JEE Main & Advanced Mathematics Straight Line Question Bank

done Critical Thinking Total Questions - 30

• question_answer1)
  The number of integral values of m, for which the x-co-ordinate of the point of intersection of the lines \[3x+4y=9\] and \[y=mx+1\]is also an integer is  [IIT Screening 2001]
  A)
             2 done clear
  B)
             0 done clear
  C)
             4      done clear
  D)
             1 done clear
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• question_answer2)
  A ray of light coming from the point (1, 2) is reflected at a point A on the x-axis and then passes through the point       (5, 3). The coordinates of the point A are                                            [Orissa JEE 2003]
  A)
  \[\left( 13/5,\ 0 \right)\]          done clear
  B)
  \[\left( 5/13,\ 0 \right)\] done clear
  C)
  (- 7, 0)                                        done clear
  D)
  None of these done clear
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• question_answer3)
  If the co-ordinates of the middle point of the portion of a line intercepted between coordinate axes (3,2), then the equation of the line will be            [RPET 1985; MP PET 1984]
  A)
             \[2x+3y=12\]                              done clear
  B)
             \[3x+2y=12\] done clear
  C)
             \[4x-3y=6\]                                done clear
  D)
             \[5x-2y=10\] done clear
  View Solution play_arrow

• question_answer4)
  A line through \[A(-5,-\ 4)\] meets the lines \[x+3y+2=0,\] \[2x+y+4=0\] and \[x-y-5=0\] at B, C and D respectively. If \[{{\left( \frac{15}{AB} \right)}^{2}}+{{\left( \frac{10}{AC} \right)}^{2}}={{\left( \frac{6}{AD} \right)}^{2}},\] then the equation of the line is                                                    [IIT 1993] 
  A)
             \[2x+3y+22=0\]                          done clear
  B)
             \[5x-4y+7=0\] done clear
  C)
             \[3x-2y+3=0\]                            done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer5)
  The equation of perpendicular bisectors of the sides AB and AC of a triangle ABC are \[x-y+5=0\] and \[x+2y=0\] respectively. If the point A is \[(1,\ -\ 2)\], then the equation of line BC is                                         [IIT 1986]
  A)
             \[23x+14y-40=0\]                      done clear
  B)
             \[14x-23y+40=0\] done clear
  C)
             \[{{\tan }^{-1}}(2)\]                   done clear
  D)
             \[14x+23y-40=0\] done clear
  View Solution play_arrow

• question_answer6)
  The medians AD and BE of a triangle with vertices \[A\ (0,\ b),\ B\ (0,\ 0)\] and \[C\ (a,\ 0)\] are perpendicular to each other, if [Karnataka CET 2000]
  A)
             \[a=\sqrt{2}\ b\]                        done clear
  B)
             \[a=-\sqrt{2}\ b\] done clear
  C)
             Both (a) and (b)                         done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer7)
  Let PS be the median of the triangle with vertices \[P(2,\ 2),\ Q(6,\ -\ 1)\]and \[R(7,\ 3)\]. The equation of the line passing through (1,? 1) and parallel to PS is  [IIT Screening 2000]
  A)
             \[2x-9y-7=0\]                             done clear
  B)
             \[2x-9y-11=0\] done clear
  C)
             \[2x+9y-11=0\]                          done clear
  D)
             \[2x+9y+7=0\] done clear
  View Solution play_arrow

• question_answer8)
  The equation of straight line passing through \[(-a,\ 0)\] and making the triangle with axes of area ?T? is      [RPET 1987]
  A)
             \[2Tx+{{a}^{2}}y+2aT=0\]          done clear
  B)
             \[2Tx-{{a}^{2}}y+2aT=0\] done clear
  C)
             \[2Tx-{{a}^{2}}y-2aT=0\]           done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer9)
  The equations of two equal sides of an isosceles triangle are \[7x-y+3=0\] and \[x+y-3=0\] and the third side passes through the point (1, ? 10). The equation of the third side is                                                     [IIT 1984]
  A)
             \[y=\sqrt{3}x+9\] but not \[{{x}^{2}}-9{{y}^{2}}=0\] done clear
  B)
             \[3x+y+7=0\] but not \[{{60}^{o}}\] done clear
  C)
             \[3x+y+7=0\] or \[x-3y-31=0\] done clear
  D)
             Neither \[3x+y+7\] nor \[x-3y-31=0\] done clear
  View Solution play_arrow

