222 =abcabc (C) 111222= abcabc (D)1122 smallest value of k for which the equation x2 + kx + 9 = 0 has real roots, is(A) 6(B) 6(C) 36(D) coordinates of the points P and Q are (4, 3) and ( 1, 7).

5 Then the abscissa ofa point R on the line segment PQ such that PR3PQ5= is03/05/18 DESIGN OF THE QUESTION PAPER , SET-I207(A) 185(B) 175(C) 178 (D) the adjoining figure, PA and PB are tangents from apoint P to a circle with centre O. Then the quadrilateralOAPB must be a(A) square(B) rhombus(C) cyclic quadrilateral(D) for some angle , cot 2 = 13, then the value ofsin3 , 2 (A) 12(B) 1(C) 0(D) each corner of a square of side 4 cm, a quadrantof a circle of radius 1 cm is cut and also a circle ofdiameter 2 cm is cut as shown in figure. The area of theremaining (shaded) portion is(A) (16 2 ) cm2(B) (16 5 ) cm2(C) 2 cm2(D) 5 letter of English alphabets is chosen at random.

6 Theprobability that it is a letter of the word Mathematics is(A) 1126(B) 513(C) 926(D) 413 SECTION there any natural number n for which 4n ends with the digit 0? Give reasons insupport of your using the formula for the nth term, find which term of the AP : 5, 17, 29, 41,.. will be 120 more than its 15th term? Justify your 144 a term of the AP : 3, 7, 11, .. ? Justify your coordinates of the points P, Q and R are (3, 4), (3, 4) and ( 3, 4), the area of PQR 24 sq. units? Justify your length of a line segment is 10 units. If one end is (2, 3) and the abscissa of theother end is 10, then its ordinate is either 3 or 9.

7 Give justification for the is the maximum value of 3cosec ? Justify your the zeroes of the polynomial p (x) = 243 23 23xx and verify therelationship between the zeroes and the dividing the polynomial f (x) = x3 5x2 + 6x 4 by a polynomial g(x), thequotient q (x) and remainder r (x) are x 3, 3x + 5, respectively. Find the polynomialg (x). the equations 5x y = 5 and 3x y = 3 the sum of the first n terms of an AP is 4n n2, what is the10th term and the nthterm?ORHow many terms of the AP : 9, 17, 25, .. must be taken to give a sum 636? (1, 2), (4, y), (x, 6) and (3, 5) are the vertices of a parallelogram taken in order,find the values of x and sides AB, BC and median AD of a ABC are respectively propotional to thesides PQ, QR and the median PM of PQR.

8 Show that ABC ~ triangle ABC is drawn to circumscribe a circle of radius 4 cm such that thesegments BD and DC into which BC is divided by the point of contact D are oflengths 8 cm and 7 cm, respectively. Find the sides AB and an isosceles triangle whose base is 6 cm and altitude 5 cm and thenanother triangle whose sides are 75 of the corresponding sides of the that cos sin11sincos 1cosec cot += + .OREvaluate:23cos43cos37cosec53 sin47tan5tan25tan45tan65tan85 03/05/18 DESIGN OF THE QUESTION PAPER , the figure, ABC is a triangle right angled at A.

9 Semicircles are drawn on AB,AC and BC as diameters. Find the area of the shaded bag contains white, black and red balls only. A ball is drawn at random from thebag. The probability of getting a white ball is 310 and that of a black ball is 25. Findthe probability of getting a red ball. If the bag contains 20 black balls, then find thetotal number of balls in the the price of a book is reduced by Rs 5, a person can buy 5 more books forRs 300. Find the original list price of the sum of the ages of two friends is 20 years. Four years ago, the product of theirages in years was 48.

10 Is this situation possible? If so, determine their present that the lengths of the tangents drawn from an external point to a circle the above theorem, prove that:If quadrilateral ABCD is circumscribing a circle , then AB + CD = AD + that the ratio of the areas of two similar triangles is equal to the ratio of thesquares of the corresponding the above theorem, do the following :ABC is an iscosceles triangle right angled at B. Two equilateral triangles ACD andABE are constructed on the sides AC and AB, respectively. Find the ratio of theareas of and angles of depression of the top and bottom of a building 50 metres high asobserved from the top of a tower are 30 and 60 , respectively.