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Downloaded from www.examguesspapers.com | Be a part of the growing student community online D ate:l2 Jan 2009 THE CATHEDRAL & JOHN CONNON SCHOOL Preliminarv Examination 2008-09 CLASS XII {nI'l[arks: 100 T ime : 3 h p u r s MATHEMATICS Section A: Answer Question I (compulsory) and FIVE other questions. Section B & Section C: Answer any TWO questionsfrom eilher Section B or Section C. AII essential working must he clearly shown on the same sheet as the rest of the answer. SectionA (Answer Question I and ony other FIVE questions) Questionl: I l0 x 3 :30 marksI (a) [-r -tanel f r showthatl lx | ftanO (b) lf | _l I ,urrol lcos2e -sin2ol | -l I l_-tanO lJ !in20 cosr0 | rt for a, I e, +. . I is a Booleanalgebra all the elements b, c of B, TJ provethat(a + b) (b'+ c) + b(a'+ c') : ab'* ac + b. (c) Find the equationof the tangentto the parabola!' : l6x which is pcrpendicular to the line 3r- 4y + 5: 0. Also find the point ol'contact. (d) In a singlethrow of two dice, what is the probability of getting a total o1' at most 9 ? (e) Determine so that the line y:2x + I may touchthe ellipse3x'+ 5y: l" (0 Solvethe dilfcrentialequatio ", (g) # "r** 15. : e'-v Find the angle betweenthe lines and the equation of the bisectorsof the angle betweenthe pair of lines given by 2x2* 7xy + 3 )F:0. Continued on page 2
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