1
IIT-JEE 2005 Screening
MCQ (Single Correct Answer)
+1
-0.25
The number of radial nodes of 3s and 2p orbitals are respectively
A
2, 0
B
0, 2
C
1, 2
D
2, 1
2
IIT-JEE 2005 Screening
MCQ (Single Correct Answer)
+3
-0.75
$$\int\limits_{ - 2}^0 {\left\{ {{x^3} + 3{x^2} + 3x + 3 + \left( {x + 1} \right)\cos \left( {x + 1} \right)} \right\}\,\,dx} $$ is equal to
A
$$-4$$
B
$$0$$
C
$$4$$
D
$$6$$
3
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
$$\left( {\overrightarrow a ,\overrightarrow {{b_2}} ,\overrightarrow {{c_2}} } \right)$$
4
IIT-JEE 2005 Screening
MCQ (Single Correct Answer)
+4
-1
A variable plane at a distance of the one unit from the origin cuts the coordinates axes at $$A,$$ $$B$$ and $$C.$$ If the centroid $$D$$ $$(x, y, z)$$ of triangle $$ABC$$ satisfies the relation $${1 \over {{x^2}}} + {1 \over {{y^2}}} + {1 \over {{z^2}}} = k,$$ then the value $$k$$ is
A
$$3$$
B
$$1$$
C
$${1 \over 3}$$
D
$$9$$
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