Mathematics Objective Questions Part 7
Transcript of Mathematics Objective Questions Part 7
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IC.S.£ Pre-l999
I
ol
Il l
M THEM TICS
1
2,
3,
4.
5,
T he number of arbitrary consl
an
t in
lhe
com plete pn1mtive of the
diiTenltl\ial
equ:\IIOn
¢.
{
r,
x
,
tl'
=
0
is
dr
'
2
c.
3
cl
file
dlt.Jerentin
l equallon
of Ute
system
of
circles 1ouclung
lhe x 1 ~ at
origin is
, , dv
0
.
(1C
-y' ) ~ -
2Ay =
(
, '
dl
b >c-y·) 2 ~ =
dx
,
.
d\
o.
(x
- 1 .-) --- +
2xv
=( I
-
tlx
•
d
. r
(x-+y' )
dx
-1 2xy
=
()
The
smgular solution
of the
equauon
4xyp+8p
=c) (p..
:t
27y
= 4x
b =
c. 27y = -lx
cl .n
l
= 4x
r he solutions
\lf
1he diiTerential equa1on
2 y ( y ' + 2 l - ~ ' Y
are the
i't
mction
J_ y=()
2. y =-
-lx
Select
the
correct
ans11
'
er
usillg
the
codes
gh
•
er1
belo .
a
No
ne or I nnd l1s as1ngulnrsolution
b. both I .
nnd
?.arc smgular solullo
ns
~ I is a singular solution but2 is not
cl 2
is a singular so
Ui
ion bu l is not
The o
nhogc)llnl
trajectories of ibe system
ol
curves
1
sm
ffil=K" are
a y cos oa = a
b. y cosO = a
c f cosnO=a
7
d. 1
tun
n9 = a
The equati1111 whose s.olution
fam
il) 1s self
orthogomd
1s
I ,
d1•
a.
p-
p
= - -
p dr
dv
b \'PX+yl(x ,. yp)- J..p= 0. p :
ck
dy
c, (px-y)(' YP)-A.p
=
o, p=-,
u
dy
d.
(px+y-
)(X·)'p)-A.[F0,
dt
Which of the followtog
smtemen
(s
associated with n lirst order non-
li
near
diJrerential equation
llx. y. d) /
dx
) : (I are
correct'
/
l
Its general
so
lution must contain ooly
one arbitrruy cooslrutt.
2 Its singularsolutioo can
be
obtained
by
subsututing partJculnr ' 'alue of U1e
arbitrary
constam in JJS general
solullon
3
It
s stngular solution
ls
an envelope of
hs general sol
uti
on
which also satisfies
tile
equal ion
Select lhe correct answer using the codes
given 11elow:
a. L nd
.3
b I an
d 2
c.
I
and 3
d. 1
and
3
A
particular
integral
d:v dy ,
---"c -
1> b
+ l b,l'
=
Q(.t)LS
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9.
n. ax1by = c
b• • .: - by = I)
cJ
aX:
• b). =1
d. I
t;j -
0
I0. A vari:oble lines p3S$t.."S through the lixcd
0
inJ ' '
b). Th e
locUJ
••
f
Ue
t i d d l ~ t•. -
16
; l
,,.t
c . -
- j
12 t"
d.
- t
l
l n drclo cuts lhc rcctangulnr hyp ·boln
XY -
. _ ~
in points Cx,.. y,) I r = 1, 2.3.4 )
.tl1en
3. X 1 _ l ~ X , j -
h.
X :X3 X,, -
c
j
il.
:il '
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20
21.
I f ~ slr.light line lllllk.;, 3ngle.
6fi
45"
ron . - y ~
11 :l
yz +
I izx +
15:<
y= t)
24 . Thd equation bf tho oylinJcr. generated b.)'
llnos
p a ~ ' I I U d
to the l il'ed line
. .,.L
= . .
I
" '
f•
nnd bavintt tl1e ellipse z:
ll
. a.x> by'-=1 • as
the guiding CIUYclS
. . =
a. a(nx - b ( n y J 1 Z )
.
.
'
b,
a(llx h )"
b(n.)'·mz}· n·
c.
a(m
,:: - lzf·bttt
y·
m:>) 'n:
il
.
;l(nx- " ' n ~
25. A unit vect
or
·perpandiculnr to th" two
vc
cto"' i
J j
- In
od 2 i
•3j
l
,i i•
••
s 3j
t
h.
p o ~ i t i o n vectors
are a 3 ; 4 / 4 i • 2 i - j - : t . ~ ; .
3]
-
Si are
a. fin lri
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'35
.
