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(12) rhe order of ( p,Q,) where r = [] : ;) and Q = [j j] "A6 B.3x2 C.2x2 D.3x3{i3) A and B are trvo events such that P(not A) : 0.6 and P(B) = 0.286 , thenP(A) + F(not B) =A, A.7A B. 0.286

8.2x3

c. 1.ii4 D. 0.886 E. none of these

c. 55"

c. 16

(14) A bag contains 12 white balls and some red balls, The probability of drawing a red ball\ir fi. The number 'cf red ball ish. Lt B. i0 c.22 D.5 E. none of these

(15) O is the centre of the circle MPQN and IPQN : 125', then /MNP =

(16) AB and EF are tangents to the circle at A and F respectively. If AB : 6.BC = 3, DE = 16, then EF:

A.25'D. 65"

A. 15D,20

A1)

B. 35"8.75"

B. 12E.2s

B+-l r3"'4

(17) Two corresponding altitudes of twa similar triangles are 8cm and 1Ocm. Thenu(smallerA) : u(larger A) =A.4: 5 8.3:4 C.9:25 D. 9: 16 E. \6:25

(18) The position vectors of the points A and B relative to an original O are +i - O j anA^i i8i -p j respectively. If O, A and B are collinear. then p:A. -12 B. -8 C" I D. 12 E. 36-> -)(19) A, b and i are three nonzero vectors such that every two of them are non- parallel.r -'+ --+If(x +y- 3)T : ty + z- 4)b : (z+x- 5) i, then x+y + z:A.3 8.4 c.5 D.6 8,7

(20) IfO is an acute angle and cos 0 : !, tn.n tan( 90' - 0) :D. + E. ncne of these

(21) Iftan 0 =x, tan20 = 3x and 0

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(23) The equation of the normal to the curve y = 3e" at x: 0 isA.3x*y:9 B.x+3y=9 C.3x-y=9 D.x-3y:9 E.x+y:9(24) It nis a rationai number, l* Gl*d :

A. n B. xn C. nxn-' D. (n - 1) xn E. xn- I(25) The stationary points of the curve y : x3 * 3x * 2 areA.(i, 4) and ( -1,0)D. (-1,4)

B,(-1,4) and (1.0)E. none of these

c. (1,0)(25 marks)

SECTTON (B)(Answer A"LL questions)2.If f:x*>2x+bandg: x H3a-2x,suchthat f og : gof ,findtherelaticnshipbetween

a and b. (3 marks)Giventhat when x2 + ax + b and *'*flO*Yk are divided by x *F,rheirremainder are

m * n = 1, show that A, B, and C are collinear.5. Solvethe equationcosx-2 cos2X =0, for 0

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(b) An A' P is such that the 5th term is three times the 2nd term" Show that the sum of thefirst eight terms is fow times the sum of the first four terms. (5 marks)10.(a) The first three terms of an A.P are x, y, z.If these numbers x, y, z are also the first,third and fourth terms of a G.P. Show that (Zy - z) z2 = ,3 . (5 marks)

(b) showthat A=[t:.t" sincr'l satisfies A2 + I = 2Acos a where I is the unitmatrix\-srncr cosu/of order 2. (5 marks)11.(a) Write down the inverse matrix of thern"rn>< [] -ll *o use it to solve the following\z r)simultaneous equations 9x - 2 y - 13 : 0 and 2x + 3y* 4 = 0. (5 marks)

ft) Make a table of order pairs (first die, second die) for rolling two dice. Use the table tofind the probability that the sum of the scores is odd, G product of the scores isgreater than 15 and the product of the score is a multiple of 6. (5 marks)12.(a) If P, Q, R are three points on the circumference of a circle such that the chords pe isequal to the chord PR, prove that the tangent at P bisects the exterior angle between pe(5 marks)nd PR.

(b) Two circles intersect at A and B. A point P is taken on one so that pA and pB cut theother at Q and R respectively, The tangents at Q and R meet the tangent at p in S and Trespectively. Prove that ITPR = ZBRe and pBeS is cyclic, (5 marks)

(b) Solve AABC with b = 13, a: 10, c : 9. (5 marks)

13.(a) In AABC, ZBAC = 90"and ADl BC. If DC = g BD, prove thar BC = 3AB. (5 marks)(b) The position vectors of A and B relative to an origin o are [,t l *o ft:lrespectively.us/ [3i

Given that C lies on AB and has position vector fttitl, find rhe value of t and the\. t+I )'ratio AC: CB. (5 marks)H.(a) Given that ffi#=t, pro'n, that cos c{, cos F = 6 sin cr sin p and deduce arelationship between tan a and tan B. Given further that s, + F : 45,, calculate thevalue of tan cl + tan B. (5 marks)15.(a) Show that the equation of the tangent to the curve y : (2x + a)3 at the point wherey = a3 is y = a2 (a + 6y1. ' r \--- (5 marks)

(b) If x * y : 42, find the maximum value of xy, (5 marks)