1
IIT-JEE 2010 Paper 2 Offline
Numerical
+4
-0
Consider a triangle $$ABC$$ and let $$a, b$$ and $$c$$ denote the lengths of the sides opposit to vertices $$A, B$$ and $$C$$ respectively. Suppose $$a = 6,b = 10$$ and the area of the triangle is $$15\sqrt 3 $$, if $$\angle ACB$$ is obtuse and if $$r$$ denotes the radius of the incircle of the triangle, then r2 is equal to :
Your input ____
2
IIT-JEE 2010 Paper 2 Offline
MCQ (Single Correct Answer)
+4
-1
If the distance of the point $$P(1, -2, 1)$$ from the plane $$x+2y-2z$$$$\, = \alpha ,$$ where $$\alpha > 0,$$ is $$5,$$ then the foot of the perpendicular from $$P$$ to the planes is
A
$$\left( {{8 \over 3},{4 \over 3}, - {7 \over 3}} \right)$$
B
$$\left( {{4 \over 3},-{4 \over 3}, {1 \over 3}} \right)$$
C
$$\left( {{1 \over 3},{2 \over 3}, {10 \over 3}} \right)$$
D
$$\left( {{2 \over 3},-{1 \over 3}, {5 \over 3}} \right)$$
3
IIT-JEE 2010 Paper 2 Offline
Numerical
+4
-0
Two parallel chords of a circle of radius 2 are at a distance $$\sqrt 3 + 1$$ apart. If the chords subtend at the center , angles of $${\pi \over k}$$ and $${{2\pi } \over k},$$ where$$k > 0,$$ then the value of $$\left[ k \right]$$ is

[Note :[k] denotes the largest integer less than or equal to k ]

Your input ____
4
IIT-JEE 2010 Paper 2 Offline
MCQ (Single Correct Answer)
+4
-1
For $$r = 0,\,1,....,$$ let $${A_r},\,{B_r}$$ and $${C_r}$$ denote, respectively, the coefficient of $${X^r}$$ in the expansions of $${\left( {1 + x} \right)^{10}},$$ $${\left( {1 + x} \right)^{20}}$$ and $${\left( {1 + x} \right)^{30}}.$$
Then $$\sum\limits_{r = 1}^{10} {{A_r}\left( {{B_{10}}{B_r} - {C_{10}}{A_r}} \right)} $$ is equal to
A
$$\left( {{B_{10}} - {C_{10}}} \right)$$
B
$${A_{10}}\left( {{B^2}_{10}{C_{10}}{A_{10}}} \right)$$
C
$$0$$
D
$${{C_{10}} - {B_{10}}}$$
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