1
IIT-JEE 1995 Screening
+1
-0.25
The slope of the tangent to a curve $$y = f\left( x \right)$$ at $$\left[ {x,\,f\left( x \right)} \right]$$ is $$2x+1$$. If the curve passes through the point $$\left( {1,2} \right)$$, then the area bounded by the curve, the $$x$$-axis and the line $$x=1$$ is
A
$${5 \over 6}$$
B
$${6 \over 5}$$
C
$${1 \over 6}$$
D
$$6$$
2
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 $$\left( { - \infty , - 1} \right)$$
3
IIT-JEE 1994
+1
-0.25
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
$${x^2} = 4ay$$
4
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
$$\left( {{{3\pi } \over 2},2\pi } \right)$$
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