1
IIT-JEE 1984
Subjective
+2
-0
Evaluate the following $$\int\limits_0^{{1 \over 2}} {{{x{{\sin }^{ - 1}}x} \over {\sqrt {1 - {x^2}} }}dx} $$
2
IIT-JEE 1984
Subjective
+4
-0
Given a function $$f(x)$$ such that
(i) it is integrable over every interval on the real line and
(ii) $$f(t+x)=f(x),$$ for every $$x$$ and a real $$t$$, then show that
the integral $$\int\limits_a^{a + 1} {f\,\,\left( x \right)} \,dx$$ is independent of a.
3
IIT-JEE 1984
Subjective
+4
-0
Find the area of the region bounded by the $$x$$-axis and the curves defined by $$$y = \tan x, - {\pi \over 3} \le x \le {\pi \over 3};\,\,y = \cot x,{\pi \over 6} \le x \le {{3\pi } \over 2}$$$
4
IIT-JEE 1984
MCQ (Single Correct Answer)
+2
-0.5
Three identical dice are rolled. The probability that the same number will appear on each of them is
A
$$1/6$$
B
$$1/36$$
C
$$1/18$$
D
$$3/28$$
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