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## Numerical

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Consider the lines L1 and L2 defined by $${L_1}:x\sqrt 2 + y - 1 = 0$$ and $${L_2}:x\sqrt 2 - y + 1 = 0$$For a fixed c...
JEE Advanced 2021 Paper 1 Online
Consider the lines L1 and L2 defined by $${L_1}:x\sqrt 2 + y - 1 = 0$$ and $${L_2}:x\sqrt 2 - y + 1 = 0$$For a fixed c...
JEE Advanced 2021 Paper 1 Online
For a point $$P$$ in the plane, Let $${d_1}\left( P \right)$$ and $${d_2}\left( P \right)$$ be the distance of the point...
JEE Advanced 2014 Paper 1 Offline

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For $$a &gt; b &gt; c &gt; 0,$$ the distance between $$(1, 1)$$ and the point of intersection of the lines $$ax + by + c... JEE Advanced 2013 Paper 1 Offline A straight line$$L$$through the point$$(3, -2)$$is inclined at an angle$${60^ \circ }$$to the line$$\sqrt {3x} +...
IIT-JEE 2011 Paper 1 Offline
The lines $${L_1}:y - x = 0$$ and $${L_2}:2x + y = 0$$ intersect the line $${L_3}:y + 2 = 0$$ at $$P$$ and $$Q$$ respect...
IIT-JEE 2007
Let $$O\left( {0,0} \right),P\left( {3,4} \right),Q\left( {6,0} \right)$$ be the vertices of the triangles $$OPQ$$. The ...
IIT-JEE 2007
Area of the triangle formed by the line $$x + y = 3$$ and angle bisectors of the pair of straight line $${x^2} - {y^2} ... IIT-JEE 2004 Screening Orthocentre of triangle with vertices$$\left( {0,0} \right),\left( {3,4} \right)$$and$$\left( {4,0} \right)$$is IIT-JEE 2003 Screening The number of integral points (integral point means both the coordinates should be integer) exactly in the interior of t... IIT-JEE 2003 Screening The pair of lines represented by$$3a{x^2} + 5xy + \left( {{a^2} - 2} \right){y^2} = 0$$are perpendicular to each othe... IIT-JEE 2002 If the pair of lines$$a{x^2} + 2hxy + b{y^2} + 2gx + 2fy + c = 0$$intersect on the$$y$$axis then IIT-JEE 2002 Locus of mid point of the portion between the axes of$$x\cos \alpha + y\sin \alpha = p$$where$$p$$is constant... IIT-JEE 2002 A triangle with vertices$$(4, 0), (-1, -1), (3, 5)$$is IIT-JEE 2002 A straight line through the origin$$O$$meets the parallel lines$$4x+2y=9$$and$$2x+y+6=0$$at points$$P$$and$$Q$$... IIT-JEE 2002 Screening Let$$P = \left( { - 1,\,0} \right),\,Q = \left( {0,\,0} \right)$$and$$R = \left( {3,\,3\sqrt 3 } \right)$$be three p... IIT-JEE 2002 Screening Let$$0 &lt; \alpha &lt; {\pi \over 2}$$be fixed angle. If$$P = \left( {\cos \theta ,\,\sin \theta } \right)$$and ... IIT-JEE 2002 Screening Area of the parallelogram formed by the lines$$y = mx$$,$$y = mx + 1$$,$$y = nx$$and$$y = nx + 1$$equals IIT-JEE 2001 Screening The number of integer values of$$m$$, for which the$$x$$-coordinate of the point of intersection of the lines$$3x + 4...
