JEE Main & Advanced Mathematics Straight Line Question Bank

done Mock Test - Straight Lines Total Questions - 25

• question_answer1)
  The straight line \[ax+by+c=0\], where \[abc\ne 0\], will pass through the first quadrant if
  A)
   \[ac>0,bc>0\] done clear
  B)
   \[c>0\,and\,bc<0\] done clear
  C)
   \[bc>0\,and/or\,ac>0\] done clear
  D)
   \[ac<0\,and/or\,bc<0\] done clear
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• question_answer2)
  The lines y\[y={{m}_{1}}x,\] \[y={{m}_{2}}x,\]and \[y={{m}_{3}}x,\]make equal intercepts on the line\[x+y=1\]. Then
  A)
   \[2(1+{{m}_{1}})(1+{{m}_{3}})=(1+{{m}_{2}})(2+{{m}_{1}}+{{m}_{3}})\] done clear
  B)
   \[(1+{{m}_{1}})(1+{{m}_{3}})=(1+{{m}_{2}})(1+{{m}_{1}}+{{m}_{3}})\] done clear
  C)
   \[(1+{{m}_{1}})(1+{{m}_{2}})=(1+{{m}_{3}})(2+{{m}_{1}}+{{m}_{3}})\] done clear
  D)
   \[2(1+{{m}_{1}})(1+{{m}_{3}})=(1+{{m}_{2}})(1+{{m}_{1}}+{{m}_{3}})\] done clear
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• question_answer3)
  The condition on a and b, such that the portion of the line \[ax+by-1=0\]intercepted between the lines \[ax+y=0\]and \[x+by=0\]subtends a right angle at the origin, is
  A)
  \[a=b\] done clear
  B)
  \[a+b=0\] done clear
  C)
  \[a=2b\]           done clear
  D)
  \[2a=b\] done clear
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• question_answer4)
  If each of the points, \[({{x}_{1}},4)\], \[(-2,{{y}_{1}})\]lies on the line joining the points (2, -1) and (5, -3), then the point \[p({{x}_{1}},{{y}_{1}})\]lies on the line
  A)
  \[6(x+y)-25=0\] done clear
  B)
  \[2x+6y+1=0\] done clear
  C)
  \[2x+3y-6=0\] done clear
  D)
  \[6(x+y)+25=0\] done clear
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• question_answer5)
  If \[u={{a}_{1}}x+{{b}_{1}}y={{c}_{1}}=0\], \[v={{a}_{2}}x+{{b}_{2}}y+{{c}_{2}}=0\]and \[{{a}_{1}}/{{a}_{2}}={{b}_{1}}/{{b}_{2}}={{c}_{1}}/{{c}_{2}}\], then the curve \[u+kv=0\]is
  A)
  the same straight line u done clear
  B)
   different straight line done clear
  C)
   not a straight line done clear
  D)
   none of these done clear
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• question_answer6)
  The point A (2, 1) is translated parallel to the line x-y=3 by a distance of 4 units, if the new position A' is in the third quadrant, then the coordinates of A' are
  A)
  \[(2+2\sqrt{2,}\,1+2\sqrt{2})\] done clear
  B)
  \[(-2+\sqrt{2,}\,-1-2\sqrt{2})\] done clear
  C)
  \[(2-2\sqrt{2,}\,1-2\sqrt{2})\] done clear
  D)
  None of these done clear
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• question_answer7)
  A line of fixed length 2 units moves so that its ends are on the positive x-axis and that part of the line x+y=0 which lies in the second quadrant. Then the locus of the midpoint of the line has equation
  A)
   \[{{x}^{2}}+5{{y}^{2}}+4xy-1=0\] done clear
  B)
   \[{{x}^{2}}+5{{y}^{2}}+4xy+1=0\] done clear
  C)
   \[{{x}^{2}}+5{{y}^{2}}-4xy-1=0\] done clear
  D)
   \[4{{x}^{2}}+5{{y}^{2}}+4xy+1=0\] done clear
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• question_answer8)
  The line\[\frac{x}{a}+\frac{y}{b}=1\]meets the x-axis at A, the y-axis at B, and the line y=x at C such that the area of \[\Delta AOC\]is twice the area of \[\Delta BOC\]. Then the coordinates of C are
