Mathematics Objective Questions Part 2
Transcript of Mathematics Objective Questions Part 2
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0
_,
3,
s.
1Ot'J
M THEM TICS
J
If the equati
on
of the base of
an
egtillateral
triangle is x + y = Md
the
•·ertex 1s (2. -J)
, then the length or ts side is
11
d. None ol' tbe above
The line(s) passing through
the
intersection
of
4x- 3y- =0 and 2-.- + 3
:{)
3lld
i qually inclined u
>
the axes wiU
huve
.a. )
= ±
x
as
i qurtllons
b,
' =
x, x
+y=
2 as the e ~ J t l a t l o n s
c.
(y- ~ = tl as
the
q u a t i o n s
d. an tndefinite num ber
of
strmgbt lmes
If the three vert1ces
of
a parallelogram
ABCD are
A{
I.
OJ, B(2. 3), C(3,
2)
,
then
the
C O > rd
i
n:He
s
of
the fo
urth Yenex
0
wi
ll
be
a (2. I)
b (2 , -1)
c.
(-1
, '2)
d. none
of
above
Coosider the followmg statements
Assc>nion (A): The tangent and normal at
point I
>
n an e
ll
ipse bis
ect the
e.xtemal and internal angles betwceu the.
focal
distances of P,
Reaso
n(R): The straigbl ltne joining lhe
.foc t
or
tlltl ellip$e subtcnds a rtghl angle at
p
Of
these
statemenlS
a.
Bot
h A
and
R
are
true
and
R
ts
the
correct explanation oJ A
b,
Both
A
nod
R are true
btu
R is not a
CO
II'CCt t Xp
lao.;liion
of
A
t
A is true but Rfs false
d. A 1s false but R IS tme
The condition
th.at
the slrnlghl line l n
r
C
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'L of lhe ~ l x l
II
. T he lina I
<
-tmy =n
i•
n normnl to the
.
'
p ~ e . .;+4=
1.
if
n
h
u.
~ = ; ) \ , :
•'
b'
1 ;
lfr
.
. - +
J. , ,,. , -'
c.
mL
T
b
fd'
-b >
d, b
1
f ·a
1
m
=
n'-bi
1
n
1
IZ. Jn the cqu:nion
• b
l '
y ~ · 2 g z x
1 2 f y z 2 w z 1
if
•
~ b ; e '" k ~ constunt nod
J"' g
- h -
O, then
th
e
olwve
eqn.11iun would repn:sent
a. • pn1r ofs l7atght lln..,.
b.
11
pl• no
c
ci
r
cle
d.
a
sphere
13
. I he eqttation nt'
Ot
e
righl
circ
ubt CQ
ne
IVh
QS¢
axis
is
lC
=
y
=
Z • n
iS lhe
ori
f',
ill Jlnd
Uti:
angle i
s.
45
1
' I&
gi
ven
"·
:t +
·•
z' - 0
b.
2 ( x ~
l J - z ~
~ ( x 4
y>z)
1
.,.- '
:
IL . 3 ~ ' < ·
•2(x+y- t )
. ._ ' 2 2 ...., 0
~ x·· y · z
x y J z z x
~
14. The
senor•
I
'(
U3ti
on
of Ute COR
\
which
pa
sses
through the coordinat
-e
ax
e•
;..
II , x ' + - h J ~ < ~ : - 2 f y 7 - 2 g 7 ~ - V > ) = (l
• b '
l . .
b.
ax·-
y--k:z - 0
c.
fYz
- 12"-
h
xy = ()
tL ' t - ' r . . ~ + xy
=
15. fh e equation ofthe
ng
hl circul$r cylinder
whose
md
lusJs.r and .:uds ts U1e z-ax is ill
,
l ..
'
:t .x-
- y
-r"
b.
~ ' r '
C. Xi I
f l
I ZX -
r
d.
~
,
-
-
16, Forces
of nlagtli tuJe. 5
.
