1
IIT-JEE 1987
+2
-0.5
Let $$f$$ and $$g$$ be increasing and decreasing functions, respectively from $$\left[ {0,\infty } \right)$$ to $$\left[ {0,\infty } \right)$$. Let $$h\left( x \right) = f\left( {g\left( x \right)} \right).$$ If $$h\left( 0 \right) = 0,$$ then $$h\left( x \right) - h\left( 1 \right)$$ is
A
always zero
B
always negative
C
always positive
D
strictly increasing
2
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
3
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
4
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
Physics
Mechanics
Electricity
Optics
Modern Physics
Chemistry
Physical Chemistry
Inorganic Chemistry
Organic Chemistry
Mathematics
Algebra
Trigonometry
Coordinate Geometry
Calculus
EXAM MAP
Joint Entrance Examination