1
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
$$F\left( t \right) = t{e^t}$$.
2
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
$$e - {{{e^2}} \over 2} - {3 \over 2}$$
3
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
$$\,{{b - a} \over 2}\int\limits_a^b {f\left( x \right)dx} $$
4
AIEEE 2003
MCQ (Single Correct Answer)
+4
-1
The value of the integral $$I = \int\limits_0^1 {x{{\left( {1 - x} \right)}^n}dx} $$ is
A
$${1 \over {n + 1}} + {1 \over {n + 2}}$$
B
$${1 \over {n + 1}}$$
C
$${1 \over {n + 2}}$$
D
$${1 \over {n + 1}} - {1 \over {n + 2}}$$
JEE Main Subjects
EXAM MAP
Medical
NEET
Graduate Aptitude Test in Engineering
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
Civil Services
UPSC Civil Service
Defence
NDA
CBSE
Class 12