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Select the correct alternative : (Only one is correct) Q.1 If the lines x + y + 1 = 0 ; 4x + 3y + 4 = 0 and x + αy + β = 0, where α2 + β2 = 2, are concurrent then (A) α = 1, β = – 1 (B) α = 1, β = ± 1 (C) α = – 1, β = ± 1 (D) α = ± 1, β = 1 Q.2 The axes are translated so that the new equation of the circle x²+y²– 5x+ 2y – 5 = 0 has no first degree terms. Then the new equation is : (A) x2 + y2 = 9 (B) x2 + y2 = 49 4 (C) x2 + y2 = 81 16 (D) none of these Q.3 Given the family of lines, a(3x + 4y + 6) + b(x + y + 2) = 0 . The line of the family situated at the greatest distance from the point P (2, 3) has equation : (A) 4x + 3y + 8 = 0 (B) 5x + 3y + 10 = 0 (C) 15x + 8y + 30 = 0 (D) none Q.4 The ends of a quadrant of a circle have the coordinates (1, 3) and (3, 1) then the centre of the such a circle is (A) (1, 1) (B) (2, 2) (C) (2, 6) (D) (4, 4) Q.5 The straight line, ax + by = 1 makes with the curve px2 + 2axy + qy2 = r a chord which subtends a right angle at the origin . Then : (A) r (a2 + b2) = p + q (B) r (a2 + p2) = q + b (C) r (b2 + q2) = p + a (D) none Q.6 The circle described on the line joining the points (0 , 1), (a, b) as diameter cuts the x–axis in points whose abscissae are roots of the equation : (A) x² + ax + b = 0 (B) x² – ax + b = 0 (C) x² + ax – b = 0 (D) x² – ax – b = 0 Q.7 Centroid of the triangle, the equations of whose sides are 12x2 – 20xy + 7y2 = 0 and 2x – 3y + 4=0 is ( 8 , 8 ( 3, 8 ( 8 , 3 (A) (3, 3) (B) 3 (C) 3 (D) Q.8 The line 2x – y + 1 = 0 is tangent to the circle at the point (2, 5) and the centre of the circles lies on x – 2y = 4. The radius of the circle is (A) 3 (B) 5 (C) 2 (D) 5 Q.9 The line x + 3y – 2 = 0 bisects the angle between a pair of straight lines of which one has equation x – 7y + 5 = 0 . The equation of the other line is : (A) 3x + 3y – 1 = 0 (B) x – 3y + 2 = 0 (C) 5x + 5y – 3 = 0 (D) none Q.10 Given two circles x² + y² – 6x – 2y+ 5 = 0 & x² + y² + 6x + 22y+ 5 = 0. The tangent at (2, –1) to the first circle : (A) passes outside the second circle (B) touches the second circle (C) intersects the second circle in 2 real points (D) passes through the centre of the second circle. Q.11 A variable rectangle PQRS has its sides parallel to fixed directions. Q & S lie respectively on the lines x = a, x = – a & P lies on the x – axis . Then the locus of R is : (A) a straight line (B) a circle (C) a parabola (D) pair of straight lines Q.12 To which of the following circles, the line y– x + 3 = 0 is normal at the point ( 3+ 3 3 ( 3 2 ( 3 2 ( 3 2 ( 3 2 (A) x – 3– + y – = 9 (B) x – + y – = 9 2 2 2 2 (C) x² + (y – 3)² = 9 (D) (x – 3)² + y² = 9 Q.13 On the portion of the straight line, x + 2y = 4 intercepted between the axes, a square is constructed on the side of the line away from the origin. Then the point of intersection of its diagonals has co-ordinates (A) (2, 3) (B) (3, 2) (C) (3, 3) (D) (2

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Select the correct alternative : (Only one is correct) Q.1 If the lines x + y + 1 = 0 ; 4x + 3y + 4 = 0 and x + αy + β = 0, where α2 + β2 = 2, are concurrent then (A) α = 1, β = – 1 (B) α = 1, β = ± 1 (C) α = – 1, β = ± 1 (D) α = ± 1, β = 1 Q.2 The axes are translated so that the new equation of the circle x²+y²– 5x+ 2y – 5 = 0 has no first degree terms. Then the new equation is : (A) x2 + y2 = 9 (B) x2 + y2 = 49 4 (C) x2 + y2 = 81 16 (D) none of these Q.3 Given the family of lines, a(3x + 4y + 6) + b(x + y + 2) = 0 . The line of the family situated at the greatest distance from the point P (2, 3) has equation : (A) 4x + 3y + 8 = 0 (B) 5x + 3y + 10 = 0 (C) 15x + 8y + 30 = 0 (D) none Q.4 The ends of a quadrant of a circle have the coordinates (1, 3) and (3, 1) then the centre of the such a circle is (A) (1, 1) (B) (2, 2) (C) (2, 6) (D) (4, 4) Q.5 The straight line, ax + by = 1 makes with the curve px2 + 2axy + qy2 = r a chord which subtends a right angle at the origin . Then : (A) r (a2 + b2) = p + q (B) r (a2 + p2) = q + b (C) r (b2 + q2) = p + a (D) none Q.6 The circle described on the line joining the points (0 , 1), (a, b) as diameter cuts the x–axis in points whose abscissae are roots of the equation : (A) x² + ax + b = 0 (B) x² – ax + b = 0 (C) x² + ax – b = 0 (D) x² – ax – b = 0 Q.7 Centroid of the triangle, the equations of whose sides are 12x2 – 20xy + 7y2 = 0 and 2x – 3y + 4=0 is ( 8 , 8 ( 3, 8 ( 8 , 3 (A) (3, 3) (B) 3 (C) 3 (D) Q.8 The line 2x – y + 1 = 0 is tangent to the circle at the point (2, 5) and the centre of the circles lies on x – 2y = 4. The radius of the circle is (A) 3 (B) 5 (C) 2 (D) 5 Q.9 The line x + 3y – 2 = 0 bisects the angle between a pair of straight lines of which one has equation x – 7y + 5 = 0 . The equation of the other line is : (A) 3x + 3y – 1 = 0 (B) x – 3y + 2 = 0 (C) 5x + 5y – 3 = 0 (D) none Q.10 Given two circles x² + y² – 6x – 2y+ 5 = 0 & x² + y² + 6x + 22y+ 5 = 0. The tangent at (2, –1) to the first circle : (A) passes outside the second circle (B) touches the second circle (C) intersects the second circle in 2 real points (D) passes through the centre of the second circle. Q.11 A variable rectangle PQRS has its sides parallel to fixed directions. Q & S lie respectively on the lines x = a, x = – a & P lies on the x – axis . Then the locus of R is : (A) a straight line (B) a circle (C) a parabola (D) pair of straight lines Q.12 To which of the following circles, the line y– x + 3 = 0 is normal at the point ( 3+ 3 3 ( 3 2 ( 3 2 ( 3 2 ( 3 2 (A) x – 3– + y – = 9 (B) x – + y – = 9 2 2 2 2 (C) x² + (y – 3)² = 9 (D) (x – 3)² + y² = 9 Q.13 On the portion of the straight line, x + 2y = 4 intercepted between the axes, a square is constructed on the side of the line away from the origin. Then the point of intersection of its diagonals has co-ordinates (A) (2, 3) (B) (3, 2) (C) (3, 3) (D) (2

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- 2. Select the correct alternative : (Only one is correct) Q.1 If the lines x + y+ 1 = 0 ; 4x + 3y+ 4 = 0 and x + y+ = 0, where 2 + 2 = 2, are concurrent then (A) = 1, = – 1 (B) = 1, = ± 1 (C) = – 1, = ± 1 (D) = ± 1, = 1 Q.2 The axes aretranslated sothat the new equation of thecircle x²+y²5x+2y–5 =0has no first degree terms. Thenthenewequationis : (A) x2 + y2 = 9 (B) x2 + y2 = 49 4 (C) x2 + y2 = 81 16 (D) none of these Q.3 Giventhefamilyoflines, a(3x+4y+6)+b(x +y+2)=0.Thelineofthefamilysituatedat thegreatest distance from thepoint P (2, 3)has equation : (A) 4x + 3y + 8 = 0 (B) 5x + 3y + 10 = 0 (C) 15x + 8y + 30 = 0 (D) none Q.4 The ends of a quadrant of a circle have the coordinates (1, 3) and (3, 1) then the centre of the such a circleis (A) (1, 1) (B) (2, 2) (C) (2, 6) (D) (4, 4) Q.5 Thestraight line,ax+by=1 makes withthecurve px2 +2axy+qy2 =r achord whichsubtends aright angleat theorigin.Then: (A) r (a2 + b2) = p + q (B) r (a2 + p2) = q + b (C) r (b2 + q2) = p + a (D) none Q.6 The circle described onthelinejoiningthe points (0,1), (a,b) as diameter cuts thexaxis in points whose abscissae are roots of the equation : (A) x² + ax + b = 0 (B) x² ax + b = 0 (C) x² + ax b = 0 (D) x² ax b = 0 Q.7 Centroid of the triangle, the equations of whose sides are 12x2 – 20xy + 7y2 = 0 and 2x – 3y+ 4=0 is (A) (3, 3) (B) 3 8 , 3 8 (C) 3 8 , 3 (D) 3 , 3 8 Q.8 The line 2x – y + 1 = 0 is tangent to the circle at the point (2, 5) and the centre of the circles lies on x – 2y= 4. The radius of the circle is (A) 5 3 (B) 3 5 (C) 5 2 (D) 2 5 Q.9 The line x + 3y 2 = 0 bisects the angle between a pair of straight lines of which one has equation x 7y+ 5 = 0 . The equation of the other line is : (A) 3x + 3y 1 = 0 (B) x 3y + 2 = 0 (C) 5x + 5y 3 = 0 (D) none Q.10 Given two circles x² + y² 6x 2y+ 5 = 0 & x² + y² + 6x + 22y+ 5 = 0. The tangent at (2, 1) to the first circle: (A) passes outside the second circle (B) touches the second circle (C) intersects the second circle in 2 real points (D) passes through the centre of the second circle. Q.11 A variable rectanglePQRS has its sides parallel to fixed directions. Q& S lie respectivelyon the lines x = a, x = a & P lies on the xaxis . Then the locus of R is : (A) astraight line (B) a circle (C) a parabola (D) pairofstraight lines Q.12 To which of the following circles, the line yx+3 = 0 is normal at the point 3 3 2 3 2 , ? (A) x y 3 3 2 3 2 9 2 2 (B) x y 3 2 3 2 9 2 2 (C) x² + (y 3)² = 9 (D) (x 3)² + y² = 9
- 3. Q.13 On the portion of the straight line, x + 2y= 4 intercepted between the axes, a square is constructed on theside ofthelineawayfromtheorigin. Thenthe pointofintersection ofitsdiagonals has co-ordinates (A) (2, 3) (B) (3, 2) (C) (3, 3) (D) (2, 2) Q.14 The locus of the mid point of a chord of the circle x²+y² = 4 which subtends a right angleat the origin is (A) x + y = 2 (B) x² + y² = 1 (C) x² + y² = 2 (D) x + y = 1 Q.15 Given the familyoflines, a(2x +y+ 4)+ b(x 2y 3)=0.Amongthe lines ofthefamily, the number of lines situated at a distance of 10 from the point M(2, 3) is : (A) 0 (B) 1 (C) 2 (D) Q.16 The equation of the line passing through the points of intersection of the circles ; 3x² + 3y² 2x + 12y 9 = 0 & x² + y² + 6x + 2y 15 = 0 is : (A) 10x 3y 18 = 0 (B) 5x + 3y 18 = 0 (C) 5x 3y 18 = 0 (D) 10x + 3y+ 1 = 0 Q.17 ThroughapointAonthex-axisastraight lineisdrawnparallelto y-axis soasto meet thepairofstraight lines ax2 + 2hxy + by2 = 0 in B and C. IfAB = BC then (A) h2 = 4ab (B) 8h2 = 9ab (C) 9h2 = 8ab (D) 4h2 = ab Q.18 The number of common tangent(s) to the circles x2 +y2 +2x +8y –23 = 0 and x2 + y2 – 4x – 10y+ 19 = 0 is (A) 1 (B) 2 (C) 3 (D) 4 Q.19 A, B and C are points in the xy plane such thatA(1, 2) ; B (5, 6) andAC = 3BC. Then (A)ABC isauniquetriangle (B) Therecan be onlytwo such triangles. (C) No suchtriangle is possible (D)Therecan beinfinitenumberofsuch triangles. Q.20 From the point A(0, 3) on the circle x² +4x +(y3)² = 0 a chord AB is drawn & extended to a point M such that AM = 2AB. The equation of the locus of M is : (A) x² + 8x + y² = 0 (B) x² + 8x + (y 3)² = 0 (C) (x 3)² + 8x + y² = 0 (D) x² + 8x + 8y² = 0 Q.21 IfA(1, p2) ; B (0, 1) and C (p, 0) are the coordinates of three points then the value of p for which the areaofthetriangleABCisminimum,is (A) 3 1 (B) – 3 1 (C) 3 1 or – 3 1 (D) none Q.22 The area of the quadrilateral formed by the tangents from the point (4 , 5) to the circle x²+ y² 4x2y11 = 0 with the pair of radii through the points of contact of the tangents is : (A) 4 sq.units (B) 8 sq.units (C) 6 sq.units (D) none Q.23 The area of triangle formed by the lines x + y – 3 = 0 , x – 3y + 9 = 0 and 3x – 2y + 1= 0 (A) 7 16 sq. units (B) 7 10 sq. units (C) 4 sq. units (D) 9 sq. units Q.24 Two circles of radii 4cms & 1cm touch each other externallyand is the angle contained by their direct common tangents. Then sin = (A) 25 24 (B) 25 12 (C) 4 3 (D) none Q.25 The set of lines ax + by + c = 0, where 3a + 2b + 4c = 0, is concurrent at the point : (A) 3 4 3 4 , (B) 1 2 1 2 , (C) 3 4 1 2 , (D) (1, 1)
- 4. Q.26 The locus of poles whose polar with respect to x² +y² = a² always passes through (K , 0) is (A) Kx a² = 0 (B) Kx + a² = 0 (C) Ky + a² = 0 (D) Ky a² = 0 Q.27 The coordinates of the point of reflection of the origin (0, 0) in the line 4x 2y 5 = 0 is : (A) (1, 2) (B) (2, 1) (C) 4 5 2 5 , (D) (2, 5) Q.28 Thelocus ofthemidpoints ofthechords of the circle x2+ y2 axby=0 which subtend a right angle at a 2 b 2 , is (A) ax + by = 0 (B) ax + by = a2 + b2 (C) x2 + y2 ax by+ 8 b a 2 2 = 0 (D) x2 + y2 ax by 8 b a 2 2 = 0 Q.29 Arayof light passingthrough the point A(1, 2) is reflected at a point B on the xaxis and then passes through (5, 3).Then the equation ofAB is : (A) 5x + 4y = 13 (B) 5x 4y = 3 (C) 4x + 5y = 14 (D) 4x 5y = 6 Q.30 From (3,4)chords are drawntothe circle x² + y²4x =0. The locus of the mid points of the chords is (A) x² + y² 5x 4y + 6 = 0 (B) x² + y² + 5x 4y + 6 = 0 (C) x² + y² 5x + 4y + 6 = 0 (D) x² + y² 5x 4y 6 = 0 Q.31 m, nare integerwith 0< n< m.Ais thepoint(m, n) onthe cartesian plane. Bis thereflection ofAin the liney=x.CisthereflectionofBinthey-axis,Dis thereflection ofCinthex-axis andEisthereflection of Din the y-axis.The area of the pentagonABCDE is (A) 2m(m + n) (B) m(m + 3n) (C) m(2m + 3n) (D) 2m(m + 3n) Q.32 Which one of the following is false ? The circles x² + y² 6x 6y+ 9 = 0 & x² + y² + 6x + 6y+ 9 = 0 are such that : (A) theydo not intersect (B) theytouch each other (C) theirexterior common tangents are parallel (D) their interior common tangents are perpendicular. Q.33 The lines y y1 = m (x x1) ± a 1 2 m are tangents to the same circle . The radius of the circle is (A) a/2 (B) a (C) 2a (D) none Q.34 The centre of the smallest circle touching the circles x² + y² 2y3 = 0 and x² + y² 8x 18y + 93 = 0 is : (A) (3 , 2) (B) (4 , 4) (C) (2 , 7) (D) (2 , 5) Q.35 The ends of the base ofan isosceles triangle areat (2, 0) and(0, 1) and theequation of one sideis x = 2 thenthe orthocentreofthetriangleis (A) 2 3 , 4 3 (B) 1 , 4 5 (C) 1 , 4 3 (D) 12 7 , 3 4 Q.36 A rhombus is inscribed in the region common to the two circles x2 + y2 4x 12 = 0 and x2 +y2 +4x12=0 withtwoofits verticesonthe linejoiningthecentres ofthecircles. The areaof the rhombousis (A) 8 3 sq.units (B) 4 3 sq.units (C) 16 3 sq.units (D) none
- 5. Q.37 Avariablestraight linepasses throughafixed point (a,b)intersectingthecoordinates axesatA&B. If 'O'is the origin then thelocus ofthe centroid of the triangle OABis : (A) bx + ay 3xy = 0 (B) bx + ay 2xy = 0 (C) ax + by 3xy = 0 (D) none Q.38 The angle between the two tangents from the origin to the circle (x7)2 + (y+1)2 = 25 equals (A) 4 (B) 3 (C) 2 (D) none Q.39 If P = (1, 0); Q = (1, 0) & R = (2, 0) are three given points, then the locus of the points S satisfying the relation, SQ2 + SR2 = 2 SP2 is : (A) astraight lineparalleltoxaxis (B) a circlepassing throughtheorigin (C) acircle with the centreat the origin (D) astraight lineparallel to yaxis. Q.40 The equation of the circle having normal at (3, 3) as the straight line y= x and passing through the point (2, 2) is : (A) x² + y² 5x + 5y + 12 = 0 (B) x² + y² + 5x 5y + 12 = 0 (C) x² + y² 5x 5y 12 = 0 (D) x² + y² 5x 5y + 12 = 0 Q.41 The equation of the baseofanequilateral triangleABC is x +y= 2 and thevertex is (2, 1).The area of the triangleABC is : (A) 2 6 (B) 3 6 (C) 3 8 (D) none Q.42 InarighttriangleABC, rightangledatA,onthe legACasdiameter,asemicircleisdescribed.Thechord joiningAwiththepointofintersectionDofthehypotenuseandthesemicircle,thenthelengthACequalsto (A) AB AD AB AD 2 2 (B) AB AD AB AD (C) AB AD (D) AB AD AB AD 2 2 Q.43 The equation ofthe pair of bisectors of the angles between twostraight lines is, 12x2 7xy 12y2 = 0. If the equation of one line is 2y x = 0 then the equation of the other line is : (A) 41x 38y = 0 (B) 38x 41y = 0 (C) 38x + 41y = 0 (D) 41x + 38y = 0 Q.44 If the circle C1 : x2 + y2 = 16 intersects another circle C2 of radius 5 in such a manner that the commonchordisofmaximumlengthand has aslopeequal to3/4,thentheco-ordinates of thecentreof C2 are : (A) 9 5 12 5 , (B) 9 5 12 5 , (C) 12 5 9 5 , (D) 12 5 9 5 , Q.45 Area of the rhombus bounded bythe four lines, ax ± by± c = 0 is : (A) c ab 2 2 (B) 2 2 c ab (C) 4 2 c ab (D) ab c 4 2 Q.46 Two lines p1x + q1y + r1 = 0 & p2x + q2y + r2 = 0 are conjugate lines w.r.t. the circle x² + y² = a² if (A) p1p2 + q1q2 = r1r2 (B) p1p2 + q1q2 + r1r2 = 0 (C) a²(p1p2 + q1q2) = r1r2 (D) p1p2 + q1q2 = a² r1r2 Q.47 Area of the quadrilateral formed bythe lines x + y = 2 is : (A) 8 (B) 6 (C) 4 (D) none Q.48 If the two circles (x1)² + (y3)² = r² & x²+y²8x+2y+ 8 = 0 intersect in two distinct points then (A) 2 < r < 8 (B) r < 2 (C) r = 2 (4) r > 2
