1
IIT-JEE 2003 Screening
MCQ (Single Correct Answer)
+2
-0.5
If $$y(t)$$ is a solution of $$\left( {1 + t} \right){{dy} \over {dt}} - ty = 1$$ and $$y\left( 0 \right) = - 1,$$ then $$y(1)$$ is equal to
A
$$ - 1/2$$
B
$$e+1/2$$
C
$$e-1/2$$
D
$$ 1/2$$
2
IIT-JEE 2003 Screening
MCQ (Single Correct Answer)
+3
-0.75
If $$f\left( x \right) = \int\limits_{{x^2}}^{{x^2} + 1} {{e^{ - {t^2}}}} dt,$$ then $$f(x)$$ increases in
A
$$(-2, 2)$$
B
no value of $$x$$
C
$$\left( {0,\infty } \right)$$
D
$$\left( { - \infty ,0} \right)$$
3
IIT-JEE 2003 Screening
MCQ (Single Correct Answer)
+3
-0.75
The area bounded by the curves $$y = \sqrt x ,2y + 3 = x$$ and
$$x$$-axis in the 1st quadrant is
A
$$9$$
B
$$27/4$$
C
$$36$$
D
$$18$$
4
IIT-JEE 2003 Screening
MCQ (Single Correct Answer)
+2
-0.5
If $$\,\left| z \right| = 1$$ and $$\omega = {{z - 1} \over {z + 1}}$$ (where $$z \ne - 1$$), then $${\mathop{\rm Re}\nolimits} \left( \omega \right)$$ is
A
0
B
$$ - {1 \over {{{\left| {z + 1} \right|}^2}}}$$
C
$$\left| {{z \over {z + 1}}} \right|.{1 \over {{{\left| {z + 1} \right|}^2}}}$$
D
$$\,{{\sqrt 2 } \over {{{\left| {z + 1} \right|}^2}}}$$
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