1
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
2
IIT-JEE 1983
+1
-0.25
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
3
IIT-JEE 1983
+1
-0.25
$$AB$$ 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
+1
-0.25
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
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