Question 1 [2x15 = 30]

Transcription

1 MTHEMTIS Three hours and a quarter (The first 5 minutes of the eamination are for reading the paper onl. andidates must NOT start writing during this time). Total marks: nswer Question from Section and 0 questions from Section. ll working, including rough work, should e done on the same sheet adjacent to the rest of the answers. The intended marks for questions or parts of questions are given in rackets [ ]. Mathematical formulae are given at the end of this question paper. The use of calculator (F-8)/(F-00) is allowed SETION (nswer LL questions) Directions: Read the following questions carefull. For each question there are four alternatives,,, and D. hoose the correct alternative and write it in our answer sheet. Question [5 = 0] 4 (i) If then will e equal to 5 7 D (ii) The distance of the point (,,) from the origin is 5 D 9 HSE/0/0 Page of This ooklet contains pages

2 (iii) The value of sin d cos c sin c 4 sin c 4 D sin c (iv) If f () - e 0 cos e, then f ' is D (v) The direction cosines of the normal to the plane 9 6z55 0 are 9 6,, 9 6,,, 9, 6 D, 9, 55 d (vi) The solution of the differential equation sec d for when = is sin tan sec tan D sin HSE/0/0 Page of

3 (vii) t what value of is the function sin maimum? 0 D (viii) The centre of the ellipse 5 (,5) (, 5) 6 9 is at (5, ) D ( 5, ) (i) If is a cue root of unit, then 0 D is equal to () ag contains 4 red, 5 green and 6 lue alls. all is drawn at random, the proailit of getting a green or red all is 5 D HSE/0/0 Page of

4 (i) In the diagram given elow, what is the area of the shaded portion? 8 sq. units = D 8 sq. units sq. units 6 sq. units (ii) The standard deviation of the first five even numers is. 8 4 D (iii) If cos, 0, D 5, then 5 d is equal to 0 HSE/0/0 Page 4 of

5 (iv) The point of intersection of the pair of lines given (, 0) (, 0) (,) D (0,0) 0 0 is (v) The tale elow represents the ranks of five students in two different sujects. Suject 5 4 Suject 4 5 Which statement elow est descries the relation etween the ranks in two sujects? No correlation D Perfect positive correlation Perfect negative correlation Moderate negative correlation SETION nswer an 0 questions. ll questions in this section have equal marks Question Using the properties of determinants prove that [] p q r q p r 0 r p q Find d d if tan [4] HSE/0/0 Page 5 of

6 Question If sin(cos ), find the values of. [] Show that the four points (0,,), (,, ), (,,) and (0,,) are coplanar. [4] Question 4 Evaluate: log d [] The proailit that Dorji will pass in Dzongkha test is 4 5 and the proailit that he will not pass in English test is. If the proailit of passing in at least one 8 of the tests is, what is the proailit that he will pass in oth the tests? [4] 4 Question 5 Find the equation of the paraola whose focus is (, ) and the directri is 0. [] d Solve the differential equation cos, given that d and d d 0, when 0. [4] Question 6 The mean monthl salar paid to all emploees of a compan was Nu 500. The mean annual salaries of male and female emploees were Nu 600 and Nu 00 respectivel. Determine the percentage of males and females emploed the compan. [] Ten teachers were invited for a meeting the Principal. In how man was can the teachers and the Principal e seated around a circular tale? In how man was will two particular teachers e seated on either side of the Principal? [4] HSE/0/0 Page 6 of

7 Question 7 Solve: d ( ) [] d Evaluate: sin tan 5 tan 4 [4] Question 8 Evaluate: d [] 6 Differentiate with respect to : sin ( 4 ) [4] Question 9 Find the equation of a plane which passes through the point (4,0,) and is parallel to the plane 4 z 6 0 [] Find the value of so that the equation represents a pair of straight lines. [4] Question 0 The arithmetic mean of the points scored four archers Pema, Dawa, Tshering and Tashi are 70, 90, 60, and 40 respectivel. The standard deviations of their points are, 6, 9 and 8. Who is the most consistent archer of the four? [] Find the vertices and foci of the hperola [4] Question Find the modulus and amplitude of i i. [] The marks of five candidates in Mathematics and Phsics tests were as follows. Mathematics Phsics candidate who scored 75 in Mathematics was asent from the Phsics test. Estimate his proale score in Phsics finding the appropriate regression equation. [4] HSE/0/0 Page 7 of

8 Question If 5, find d d. [] Using De Moivre s theorem, find all the values of ( i). lso find the continued product of the values. [5] Question Find the length of latus rectum of the ellipse [] 9 6 Using matri method, solve the following sstem of linear equations. [5] a 4c 4 ac 0 Question 4 Given that (,,5), (,,) and (7,0, ) are collinear. Find the ratio in which divides. [] right circular clinder is to e made so that the sum of its radius and its height is 9 metres. Find the maimum volume of the clinder. [5] HSE/0/0 Page 8 of

9 MTHEMTIS FORMULE Trigonometr sin cos tan sin sin sin cos cos cos tan tan tan, tan tan sin cos cos ec sin sec cos cot tan omple Numers r a tan tan a a z r cos i sin then If n n z r cosn isinn n n k k z r cos isin, n n k 0,,,,... n o-ordinate Geometr D z z m m m m mz mz (,, z),, m m m m m m a c z 0and a c z 0 z c c c a c a a a ngleetweentwo planes, cos a a c c a c a c a cz d distanceof a point froma plane a c m m m m,, m m m m ngleetween thelinesa h 0, h a tan a equation of i sec tor, a h hf g gh af points of intersection,, a h a h lgera a a a a a a a Inthe quadratic equation a c 0, n n p ij r r n! n r! n! r! n r! i j M I adj det ij 4ac HSE/0/0 Page 9 of

10 D D Dz,, z D D D... 6 n nn n nn n... n n... n LULUS = n n, n, = cf(), cf (), d du dv If = u ± v,then = ± d d d d dv du If = uv,then = u + v d d d du dv v - u u d d d If =, then = v d v d d d du du d du uv d u vd vd d. d n f ( ) d lim h f ( a rh) h0 a r0 d pd p Q, I. F e, d general solution,. IF ( Q. IF) d c V d a d a Volumeof one 4 Volume of Sphere Volume of linder r h r h r h S. rea of one rl r S. rea of Sphere 4 r S. rea of linder rh r Data and Proailit X f f Median l m c f l l ( ) i or n n n f f f f m n X m n ov r r n n n d n d n n X, Y X XY Y n n n n n 6 r nn r ( ). d HSE/0/0 Page 0 of

11 YX XY r r n n n n XY cov, Y Y X X r X X XY cov, X X Y Y r Y Y = r na a r P P P P P P P P P P P P HSE/0/0 Page of

12 Rough Work HSE/0/0 Page of