- 6. Q.49 Let the algebraic sum of theperpendicular distances from the points (3, 0), (0, 3) & (2, 2) to a variable straight linebezero, then theline passes through afixed point whose co-ordinates are : (A) (3, 2) (B) (2, 3) (C) 3 5 3 5 , (D) 5 3 5 3 , Q.50 If a circle passes through the point (a , b) & cuts the circle x² + y² = K² orthogonally, then the equation of the locus of its centre is : (A) 2ax + 2by (a² + b² + K²) = 0 (B) 2ax + 2by (a² b² + K²) = 0 (C) x² + y² 3ax 4by + (a² + b² K²) = 0 (D) x² + y² 2ax 3by + (a² b² K²) = 0 Q.51 Consider a quadratic equation in Zwith parameters x and yas Z2 – xZ + (x – y)2 = 0 The parameters x and y are the co-ordinates of a variable point P w.r.t. an orthonormal co-ordinate system ina plane. If thequadratic equation has equal roots then the locus of P is (A) a circle (B) a linepair through the originof co-ordinates with slope 1/2 and 2/3 (C) a linepair through the originof co-ordinates with slope 3/2 and 2 (D) a linepair through the originof co-ordinates with slope3/2 and 1/2 Q.52 Consider the circle S x2 + y2 –4x – 4y+4 = 0. If another circle of radius 'r' less than the radius of the circle S is drawn, touching the circle S, and the coordinate axes, then the valueof 'r' is (A) 3 – 2 2 (B) 4 – 2 2 (C) 7 – 2 4 (D) 6 – 2 4 Q.53 Vertices of a parallelogram ABCD are A(3, 1), B(13, 6), C(13, 21) and D(3, 16). If a line passing throughtheorigindivides theparallelogramintotwocongruent partsthen theslopeofthelineis (A) 12 11 (B) 8 11 (C) 8 25 (D) 8 13 Q.54 The distance between the chords of contact of tangents to the circle ; x2+y2 +2gx+2fy+ c =0 from the origin & the point (g, f) is : (A) g f 2 2 (B) g f c 2 2 2 (C) g f c g f 2 2 2 2 2 (D) g f c g f 2 2 2 2 2 Q.55 Two mutuallyperpendicular straight lines through the origin from an isosceles triangle with the line 2x + y= 5. Then the area of the triangle is (A) 5 (B) 3 (C) 5/2 (D) 1 Q.56 The locus of the centers of the circles which cut the circles x2 + y2 + 4x 6y + 9 = 0 and x2 +y2 5x +4y2 = 0 orthogonally is (A) 9x + 10y 7 = 0 (B) x y+ 2 = 0 (C) 9x 10y+ 11=0 (D) 9x + 10y+ 7 = 0 Q.57 Distance between thetwo lines represented bythe line pair, x2 4xy + 4y2 + x 2y 6 = 0 is : (A) 1 5 (B) 5 (C) 2 5 (D) none Q.58 The locus of the center of the circles such that the point (2 , 3) is the mid point of the chord 5x + 2y = 16 is : (A) 2x 5y + 11 = 0 (B) 2x + 5y 11 = 0 (C) 2x + 5y+ 11 = 0 (D) none
- 7. Q.59 The distance between the two parallel lines is 1 unit.Apoint 'A' is chosen to lie between the lines at a distance'd'from oneofthem.TriangleABC is equilateralwith B on onelineand C ontheotherparallel line.Thelengthofthesideoftheequilateraltriangleis (A) 1 d d 3 2 2 (B) 3 1 d d 2 2 (C) 1 d d 2 2 (D) 1 d d2 Q.60 The locus of the midpointsofthe chords ofthecircle x²+y²+4x6y12=0 which subtend an angle of 3 radians at its circumferenceis : (A) (x 2)² + (y + 3)² = 6.25 (B) (x + 2)² + (y 3)² = 6.25 (C) (x + 2)² + (y 3)² = 18.75 (D) (x + 2)² + (y + 3)² = 18.75 Q.61 GivenA(0,0) and B(x, y)with x (0, 1) and y> 0. Let the slopeof the lineAB equals m1. Point C lies on the linex = 1 such that the slope ofBC equals m2 where 0 < m2 < m1. Ifthe area of thetriangleABC can be expressed as (m1 – m2) f (x), then the largest possible value of f (x) is (A) 1 (B) 1/2 (C) 1/4 (D) 1/8 Q.62 If two chords of the circle x2 + y2 ax by = 0, drawn from the point (a, b) is divided by the xaxis in the ratio 2: 1 then: (A) a2 > 3 b2 (B) a2 < 3 b2 (C) a2 > 4 b2 (D) a2 < 4 b2 Q.63 P lies on the line y = x and Q lies on y = 2x. The equation for the locus of the mid point of PQ, if | PQ | = 4, is (A) 25x2 + 36xy + 13y2 = 4 (B) 25x2 – 36xy + 13y2 = 4 (C) 25x2 – 36xy – 13y2 = 4 (D) 25x2 + 36xy – 13y2 = 4 Q.64 The points (x1, y1), (x2, y2), (x1, y2) & (x2, y1) are always : (A)collinear (B)concyclic (C) vertices of a square (D) vertices of a rhombus Q.65 If the vertices Pand Q of a triangle PQR are given by(2, 5) and (4, –11) respectively, and the point R moves alongthe line N: 9x + 7y+ 4 = 0, then the locus of the centroid of the triangle PQRis a straight lineparallelto (A) PQ (B) QR (C) RP (D) N Q.66 The angle at which the circles (x – 1)2 + y2 = 10 and x2 + (y – 2)2 = 5 intersect is (A) 6 (B) 4 (C) 3 (D) 2 Q.67 The coordinates of the points A, B, C are ( 4, 0) , (0, 2) & ( 3, 2) respectively. The point of intersectionofthelinewhichbisectstheangleCABinternallyandthelinejoiningCtothemiddlepointof ABis (A) 7 3 4 3 , (B) 5 2 13 2 , (C) 7 3 10 3 , (D) 5 2 3 2 , Q.68 Twocongruentcircleswithcentres at(2, 3)and(5,6)whichintersectatrightangles hasradiusequal to (A) 2 2 (B) 3 (C) 4 (D) none Q.69 Three lines x + 2y + 3 = 0 ; x + 2y – 7 = 0 and 2x – y – 4 = 0 form the three sides of two squares. The equation to the fourth side of each square is (A) 2x – y + 14 = 0 & 2x – y + 6 = 0 (B) 2x – y + 14 = 0 & 2x – y – 6 = 0 (C) 2x – y – 14 = 0 & 2x – y – 6 = 0 (D) 2x – y – 14 = 0 & 2x – y + 6 = 0
