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 2007
+3
-0.75
Consider the planes $$3x-6y-2z=15$$ and $$2x+y-2z=5.$$

STATEMENT-1: The parametric equations of the line of intersection of the given planes are $$x=3+14t,y=1+2t,z=15t.$$ because

STATEMENT-2: The vector $${14\widehat i + 2\widehat j + 15\widehat k}$$ is parallel to the line of intersection of given planes.

A
Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1
B
Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1
C
Statement-1 is True, Statement-2 is False
D
Statement-1 is False, Statement-2 is True.
3
IIT-JEE 2007
+3
-0.75
Let the vectors $$\overrightarrow {PQ} ,\,\,\overrightarrow {QR} ,\,\,\overrightarrow {RS} ,\,\,\overrightarrow {ST} ,\,\,\overrightarrow {TU} ,$$ and $$\overrightarrow {UP} ,$$ represent the sides of a regular hexagon.

STATEMENT-1: $$\overrightarrow {PQ} \times \left( {\overrightarrow {RS} + \overrightarrow {ST} } \right) \ne \overrightarrow 0 .$$ because
STATEMENT-2: $$\overrightarrow {PQ} \times \overrightarrow {RS} = \overrightarrow 0$$ and $$\overrightarrow {PQ} \times \overrightarrow {ST} \ne \overrightarrow 0 \,\,.$$

A
Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.
B
Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.
C
Statement-1 is True, Statement-2 is False
D
Statement-1 is False, Statement-2 is True.
4
IIT-JEE 2007
+6
-1.5
Some physical quantities are given in Column I and some possible SI units in which these quantities may be expressed are given in Column II. Match the physical quantities in Column I with the units in Column II.

Column I

(A) GMeMs ,
G $$\to$$ universal gravitational constant, Me $$\to$$ mass of the earth, Ms $$\to$$ mass of the Sun

(B) $${{3RT} \over M}$$,
R $$\to$$ universal gas constant, T $$\to$$ absolute temperature, M $$\to$$ molar mass

(C) $${{{F^2}} \over {{q^2}{B^2}}}$$ ,
F $$\to$$ force, q $$\to$$ charge, B $$\to$$ magnetic field

(D) $${{G{M_e}} \over {{R_e}}}$$,
G $$\to$$ universal gravitational constant, Me $$\to$$ mass of the earth, Re $$\to$$ radius of the earth

Column II

(p) (volt) (coulomb) (metre)

(q) (kilogram) (metre)3 (second)−2

(r) (meter)2(second)−2

A
A $$\to$$ (p) & (q), B $$\to$$ (r) & (s), C $$\to$$ (r) & (s), D $$\to$$ (r) & (s)
B
A $$\to$$ (p), B $$\to$$ (r) & (s), C $$\to$$ (r) & (s), D $$\to$$ (r) & (s)
C
A $$\to$$ (p) & (q), B $$\to$$ (r) & (s), C $$\to$$ (r) & (s), D $$\to$$ (r)
D
A $$\to$$ (p) & (q), B $$\to$$ (r), C $$\to$$ (r) & (s), D $$\to$$ (r) & (s)
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