1
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
$${\sqrt 3 }$$
2
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
$${4 \sqrt 3 }$$
3
IIT-JEE 2007
+3
-0.75
Let $$ABCD$$ be a quadrilateral with area $$18$$, with side $$AB$$ parallel to the side $$CD$$ and $$2AB=CD$$. Let $$AD$$ be perpendicular to $$AB$$ and $$CD$$. If a circle is drawn inside the quadrilateral $$ABCD$$ touching all the sides, then its radius is
A
$$3$$
B
$$2$$
C
$${3 \over 2}$$
D
$$1$$
4
IIT-JEE 2006
+3
-0.75
One angle of an isosceles $$\Delta$$ 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
$$4\pi$$
EXAM MAP
Medical
NEET