• question_answer10)
  The graph of the function \[\cos x\ \cos (x+2)-{{\cos }^{2}}(x+1)\] is [IIT 1997 Re-Exam]
  A)
             A straight line passing through \[(0,\,\,-{{\sin }^{2}}1)\]with slope 2      done clear
  B)
             A straight line passing through (0, 0) done clear
  C)
             A parabola with vertex \[{{75}^{o}}\] done clear
  D)
             A straight line passing through the point \[\left( \frac{\pi }{2},-{{\sin }^{2}}1 \right)\] and parallel to the x?axis                done clear
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• question_answer11)
  If the equation of base of an equilateral triangle is \[2x-y=1\] and the vertex is (?1, 2), then the length of the side of the triangle is [Kerala (Engg.) 2005]
  A)
             \[\sqrt{\frac{20}{3}}\]               done clear
  B)
             \[\frac{2}{\sqrt{15}}\] done clear
  C)
             \[\sqrt{\frac{8}{15}}\]               done clear
  D)
             \[\sqrt{\frac{15}{2}}\] done clear
  View Solution play_arrow

• question_answer12)
  If \[{{x}_{1}},{{x}_{2}},{{x}_{3}},\,\,\text{and }\,{{y}_{1}},{{y}_{2}},{{y}_{3}}\] are both in G.P. with the same common ratio, then the points \[({{x}_{1}},{{y}_{1}}),\] \[({{x}_{2}},\,{{y}_{2}})\] and \[({{x}_{3}},\,{{y}_{3}})\][AIEEE 2003]
  A)
             Lie on a straight line                  done clear
  B)
             Lie on an ellipse done clear
  C)
             Lie on a circle                             done clear
  D)
             Are vertices of a triangle done clear
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• question_answer13)
  A line \[4x+y=1\]passes through the point \[A(2,\ -\ 7)\] meets the line BC whose equation is \[3x-4y+1=0\] at the point B. The equation to the line AC so that AB = AC, is                                [IIT 1971]
  A)
             \[52x+89y+519=0\]                    done clear
  B)
             \[\beta \] done clear
  C)
             \[89x+52y+519=0\]                    done clear
  D)
             \[89x+52y-519=0\] done clear
  View Solution play_arrow

• question_answer14)
  In what direction a line be drawn through the point (1, 2) so that its points of intersection with the line \[x+y=4\] is at a distance \[\frac{\sqrt{6}}{3}\] from the given point                             [IIT 1966; MNR 1987]
  A)
             \[{{30}^{o}}\]                             done clear
  B)
             \[{{45}^{o}}\] done clear
  C)
             \[{{60}^{o}}\]                             done clear
  D)
             \[{{75}^{o}}\] done clear
  View Solution play_arrow

• question_answer15)
  If straight lines \[ax+by+p=0\] and \[x\cos \alpha +y\sin \alpha -p=0\] include an angle \[\pi /4\] between them and meet the straight line \[x\sin \alpha -y\cos \alpha =0\] in the same point, then the value of \[{{a}^{2}}+{{b}^{2}}\]is equal to
  A)
             1      done clear
  B)
             2 done clear
  C)
             3      done clear
  D)
             4 done clear
  View Solution play_arrow

• question_answer16)
  The sides \[AB,BC,CD\] and \[DA\]of a quadrilateral are \[x+2y=3,\,x=1,\] \[x-3y=4,\,\] \[\,5x+y+12=0\] respectively.  The angle between diagonals \[AC\]and \[BD\]is  [Roorkee 1993]
  A)
             \[{{45}^{o}}\]                             done clear
  B)
             \[{{60}^{o}}\] done clear
  C)
             \[{{90}^{o}}\]                             done clear
  D)
             \[{{30}^{o}}\] done clear
  View Solution play_arrow

• question_answer17)
  Given vertices \[A(1,\,1),B(4,\,-2)\]and \[C(5,\,5)\]of a triangle, then the equation of the perpendicular dropped from C to the interior bisector of the angle A is                                              [Roorkee 1994]
  A)
             \[y-5=0\]                                    done clear
  B)
             \[x-5=0\] done clear
  C)
             \[y+5=0\]                                   done clear
  D)
             \[x+5=0\] done clear
  View Solution play_arrow

• question_answer18)
  If the straight line through the point \[P(3,\,4)\]makes an angle \[\frac{\pi }{6}\]with the x-axis and meets the line \[12x+5y+10=0\] at Q, then the length \[PQ\]is
  A)
             \[\frac{132}{12\sqrt{3}+5}\]     done clear
  B)
             \[\frac{132}{12\sqrt{3}-5}\] done clear
  C)
             \[\frac{132}{5\sqrt{3}+12}\]     done clear
  D)
             \[\frac{132}{5\sqrt{3}-12}\] done clear
  View Solution play_arrow

• question_answer19)
  The vertices of a triangle are (2, 1), (5, 2) and    (4, 4). The lengths of the perpendicular from these vertices on the opposite sides are [IIT 1962]
  A)
             \[\frac{7}{\sqrt{5}},\frac{7}{\sqrt{13}},\frac{7}{\sqrt{6}}\]         done clear
  B)
             \[\frac{7}{\sqrt{6}},\frac{7}{\sqrt{8}},\frac{7}{\sqrt{10}}\] done clear
  C)
             \[\frac{7}{\sqrt{5}},\frac{7}{\sqrt{8}},\frac{7}{\sqrt{15}}\]         done clear
  D)
             \[\frac{7}{\sqrt{5}},\frac{7}{\sqrt{13}},\frac{7}{\sqrt{10}}\] done clear
  View Solution play_arrow