- 8. Q.70 Acircleof radius unityis centred at origin.Two particles start moving at the same time from the point (1, 0) and move around the circle in opposite direction. One of the particle moves counterclockwise with constant speed v and the other moves clockwise with constant speed 3v.After leaving (1, 0), the two particles meet first at apoint P, andcontinueuntil theymeet next at point Q.Thecoordinates of the point Q are (A) (1, 0) (B) (0, 1) (C) (0, –1) (D) (–1, 0) Q.71 The pointsA(a, 0), B(0, b), C(c, 0) & D(0, d) are such that ac = bd & a, b, c, d are all nonzero.The thepoints (A) form aparallelogram (B) do not lie on a circle (C) forma trapezium (D) are concyclic Q.72 The value of 'c' for which the set, {(x, y)x2 + y2 + 2x 1} {(x, y)x y + c 0} contains only onepoint incommonis: (A) (, 1] [3, ) (B) {1, 3} (C) {3} (D) { 1 } Q.73 GivenA (1,1) andABis anylinethrough it cuttingthex-axis in B.IfAC is perpendiculartoABand meets the y-axis in C, then the equation of locus of mid- point P of BC is (A) x + y = 1 (B) x + y = 2 (C) x + y = 2xy (D) 2x + 2y = 1 Q.74 Acircle is inscribed into a rhombousABCD with one angle 60º.The distance from the centre of the circle to thenearest vertex is equal to 1 . If P is anypoint of the circle, then PA PB PC PD 2 2 2 2 is equal to : (A) 12 (B) 11 (C) 9 (D) none Q.75 Thenumberofpossiblestraightlines,passingthrough(2,3)andformingatrianglewithcoordinateaxes, whose area is 12 sq. units , is (A) one (B) two (C) three (D)four Q.76 P is a point (a, b) in the first quadrant. If the two circles which pass through P and touch both the co-ordinate axes cut at right angles, then : (A) a2 6ab + b2 = 0 (B) a2 + 2ab b2 = 0 (C) a2 4ab + b2 = 0 (D) a2 8ab + b2 = 0 Q.77 In a triangleABC , ifA(2, – 1) and 7x – 10y+ 1 = 0 and 3x – 2y + 5 = 0 are equations of an altitude and an angle bisector respectivelydrawnfrom B, then equation of BC is (A) x + y + 1 = 0 (B) 5x + y + 17 = 0 (C) 4x + 9y + 30 = 0 (D) x – 5y – 7 = 0 Q.78 The range of values of 'a' such that the angle between the pair of tangents drawn from the point (a, 0) to the circle x2 + y2 = 1 satisfies 2 < < is : (A) (1, 2) (B) 1 2 , (C) 2 1 , (D) 2 1 , 1 2 , Q.79 Distance of the point (2, 5) from the line 3x + y + 4 = 0 measured parallel to the line 3x 4y + 8 = 0 is (A) 15/2 (B) 9/2 (C) 5 (D) None Q.80 Threeconcentriccirclesofwhichthebiggestis x2 +y2 =1,havetheirradiiinA.P.Iftheliney = x + 1 cuts allthecirclesinrealanddistinctpoints.TheintervalinwhichthecommondifferenceoftheA.P.willlieis (A) 0 1 4 , (B) 0 1 2 2 , (C) 0 2 2 4 , (D) none
- 9. Q.81 Theco-ordinatesofthevertices P,Q,R & SofsquarePQRS inscribed inthetriangleABCwith vertices A (0, 0), B (3, 0) & C (2, 1)given that two of its vertices P, Q are on the sideABare respectively (A) 1 4 0 3 8 0 3 8 1 8 1 4 1 8 , , , , , & , (B) 1 2 0 3 4 0 3 4 1 4 1 2 1 4 , , , , , & , (C) (1, 0) , 3 2 0 3 3 1 2 1 1 2 , , , & , (D) 3 2 0 9 4 0 9 4 3 4 3 2 3 4 , , , , , & , Q.82 A tangent at a point on the circle x2 + y2 = a2 intersectsa concentriccircle C at two points P and Q. The tangents to thecircleX at P andQ meet at apoint onthecircle x2 + y2 = b2 thentheequation ofcircle is (A) x2 + y2 = ab (B) x2 + y2 = (a – b)2 (C) x2 + y2 = (a + b)2 (D) x2 + y2 = a2 + b2 Q.83 AB is the diameter of a semicircle k, C is an arbitrary point on the semicircle (otherthanAor B) andS is the centre ofthecircle inscribed intotriangleABC,thenmeasureof (A) angleASB changes as C moves on k. (B)angleASBis thesameforall positionsofCbutitcannotbedeterminedwithoutknowingtheradius. (C) angleASB = 135° for all C. (D) angleASB = 150° for all C. Q.84 Tangents are drawn to the circle x2 + y2 = 1 at the points where it is met by the circles, x2 + y2 ( + 6)x + (8 2) y 3 = 0 . being the variable . The locus of the point of intersection of thesetangentsis : (A) 2x y+ 10 = 0 (B) x + 2y 10 = 0 (C) x 2y+ 10 = 0 (D) 2x + y 10 = 0 Q.85 Given x a y b = 1 and ax + by= 1 are two variable lines, 'a' and 'b' being the parameters connected by the relation a2 + b2 = ab. The locus of the point of intersection has the equation (A) x2 + y2 + xy 1 = 0 (B) x2 + y2 – xy + 1 = 0 (C) x2 + y2 + xy + 1 = 0 (D) x2 + y2 – xy – 1 = 0 Q.86 B & C arefixed points havingcoordinates (3, 0) and (3, 0)respectively. Ifthe vertical angle BAC is 90º, then the locus of the centroid of the ABC has the equation : (A) x2 + y2 = 1 (B) x2 + y2 = 2 (C) 9 (x2 + y2) = 1 (D) 9 (x2 + y2) = 4 Q.87 The set ofvalues of 'b' for which theorigin and the point (1, 1) lie on the same side ofthe straight line, a2x + a by + 1 = 0 a R, b > 0 are : (A) b (2, 4) (B) b (0, 2) (C) b [0, 2] (D) (2, ) Q.88 If a a , 1 , b b , 1 , c c , 1 & d d , 1 are four distinct points on a circle of radius 4 units then, abcd is equal to (A) 4 (B) 1/4 (C) 1 (D) 16 Q.89 Triangle formed by the lines x + y = 0 , x – y = 0 and lx + my = 1. If l and m vary subject to the condition l 2 + m2 = 1 then the locus of its circumcentre is (A) (x2 – y2)2 = x2 + y2 (B) (x2 + y2)2 = (x2 – y2) (C) (x2 + y2) = 4x2 y2 (D) (x2 – y2)2 = (x2 + y2)2 Q.90 Tangents aredrawntoaunitcirclewithcentreatthe originfrom eachpoint on theline 2x +y=4.Then the equation to the locus of themiddle point of the chordof contact is (A) 2 (x2 + y2) = x + y (B) 2 (x2 + y2) = x + 2 y (C) 4 (x2 + y2) = 2x + y (D) none
