1
IIT-JEE 1998
Subjective
+8
-0
Prove that a triangle $$ABC$$ is equilateral if and only if $$\tan A + \tan B + \tan C = 3\sqrt 3 $$.
2
IIT-JEE 1998
Subjective
+8
-0
A bird flies in a circle on a horizontal plane. An observer stands at a point on the ground. Suppose $${60^ \circ }$$ and $${30^ \circ }$$ are the maximum and the minimum angles of elevation of the bird and that they occur when the bird is at the points $$P$$ and $$Q$$ respectively on its path. Let $$\theta $$ be the angle of elevation of the bird when it is a point on the are of the circle exactly midway between $$P$$ and $$Q$$. Find the numerical value of $${\tan ^2}\theta $$. (Assume that the observer is not inside the vertical projection of the path of the bird.)
3
IIT-JEE 1998
MCQ (More than One Correct Answer)
+2
-0.5
If $${\omega}$$ is an imaginary cube root of unity, then $${(1\, + \omega \, - {\omega ^2})^7}$$ equals
A
$$128\omega $$
B
$$ - 128\omega $$
C
$$128{\omega ^2}$$
D
$$ - 128{\omega ^2}$$
4
IIT-JEE 1998
MCQ (Single Correct Answer)
+2
-0.5
If in a triangle $$PQR$$, $$\sin P,\sin Q,\sin R$$ are in $$A.P.,$$ then
A
the altitudes are in $$A.P.$$
B
the altitudes are in $$H.P.$$
C
the medians are in $$G.P.$$
D
the medians are in $$A.P$$
JEE Advanced Papers
EXAM MAP