• question_answer20)
  The equation of the line joining the point (3, 5)to the point of intersection of the lines \[4x+y-1=0\] and \[7x-3y-35=0\] is equidistant from the points (0, 0) and   (8, 34)                                                                 [Roorkee 1984]
  A)
             True                                            done clear
  B)
             False done clear
  C)
             Nothing can be said                   done clear
  D)
             None of these done clear
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• question_answer21)
  A variable line passes through a fixed point P. The algebraic sum of the perpendicular drawn from (2,0), (0, 2) and        (1, 1) on the line is zero, then the coordinates of the P are [IIT 1991; AMU 2005]                                       
  A)
             (1, -1)                                         done clear
  B)
             (1, 1) done clear
  C)
             (2, 1)                                          done clear
  D)
             (2, 2)                 done clear
  View Solution play_arrow

• question_answer22)
  Given the four lines with equations \[x+2y=3,\] \[3x+4y=7,\,\,2x+3y=4\,\,\] and \[4x+5y=6,\] then these lines are [IIT 1980; Pb. CET 2003]
  A)
             Concurrent                                 done clear
  B)
             Perpendicular done clear
  C)
             The sides of a rectangle            done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer23)
  The line \[3x+2y=24\]meets \[y\]-axis at A and x-axis at B. The perpendicular bisector of \[AB\]meets the line through \[(0,-1)\] parallel to x-axis at C. The area of the triangle \[ABC\] is 
  A)
             \[182sq.\]units                          done clear
  B)
             \[91sq.\]units done clear
  C)
             \[48sq.\]units                            done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer24)
  A pair of straight lines drawn through the origin form with the line \[2x+3y=6\]an isosceles right angled triangle, then the lines and the area of the triangle thus formed is                                                    [Roorkee 1993]
  A)
             \[x-5y=0\]\[5x+y=0\]\[\Delta =\frac{36}{13}\]                            done clear
  B)
             \[3x-y=0\]\[x+3y=0\]\[\Delta =\frac{12}{17}\] done clear
  C)
             \[5x-y=0\]\[x+5y=0\]\[\Delta =\frac{13}{5}\]                              done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer25)
  The diagonals of a parallelogram \[PQRS\]are along the lines \[x+3y=4\]and \[6x-2y=7\]. Then \[PQRS\] must be a    [IIT 1998]
  A)
             Rectangle                                   done clear
  B)
             Square done clear
  C)
             Cyclic quadrilateral                    done clear
  D)
             Rhombus done clear
  View Solution play_arrow

• question_answer26)
  The area enclosed within the curve \[|x|+|y|=1\]is   [RPET 1990, 1997; IIT 1981; UPSEAT 2003]
  A)
             \[\sqrt{2}\]                                done clear
  B)
             1 done clear
  C)
             \[\sqrt{3}\]                                done clear
  D)
             2 done clear
  View Solution play_arrow

• question_answer27)
  The area of triangle formed by the lines \[x=0,y=0\] and \[\frac{x}{a}+\frac{y}{b}=1\], is                                                 [RPET 1984]
  A)
             \[ab\]                                         done clear
  B)
             \[\frac{ab}{2}\] done clear
  C)
             \[2ab\]                                       done clear
  D)
             \[\frac{ab}{3}\] done clear
  View Solution play_arrow

• question_answer28)
  A line L passes through the points (1, 1) and    (2, 0) and another line \[{L}'\] passes through \[\left( \frac{1}{2},0 \right)\] and perpendicular to L. Then the area of the triangle formed by the lines \[L,L'\] and y- axis, is                                      [RPET 1991]
  A)
             15/8                                           done clear
  B)
             25/4 done clear
  C)
             25/8                                           done clear
  D)
             25/16 done clear
  View Solution play_arrow

• question_answer29)
  The image of the point (4, - 3) with respect to the line y = x is                                                            [RPET 2002]
  A)
             (- 4, - 3)                                      done clear
  B)
             (3, 4) done clear
  C)
             (- 4, 3)                                        done clear
  D)
             (- 3, 4) done clear
  View Solution play_arrow

• question_answer30)
  The locus of a point P which divides the line joining (1, 0) and \[(2\cos \theta ,2\sin \theta )\]internally in the ratio 2 : 3 for all \[\theta \], is a  [IIT 1986]
  A)
             Straight line                               done clear
  B)
             Circle done clear
  C)
             Pair of straight lines    done clear
  D)
             Parabola done clear
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