36.
equ
ilibri
um n
that the s
um
oflhe momenu
ofall the
fp
r
ce< :lbou
t
{1, a t) )int i.s 7.ero
b. any 11vo pootts is zoru
c. any three non
-oo
llineru: pointS
IS
zeoo
,
1. ;I
n
ttxi• i&
7,A t"i)
l f
a
p.miclu in
eq
uilibrium i• •
ub
jec
t
ed
to
four f m·ccs viz F
1
2t
- 5 J1
6t . r
3 •
.
"
7 F
3
=
2;
-2J - t :md F., then • egu:ol
to
b ~ t - 4 5
J·
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a lirut
of A
c.
A
IS true bu
t R
f ~ l < e
d. A is
fa lse but
R true
44. Ass
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- . · · ·
hlhf
x l ll lilctor x: . : ~ x - l l , I ,.,,
value
ora
i$
u. 1)
b. ]
c.
2
d. 3
53. A
q u a d r o 1 i
equation
wilh
rntion 1l
coeflicients and
with
one roo
a M
l-
..fi
i•
u.
- 4 1 1 ~ ~
b. x ~ + 4 : < +
~ 1
c.
x -4, 1=0
• - •
54.
II
' v a l u ~ : o f ( u .
p) .
55 .
56.
57
~ a c
1 - 4ac
h.
d.
b
·Ia•
2
b r T C
2
A r ~ c a t e d cool
of
ll d cquution
3 - . < l
is
;t. 0
b.
- 1
c...
I
d. 2
llto values
ofi
11
• Arc
lr
rr
SU\
T I .:08 - . II I. s 9. 13. 7.
l2 12
2 1
/
l l f
•
r
1 • " I' 17
b C 5 - " - I SU\
.
II - -. l .
12 12
2 1
•
mr
. 111r
0
1
2." ,, "
c. s
ut -
n = , • .,,
...
.
. ,
6 6
it C
A.B aod C wblch one
of
the fo llow inl' stot=ents i.>
U( l'n:(;
t?
.'\ 'Ill
- ~
= = A
B
C
=
Ill
L
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m
'
II
In Ia
n
n m
I
q
It>
I n
I n
l d m n
Ia
I a I n 11
m
-
.OJ
II
IP Ia
Ill
IU
Ul Ul I l l
n
m n
m
n
I n
m
I D l l In
lq
m Ia m Ia
Then
wh1ch
one or
the fo l
io
\\
fng
l•
rtc :t•
a.
(R,
~
)
i<
•
group , Inn (R, -t,.J ,. not•
l ing
h. (R,
+,
.1
i•
with
uni
ty
1 .. (R.
•. m m ~ l l l t l \
ring
d.
R
• .) is a non-conuliUiliU
V
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70.
71.
72.
7
.3
.
h, -K
· K
d. - 3K
fA H -;· 1 cn
i o w r s ~ of ~ l r f : <
A
will
b.,
.. l
h. [ - ;,)
- 1 I 0
c.
~
d.
u
J
Co1uidcr the equation ~ B. where A=
( - ~ a l l t ~ u
lhe equ•tlon no so lution
h. solution nf theequorion
c. lhor
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RoUe '$ th
eorem
docs not apply to
f i
n
1·1.
I)
b. Roll
e"s th
eorem
applieo,
to/ in
(·
I, 1]
l l . fis
not eonlinuou;,
x
0
d.
f
(0)
=
0
NQ
The
expansion of
an in
w ~ 11r1' by
Maclaurin
5
theor
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1(0, yJ=y
2
sin . .
when
y= n
•
1{0, 0) 0,
then ut (0,
0)
o. ·IX is continuous
hut
not f
b.
I)> continuous
hut
not fs
c. IX
and
J Y ; ~ r e
hotll
coulinu
ous
d. neither
fx. 3Jld
.iJ;
eonlinuoll
91. I he double point on the cucve (x-
2) =
,) () - 1)
2
is
n. t l .
2)
1)
, (3, 4)
c. 3)
d. (2. I )
92.
T he
va
l
ue
M l
;ff J;m;
J.ot
i
~ ~ x z
stnx
93.
?4.
tl 1
/2
b. n/4
c..
n•8
d.
1'hc \'Olue )
IS
£\
1--Ji))
95
.
11ce
:o
oo
of
the crudiod
p
a( H
cosO
I
is
equal
to
iL 4 o t
1
b.
Sli3
c.
)lTD
d.
2n.; :
96
Tha volume of the solid ganerallld by
re\'Oiving d1e curve
:'p
to
the •urn
I
l.
c.