1
IIT-JEE 2008 Paper 1 Offline
+3
-1
If $$0 < x < 1$$, then

$$\sqrt {1 + {x^2}} {\left[ {{{\left\{ {x\cos \left( {{{\cot }^{ - 1}}x} \right) + \sin \left( {{{\cot }^{ - 1}}x} \right)} \right\}}^2} - 1} \right]^{1/2}} =$$
A
$${x \over {\sqrt {1 + {x^2}} }}$$
B
$$x$$
C
$$x\sqrt {1 + {x^2}}$$
D
$$\sqrt {1 + {x^2}}$$
2
IIT-JEE 2004 Screening
+2
-0.5
The value of $$x$$ for which $$sin\left( {{{\cot }^{ - 1}}\left( {1 + x} \right)} \right) = \cos \left( {{{\tan }^{ - 1}}\,x} \right)$$ is
A
$$1/2$$
B
$$1$$
C
$$0$$
D
$$-1/2$$
3
IIT-JEE 2001 Screening
+2
-0.5
If $${\sin ^{ - 1}}\left( {x - {{{x^2}} \over 2} + {{{x^3}} \over 4} - ....} \right)$$ $$+ {\cos ^{ - 1}}\left( {{x^2} - {{{x^4}} \over 2} + {{{x^6}} \over 4} - ....} \right) = {\pi \over 2}$$\$
for $$0 < \left| x \right| < \sqrt 2 ,$$ then $$x$$ equals
A
$$1/2$$
B
$$1$$
C
$$-1/2$$
D
$$-1$$
4
IIT-JEE 1999
+2
-0.5
The number of real solutions of
$${\tan ^{ - 1}}\,\,\sqrt {x\left( {x + 1} \right)} + {\sin ^{ - 1}}\,\,\sqrt {{x^2} + x + 1} = \pi /2$$ is
A
zero
B
one
C
two
D
infinite
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