1
IIT-JEE 2011 Paper 1 Offline
+4
-1
A straight line $$L$$ through the point $$(3, -2)$$ is inclined at an angle $${60^ \circ }$$ to the line $$\sqrt {3x} + y = 1.$$ If $$L$$ also intersects the x-axis, then the equation of $$L$$ is
A
$$y + \sqrt {3x} + 2 - 3\sqrt 3 = 0$$
B
$$y - \sqrt {3x} + 2 + 3\sqrt 3 = 0$$
C
$$\sqrt {3y} - x + 3 + 2\sqrt 3 = 0$$
D
$$\sqrt {3y} + x - 3 + 2\sqrt 3 = 0$$
2
IIT-JEE 2008 Paper 2 Offline
+3
-1

Consider three points $$P = ( - \sin (\beta - \alpha ), - cos\beta ),Q = (cos(\beta - \alpha ),\sin \beta )$$ and $$R = (\cos (\beta - \alpha + \theta ),\sin (\beta - \theta ))$$ where $$0 < \alpha ,\beta ,\theta < {\pi \over 4}$$. Then :

A
P lies on the line segment RQ
B
Q lies on the line segment PR
C
R lies on the line segment QP
D
P, Q, R are non-collinear
3
IIT-JEE 2008 Paper 2 Offline
+4
-1

Consider the lines given by:

$${L_1}:x + 3y - 5 = 0$$

$${L_2}:3x - ky - 1 = 0$$

$${L_3}:5x + 2y - 12 = 0$$

Match the Statement/Expressions in Column I with the Statements/Expressions in Column II.

Column I Column II
(A) L$$_1$$, L$$_2$$, L$$_3$$ are concurrent, if (P) $$K = - 9$$
(B) One of L$$_1$$, L$$_2$$, L$$_3$$ is parallel to atleast one of the other two, if (Q) $$K = - {6 \over 5}$$
(C) L$$_1$$, L$$_2$$, L$$_3$$ form a triangle, if (R) $$K = {5 \over 6}$$
(D) L$$_1$$, L$$_2$$, L$$_3$$ do not form a triangle, if (S) $$K = 5$$

A
A - iv; B - ii; C - iii; D - i, ii
B
A - iv; B - i, ii; C - iii; D - i, ii, iv
C
A - iv; B - i; C - iii; D - i, ii
D
A - ii; B - i, iii; C - iii; D - i, ii, iv
4
IIT-JEE 2007
+3
-0.75
Let $$O\left( {0,0} \right),P\left( {3,4} \right),Q\left( {6,0} \right)$$ be the vertices of the triangles $$OPQ$$. The point $$R$$ inside the triangle $$OPQ$$ is such that the triangles $$OPR$$, $$PQR$$, $$OQR$$ are of equal area. The coordinates of $$R$$ are
A
$$\left( {{4 \over 3},3} \right)$$
B
$$\left( {3,{2 \over 3}} \right)$$
C
$$\left( {3,{4 \over 3}} \right)$$
D
$$\left( {{4 \over 3},{2 \over 3}} \right)$$
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