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1

### IIT-JEE 1994

The function defined by $$f\left( x \right) = \left( {x + 2} \right){e^{ - x}}$$
A
decreasing for all $$x$$
B
decreasing in $$\left( { - \infty , - 1} \right)$$ and increasing in $$\left( { - 1,\infty } \right)$$
C
increasing for all $$x$$
D
decreasing in $$\left( { - 1,\infty } \right)$$ and increasing in $$\left( { - \infty , - 1} \right)$$
2

### IIT-JEE 1994

Which one of the following curves cut the parabola $${y^2} = 4ax$$ at right angles?
A
$${x^2} + {y^2} = {a^2}$$
B
$$y = {e^{ - x/2a}}$$
C
$$y = ax$$
D
$${x^2} = 4ay$$
3

### 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
4

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

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Class 12