1
AIEEE 2003
MCQ (Single Correct Answer)
+4
-1
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The value of $$\mathop {\lim }\limits_{x \to 0} {{\int\limits_0^{{x^2}} {{{\sec }^2}tdt} } \over xsinx}$$ is
A
0
B
3
C
2
D
1
2
AIEEE 2003
MCQ (Single Correct Answer)
+4
-1
If $$f\left( {a + b - x} \right) = f\left( x \right)$$ then $$\int\limits_a^b {xf\left( x \right)dx} $$ is equal to
A
$${{a + b} \over 2}\int\limits_a^b {f\left( {a + b + x} \right)dx} $$
B
$${{a + b} \over 2}\int\limits_a^b {f\left( {b - x} \right)dx} $$
C
$${{a + b} \over 2}\int\limits_a^b {f\left( x \right)dx} $$
D
$$\,{{b - a} \over 2}\int\limits_a^b {f\left( x \right)dx} $$
3
AIEEE 2003
MCQ (Single Correct Answer)
+4
-1
Let $$f(x)$$ be a function satisfying $$f'(x)=f(x)$$ with $$f(0)=1$$ and $$g(x)$$ be a function that satisfies $$f\left( x \right) + g\left( x \right) = {x^2}$$. Then the value of the integral $$\int\limits_0^1 {f\left( x \right)g\left( x \right)dx,} $$ is
A
$$e + {{{e^2}} \over 2} + {5 \over 2}$$
B
$$e - {{{e^2}} \over 2} - {5 \over 2}$$
C
$$e + {{{e^2}} \over 2} - {3 \over 2}$$
D
$$e - {{{e^2}} \over 2} - {3 \over 2}$$
4
AIEEE 2003
MCQ (Single Correct Answer)
+4
-1
If $$f\left( y \right) = {e^y},$$ $$g\left( y \right) = y;y > 0$$ and

$$F\left( t \right) = \int\limits_0^t {f\left( {t - y} \right)g\left( y \right)dy,} $$ then :
A
$$F\left( t \right) = t{e^{ - t}}$$
B
$$F\left( t \right) = 1t - t{e^{ - 1}}\left( {1 + t} \right)$$
C
$$F\left( t \right) = {e^t} - \left( {1 + t} \right)$$
D
$$F\left( t \right) = t{e^t}$$.
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