- 10. Q.91 The coordinates ofthreepoints A(4, 0); B(2, 1)and C(3, 1)determine the vertices ofan equilateral trapeziumABCD.The coordinates ofthe vertex Dare : (A) (6, 0) (B) ( 3, 0) (C) ( 5, 0) (D) (9, 0) Q.92 ABCDisasquare ofunitarea.Acircle istangent to two sidesofABCD and passesthrough exactlyone of its vertices. The radius of the circle is (A) 2 2 (B) 1 2 (C) 2 1 (D) 2 1 Q.93 Aparallelogramhas 3 ofits vertices as (1, 2),(3, 8)and(4, 1).Thesum ofallpossible x-coordinates for the 4th vertex is (A) 11 (B) 8 (C) 7 (D) 6 Q.94 Apair of tangents are drawn to a unit circle with centre at the origin and these tangents intersect atA enclosing an angle of 60°. The area enclosed bythese tangents and the arc of the circle is (A) 3 2 – 6 (B) 3 – 3 (C) 3 – 6 3 (D) 6 1 3 Q.95 The image of the pair of lines represented by ax2 + 2h xy + by2 = 0 by the line mirror y= 0 is (A) ax2 2h xy by2 = 0 (B) bx2 2h xy + ay2 = 0 (C) bx2 + 2h xy + ay2 = 0 (D) ax2 2h xy + by2 = 0 Q.96 A straight line with slope 2 and y-intercept 5 touches the circle, x2 + y2 + 16x + 12y+ c = 0 at a point Q. Then the coordinates of Q are (A) (–6, 11) (B) (–9, –13) (C) (–10, – 15) (D) (–6, –7) Q.97 Theacuteanglebetweentwostraightlines passingthroughthepoint M(6,8)and thepointsinwhich the line segment 2x + y + 10 = 0 enclosed between the co-ordinate axes is divided in the ratio 1:2:2inthedirectionfromthepointofitsintersectionwiththex-axistothepointofintersectionwiththe y-axisis (A) /3 (B) /4 (C) /6 (D) /12 Q.98 Avariable circle cuts each of the circles x2 + y2 2x = 0 & x2 + y2 4x 5 = 0 orthogonally. The variable circle passes throughtwo fixed points whose coordinates are : (A) 5 3 2 0 , (B) 5 3 5 2 0 , (C) 5 5 3 2 0 , (D) 5 5 2 0 , Q.99 If in triangle ABC , A (1, 10) , circumcentre 1 3 2 3 , and orthocentre 11 3 4 3 , then the co-ordinates of mid-point of side opposite toAis : (A) (1, 11/3)(B) (1, 5) (C) (1, 3) (D) (1, 6) Q.100 TheradicalcentreofthreecirclestakeninpairsdescribedonthesidesofatriangleABCasdiametresisthe (A) centroid of the ABC (B) incentre of the ABC (C) circumcentre o the ABC (D) orthocentre of the ABC Q.101 The line x + y= p meets the axis of x & y atA& B respectively.AtriangleAPQ is inscribed in the triangle OAB, Obeing the origin, with right angle at Q. Pand Q lierespectivelyon OB andAB. If the area of the triangleAPQ is 3/8th of the area of the triangle OAB, then AQ BQ is equal to : (A) 2 (B) 2/3 (C) 1/3 (D) 3
- 11. Q.102 Twocirclesaredrawnthroughthepoints(1,0)and(2,1)totouchtheaxisof y.Theyintersectatanangle (A) cot–1 3 4 (B) cos 1 4 5 (C) 2 (D) tan1 1 Q.103 In a triangle ABC, side AB has the equation 2 x + 3 y = 29 and the side AC has the equation, x + 2y = 16 . If the midpoint of BC is (5, 6) then the equation of BC is : (A) x y = 1 (B) 5 x 2 y = 13 (C) x + y = 11 (D) 3 x 4 y = 9 Q.104 If the line x cos + y sin = 2 is the equation of a transverse common tangent to the circles x2 + y2 = 4 and x2 + y2 6 3 x 6y + 20 = 0, then the value of is : (A) 5/6 (B) 2/3 (C) /3 (D) /6 Q.105 ABC is an isosceles triangle. If the co-ordinates of the base are (1, 3) and ( 2, 7), then co-ordinates of vertexAcan be : (A) 1 2 5 , (B) 1 8 5 , (C) 5 6 5 , (D) 7 1 8 , Q.106 Acircleisdrawnwithy-axis as atangent andits centreat thepoint whichis thereflection of (3,4)inthe line y=x.The equation ofthe circle is (A) x2 + y2 – 6x – 8y + 16 = 0 (B) x2 + y2 – 8x – 6y + 16 = 0 (C) x2 + y2 – 8x – 6y + 9 = 0 (D) x2 + y2 – 6x – 8y + 9 = 0 Q.107 Aisapointoneitheroftwolinesy+ 3 x=2atadistanceof 4 3 unitsfromtheirpointofintersection. The co-ordinates of the foot of perpendicular fromAon the bisector of the anglebetween them are (A) 2 3 2 , (B) (0, 0) (C) 2 3 2 , (D) (0, 4) Q.108 A circle of constant radius 'a' passes through origin 'O' and cuts the axes of coordinates in points P and Q, then the equation of the locus of the foot of perpendicular from O to PQ is : (A) (x2 + y2) 1 1 2 2 x y = 4 a2 (B) (x2 + y2)2 1 1 2 2 x y = a2 (C) (x2 + y2)2 1 1 2 2 x y = 4 a2 (D) (x2 + y2) 1 1 2 2 x y = a2 Q.109 ThreestraightlinesaredrawnthroughapointPlyingintheinteriorofthe ABCandparalleltoitssides. The areas ofthe three resulting triangles with P as the vertex are s1, s2 and s3. The area of the triangle in terms of s1, s2 and s3 is : (A) s s s s s s 1 2 2 3 3 1 (B) s s s 1 2 3 3 (C) s s s 1 2 3 2 (D) none Q.110 The circle passing throughthe distinct points (1, t), (t, 1) & (t, t) forall values of 't' , passes through thepoint: (A) ( 1, 1) (B) ( 1, 1) (C) (1, 1) (D) (1, 1) Q.111 The sides of a ABC are 2x y + 5 = 0 ; x + y 5 = 0 and x 2y 5 = 0 . Sum of the tangents ofitsinterioranglesis : (A) 6 (B) 27/4 (C) 9 (D) none
