1
IIT-JEE 1995 Screening
MCQ (Single Correct Answer)
+2
-0.5
The probability of India winning a test match against West Indies is $$1/2$$. Assuming independence from match to match the probability that in a $$5$$ match series India's second win occurs at third test is
A
$$1/8$$
B
$$1/4$$
C
$$1/2$$
D
$$2/3$$
2
IIT-JEE 1995 Screening
MCQ (Single Correct Answer)
+2
-0.5
Three of six vertices of a regular hexagon are chosen at random. The probability that the triangle with three vertices is equilateral, equals
A
$$1/2$$
B
$$1/5$$
C
$$1/10$$
D
$$1/20$$
3
IIT-JEE 1995 Screening
MCQ (More than One Correct Answer)
+2
-0.5
Let $$0 < P\left( A \right) < 1,0 < P\left( B \right) < 1$$ and
$$P\left( {A \cup B} \right) = P\left( A \right) + P\left( B \right) - P\left( A \right)P\left( B \right)$$ then
A
$$P\left( {B/A} \right) = P\left( B \right) - P\left( A \right)$$
B
$$P\left( {A' - B'} \right) = P\left( {A'} \right) - P\left( {B'} \right)$$
C
$$P\left( {A \cup B} \right)' = P\left( {A'} \right) - P\left( {B'} \right)$$
D
$$P\left( {A/B} \right) = P\left( A \right)$$
4
IIT-JEE 1995 Screening
MCQ (Single Correct Answer)
+4
-1
Let $$\overrightarrow a = \widehat i - \widehat j,\overrightarrow b = \widehat j - \widehat k,\overrightarrow c = \widehat k - \widehat i.$$ If $$\overrightarrow d $$ is a unit vector such that $$\overrightarrow a .\overrightarrow d = 0 = \left[ {\overrightarrow b \overrightarrow c \overrightarrow d } \right],$$ then $$\overrightarrow d $$ equals
A
$$ \pm {{\widehat i + \widehat j - 2k} \over {\sqrt 6 }}$$
B
$$ \pm {{\widehat i + \widehat j - k} \over {\sqrt 3 }}$$
C
$$ \pm {{\widehat i + \widehat j + k} \over {\sqrt 3 }}$$
D
$$ \pm \widehat k$$
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