VIEWS: 36 PAGES: 4 CATEGORY: Education POSTED ON: 2/15/2012 Public Domain
IB GUESS PAPER II Section A ANSWER ALL QUESTIONS 10X2=20 1 Find the foot of the perpendicular drawn from (-1, 3) on the line 5x – y = 18. OR Prove that the points (1, 11), (2, 15) and (-3, -5) are collinear and find the equation of the straight line containing them. OR Find the area of the triangle formed by the straight lines and the co-ordinates axes i) 2 x 4 y 7 0 ii) xcosα+ysinα=p 2 find distance between parallel lines given by 5x-3y-4=0 and 10x-6y-9=0 OR If θ is angle between lines x/a +y/b=1&x/b+y/a=1 find the value of sin θ OR Find value of “x” if slope of the line joining points (2,5) and (x,3) is 2 3 If (2,4,-1) (3,6,-1) (4,5,1) are three vertices of a parallelogram find 4 vertex OR show that points (0,4,1) (2,3,-1) (4,5,0) and (2,6,2) are vertices of square OR If extremities of a diagonals of square are (1,-2,3) and ( 2,-3,5) then find the length of side of square 4 Find equation of plane which intercepts on axes 3,4 -5 OR Find the angle between planes 6 x 3 y 2 z 1 0; x 2 y 2 z 1 0 OR Find distance between plane x 3 y 4 z 7 0; 2 x 6 y 8z 16 0 OR Find distance from (2, 1, -1)to plane 6 x 3 y 2 z 14 0 x 1 cos 2mx 5 Compute lim OR Compute lim OR Compute 1 x 1 x sin nx x0 x 0 2 sin(a bx) sin(a bx) lim x 0 x 6 If f(x) = log (sec x tan x), find f(x) OR if y=Cos(log(cotx)) find dy/dx OR find derivative of y= cos-1(4x3-3x) 1 cos x 7 y tan 1 1 cos x find dy/dx OR if x=at y=2at find dy/dx OR if y=x find dy/dx 2 x Page -2- 8 Find derivative of sin tan 1 e x OR If x= a(cost+tsint) y=a(sint-tcost) find dy/dx OR find dy/dx if x=3cost-2cos3t y= 3sint-2sin 3t 9 Find y and dy for y=logx when x=3 x=0.003 OR Find equation of tangent and normal of y4=ax3 at (a,a) OR The radius of circular plate is increasing in length at 0.01 cm/sec. What is the rate at which the area increasing , when the radius is 12 cm 10 Find the approximate value of 82 OR show that length of sub-normal at any point on the curve 2 y =4ax is constant OR If the increase in the side of cube is 3% find the percentage of change in the volume in the cube Section B ANSWER ANY 5 QUESTIONS 4X5=20 11 Find the equation of locus of P, if A = (4, 0), B(-4, 0) and PA - PB = 4 OR A(2, 3) and B(-3, 4) be two given points. Find the equation fo the locus of P so that the area of the triangle PAB is 8.5 sq.units.OR Find the of locus of P if line segment joining (2,3) and (-1, 5) subtends a right angle at P. 12 Find the transformed equation of the curve 3x 2 10 xy 3 y 2 9 when the axes are rotated through an angle OR If the transformed equation of a curve is x 2 3xy 2 y 2 17 x 7 y 11 0 , when the origin is 4 shifted to the point (2,3), the find the original equation of the curve OR Show that the axes are rotated through 1 2h an angle of Tan 1 so as to remove the xy term from the equation ax 2hxy by 0 2 2 2 ab 13 If 3a+2b+4c=0 then show that ax+by+c=0 represents a family of lines and find point of concurrency OR Find the equation line perpendicular to the line 3x+4y+6=0 making an intercept -4 on the X axis OR Find the equation of lines passing from point of intersection of lines 3x + 2y + 4 = 0 ; 2x + 5y = 1 and whose distance from (2, -1) is ‘2’ 3 (1 x) 2 1 3 1 x 3 1 x 14 compute lim x 0 OR Compute lim x 0 x x Page -3- ax 3 if x3 OR f is defined by f(x) = is continuous at x=3 find "a" 3 x 2x x0 2 if 15 Find the derivative function tan2xfrom the first principles OR Find derivative of 1 x2 1 1 1 f(x)= tan with respect of g(x) = tan x OR Find the derivative of sec2x from the first x principles dy sin 2 (a y ) 16 If sin y x sin(a y), then show that OR dx sin a dy log x If x y e x y then show that dx (1 log x) 2 17 If z = log( tan x tan y ) , show that (sin 2 x) z x (sin 2 y ) z y 2 OR Using Euler’s theorem show that 1 x y xu x yu y tan u for the function u sin 1 2 x y Section C ANSWER ANY 5 QUESTIONS 7X5=35 18 If p and q are the length of the perpendicular from the origin to the straight lines x sec y cosec a and x cos y sin a cos 2 , prove that 4 p 2 q 2 a 2 OR If Q (h, k) is the image of the point p ( x1 , y1 ) h x1 k y1 2(ax1 by1 c) w.r.t. the line ax by c 0 then show that a b a 2 b2 19 If second degree equation S ax 2 2hxy by 2 2 gx 2 fy c 0, in the two variables x and y i) abc 2 fgh af 2 bg 2 ch2 0 represents pair of lines then ii) h 2 ab g 2 ac f 2 bc OR If the equation mx2-10xy+12y2+5x-16y-3=0 represents pair of lines find “m” and also find angle and point of intersection for this value of “m” 20 Find the value of k, if the lines joining the origin to the points of intersection of the curve 2 x 2 2 xy 3 y 2 2 x y 1 0 and the line x 2 y k are mutually OR Find angle between the lines joining the origin to the points of intersection of curves x 2 2 xy y 2 2 x 2 y 5 0, and line 3x-y+1=0 Page -4- 1 21 Show that cos 1 is the angle between two non-parallel lines whose direction ratios satisfy the equations 6 3l m 5n 0 and 6mn 2 ln 5lm 0 .OR Find angle between two diagonals of cube 2 3 (1 2 x) 3 (1 3x) 4 dy 22 If y 5 6 find OR dx (1 6 x) (1 7 x) 6 7 dy if y= x x 2 a 2 a 2 log( x x 2 a 2 ) show that 2 x2 a2 dx 23 Find the dimensions of the right circular cylinder with the greatest volume that can be inscribed in a sphere of radius “a.”OR If tangent at any point on the curve xmyn=am+n meets coordinate axes at A,B then show that AP:BP is constant 24 Water is dripping out from a conical funnel, at a uniform rate of 2cm3/sec, through a tiny hole at the vertex at the bottom. When the slant height of the water is 4cm, find the rate of decrease of the slant height of the water given that the vertical angle of the funnel is 120. OR A man 6ft. high walks at a uniform rate of 4 miles per hour away from a lamp 20 ft. high. Find the rate at which the length of is shadow increase. (1mile = 5280 ft.)