1
IIT-JEE 2007 Paper 1 Offline
MCQ (Single Correct Answer)
+3
-1
Consider the following linear equations
$$ax + by + cz = 0$$
$$bx + cy + az = 0$$
$$cx + ay + bz = 0$$
Match the conditions/expressions in Column I with statements in Column II.
| Column I | Column II | ||
|---|---|---|---|
| (A) | $$a + b + c \ne 0$$ and $${a^2} + {b^2} + {c^2} = ab + bc + ca$$ | (P) | the equations represent planes meeting only at a single point. |
| (B) | $$a + b + c = 0$$ and $${a^2} + {b^2} + {c^2} \ne ab + bc + ca$$ | (Q) | the equations represent the line $$x=y=z$$. |
| (C) | $$a + b + c \ne 0$$ and $${a^2} + {b^2} + {c^2} \ne ab + bc + ca$$ | (R) | the equations represent identical planes. |
| (D) | $$a + b + c = 0$$ and $${a^2} + {b^2} + {c^2} = ab + bc + ca$$ | (S) | the equations represent the whole of the three dimensional space. |
2
IIT-JEE 2005 Mains
MCQ (Single Correct Answer)
+3
-0
The area of the triangle formed by the intersection of a line parallel to X-axis and passing through $$(h, k)$$ with the lines $$y=x$$ and $$x+y=2$$ is $$4 h^{2}$$. Find the locus of point $$P$$.
3
IIT-JEE 2004 Screening
MCQ (Single Correct Answer)
+3
-0.75
Area of the triangle formed by the line $$x + y = 3$$ and angle bisectors of the pair of straight line $${x^2} - {y^2} + 2y = 1$$ is
4
IIT-JEE 2003 Screening
MCQ (Single Correct Answer)
+3
-0.75
Orthocentre of triangle with vertices $$\left( {0,0} \right),\left( {3,4} \right)$$ and $$\left( {4,0} \right)$$ is
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