1
IIT-JEE 2006
MCQ (Single Correct Answer)
+3
-1

For $x>0, \mathop {\lim }\limits_{x \to 0}\left((\sin x)^{1 / x}+(1 / x)^{\sin x}\right)$ is :

A

0

B

-1

C

1

D

2

2
IIT-JEE 2006
MCQ (Single Correct Answer)
+3
-1

$\int \frac{x^2-1}{x^3 \sqrt{2 x^4-2 x^2+1}} d x$ is equal to

A

$\frac{\sqrt{2 x^4-2 x^2+1}}{x^2}+\mathrm{C}$

B

$\frac{\sqrt{2 x^4-2 x^2+1}}{x^3}+\mathrm{C}$

C

$\frac{\sqrt{2 x^4-2 x^2+1}}{x}+\mathrm{C}$

D

$\frac{\sqrt{2 x^4-2 x^2+1}}{2 x^2}+C$

3
IIT-JEE 2006
MCQ (Single Correct Answer)
+3
-1

Given an isosceles triangle, whose one angle is $120^{\circ}$ and radius of its incircle $=\sqrt{3}$. Then the area of the triangle in sq. units is

A

$7+12 \sqrt{3}$

B

$12-7 \sqrt{3}$

C

$12+7 \sqrt{3}$

D

$4 \pi$

4
IIT-JEE 2006
MCQ (Single Correct Answer)
+3
-1

If $0<\theta<2 \pi$, then the intervals of values of $\theta$ for which $2 \sin ^2 \theta-5 \sin \theta+2>0$, is

A

$\left(0, \frac{\pi}{6}\right) \cup\left(\frac{5 \pi}{6}, 2 \pi\right)$

B

$\left(\frac{\pi}{8}, \frac{5 \pi}{6}\right)$

C

$\left(0, \frac{\pi}{8}\right) \cup\left(\frac{\pi}{6}, \frac{5 \pi}{6}\right)$

D

$\left(\frac{41 \pi}{48}, \pi\right)$

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