  A)
  \[\left( \frac{b}{3},\frac{b}{3} \right)\]    done clear
  B)
  \[\left( \frac{2a}{3},\frac{2a}{3} \right)\] done clear
  C)
  \[\left( \frac{2b}{3},\frac{2b}{3} \right)\] done clear
  D)
  none of these done clear
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• question_answer9)
  If the straight lines \[2x+3y-1=0,\text{ }x+2y-1=0,~\text{ }x+2y-1=0,\text{ }and\text{ }ax+by-1=0\] form a triangle with the origin as orthocenter, then (a, b) is given by
  A)
  (6, 4)     done clear
  B)
  (-3, 3) done clear
  C)
  (-8, 8)   done clear
  D)
  (0, 7) done clear
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• question_answer10)
  The equations of the sides of a triangle are \[x+y-5=0,\text{ }x-y+1=0,\text{ }and\text{ }y-1=0,\] then the coordinates of the circumcenter are
  A)
  (2, 1)     done clear
  B)
  (1, 2) done clear
  C)
  (2, -2)   done clear
  D)
  (1, -2) done clear
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• question_answer11)
  The foot of the perpendicular on the line 3x+y=\[\lambda \]drawn from the origin is C. if the line cuts the x-and the y-axis at A and B, respectively, then BC:CA is
  A)
  1 : 3                  done clear
  B)
  3 : 1 done clear
  C)
  1 : 3                 done clear
  D)
  9 : 1 done clear
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• question_answer12)
  A light ray coming along the line \[3x+4y=5\] gets reflected from the line \[ax+by=1\]and goes along the line\[5x-12y=10\]. Then
  A)
   \[a=64/115,\text{ }b=112/15\] done clear
  B)
   \[a=14/15,\text{ }b=-8/115\] done clear
  C)
   \[a=64/115,\text{ }b=-8/115\] done clear
  D)
   \[a=64/15,\text{ }b=14/15\] done clear
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• question_answer13)
  If the quadrilateral formed by the lines \[ax+by+c=0,\text{ }a'x+b'y+c'=0,\text{ }ax+by+c'=0,\text{ }a'x+b'y+c'=0\]has perpendicular diagonals, then
  A)
   \[{{b}^{2}}+{{c}^{2}}=b{{'}^{2}}+c{{'}^{2}}\] done clear
  B)
   \[{{c}^{2}}+{{a}^{2}}=c{{'}^{2}}+a{{'}^{2}}\] done clear
  C)
   \[{{a}^{2}}+{{b}^{2}}=a{{'}^{2}}+b{{'}^{2}}\] done clear
  D)
   none of these done clear
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• question_answer14)
  Line \[ax+by+p=0\]makes angle \[\pi /4\] with \[xcos\,\alpha +ysin\,\alpha =p,\text{ }p\in {{R}^{+}}\]. if these lines and the line \[x\text{ }sin\,\alpha -y\text{ }cos\,\alpha =0\] are concurrent, then
  A)
  \[{{a}^{2}}+{{b}^{2}}=1\] done clear
  B)
  \[{{a}^{2}}+{{b}^{2}}=2\] done clear
  C)
  \[2({{a}^{2}}+{{b}^{2}})=1\] done clear
  D)
  none of these done clear
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• question_answer15)
  If the equation of the locus of a point equidistant from the points (\[{{a}_{1,}}{{b}_{1}}\]) and (\[{{a}_{2,}}{{b}_{2}}\]) is (\[{{a}_{1,-}}{{a}_{2}}\])x+(\[{{b}_{1,-}}{{b}_{2}}\])\[y+c=0\] then the value of c is
  A)
  \[\frac{1}{2}({{a}_{2}}^{2}+{{b}_{2}}^{2}-{{a}_{1}}^{2}-{{b}_{1}}^{2})\] done clear
  B)
  \[{{a}_{1}}^{2}+{{a}_{2}}^{2}+{{b}_{1}}^{2}-{{b}_{2}}^{2}\] done clear
  C)
  \[\frac{1}{2}({{a}_{1}}^{2}+{{a}_{2}}^{2}-{{b}_{1}}^{2}-{{b}_{2}}^{2})\] done clear
  D)
  \[\sqrt{{{a}_{1}}^{2}+{{b}_{2}}^{2}-{{a}_{2}}^{2}-{{b}_{2}}^{2}}\] done clear
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• question_answer16)
