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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
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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
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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
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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)
\[a=\sqrt{2}\ b\] done
clear
B)
\[a=-\sqrt{2}\ b\] done
clear
C)
Both (a) and (b) done
clear
D)
None of these done
clear
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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)
\[2x-9y-7=0\] done
clear
B)
\[2x-9y-11=0\] done
clear
C)
\[2x+9y-11=0\] done
clear
D)
\[2x+9y+7=0\] done
clear
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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)
\[2Tx+{{a}^{2}}y+2aT=0\] 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
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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
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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
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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 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
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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)
\[{{30}^{o}}\] done
clear
B)
\[{{45}^{o}}\] done
clear
C)
\[{{60}^{o}}\] done
clear
D)
\[{{75}^{o}}\] done
clear
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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 done
clear
B)
2 done
clear
C)
3 done
clear
D)
4 done
clear
View Solution play_arrow
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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
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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)
\[y-5=0\] done
clear
B)
\[x-5=0\] done
clear
C)
\[y+5=0\] done
clear
D)
\[x+5=0\] done
clear
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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
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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)
\[\frac{7}{\sqrt{5}},\frac{7}{\sqrt{13}},\frac{7}{\sqrt{6}}\] 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
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question_answer20)
The equation of the line joining the point (3, 5)to the point of intersection of the lines \[4x+y-1=0\] 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
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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 done
clear
B)
Perpendicular done
clear
C)
The sides of a rectangle done
clear
D)
None of these done
clear
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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
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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)
\[x-5y=0\]\[5x+y=0\]\[\Delta =\frac{36}{13}\] 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
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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
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question_answer26)
The area enclosed within the curve \[|x|+|y|=1\]is [RPET 1990, 1997; IIT 1981; UPSEAT 2003]
A)
\[\sqrt{2}\] done
clear
B)
1 done
clear
C)
\[\sqrt{3}\] done
clear
D)
2 done
clear
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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)
\[ab\] done
clear
B)
\[\frac{ab}{2}\] done
clear
C)
\[2ab\] done
clear
D)
\[\frac{ab}{3}\] done
clear
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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 done
clear
B)
25/4 done
clear
C)
25/8 done
clear
D)
25/16 done
clear
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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) done
clear
B)
(3, 4) done
clear
C)
(- 4, 3) done
clear
D)
(- 3, 4) done
clear
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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 done
clear
B)
Circle done
clear
C)
Pair of straight lines done
clear
D)
Parabola done
clear
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