1
IIT-JEE 1998
MCQ (More than One Correct Answer)
+2
-0.5
Let $$h\left( x \right) = f\left( x \right) - {\left( {f\left( x \right)} \right)^2} + {\left( {f\left( x \right)} \right)^3}$$ for every real number $$x$$. Then
A
$$h$$ is increasing whenever $$f$$ is increasing
B
$$h$$ is increasing whenever $$f$$ is decreasing
C
$$h$$ is decreasing whenever $$f$$ is decreasing
D
nothing can be said in general.
2
IIT-JEE 1998
MCQ (Single Correct Answer)
+2
-0.5
The number of values of $$x$$ where the function
$$f\left( x \right) = \cos x + \cos \left( {\sqrt 2 x} \right)$$ attains its maximum is
A
$$0$$
B
$$1$$
C
$$2$$
D
infinite
3
IIT-JEE 1998
Subjective
+8
-0
Prove that a triangle $$ABC$$ is equilateral if and only if $$\tan A + \tan B + \tan C = 3\sqrt 3 $$.
4
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.)
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