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1

### IIT-JEE 2002 Screening

The integral $$\int\limits_{ - 1/2}^{1/2} {\left( {\left[ x \right] + \ell n\left( {{{1 + x} \over {1 - x}}} \right)} \right)dx}$$ equal to
A
$$- {1 \over 2}$$
B
$$0$$
C
$$1$$
D
$$2\ell n\left( {{1 \over 2}} \right)$$
2

### IIT-JEE 2002 Screening

The area bounded by the curves $$y = \left| x \right| - 1$$ and $$y = - \left| x \right| + 1$$ is
A
$$1$$
B
$$2$$
C
$$2\sqrt 2$$
D
$$4$$
3

### IIT-JEE 2001 Screening

The value of $$\int\limits_{ - \pi }^\pi {{{{{\cos }^2}x} \over {1 + {a^x}}}dx,\,a > 0,}$$ is
A
$$\pi$$
B
$$a\pi$$
C
$$\pi /2$$
D
$$2\pi$$
4

### IIT-JEE 2000 Screening

The value of the integral $$\int\limits_{{e^{ - 1}}}^{{e^2}} {\left| {{{{{\log }_e}x} \over x}} \right|dx}$$ is :
A
$$3/2$$
B
$$5/2$$
C
$$3$$
D
$$5$$

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NEET

Class 12