IIT-JEE 2001 Screening
The incentre of the triangle with vertices $$\left( {1,\,\sqrt 3 } \right),\left( {0,\,0} \right)$$ and $$\left( {2,\,0}... IIT-JEE 2000 Screening Let$$PS$$be the median of the triangle with vertices$$P(2, 2),Q(6, -1)$$and$$R(7, 3).$$The equation of the li... IIT-JEE 2000 Screening If$${x_1},\,{x_2},\,{x_3}$$as well as$${y_1},\,{y_2},\,{y_3}$$, are in G.P. with the same common ratio, then the poin... IIT-JEE 1999 Lt$$PQR$$be a right angled isosceles triangle, right angled at$$P(2, 1)$$. If the equation of the line$$QR$$is$$2x...
IIT-JEE 1999
If $$\left( {P\left( {1,2} \right),\,Q\left( {4,6} \right),\,R\left( {5,7} \right)} \right)$$ and $$S\left( {a,b} \right... IIT-JEE 1998 The diagonals of a parralleogram$$PQRS$$are along the lines$$x + 3y = 4$$and$$6x - 2y = 7$$. Then$$PQRS$$must be ... IIT-JEE 1998 The orthocentre of the triangle formed by the lines$$xy=0$$and$$x+y=1$$is IIT-JEE 1995 The equations to a pair of opposites sides of parallelogram are$${x^2} - 5x + 6 = 0$$and$${y^2} - 6y + 5 = 0,$$the e... IIT-JEE 1994 The locus of a variable point whose distance from$$\left( { - 2,\,0} \right)$$is$$2/3$$times its distance from the ... IIT-JEE 1994 If the sum of the distances of a point from two perpendicular lines in a plane is 1, then its locus is IIT-JEE 1992 Line$$L$$has intercepts$$a$$and$$b$$on the coordinate axes. When the axes are rotated through a given angle, keepi... IIT-JEE 1990 If$$P=(1, 0),Q=(-1, 0)$$and$$R=(2, 0)$$are three given points, then locus of the point$$S$$satisfying the rel... IIT-JEE 1988 A vector$$\overline a $$has components$$2p$$and$$1$$with respect to a rectangular cartesian system. This system is... IIT-JEE 1986 The points$$\left( {0,{8 \over 3}} \right),\,\,\left( {1,\,3} \right)$$and$$\left( {82,\,30} \right)$$are vertices o... IIT-JEE 1986 The straight lines$$x + y = 0,\,3x + y - 4 = 0,\,x + 3y - 4 = 0$$form a triangle which is IIT-JEE 1983 The point$$\,\left( {4,\,1} \right)$$undergoes the following three transformations successively. Reflection about the ... IIT-JEE 1980 The points$$\left( { - a,\, - b} \right),\,\left( {0,\,0} \right),\,\left( {a,\,b} \right)$$and$$\left( {{a^2},\,ab} ...
IIT-JEE 1979

