1
IIT-JEE 2005 Screening
MCQ (Single Correct Answer)
+4
-1
If $$\overrightarrow a \,,\,\overrightarrow b ,\overrightarrow c $$ are three non-zero, non-coplanar vectors and
$$\overrightarrow {{b_1}} = \overrightarrow b - {{\overrightarrow b .\,\overrightarrow a } \over {{{\left| {\overrightarrow a } \right|}^2}}}\overrightarrow a ,\overrightarrow {{b_2}} = \overrightarrow b + {{\overrightarrow b .\,\overrightarrow a } \over {{{\left| {\overrightarrow a } \right|}^2}}}\overrightarrow a ,$$
$$\overrightarrow {{c_1}} = \overrightarrow c - {{\overrightarrow c .\,\overrightarrow a } \over {{{\left| {\overrightarrow a } \right|}^2}}}\overrightarrow a + {{\overrightarrow b .\,\overrightarrow c } \over {{{\left| c \right|}^2}}}{\overrightarrow b _1},\,\,\overrightarrow {{c_2}} = \overrightarrow c - {{\overrightarrow c .\,\overrightarrow a } \over {{{\left| {\overrightarrow a } \right|}^2}}}\overrightarrow a - {{\overrightarrow b \,.\,\overrightarrow c } \over {{{\left| {{{\overrightarrow b }_1}} \right|}^2}}}{\overrightarrow b _1},$$
$$\overrightarrow {{c_3}} = \overrightarrow c - {{\overrightarrow c .\,\overrightarrow a } \over {{{\left| {\overrightarrow c } \right|}^2}}}\overrightarrow a + {{\overrightarrow b .\,\overrightarrow c } \over {{{\left| c \right|}^2}}}{\overrightarrow b _1},\,\,\overrightarrow {{c_4}} = \overrightarrow c - {{\overrightarrow c .\,\overrightarrow a } \over {{{\left| {\overrightarrow c } \right|}^2}}}\overrightarrow a - {{\overrightarrow b \,.\,\overrightarrow c } \over {{{\left| {{{\overrightarrow b }_1}} \right|}^2}}}{\overrightarrow b _1},$$
then the set of orthogonal vectors is
A
$$\left( {\overrightarrow a ,\overrightarrow {{b_1}} ,\overrightarrow {{c_3}} } \right)$$
B
$$\left( {\overrightarrow a ,\overrightarrow {{b_1}} ,\overrightarrow {{c_2}} } \right)$$
C
$$\left( {\overrightarrow a ,\overrightarrow {{b_1}} ,\overrightarrow {{c_1}} } \right)$$
D
$$\left( {\overrightarrow a ,\overrightarrow {{b_2}} ,\overrightarrow {{c_2}} } \right)$$
2
IIT-JEE 2005 Screening
MCQ (Single Correct Answer)
+2
-0.5
Which of the following set have different dimensions?
A
Pressure, Young's modulus, Stress
B
EMF, Potential difference, Electric potential
C
Heat, Work done, Energy
D
Dipole moment, Electric flux, Electric field
3
IIT-JEE 2005 Screening
MCQ (Single Correct Answer)
+2
-0.5
A simple pendulum has time period T1. The point of suspension is now moved upward according to the relation y = Kt2, (K = 1 m/s2) where y is the vertical displacement. The time period now become T2. The ratio of $${{T_1^2} \over {T_2^2}}$$ is (g = 10 m/s2)
A
$${5 \over 6}$$
B
$${6 \over 5}$$
C
1
D
$${4 \over 5}$$
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