- 12. Q.112 If a circle of constant radius 3k passes through the origin 'O' and meets co-ordinate axes atAand B then the locus ofthe centroid of thetriangleOAB is (A) x2 + y2 = (2k)2 (B) x2 + y2 = (3k)2 (C) x2 + y2 = (4k)2 (D) x2 + y2 = (6k)2 Q.113 Chords ofthecurve 4x2 + y2 x +4y=0 which subtend aright angleat theorigin passthrough afixed point whose co-ordinates are (A) 1 5 4 5 , (B) 1 5 4 5 , (C) 1 5 4 5 , (D) 1 5 4 5 , Q.114 Let x&ybetherealnumberssatisfyingtheequationx2 4x+y2 +3=0.Ifthemaximumandminimum values of x2 + y2 are M & m respectively, then the numerical value of M m is : (A) 2 (B) 8 (C) 15 (D) none of these Q.115 Ifthestraightlines joiningtheoriginandthepointsofintersectionofthecurve 5x2 + 12xy 6y2 + 4x 2y + 3 = 0 and x + ky 1 = 0 are equallyinclined to the co-ordinate axes then the value of k : (A) is equal to 1 (B) is equal to 1 (C) is equal to 2 (D) does not exist in the set of real numbers . Q.116 A line meets the co-ordinate axes in A & B. A circle is circumscribed about the triangle OAB. If d1 & d2 arethe distances of thetangent to thecircleat the originOfrom thepointsAand B respectively, the diameterofthecircleis : (A) 2 d d 2 2 1 (B) 2 d 2 d 2 1 (C) d1 + d2 (D) 2 1 2 1 d d d d Q.117 A pair of perpendicular straight lines is drawn through the origin forming with the line 2x + 3y= 6 an isosceles trianglerightangledatthe origin.Theequationto thelinepairis : (A) 5x2 24xy 5y2 = 0 (B) 5x2 26xy 5y2 = 0 (C) 5x2 + 24xy 5y2 = 0 (D) 5x2 + 26xy 5y2 = 0 Q.118 The equation of a line inclined at an angle 4 to the axis X, such that the two circles x2 + y2 = 4, x2 + y2 – 10x – 14y + 65 = 0 intercept equal lengths on it, is (A) 2x – 2y – 3 = 0 (B) 2x – 2y + 3 = 0 (C) x – y + 6 = 0 (D) x – y – 6 = 0 Q.119 If the line y= mx bisects the angle between the lines ax2 + 2h xy+ by2 = 0 then m is a root of the quadraticequation: (A) hx2 + (a b) x h = 0 (B) x2 + h (a b) x 1 = 0 (C) (a b) x2 + hx (a b) = 0 (D) (a b) x2 hx (a b) = 0 Q.120 Tangents are drawn from anypoint on the circle x2 + y2 = R2 to the circle x2 + y2 = r2. Ifthe line joining thepoints ofintersection of these tangents with thefirst circle also touch thesecond, then R equals (A) 2 r (B) 2r (C) 2 2 3 r (D) 4 3 5 r Q.121 An equilateral triangle has each of its sides of length 6 cm . If (x1, y1); (x2, y2) & (x3, y3) areits vertices thenthevalueofthedeterminant, 2 3 3 2 2 1 1 1 y x 1 y x 1 y x is equal to : (A) 192 (B) 243 (C) 486 (D) 972
- 13. Q.122 Avariable circleC has theequation x2 + y2 – 2(t2 – 3t + 1)x – 2(t2 + 2t)y + t = 0, where t is a parameter. If the power of point P(a,b) w.r.t. the circle C is constant then the ordered pair (a, b) is (A) 10 1 , 10 1 (B) 10 1 , 10 1 (C) 10 1 , 10 1 (D) 10 1 , 10 1 Q.123 Points A&Bareinthefirst quadrant;point 'O'is theorigin . IftheslopeofOAis1, slopeofOBis7 and OA= OB, then the slope ofAB is: (A) 1/5 (B) 1/4 (C) 1/3 (D) 1/2 Q.124 Let C bea circle with twodiameters intersecting at an angle of 30 degrees.Acircle S is tangent to both the diameters andto C, and has radius unity.The largest radius of C is (A) 1 + 2 6 (B) 1 + 2 6 (C) 2 6 – 1 (D) none of these Q.125 The co-ordinates of a point Pon the line 2x y+ 5 = 0 such that PA PB is maximum where A is (4, 2) and B is (2, 4) will be : (A) (11, 27) (B) ( 11, 17) (C) ( 11, 17) (D) (0, 5) Q.126 A straight line l1 with equation x – 2y+ 10 = 0 meets the circle with equation x2 + y2 = 100 at B in the first quadrant.Aline through B, perpendicular to l1 cuts the y-axis at P(0, t).The value of 't' is (A) 12 (B) 15 (C) 20 (D) 25 Q.127 Avariable circleC has theequation x2 + y2 – 2(t2 – 3t + 1)x – 2(t2 + 2t)y + t = 0, where t is a parameter. The locus of the centre of the circle is (A) a parabola (B)anellipse (C) a hyperbola (D)pairofstraightlines Q.128 Letaandbrepresent thelengthofarighttriangle's legs. Ifdisthediameter of a circle inscribed into the triangle, and D is the diameter of a circle superscribed onthe triangle, then d + D equals (A) a + b (B) 2(a + b) (C) 2 1 (a + b) (D) 2 2 b a Select the correct alternatives : (More than one are correct) Q.129 The area of triangleABC is 20 cm2. The coordinates of vertex Aare (5, 0) and B are (3, 0). The vertex C lies on the line, x y= 2 . The coordinates of C are (A) (5, 3) (B) ( 3, 5) (C) ( 5, 7) (D) (7, 5) Q.130 Apoint (x1, y1) is outsidethe circle, x2 + y2 + 2gx + 2fg + c= 0 with centreat the origin andAP,AQare tangents tothecircle. Then: (A)area ofthequadriletralformedbythepairoftangentsandthecorrespondingradiithroughthepoints of contact is g f c x y gx fy c 2 2 1 2 1 2 1 1 2 2 (B) equation of the circle circumscribing the APQ is, x2 + y2 + x(g – x1) + y(f y1) – (gx1 + fy1) = 0 (C) least radius of a circle passing through the points 'A'& the origin is, ( ) ( ) x g y f 1 2 1 2 (D) the between the two tangent is, 1 2 2 2 2 1 2 2 1 2 1 2 1 1 1 2 1 2 sin ( ) ( ) g f c x y gx fy c x g y f Q.131 Let u ax + by + a b 3 = 0 v bx ay + b a 3 = 0 a, b R be two straight lines. The equation of the bisectors of the angle formed by k1u k2v = 0 & k1u + k2v = 0 for non zero real k1 & k2 are: (A) u = 0 (B) k2u + k1v = 0 (C) k2u k1v = 0 (D) v = 0
