1
IIT-JEE 1993
MCQ (Single Correct Answer)
+1
-0.25
An unbiased die with faces marked $$1,2,3,4,5$$ and $$6$$ is rolled four times. Out of four face values obtained, the probability that the minimum face value is not less than $$2$$ and the maximum face value is not greater than $$5,$$ is then:
A
$$16/81$$
B
$$1/81$$
C
$$80/81$$
D
$$65/81$$
2
IIT-JEE 1993
MCQ (More than One Correct Answer)
+2
-0.5
$$E$$ and $$F$$ are two independent events. The probability that both $$E$$ and $$F$$ happen is $$1/12$$ and the probability that neither $$E$$ nor $$F$$ happens is $$1/2.$$ Then,
A
$$\,P\left( E \right) = 1/3,P\left( F \right) = 1/4$$
B
$$\,P\left( E \right) = 1/2,P\left( F \right) = 1/6$$
C
$$\,P\left( E \right) = 1/6,P\left( F \right) = 1/2$$
D
$$\,P\left( E \right) = 1/4,P\left( F \right) = 1/3$$
3
IIT-JEE 1993
Subjective
+5
-0
Numbers are selected at random, one at a time, from the two- digit numbers $$00, 01, 02 ......, 99$$ with replacement. An event $$E$$ occurs if only if the product of the two digits of a selected number is $$18$$. If four numbers are selected, find probability that the event $$E$$ occurs at least $$3$$ times.
4
IIT-JEE 1993
MCQ (Single Correct Answer)
+1
-0.25
Let $$a, b, c$$ be distinct non-negative numbers. If the vectors $$a\widehat i + a\widehat j + c\widehat k,\widehat i + \widehat k$$ and $$c\widehat i + c\widehat j + b\widehat k$$ lie in a plane, then $$c$$ is
A
the Arithmetic Mean of $$a$$ and $$b$$
B
the Geometric Mean of $$a$$ and $$b$$
C
the Harmonic Mean of $$a$$ and $$b$$
D
equal to zero
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