1
JEE Advanced 2014 Paper 2 Offline
+3
-1
In a triangle the sum of two sides is $$x$$ and the product of the same sides is $$y$$. If $${x^2} - {c^2} = y$$, where $$c$$ is the third side of the triangle, then the ratio of the in radius to the circum-radius of the triangle is
A
$${{3y} \over {2x\left( {x + c} \right)}}$$
B
$${{3y} \over {2c\left( {x + c} \right)}}$$
C
$${{3y} \over {4x\left( {x + c} \right)}}$$
D
$${{3y} \over {4c\left( {x + c} \right)}}$$
2
IIT-JEE 2012 Paper 2 Offline
+4
-1
Let $$PQR$$ be a triangle of area $$\Delta$$ with $$a=2$$, $$b = {7 \over 2}$$ and $$c = {5 \over 2}$$; where $$a, b,$$ and $$c$$ are the lengths of the sides of the triangle opposite to the angles at $$P.Q$$ and $$R$$ respectively. Then $${{2\sin P - \sin 2P} \over {2\sin P + \sin 2P}}$$ equals.
A
$${3 \over {4\Delta }}$$
B
$${45 \over {4\Delta }}$$
C
$${\left( {{3 \over {4\Delta }}} \right)^2}$$
D
$${\left( {{45 \over {4\Delta }}} \right)^2}$$
3
IIT-JEE 2010 Paper 1 Offline
+4
-1
If the angles $$A, B$$ and $$C$$ of a triangle are in an arithmetic progression and if $$a, b$$ and $$c$$ denote the lengths of the sides opposite to $$A, B$$ and $$C$$ respectively, then the value of the expression $${a \over c}\sin 2C + {c \over a}\sin 2A$$ is
A
$${1 \over 2}$$
B
$${{\sqrt 3 } \over 2}$$
C
$$1$$
D
$${\sqrt 3 }$$
4
IIT-JEE 2010 Paper 1 Offline
+4
-1
Let $$ABC$$ be a triangle such that $$\angle ACB = {\pi \over 6}$$ and let $$a, b$$ and $$c$$ denote the lengths of the sides opposite to $$A$$, $$B$$ and $$C$$ respectively. The value(s) of $$x$$ for which $$a = {x^2} + x + 1,\,\,\,b = {x^2} - 1\,\,\,$$ and $$c = 2x + 1$$ is (are)
A
$$- \left( {2 + \sqrt 3 } \right)$$
B
$${1 + \sqrt 3 }$$
C
$${2 + \sqrt 3 }$$
D
$${4 \sqrt 3 }$$
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