1
IIT-JEE 2010 Paper 2 Offline
+4
-1

Consider the polynomial
$$f\left( x \right) = 1 + 2x + 3{x^2} + 4{x^3}.$$
Let $$s$$ be the sum of all distinct real roots of $$f(x)$$ and let $$t = \left| s \right|.$$

The area bounded by the curve $$y=f(x)$$ and the lines $$x=0,$$ $$y=0$$ and $$x=t,$$ lies in the interval

A
$$\left( {{3 \over 4},3} \right)$$
B
$$\left( {{{21} \over {64}},{{11} \over {16}}} \right)$$
C
$$\left( {9,10} \right)$$
D
$$\left( {0,{{21} \over {64}}} \right)$$
2
IIT-JEE 2010 Paper 2 Offline
+4
-1

Consider the polynomial
$$f\left( x \right) = 1 + 2x + 3{x^2} + 4{x^3}.$$
Let $$s$$ be the sum of all distinct real roots of $$f(x)$$ and let $$t = \left| s \right|.$$

The function$$f'(x)$$ is

A
increasing in $$\left( { - t, - {1 \over 4}} \right)$$ and decreasing in $$\left( { - {1 \over 4},t} \right)$$
B
decreasing in $$\left( { - t, - {1 \over 4}} \right)$$ and increasing in $$\left( { - {1 \over 4},t} \right)$$
C
increasing in $$(-t, t)$$
D
decreasing in $$(-t, t)$$
3
IIT-JEE 2009 Paper 1 Offline
+3
-1

Let $$f$$ be a non-negative function defined on the interval $$[0,1]$$.

If $$\int\limits_0^x {\sqrt {1 - {{(f'(t))}^2}dt} = \int\limits_0^x {f(t)dt,0 \le x \le 1} }$$, and $$f(0) = 0$$, then

A
$$f\left( {{1 \over 2}} \right) < {1 \over 2}$$ and $$f\left( {{1 \over 3}} \right) > {1 \over 3}$$
B
$$f\left( {{1 \over 2}} \right) > {1 \over 2}$$ and $$f\left( {{1 \over 3}} \right) > {1 \over 3}$$
C
$$f\left( {{1 \over 2}} \right) < {1 \over 2}$$ and $$f\left( {{1 \over 3}} \right) < {1 \over 3}$$
D
$$f\left( {{1 \over 2}} \right) > {1 \over 2}$$ and $$f\left( {{1 \over 3}} \right) < {1 \over 3}$$
4
IIT-JEE 2008 Paper 2 Offline
+3
-1
The area of the region between the curves $$y = \sqrt {{{1 + \sin x} \over {\cos x}}}$$
and $$y = \sqrt {{{1 - \sin x} \over {\cos x}}}$$ bounded by the lines $$x=0$$ and $$x = {\pi \over 4}$$ is
A
$$\int\limits_0^{\sqrt 2 - 1} {{t \over {\left( {1 + {t^2}} \right)\sqrt {1 - {t^2}} }}dt}$$
B
$$\int\limits_0^{\sqrt 2 - 1} {{4t \over {\left( {1 + {t^2}} \right)\sqrt {1 - {t^2}} }}dt}$$
C
$$\int\limits_0^{\sqrt 2 + 1} {{4t \over {\left( {1 + {t^2}} \right)\sqrt {1 - {t^2}} }}dt}$$
D
$$\int\limits_0^{\sqrt 2 + 1} {{t \over {\left( {1 + {t^2}} \right)\sqrt {1 - {t^2}} }}dt}$$
Physics
Mechanics
Electricity
Optics
Modern Physics
Chemistry
Physical Chemistry
Inorganic Chemistry
Organic Chemistry
Mathematics
Algebra
Trigonometry
Coordinate Geometry
Calculus
EXAM MAP
Joint Entrance Examination