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1

IIT-JEE 1983

MCQ (Single Correct Answer)
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
2

IIT-JEE 1983

MCQ (Single Correct Answer)
The normal to the curve $$\,x = a\left( {\cos \theta + \theta \sin \theta } \right)$$, $$y = a\left( {\sin \theta - \theta \cos \theta } \right)$$ at any point $$'\theta '$$ is such that
A
it makes a constant angle with the $$x$$-axis
B
it passes through the origin
C
it is at a constant distance from the origin
D
none of these
3

IIT-JEE 1983

MCQ (Single Correct Answer)
$$AB$$ is a diameter of a circle and $$C$$ is any point on the circumference of the circle. Then
A
the area of $$\Delta ABC$$ is maximum when it is isosceles
B
the area of $$\Delta ABC$$ is minimum when it is isosceles
C
the perimeter of $$\Delta ABC$$ is minimum when it is isosceles
D
none of these
4

IIT-JEE 1983

MCQ (Single Correct Answer)
If $$a+b+c=0$$, then the quadratic equation $$3a{x^2} + 2bx + c = 0$$ has
A
at least one root in $$\left[ {0,1} \right]$$
B
one root in $$\left[ {2,3} \right]$$ and the other in $$\left[ {-2,-1} \right]$$
C
imaginary roots
D
none of these

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