1
IIT-JEE 1993
MCQ (Single Correct Answer)
+1
-0.25
The value of $$\int\limits_0^{\pi /2} {{{dx} \over {1 + {{\tan }^3}\,x}}} $$ is
A
$$0$$
B
$$1$$
C
$$\pi /2$$
D
$$\pi /4$$
2
IIT-JEE 1993
Subjective
+5
-0
Evaluate $$\int_2^3 {{{2{x^5} + {x^4} - 2{x^3} + 2{x^2} + 1} \over {\left( {{x^2} + 1} \right)\left( {{x^4} - 1} \right)}}} dx.$$
3
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
$$65/81$$
4
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
$$\,P\left( E \right) = 1/4,P\left( F \right) = 1/3$$
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