1
IIT-JEE 2007
Subjective
+4
-0
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 $$II$$ and indicate your answer by darkening the appropriate bubbles in the $$4 \times 4$$ matrix given in the $$ORS.$$

$$\,\,\,$$ Column $$I$$
(A)$$\,\,a + b + c \ne 0$$ and $${a^2} + {b^2} + {c^2} = ab + bc + ca$$
(B)$$\,\,$$ $$a + b + c = 0$$ and $${a^2} + {b^2} + {c^2} \ne ab + bc + ca$$
(C)$$\,\,a + b + c \ne 0$$ and $${a^2} + {b^2} + {c^2} \ne ab + bc + ca$$
(D)$$\,\,$$ $$a + b + c = 0$$ and $${a^2} + {b^2} + {c^2} = ab + bc + ca$$

$$\,\,\,$$ Column $$II$$
(p)$$\,\,\,$$ the equations represents planes meeting only at asingle point
(q)$$\,\,\,$$ the equations represents the line $$x=y=z.$$
(r)$$\,\,\,$$ the equations represent identical planes.
(s) $$\,\,\,$$ the equations represents the whole of the three dimensional space.

2
IIT-JEE 2006
Subjective
+6
-0
Match the folowing :
(A)$$\,\,\,$$Two rays $$x + y = \left| a \right|$$ and $$ax - y=1$$ intersects each other in the
$$\,\,\,\,\,\,\,\,\,\,$$first quadrant in interval $$a \in \left( {{a_0},\,\,\infty } \right),$$ the value of $${{a_0}}$$ is
(B)$$\,\,\,$$ Point $$\left( {\alpha ,\beta ,\gamma } \right)$$ lies on the plane $$x+y+z=2.$$
$$\,\,\,\,\,\,\,\,\,\,\,$$Let $$\overrightarrow a = \alpha \widehat i + \beta \widehat j + \gamma \widehat k,\widehat k \times \left( {\widehat k \times \overrightarrow a } \right) = 0,$$ then $$\gamma = $$
(C)$$\,\,\,$$$$\left| {\int\limits_0^1 {\left( {1 - {y^2}} \right)dy} } \right| + \left| {\int\limits_1^0 {\left( {{y^2} - 1} \right)dy} } \right|$$
(D)$$\,\,\,$$If $$\sin A\,\,\sin B\,\,\sin C + \cos A\,\,\cos B = 1,$$ then the value of $$\sin C = $$

(p)$$\,\,\,$$ $$2$$
(q)$$\,\,\,$$ $${4 \over 3}$$
(r)$$\,\,\,$$ $$\left| {\int\limits_0^1 {\sqrt {1 - xdx} } } \right| + \left| {\int\limits_{ - 1}^0 {\sqrt {1 + xdx} } } \right|$$
(s)$$\,\,\,$$ $$1$$

3
IIT-JEE 2005
Subjective
+2
-0
Find the equation of the plane containing the line $$2x-y+z-3=0,3x+y+z=5$$ and at a distance of $${1 \over {\sqrt 6 }}$$ from the point $$(2, 1, -1).$$
4
IIT-JEE 2005
Subjective
+4
-0
If the incident ray on a surface is along the unit vector $$\widehat v\,\,,$$ the reflected ray is along the unit vector $$\widehat w\,\,$$ and the normal is along unit vector $$\widehat a\,\,$$ outwards. Express $$\widehat w\,\,$$ in terms of $$\widehat a\,\,$$ and $$\widehat v\,\,.$$ IIT-JEE 2005 Mathematics - Vector Algebra and 3D Geometry Question 46 English
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