POORNIMA GROUP OF COLLEGES
ONLINE QUESTION
ENGINEERING MATHEMATICS-1(102)
FACULTY NAME Ms.HIMANSHU RATHORE
Unit-3
(s)Q.1 If the curve is y = f(x) then formula for length of curve is
b
Ans. (a) s
{1 (
x a
t2
(c) s
t1
dx
dy 2
) }dx (b) s {1 ( ) 2 }dy
dy
dx
y a
2
dx
dy
dr
{( ) 2 ( ) 2}dt (d) s {r 2 ( ) 2}d
dt
dt
d
1
(m)Q. 2 If the curve is x = f(y) then formula for length of curve is
b
Ans. (a) s
{1 (
x a
t2
dx
dy 2
) }dx
dx
(b) s
y a
dy
{1 (
dx 2
) }dy
dy
dr
2
2
2
2
(c) s {( dt ) ( dt ) }dt (d) s {r ( d ) }d
t
(h) Q.3 If the curve isx =F(t) ,y = f(t) then formula for length of curve is
b
Ans. (a) s
{1 (
x a
t2
(c) s
t1
dx
dy 2
) }dx (b) s {1 ( ) 2 }dy
dy
dx
y a
2
dx
dy
dr
{( ) 2 ( ) 2}dt (d) s {r 2 ( ) 2}d
dt
dt
d
1
(m) Q. 4 If the curve is r = f() then formula for length of curve is
b
Ans. (a) s
x a
t2
(c) s
t1
{1 (
dx
dy 2
) }dx (b) s {1 ( ) 2 }dy
dy
dx
y a
2
dx
dy
dr
{( ) 2 ( ) 2}dt (d) s {r 2 ( ) 2}d
dt
dt
d
1
(s)Q.5 Find the perimeter of the circle x2 +y2 = a2.
Ans.
(a) 2a
(b) a2
(c) 3a
(d) a
(h)Q.6 Find the length of the asteroid x2/3 + y2/3 = a2/3
Ans. (a) 3a
(b) 2/3a
(c) a
(d) 6a
(h)Q. 7 Find the length of arc of equiangular spiral r = ae cot between the
points whose radii vector are r1 and r2
Ans. (a) (r1 r2)sec
(b) (r1- r2 )cot
(c) (r1+ r2 )sec
(d) (r1+r2 )cot
(m)Q. 8 Formula for volume V of solid of revolution about x- axis is
xB
Ans. (a) s 2 y 1 (
xA
xB
dy 2
) dx
dx
xB
(b) s 2 ( y c) 1 (
xA
dy 2
) dx
dx
xB
(c) V y dx
2
(d) V ( y c) dx
xA
xA
(h) Q.9 Formula for volume V of solid of revolution about axis y =c
parallel to x- axis is
xB
dy 2
Ans. (a) s 2 y 1 ( dx ) dx
xA
xB
xB
dy
2
(b) s 2 ( y c) 1 ( dx ) dx
xA
xB
(c) V y dx
2
(d) V ( y c) dx
xA
xA
(h) Q.10 Formula for surface S of solid of revolution about x- axis is
xB
Ans. (a) s 2 y 1 (
xA
dy 2
) dx
dx
xB
2
(c) V y dx
xA
xB
(b) s 2 ( y c) 1 (
xA
dy 2
) dx
dx
xB
2
(d) V ( y c) dx
xA
(m) Q.11 Formula for surface S of solid of revolution about axis
y = c parallel x- axis is
xB
dy 2
Ans. (a) s 2 y 1 ( dx ) dx
xA
xB
(c) V y dx
xA
xB
dy
2
(b) s 2 ( y c) 1 ( dx ) dx
xA
xB
2
(d) V ( y c) dx
xA
(m) Q.12 Formula for volume V of solid of revolution about y- axis is
yB
dx 2
Ans. (a) s 2 x 1 ( dy ) dy
yA
yB
yB
dx
2
(b) s 2 ( x c) 1 ( dy ) dy
yA
yB
(c) V x dy
2
(d) V ( x c) dy
yA
yA
(m) Q.13 Formula for volume V of solid of revolution about axis
x = c parallel to y-axis is
yB
dx 2
Ans. (a) s 2 x 1 ( dy ) dy
yA
yB
yB
dx
2
(b) s 2 ( x c) 1 ( dy ) dy
yA
yB
2
(c) V x dy
2
(d) V ( x c) dy
yA
yA
(h) Q.14 Formula for surface S of solid of revolution about axis
x = c parallel to y-axis is
Ans. (a) s
yB
2 x 1 (
yA
yB
dx 2
) dy
dy
(c) V x dy
2
yA
(b) s
yB
2 ( x c)
1 (
yA
dx 2
) dy
dy
yB
2
(d) V ( x c) dy
yA
(h) Q. 15 Formula for surface S of solid of revolution about y- axis is
yB
dx 2
Ans. (a) s 2 x 1 ( dy ) dy
yA
yB
(c) V x dy
2
yA
(h) Q.16 Evaluate
yB
yA
Ans. (a) 123 / 4
(b) 124 / 3
(c) 126 / 3
(d) 125 /6
yB
2
(d) V ( x c) dy
xy(1 y x)dxdy
x 0 y 1
dx
2
(b) s 2 ( x c) 1 ( dy ) dy
yA
a b
(m) Q.17 Evaluate
(y
x 2 )dxdy
0 0
Ans
ab(a b 2 )
4
2
ab(a b 2 )
(b)
2
2
ab( a b 2 )
(c)
3
ab(a 2 b 2 )
(d)
3
2
(a)
(m) Q.18 Evaluate
1 1 x 2
Ans
1
1 x2 y 2
(a) log( 2 1)
log( 2)
4
(c) log( 2 1)
4
(d) log( 2 1)
4
(b)
(m) Q.19 Evaluate
1 1 x 2
Ans
4 xdxdy
(a) 1/3
(b) 2/3
(c) 3/4
(d) 4/3
1 x2
(m) Q.20 Evaluate
e
0 0
Ans
(a) 1/4
(b) 1/2
(c) 2/3
(d) 2/9
y/x
dxdy
dxdy
