1

### IIT-JEE 1987

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
2

### IIT-JEE 1987

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
$$\left( {{{3\pi } \over 2},2\pi } \right)$$
3

### IIT-JEE 1986

Let $$P\left( x \right) = {a_0} + {a_1}{x^2} + {a_2}{x^4} + ...... + {a_n}{x^{2n}}$$ be a polynomial in a real variable $$x$$ with
$$0 < {a_0} < {a_1} < {a_2} < ..... < {a_n}.$$ The function $$P(x)$$ has
A
neither a maximum nor a minimum
B
only one maximum
C
only one minimum
D
only one maximum and only one minimum
4

### IIT-JEE 1983

If $$y = a\,\,In\,x + b{x^2} + x$$ has its extreamum values at $$x=-1$$ and $$x=2$$, then
A
$$a = 2,b = - 1$$
B
$$a = 2,b = - {1 \over 2}$$
C
$$a = - 2,b = {1 \over 2}$$
D
none of these

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