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1

### IIT-JEE 2002 Screening

Let $$T>0$$ be a fixed real number . Suppose $$f$$ is a continuous
function such that for all $$x \in R$$, $$f\left( {x + T} \right) = f\left( x \right)$$.

If $$I = \int\limits_0^T {f\left( x \right)dx}$$ then the value of $$\int\limits_3^{3 + 3T} {f\left( {2x} \right)dx}$$ is

A
$$3/2I$$
B
$$2I$$
C
$$3I$$
D
$$6I$$
2

### IIT-JEE 2002 Screening

Let $$T>0$$ be a fixed real number . Suppose $$f$$ is a continuous
function such that for all $$x \in R$$, $$f\left( {x + T} \right) = f\left( x \right)$$.

If $$I = \int\limits_0^T {f\left( x \right)dx}$$ then the value of $$\int\limits_3^{3 + 3T} {f\left( {2x} \right)dx}$$ is

A
$$3/2I$$
B
$$2I$$
C
$$3I$$
D
$$6I$$
3

### IIT-JEE 2002 Screening

Let $$f\left( x \right) = \int\limits_1^x {\sqrt {2 - {t^2}} \,dt.}$$ Then the real roots of the equation
$${x^2} - f'\left( x \right) = 0$$ are
A
$$\pm 1$$
B
$$\pm {1 \over {\sqrt 2 }}$$
C
$$\pm {1 \over 2}$$
D
$$0$$ and $$1$$
4

### 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
$$2\ell n\left( {{1 \over 2}} \right)$$

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NEET

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