Releted MCQ Question on
Calculus >> Application of Derivatives
Releted Question 1
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
Releted Question 2
$$AB$$ 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
Releted Question 3
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
Releted Question 4
If $$y = a\ln x + b{x^2} + x$$ has its extremum values at $$x = - 1$$ and $$x = 2,$$ then
A.
$$a = 2,b = - 1$$
B.
$$a = 2,b = - \frac{1}{2}$$
C.
$$a = - 2,b = \frac{1}{2}$$
D.
none of these