
question_answer1) The number of integral values of m, for which the xcoordinate 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
B) 0
C) 4
D) 1
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question_answer2) A ray of light coming from the point (1, 2) is reflected at a point A on the xaxis and then passes through the point (5, 3). The coordinates of the point A are [Orissa JEE 2003]
A) \[\left( 13/5,\ 0 \right)\]
B) \[\left( 5/13,\ 0 \right)\]
C) ( 7, 0)
D) None of these
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question_answer3) If the coordinates 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) \[2x+3y=12\]
B) \[3x+2y=12\]
C) \[4x3y=6\]
D) \[5x2y=10\]
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question_answer4) A line through \[A(5,\ 4)\] meets the lines \[x+3y+2=0,\] \[2x+y+4=0\] and \[xy5=0\] 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) \[2x+3y+22=0\]
B) \[5x4y+7=0\]
C) \[3x2y+3=0\]
D) None of these
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question_answer5) The equation of perpendicular bisectors of the sides AB and AC of a triangle ABC are \[xy+5=0\] and \[x+2y=0\] respectively. If the point A is \[(1,\ \ 2)\], then the equation of line BC is [IIT 1986]
A) \[23x+14y40=0\]
B) \[14x23y+40=0\]
C) \[{{\tan }^{1}}(2)\]
D) \[14x+23y40=0\]
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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) \[a=\sqrt{2}\ b\]
B) \[a=\sqrt{2}\ b\]
C) Both (a) and (b)
D) None of these
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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) \[2x9y7=0\]
B) \[2x9y11=0\]
C) \[2x+9y11=0\]
D) \[2x+9y+7=0\]
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question_answer8) The equation of straight line passing through \[(a,\ 0)\] and making the triangle with axes of area ?T? is [RPET 1987]
A) \[2Tx+{{a}^{2}}y+2aT=0\]
B) \[2Tx{{a}^{2}}y+2aT=0\]
C) \[2Tx{{a}^{2}}y2aT=0\]
D) None of these
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question_answer9) The equations of two equal sides of an isosceles triangle are \[7xy+3=0\] and \[x+y3=0\] 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 \[{{x}^{2}}9{{y}^{2}}=0\]
B) \[3x+y+7=0\] but not \[{{60}^{o}}\]
C) \[3x+y+7=0\] or \[x3y31=0\]
D) Neither \[3x+y+7\] nor \[x3y31=0\]
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question_answer10) The graph of the function \[\cos x\ \cos (x+2){{\cos }^{2}}(x+1)\] is [IIT 1997 ReExam]
A) A straight line passing through \[(0,\,\,{{\sin }^{2}}1)\]with slope 2
B) A straight line passing through (0, 0)
C) A parabola with vertex \[{{75}^{o}}\]
D) A straight line passing through the point \[\left( \frac{\pi }{2},{{\sin }^{2}}1 \right)\] and parallel to the x?axis
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question_answer11) If the equation of base of an equilateral triangle is \[2xy=1\] and the vertex is (?1, 2), then the length of the side of the triangle is [Kerala (Engg.) 2005]
A) \[\sqrt{\frac{20}{3}}\]
B) \[\frac{2}{\sqrt{15}}\]
C) \[\sqrt{\frac{8}{15}}\]
D) \[\sqrt{\frac{15}{2}}\]
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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
B) Lie on an ellipse
C) Lie on a circle
D) Are vertices of a triangle
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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 \[3x4y+1=0\] at the point B. The equation to the line AC so that AB = AC, is [IIT 1971]
A) \[52x+89y+519=0\]
B) \[\beta \]
C) \[89x+52y+519=0\]
D) \[89x+52y519=0\]
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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) \[{{30}^{o}}\]
B) \[{{45}^{o}}\]
C) \[{{60}^{o}}\]
D) \[{{75}^{o}}\]
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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
B) 2
C) 3
D) 4
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question_answer16) The sides \[AB,BC,CD\] and \[DA\]of a quadrilateral are \[x+2y=3,\,x=1,\] \[x3y=4,\,\] \[\,5x+y+12=0\] respectively. The angle between diagonals \[AC\]and \[BD\]is [Roorkee 1993]
A) \[{{45}^{o}}\]
B) \[{{60}^{o}}\]
C) \[{{90}^{o}}\]
D) \[{{30}^{o}}\]
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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) \[y5=0\]
B) \[x5=0\]
C) \[y+5=0\]
D) \[x+5=0\]
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question_answer18) If the straight line through the point \[P(3,\,4)\]makes an angle \[\frac{\pi }{6}\]with the xaxis and meets the line \[12x+5y+10=0\] at Q, then the length \[PQ\]is
A) \[\frac{132}{12\sqrt{3}+5}\]
B) \[\frac{132}{12\sqrt{3}5}\]
C) \[\frac{132}{5\sqrt{3}+12}\]
D) \[\frac{132}{5\sqrt{3}12}\]
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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) \[\frac{7}{\sqrt{5}},\frac{7}{\sqrt{13}},\frac{7}{\sqrt{6}}\]
B) \[\frac{7}{\sqrt{6}},\frac{7}{\sqrt{8}},\frac{7}{\sqrt{10}}\]
C) \[\frac{7}{\sqrt{5}},\frac{7}{\sqrt{8}},\frac{7}{\sqrt{15}}\]
D) \[\frac{7}{\sqrt{5}},\frac{7}{\sqrt{13}},\frac{7}{\sqrt{10}}\]
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question_answer20) The equation of the line joining the point (3, 5)to the point of intersection of the lines \[4x+y1=0\] and \[7x3y35=0\] is equidistant from the points (0, 0) and (8, 34) [Roorkee 1984]
A) True
B) False
C) Nothing can be said
D) None of these
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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)
B) (1, 1)
C) (2, 1)
D) (2, 2)
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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
B) Perpendicular
C) The sides of a rectangle
D) None of these
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question_answer23) The line \[3x+2y=24\]meets \[y\]axis at A and xaxis at B. The perpendicular bisector of \[AB\]meets the line through \[(0,1)\] parallel to xaxis at C. The area of the triangle \[ABC\] is
A) \[182sq.\]units
B) \[91sq.\]units
C) \[48sq.\]units
D) None of these
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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) \[x5y=0\]\[5x+y=0\]\[\Delta =\frac{36}{13}\]
B) \[3xy=0\]\[x+3y=0\]\[\Delta =\frac{12}{17}\]
C) \[5xy=0\]\[x+5y=0\]\[\Delta =\frac{13}{5}\]
D) None of these
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question_answer25) The diagonals of a parallelogram \[PQRS\]are along the lines \[x+3y=4\]and \[6x2y=7\]. Then \[PQRS\] must be a [IIT 1998]
A) Rectangle
B) Square
C) Cyclic quadrilateral
D) Rhombus
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question_answer26) The area enclosed within the curve \[x+y=1\]is [RPET 1990, 1997; IIT 1981; UPSEAT 2003]
A) \[\sqrt{2}\]
B) 1
C) \[\sqrt{3}\]
D) 2
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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) \[ab\]
B) \[\frac{ab}{2}\]
C) \[2ab\]
D) \[\frac{ab}{3}\]
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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
B) 25/4
C) 25/8
D) 25/16
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question_answer29) The image of the point (4,  3) with respect to the line y = x is [RPET 2002]
A) ( 4,  3)
B) (3, 4)
C) ( 4, 3)
D) ( 3, 4)
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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
B) Circle
C) Pair of straight lines
D) Parabola
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