- 14. Q.132 x x 1 cos = y y 1 sin = r, represents : (A) equation of a straight line, if is constant & r is variable (B) equation of a circle, if r is constant & is a variable (C) a straight line passing through a fixed point & having a known slope (D) a circle witha known centre & a given radius. Q.133 All the points lyinginside the triangle formedbythe points (1, 3), (5,6) & (1, 2) satisfy (A) 3x + 2y 0 (B) 2x + y + 1 0 (C) 2x + 3y 12 0 (D) 2x + 11 0 Q.134 The equations of the tangents drawn from the origin to the circle, x² + y² 2rx 2hy+ h² = 0 are (A) x = 0 (B) y = 0 (C) (h² r²) x 2rhy = 0 (D) (h² r²)x + 2rhy = 0 Q.135 The co-ordinates of the fourth vertex of the parallelogram where three of its vertices are ( 3, 4); (0, 4) & (5, 2) can be : (A) (8, 6) (B) (2, 10) (C) ( 8, 2) (D) none Q.136 The equation of a circle with centre (4, 3) and touching the circle x2 + y2 = 1 is : (A) x2 + y2 8x 6y 9 = 0 (B) x2 + y2 8x 6y + 11 = 0 (C) x2 + y2 8x 6y 11 = 0 (D) x2 + y2 8x 6y + 9 = 0 Q.137 Two vertices of the ABC are at the pointsA(1, 1) and B(4, 5) and the third vertex lines on the straight line y= 5(x 3) . Ifthe area of the is 19/2 then thepossible coordinates of thevertex C are: (A) (5, 10) (B) (3, 0) (C) (2, 5) (D) (5, 4) Q.138 A circle passes through the points (1, 1) , (0, 6) and (5, 5) . The point(s) on this circle, the tangent(s) at whichis/areparallel tothestraight linejoiningtheorigintoits centreis/are: (A) (1, 5) (B) (5, 1) (C) ( 5, 1) (D) ( 1, 5) Q.139 Line x a y b = 1 cuts the coordinate axes at A(a, 0) & B (0, b) & the line x a y b = 1 at A (a, 0) & B(0, b). If the points A, B, A, B are concyclic then the orthocentre of the triangle ABA is: (A) (0, 0) (B) (0, b') (C) 0 , aa b (D) 0 , ' bb a Q.140 Point M moved alongthecircle (x 4)2 + (y8)2 = 20. Then it broke awayfromit and moving along a tangent to the circle, cuts the xaxis at the point (2, 0) . The coordinates of the point on the circle at which the movingpoint broke awaycan be : (A) 3 5 46 5 , (B) 2 5 44 5 , (C) (6, 4) (D) (3, 5) Q.141 If one vertex of an equilateral triangle of side 'a' lies at the origin and the other lies on the line x 3 y= 0 then the co-ordinates of the third vertex are : (A) (0, a) (B) 3 2 2 a a , (C) (0, a) (D) 3 2 2 a a , Q.142 The circles x2 + y2 + 2x + 4y 20 = 0 & x2 + y2 + 6x 8y + 10 = 0 (A) are such that the number of common tangents onthem is 2 (B) are not orthogonal (C) are such that the length of their common tangent is 5(12/5)1/4 (D) are such that the lengthof their common chord is 5 3 2 .
- 15. Q.143 Two straight lines u = 0 and v = 0 passes through the origing forming an angle of tan1 (7/9) with eachother . If theratio of the slopes of u =0 and v = 0 is 9/2 then their equations are: (A) y = 3x & 3y = 2x (B) 2y = 3x & 3y = x (C) y + 3x = 0 & 3y + 2x = 0 (D) 2y + 3x = 0 & 3y + x = 0 Q.144 The centre(s) of the circle(s) passing through the points (0, 0) , (1, 0) and touching the circle x2 + y2=9 is/are : (A) 3 2 1 2 , (B) 1 2 3 2 , (C) 1 2 21 2 , / (D) 1 2 21 2 , / Q.145 Given two straight lines x y 7= 0 and x y+ 3 = 0. Equation of a line which divides the distance between them in the ratio 3 : 2 can be : (A) x y 1 = 0 (B) x y 3 = 0 (C) y = x (D) x y + 1 = 0 Q.146 The circles x2 + y2 2x 4y + 1 = 0 and x2 + y2 + 4x + 4y 1 = 0 (A) touchinternally (B) touchexternally (C) have 3x + 4y 1 = 0 as the common tangent at the point of contact. (D) have 3x + 4y+ 1 = 0 as the common tangent at the point of contact. Q.147 Three vertices of a triangle are A(4, 3) ; B(1, 1) and C(7, k) . Value(s) of k for which centroid, orthocentre,incentre andcircumcentre of the ABC lieon the same straightline is/are : (A) 7 (B) 1 (C) 19/8 (D) none Q.148 AandB are twofixed points whose co-ordinates are(3, 2) and (5,4) respectively.The co-ordinates of apoint PifABPisan equilateral triangle, is/are: (A) 4 3 3 3 , (B) 4 3 3 3 , (C) 3 3 4 3 , (D) 3 3 4 3 , Q.149 Which of the followinglines have the intercepts of equal lengths on the circle, x2 + y2 2x +4y= 0? (A) 3x y = 0 (B) x + 3y = 0 (C) x + 3y + 10 = 0 (D) 3x y 10 = 0 Q.150 Straight lines 2x + y= 5 and x 2y= 3 intersect at the pointA. Points B and C are chosen on these two lines such that AB=AC . Thenthe equation of a line BC passing through the point (2,3) is (A) 3x y 3 = 0 (B) x + 3y 11 = 0 (C) 3x + y 9 = 0 (D) x 3y + 7 = 0 Q.151 Equationofa straight linepassingthrough the point (2, 3)and inclined atan angleof arctan 1 2 with the line y + 2x = 5 is: (A) y = 3 (B) x = 2 (C) 3x + 4y 18 = 0 (D) 4x + 3y 17 = 0 Q.152 The x co-ordinates of the vertices of a square of unit area are the roots of the equation x2 3x + 2 = 0 and the y co-ordinates of the vertices are the roots of the equation y2 3y+ 2 = 0 then the possible vertices of the square is/are : (A) (1, 1), (2, 1), (2, 2), (1, 2) (B) ( 1, 1), ( 2, 1), ( 2, 2), ( 1, 2) (C) (2, 1), (1, 1), (1, 2), (2, 2) (D) ( 2, 1), ( 1, 1), ( 1, 2), ( 2, 2) Q.153 Considertheequation y y1 =m (x x1). If m &x1 arefixed and different lines aredrawn for different values of y1,then (A) the lines will pass through a fixed point (B) therewill be a set of parallel lines (C) all the lines intersect the line x = x1 (D) all the lines will beparallel to theliney= x1.