
question_answer1) If the extremities of the base of an isosceles triangle are the points \[(2a,0)\] and \[(0,a)\] and the equation of one of the sides is \[x=2a\], then the area of the triangle is
A) \[5{{a}^{2}}sq\]. units
B) \[\frac{5}{2}{{a}^{2}}sq.\]units
C) \[\frac{25{{a}^{2}}}{2}sq.\]units
D) None of these
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question_answer2) The equation to the sides of a triangle are \[x3y=0\], \[4x+3y=5\] and \[3x+y=0\]. The line \[3x4y=0\]passes through [EAMCET 1994]
A) The incentre
B) The centroid
C) The circumcentre
D) The orthocentre of the triangle
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question_answer3) Area of the parallelogram formed by the lines \[{{a}_{1}}x+{{b}_{1}}y+{{c}_{1}}=0\],\[{{a}_{1}}x+{{b}_{1}}y+{{d}_{1}}=0\]and \[{{a}_{2}}x+{{b}_{2}}y+{{c}_{2}}=0\], \[{{a}_{2}}x+{{b}_{2}}y+{{d}_{2}}=0\]is
A) \[\frac{({{d}_{1}}{{c}_{1}})({{d}_{2}}{{c}_{2}})}{{{[(a_{1}^{2}+b_{1}^{2})(a_{2}^{2}+b_{2}^{2})]}^{1/2}}}\]
B) \[\frac{({{d}_{1}}{{c}_{1}})({{d}_{2}}{{c}_{2}})}{{{a}_{1}}{{a}_{2}}{{b}_{1}}{{b}_{2}}}\]
C) \[\frac{({{d}_{1}}+{{c}_{1}})({{d}_{2}}+{{c}_{2}})}{{{a}_{1}}{{a}_{2}}+{{b}_{1}}{{b}_{2}}}\]
D) \[\frac{({{d}_{1}}{{c}_{1}})({{d}_{2}}{{c}_{2}})}{{{a}_{1}}{{b}_{2}}{{a}_{2}}{{b}_{1}}}\]
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question_answer4) Area of the parallelogram whose sides are \[x\cos \alpha +y\sin \alpha =p\] \[x\cos \alpha +y\sin \alpha =q,\,\,\] \[x\cos \beta +y\sin \beta =r\] and \[x\cos \beta +y\sin \beta =s\] is
A) \[\pm (pq)(rs)\,\text{cosec}(\alpha \beta )\]
B) \[(p+q)(rs)\,\text{cosec }(\alpha +\beta )\]
C) \[(p+q)(r+s)\,\text{cosec }(\alpha \beta )\]
D) None of these
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question_answer5) The area of the triangle bounded by the straight line \[ax+by+c=0,\,\,\,\,(a,b,c\ne 0)\] and the coordinate axes is [AMU 2000]
A) \[\frac{1}{2}\frac{{{a}^{2}}}{bc}\]
B) \[\frac{1}{2}\frac{{{c}^{2}}}{ab}\]
C) \[\frac{1}{2}\frac{{{b}^{2}}}{ac}\]
D) 0
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question_answer6) The triangle formed by the lines \[x+y4=0,\,\] \[3x+y=4,\] \[x+3y=4\] is [RPET 2002; IIT 1983; MNR 1992; UPSEAT 2001]
A) Isosceles
B) Equilateral
C) Right?angled
D) None of these
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question_answer7) Two lines are drawn through (3, 4), each of which makes angle of 45o with the line \[xy=2\], then area of the triangle formed by these lines is [RPET 2000]
A) 9
B) 9/2
C) 2
D) 2/9
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question_answer8) The area of the triangle formed by the line \[x\sin \alpha +y\cos \alpha =\sin 2\alpha \]and the coordinates axes is
A) \[\sin 2\alpha \]
B) \[\cos 2\alpha \]
C) \[2\sin 2\alpha \]
D) \[2\cos 2\alpha \]
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question_answer9) The area of a parallelogram formed by the lines \[ax\pm by\pm c=0\], is [IIT 1973]
A) \[\frac{{{c}^{2}}}{ab}\]
B) \[\frac{2{{c}^{2}}}{ab}\]
C) \[\frac{{{c}^{2}}}{2ab}\]
D) None of these
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question_answer10) The triangle formed by \[{{x}^{2}}9{{y}^{2}}=0\]and \[x=4\]is [Orissa JEE 2004]
A) Isosceles
B) Equilateral
C) Right angled
D) None of these
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question_answer11) A point moves so that square of its distance from the point (3, 2) is numerically equal to its distance from the line \[5x12y=13\]. The equation of the locus of the point is [Roorkee 1974]
A) \[13{{x}^{2}}+13{{y}^{2}}83x+64y+182=0\]
B) \[{{x}^{2}}+{{y}^{2}}11x+16y+26=0\]
C) \[{{x}^{2}}+{{y}^{2}}11x+16y=0\]
D) None of these
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question_answer12) Locus of the points which are at equal distance from \[3x+4y11=0\]and \[12x+5y+2=0\]and which is near the origin is [MNR 1987]
A) \[21x77y+153=0\]
B) \[99x+77y133=0\]
C) \[7x11y=19\]
D) None of these
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question_answer13) A point moves such that its distance from the point \[(4,\,0)\]is half that of its distance from the line \[x=16\]. The locus of this point is [AMU 1980]
A) \[3{{x}^{2}}+4{{y}^{2}}=192\]
B) \[4{{x}^{2}}+3{{y}^{2}}=192\]
C) \[{{x}^{2}}+{{y}^{2}}=192\]
D) None of these
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question_answer14) The locus of a point so that sum of its distance from two given perpendicular lines is equal to 2 unit in first quadrant, is [Bihar CEE 1994]
A) \[x+y+2=0\]
B) \[x+y=2\]
C) \[xy=2\]
D) None of these
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question_answer15) If the sum of the distances of a point from two perpendicular lines in a plane is 1, then its locus is [IIT 1992, Karnataka CET 1999; DCE 2000,01]
A) Square
B) Circle
C) Straight line
D) Two intersecting lines
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question_answer16) If a variable line drawn through the point of intersection of straight lines \[\frac{x}{\alpha }+\frac{y}{\beta }=1\]and \[\frac{x}{\beta }+\frac{y}{\alpha }=1\] meets the coordinate axes in A and B, then the locus of the mid point of \[AB\] is
A) \[\alpha \beta (x+y)=xy(\alpha +\beta )\]
B) \[\alpha \beta (x+y)=2xy(\alpha +\beta )\]
C) \[(\alpha +\beta )(x+y)=2\alpha \beta xy\]
D) None of these
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question_answer17) The point moves such that the area of the triangle formed by it with the points (1, 5) and (3, ?7) is 21sq. unit. The locus of the point is [Kerala (Engg.) 2002]
A) \[6x+y32=0\]
B) \[6xy+32=0\]
C) \[x+6y32=0\]
D) \[6xy32=0\]
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question_answer18) A straight line through the point (1, 1) meets the xaxis at 'A' and the yaxis at 'B'. The locus of the midpoint of AB is [UPSEAT 2004]
A) \[2xy+x+y=0\]
B) \[x+y2xy=0\]
C) \[x+y+2=0\]
D) \[x+y2=0\]
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question_answer19) If A is (2, 5), B is (4, 11) and C lies on \[9x+7y+4=0\], then the locus of the centroid of the \[\Delta ABC\] is a straight line parallel to the straight line is [MP PET 1986]
A) \[7x9y+4=0\]
B) \[9x7y4=0\]
C) \[9x+7y+4=0\]
D) \[7+9y+4=0\]
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