1
IIT-JEE 1981
Fill in the Blanks
+2
-0
For a biased die the probabilities for the different faces to turn up are given below :

This die tossed and you are told that either face $$1$$ or face $$2$$ has turned up. Then the probability that it is face $$1$$ is ...............

2
IIT-JEE 1981
Subjective
+2
-0
An anti-aircraft gun can take a maximum of four shots at an enemy plane moving away from it. The probabilities of hitting the plane at the first, second, third and fourth shot are $$0.4, 0.3, 0.2$$ and $$0.1$$ respectively. What is the probability that the gun hits the plane?
3
IIT-JEE 1981
Fill in the Blanks
+2
-0
Let $$\overrightarrow A ,\overrightarrow B ,\overrightarrow C$$ be vectors of length $$3, 4, 5$$ respectively. Let $$\overrightarrow A$$ be perpendicular to $$\overrightarrow B + \overrightarrow C ,\overrightarrow B$$ to $$\overrightarrow C + \overrightarrow A$$ to $$\overrightarrow A + \overrightarrow B .$$ Then the length of vector $$\overrightarrow A + \overrightarrow B + \overrightarrow C$$ is ..........
4
IIT-JEE 1981
True or False
+2
-0
Let $$\overrightarrow A ,\overrightarrow B$$ and $${\overrightarrow C }$$ be unit vectors suppose that $$\overrightarrow A .\overrightarrow B = \overrightarrow A .\overrightarrow C = 0,$$ and thatthe angle between $${\overrightarrow B }$$ and $${\overrightarrow C }$$ is $$\pi /6.$$ Then $$\overrightarrow A = \pm 2\left( {\overrightarrow B \times \overrightarrow C } \right).$$
A
TRUE
B
FALSE
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