1
IIT-JEE 1994
+1
-0.25
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 1987
+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
$$\left( {{{3\pi } \over 2},2\pi } \right)$$
3
IIT-JEE 1987
+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
4
IIT-JEE 1986
+2
-0.5
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
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