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1

### IIT-JEE 1986

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
2

### IIT-JEE 1983

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
3

### IIT-JEE 1983

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
4

### IIT-JEE 1983

$$AB$$ 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

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