  Let A, (2,-3) and B (-2, 1) be the vertices of a triangle ABC. If the centroid of this triangle moves on the line \[2x+3y=1,\] then the locus of the vertex C is the line
  A)
  \[2x+3y=9\]     done clear
  B)
  \[2x-3y=7\] done clear
  C)
  \[3x+2y=5\]     done clear
  D)
  \[3x-2y=3\] done clear
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• question_answer17)
  The equation of the straight line passing through the point (4, 3) and making intercepts on the coordinate axes, whose sum is-1, is
  A)
   \[\frac{x}{2}+\frac{y}{3}=-1\] and \[\frac{x}{-2}+\frac{y}{1}=-1\] done clear
  B)
   \[\frac{x}{2}-\frac{y}{3}=-1\] and \[\frac{x}{-2}+\frac{y}{1}=-1\] done clear
  C)
   \[\frac{x}{2}+\frac{y}{3}=1\] and \[\frac{x}{2}+\frac{y}{3}=1\] done clear
  D)
   \[\frac{x}{2}-\frac{y}{3}=1\] and \[\frac{x}{-2}+\frac{y}{1}=1\] done clear
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• question_answer18)
  A straight line through the point A.(3, 4) is such that its intercept between the axes is bisected at A. its equation is
  A)
  \[x+y=7\]         done clear
  B)
  \[3x-4y+7=0\] done clear
  C)
  \[4x+3y=24\]    done clear
  D)
  \[3x+4y=25\] done clear
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• question_answer19)
  The line parallel to the x-axis and passing through the intersection of the lines \[ax+2by+3b=0\]and \[bx-2ay-3a=0,\]where (a, b) \[\ne \](0, 0) is
  A)
  below the x-axis at a distance of 3/2 from it. done clear
  B)
   below the x-axis at a distance of 2/3 from it. done clear
  C)
   above the x-axis at a distance of 2/3 form it. done clear
  D)
   above the x-axis at a distance of 2/3 from it. done clear
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• question_answer20)
  If \[(a,{{a}^{2}})\]falls inside the angle made by the lines y=\[\frac{x}{2}\], x>0, and \[y=3x,\text{ }x>0,\]then a belongs to
  A)
  \[\left( 0,\frac{1}{2} \right)\]       done clear
  B)
  \[\left( 3,\,\infty  \right)\] done clear
  C)
  \[\left( \frac{1}{2},3 \right)\]       done clear
  D)
  \[\left( -3,-\frac{1}{2} \right)\] done clear
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• question_answer21)
  Distance of the origin form the line \[(1+\sqrt{3})y+(1-\sqrt{3})x=10\]along the line\[y=\sqrt{3}x+k\] is ________.
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• question_answer22)
  P is a point on the line \[y+2x=1,\]and Q and R are two points on the line \[3y+6x=6\] such that triangle PQR is an equilateral triangle. The length of the side of the triangle is ________.
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• question_answer23)
  The straight lines \[7x-2y+10=0\] and \[7x+2y-10=0\] form an isosceles triangle with the line y=2. The area (sq. units) of this triangle is equal to ______.
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• question_answer24)
  If the sum of the slopes of the lines given by \[{{x}^{2}}-2cxy-7{{y}^{2}}=0\] is four times their product, then c has the value
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• question_answer25)
  If the line \[2x+y=k\] passes through the point which divides the line segment joining the points (1, 1) and (2, 4) in the ratio 3:2, then k equals ________.
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