IIT-JEE 2012 Paper 1 Offline | Application of Integration Question 19 | Mathematics

IIT-JEE 2012 Paper 1 Offline

MCQ (More than One Correct Answer)

-1

Let $$S$$ be the area of the region enclosed by $$y = {e^{ - {x^2}}}$$, $$y=0$$, $$x=0$$, and $$x=1$$; then

$$S \ge {1 \over e}$$

$$S \ge 1 - {1 \over e}$$

$$S \le {1 \over 4}\left( {1 + {1 \over {\sqrt e }}} \right)$$

$$S \le {1 \over {\sqrt 2 }} + {1 \over {\sqrt e }}\left( {1 - {1 \over {\sqrt 2 }}} \right)$$

IIT-JEE 2010 Paper 1 Offline

MCQ (More than One Correct Answer)

-1

Let $$f$$ be a real-valued function defined on the interval $$\left( {0,\infty } \right)$$
by $$\,f\left( x \right) = \ln x + \int\limits_0^x {\sqrt {1 + \sin t\,} dt.} $$ then which of the following
statement(s) is (are) true?

$$f''(x)$$ exists for all $$x \in \left( {0,\infty } \right)$$

$$f'(x)$$ exists for all $$x \in \left( {0,\infty } \right)$$ and $$f'$$ is continuous on $$\left( {0,\infty } \right)$$, but not differentiable on $$\left( {0,\infty } \right)$$

there exists $$\,\,\alpha > 1$$ such that $$\left| {f'\left( x \right)} \right| < \left| {f\left( x \right)} \right|$$ for all $$x \in \left( {\alpha ,\infty } \right)\,$$

there exists $$\beta > 0$$ such that $$\left| {f\left( x \right)} \right| + \left| {f'\left( x \right)} \right| \le \beta $$ for all $$x \in \left( {0,\infty } \right)$$

IIT-JEE 2009 Paper 1 Offline

MCQ (More than One Correct Answer)

-2

Area of the region bounded by the curve $$y = {e^x}$$ and lines $$x=0$$ and $$y=e$$ is

$$e-1$$

$$\int\limits_1^e {\ln \left( {e + 1 - y} \right)dy} $$

$$e - \int\limits_0^1 {{e^x}dx} $$

$$\int\limits_1^e {\ln y\,dy} $$

IIT-JEE 1999

MCQ (More than One Correct Answer)

-0.75

For which of the following values of $$m$$, is the area of the region bounded by the curve $$y = x - {x^2}$$ and the line $$y=mx$$ equals $$9/2$$?

$$-4$$

$$-2$$

$$2$$

$$4$$

JEE Advanced Subjects