1
IIT-JEE 1982
MCQ (Single Correct Answer)
+2
-0.5
If $$A$$ and $$B$$ are two events such that $$P\left( A \right) > 0,$$ and $$P\left( B \right) \ne 1,$$ then $$P\left( {{{\overline A } \over {\overline B }}} \right)$$ is equal to
A
$$1 - P({A \over B})$$ (Here $$\overline A $$ and $$\overline B $$ are complements of $$A$$ and $$B$$ respectively).
B
$$1 - P({{\overline A } \over B})$$ (Here $$\overline A $$ and $$\overline B $$ are complements of $$A$$ and $$B$$ respectively).
C
$${{1 - P\left( {A \cup B} \right)} \over {P\left( {\overline B } \right)}}$$ (Here $$\overline A $$ and $$\overline B $$ are complements of $$A$$ and $$B$$ respectively).
D
$${{P\left( {\overline A } \right)} \over {P\left( {\overline B } \right)}}$$ (Here $$\overline A $$ and $$\overline B $$ are complements of $$A$$ and $$B$$ respectively).
2
IIT-JEE 1982
Subjective
+2
-0
$$A$$ and $$B$$ are two candidates seeking admission in $$IIT.$$ The probability that $$A$$ is selected is $$0.5$$ and the probability that both $$A$$ and $$B$$ are selected is atmost $$0.3$$. Is it possible that the probability of $$B$$ getting selected is $$0.9$$ ?
3
IIT-JEE 1982
MCQ (Single Correct Answer)
+2
-0.5
For non-zero vectors $${\overrightarrow a ,\,\overrightarrow b ,\overrightarrow c },$$ $$\left| {\left( {\overrightarrow a \times \overrightarrow b } \right).\overrightarrow c } \right| = \left| {\overrightarrow a } \right|\left| {\overrightarrow b } \right|\left| {\overrightarrow c } \right|$$ holds if and only if
A
$$\overrightarrow a \,.\,\overrightarrow b = 0,\overrightarrow b \,.\,\overrightarrow c = 0$$
B
$$\overrightarrow b \,.\,\overrightarrow c = 0,\overrightarrow c \,.\,\overrightarrow a = 0$$
C
$$\overrightarrow c \,.\,\overrightarrow a = 0,\overrightarrow a \,.\,\overrightarrow b = 0$$
D
$$\overrightarrow a \,.\,\overrightarrow b = \overrightarrow b \,.\,\overrightarrow c = \overrightarrow c \,.\,\overrightarrow a = 0$$
4
IIT-JEE 1982
Subjective
+2
-0
$${A_1},{A_2},.................{A_n}$$ are the vertices of a regular plane polygon with $$n$$ sides and $$O$$ is its centre. Show that
$$\sum\limits_{i = 1}^{n - 1} {\left( {\overrightarrow {O{A_i}} \times {{\overrightarrow {OA} }_{i + 1}}} \right) = \left( {1 - n} \right)\left( {{{\overrightarrow {OA} }_2} \times {{\overrightarrow {OA} }_1}} \right)} $$
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