1
IIT-JEE 2006
MCQ (Single Correct Answer)
+3
-0

Match the following:

(i) $$\sum\limits_{i = 1}^\infty {{{\tan }^{ - 1}}\left( {{1 \over {2{i^2}}}} \right) = t} $$ then $$\tan t=$$ (A) 0
(ii) Sides $$a,b,c$$ of a triangle ABC are in AP and $$\cos {\theta _1} = {a \over {b + c}},\cos {\theta _2} = {b \over {a + c}},\cos {\theta _3} = {c \over {a + b}}$$, then $${\tan ^2}\left( {{{{\theta _1}} \over 2}} \right) + {\tan ^2}\left( {{{{\theta _3}} \over 2}} \right) = $$ (B) 1
(iii) A line is perpendicular to $$x + 2y + 2z = 0$$ and passes through (0, 1, 0). The perpendicular distance of this line from the origin is (C) $${{\sqrt 5 } \over 3}$$
(D) 2/3

A
(i)-(A); (ii)-(D); (iii)-(C)
B
(i)-(B); (ii)-(D); (iii)-(C)
C
(i)-(B); (ii)-(A); (iii)-(C)
D
(i)-(A); (ii)-(D); (iii)-(B)
2
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

3
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

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

4
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

$4 \pi$

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