## Subjective

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The area of the triangle formed by intersection of a line parallel to $$x$$-axis and passing through $$P (h, k)$$ with t...
IIT-JEE 2005
A straight line $$L$$ with negative slope passes through the point $$(8, 2)$$ and cuts the positive coordinate axes at p...
IIT-JEE 2002
A straight line $$L$$ through the origin meets the lines $$x + y = 1$$ and $$x + y = 3$$ at $$P$$ and $$Q$$ respectivel...
IIT-JEE 2002
Let $$a, b, c$$ be real numbers with $${a^2} + {b^2} + {c^2} = 1.$$ Show that the equation $$\left| {\matrix{ {ax -... IIT-JEE 2001 Let$$ABC$$and$$PQR$$be any two triangles in the same plane. Assume that the prependiculars from the points$$A, B, C...
IIT-JEE 2000
For points $$P\,\,\, = \left( {{x_1},\,{y_1}} \right)$$ and $$Q\,\,\, = \left( {{x_2},\,{y_2}} \right)$$ of the co-ordin...
IIT-JEE 2000
Using co-ordinate geometry, prove that the three altitudes of any triangle are concurrent.
IIT-JEE 1998
A rectangle $$PQRS$$ has its side $$PQ$$ parallel to the line $$y = mx$$ and vertices $$P, Q$$ and $$S$$ on the lines $$... IIT-JEE 1996 Tagent at a point$${P_1}$${other than$$(0, 0)$$} on the curve$$y = {x^3}$$meets the curve again at$${P_2}$$. The t... IIT-JEE 1993 A line through$$A (-5, -4)$$meets the line$$x + 3y + 2 = 0,2x + y + 4 = 0$$and$$x - y - 5 = 0$$at the points... IIT-JEE 1993 Determine all values of$$\alpha $$for which the point$$\left( {\alpha ,\,{\alpha ^2}} \right)$$lies insides the tria... IIT-JEE 1992 Find the equation of the line passing through the point$$(2, 3)$$and making intercept of length 2 units between the li... IIT-JEE 1991 Show that all chords of the curve$$3{x^2} - {y^2} - 2x + 4y = 0,$$which subtend a right angle at the origin, pass thro... IIT-JEE 1991 A line cuts the$$x$$-axis at$$A (7, 0)$$and the$$y$$-axis at$$B (0, -5)$$. A variable line$$PQ$$is drawn perpendi... IIT-JEE 1990 Straight lines$$3x + 4y = 5$$and$$4x - 3y = 15$$intersect at the point$$A$$. Points$$B$$and$$C$$are choosen on ... IIT-JEE 1990 Let$$ABC$$be a triangle with$$AB = AC$$. If$$D$$is the midpoint of$$BC, E$$is the foot of the perpendicular drawn... IIT-JEE 1989 Lines$${L_1} = ax + by + c = 0$$and$${L_2} = lx + my + n = 0$$intersect at the point$$P$$and make an angle$$\theta...
IIT-JEE 1988
Two sides of rhombus $$ABCD$$ are parallel to the lines $$y = x + 2$$ and $$y = 7x + 3$$. If the diagonals of the rhombu...
IIT-JEE 1985
One of the diameters of the circle circumscribing the rectangle $$ABCD$$ is $$4y = x + 7$$. If $$A$$ and $$B$$ are the p...
IIT-JEE 1985
Two equal sides of an isosceles triangle are given by the equations $$7x - y + 3 = 0$$ and $$x + y - 3 = 0$$ and its thi...
IIT-JEE 1984
The end $$A, B$$ of a straight line segment of constant length $$c$$ slide upon the fixed rectangular axes $$OX, OY$$ re...
IIT-JEE 1983
The coordinates of $$A, B, C$$ are $$(6, 3), (-3, 5), (4, -2)$$ respectively, and $$P$$ is any point $$(x, y)$$. Show ...
IIT-JEE 1983
IIT-JEE 1998
All points lying inside the triangle formed by the points $$\left( {1,\,3} \right),\,\left( {5,\,0} \right)$$ and $$\lef... IIT-JEE 1986 Three lines$$px + qy + r = 0$$,$$qx + ry + p = 0$$and$$rx + py + q = 0$$are concurrent if IIT-JEE 1985 ## Fill in the Blanks More The vertices of a triangle are$$A\left( { - 1, - 7} \right)B\left( {5,\,1} \right)$$and$$C\left( {1,\,4} \right).$$T... IIT-JEE 1993 Let the algebraic sum of the perpendicular distances from the points$$\left( {2,0} \right),\,\left( {0,\,2} \right)$$... IIT-JEE 1991 The orthocentre of the triangle formed by the lines$$x + y = 1,\,2x + 3y = 6$$and$$4x - y + 4 = 0$$lies in quadrant ... IIT-JEE 1985 If$$a,\,b$$and$$c$$are in A.P., then the straight line$$ax + by + c = 0$$will always pass through a fixed point wh... IIT-JEE 1984 Given the points$$A\left( {0,4} \right)$$and$$B\left( {0, - 4} \right)$$, the equation of the locus of the point$$P\...
IIT-JEE 1983
The set of lines $$ax + by + c = 0,$$ where $$3a + 2b + 4c = 0$$ is concurrent at the point ..........
IIT-JEE 1982
$$y = {10^x}$$ is the reflection of $${\log _{10}}\,x$$ in the line whose equation is ...........
IIT-JEE 1982
The area enclosed within the curve $$\left| x \right| + \left| y \right| = 1$$ is .................
IIT-JEE 1981

## True or False

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The lines $$2x + 3y + 19 = 0$$ and $$9x + 6y - 17 = 0$$ cut the coordinates axes in concyclic points.
IIT-JEE 1988
The straight line $$5x + 4y = 0$$ passes through the point of intersection of the straight lines $$x + 2y - 10 = 0$$ and...
IIT-JEE 1983

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