1
IIT-JEE 1987
MCQ (More than One Correct Answer)
+2
-0.5
In a triangle, the lengths of the two larger sides are $$10$$ and $$9$$, respectively. If the angles are in $$AP$$. Then the length of the third side can be
A
$$5 - \sqrt 6 $$
B
$$3\sqrt 3 $$
C
$$5$$
D
$$5 + \sqrt 6 $$
2
IIT-JEE 1987
Fill in the Blanks
+2
-0
The set of all $$x$$ for which $$in\left( {1 + x} \right) \le x$$ is equal to ..........
3
IIT-JEE 1987
MCQ (Single Correct Answer)
+2
-0.5
The smallest positive root of the equation, $$\tan x - x = 0$$ lies in
A
$$\left( {0,{\pi \over 2}} \right)$$
B
$$\left( {{\pi \over 2},\pi } \right)$$
C
$$\left( {\pi ,{{3\pi } \over 2}} \right)$$
D
$$\left( {{{3\pi } \over 2},2\pi } \right)$$
4
IIT-JEE 1987
MCQ (Single Correct Answer)
+2
-0.5
Let $$f$$ and $$g$$ be increasing and decreasing functions, respectively from $$\left[ {0,\infty } \right)$$ to $$\left[ {0,\infty } \right)$$. Let $$h\left( x \right) = f\left( {g\left( x \right)} \right).$$ If $$h\left( 0 \right) = 0,$$ then $$h\left( x \right) - h\left( 1 \right)$$ is
A
always zero
B
always negative
C
always positive
D
strictly increasing
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