L
L
3 3l:l olong
the sid
c.s
u.
iiC
Cii, (iii p o c t i y of
u square
ABC'D
of side
q, II
' AU and AD
nrc
,along the
X -
and
the ' '-aXi$
c t i Y d
Own tlte equut
lo
o
o.r
tt·;c line
oi
uc1i
on
along wh ich
H1
c 8in_glc r
ll8
ul
L1nl
QC
Li
i
• • 2{:(+y)= l l
b. (x-y)= 2q
C. 2(X
·
y ) = q
d.
( ·y) - '2q
J7, A
perscm
weigl1ing 8() kg i• 81nntling
em
A
liti. th
e l
in
move; upw
.:trds
with •
uniform acc
colemli
on of
..1_
9 mls' . The
•PI"'roul weig
ht (
in kg). of the por.son
, .
u.
1
(10
b. 1
20
c.
80
d. -10
Ill. A particle ai P of
~ ~
m
: Ss ol
cscri
bc:s
:w
ellip
se
under an altr.tc
tion ·f •
lo the l
l>c
lJ i
S. ~ n d an nttrac
tion flo th
e f ocus S'. If SP
: r. S'P
=
r' and the . ~ which SP and
S
'P
mnJ.c
W
iOJ t.hc t : ~ n n
at.
P i.< 0 , thctl
llic e
qualiou l l [ mot
ion in Ue direction of
nonnalt
o
theeur
el•
a.
\ ~ l p
~ i n < l f
\).
\ ~
(f •
'
)I
•
c.
\ "l ( f
I
P)
p
COli
cJ
d
~ ·ft"'.,,J.IJ
J;
,n ,J
19. The equal
iO
tl of the pa
th of
n partil:le
moving in • cenlr.l l
o
rb
it "'
' J ['"'' ]. F= tnq•
dti
NCluc of the above
20..
The
periodic limo of
t1
to QloLion described
•
by
Ute
diJ
Jeren
ltal d·
.
o
s
Jr
a, 2
b.
4
ni(L
e. 1nl
[i:
d.
4 5
21. A pan
icle is
projected with a y u •l
an
H
to lhc hOriZO nta
l.
l'lle
tim
e of
Ois
ht
i l"Utu
p 't)jectile is
u • l t
u.
~
•
b.
f ltlf'lt)
I
c.
~ C U f i t i
s
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cl . u
g
2 2
A pat tiele
proj
ected ftom
U
e lowest point
wiU1
velocity
u move-. aiOilJl tl1e iu
side
of
the
nre
of thtr
s
mooth
,,erfical
circle of
radi111<
,• II will oscillate ; ~ b o u t he lowest
point i
a. ~ 2 g r
b. u•
• e < l i•
l l .
75
kg
b. lOO kg
1:. 125 kg
d. 1
50
kg
26. l'hroc forcl3 P. Q. R are acting
al
poml
' plane. lf he antde t>etween P
3nd
(.t nnd
Q n d
R are
tso
and 1
2(1°
respectively.
then for cquiljbrium , forcds P.
Q.
R \1
ill
e
in
tlt
o m
i
o
27
u
I
2:"3
b. b2:Ji
\ .. 3:2:1
d. .{1:2.:I
l ' h r ~ vector<
4.
'i. i ore
capl•nar
if th
e
va
lue ti l
' the
>Cl WJ triple Ji'Qdlult is
•. ll
b. I
c.
2
28 ,
29.
30.
31.
n
33.
3 uf'J
d. 3
If
II is
tbe
•uglo: betwet:n Lhe vector ;; nnd
Ls
uch hal p F~ · t h e n ll
is
• . fl
h.
4,5"
c. Jl0°
d.
TWc) nOn ·'r.erq vecto,_ J •nd 8 are
par;illcl
il
'
a. i • i = o
h
1 1
'i l= t
c.
A D=o
d. i:l l
Ii i
The oispl( l)etnent
of
a poltll mo.vins
in
o
strnight l m ~ £ = St
1
- 3t - 5
s
beln
g me3sured in met
en
and
t
in
seconds. The veJncily when
f h ~
dil plnecment
is
zero.
i5
•· 3ml .s-oc
b. 13m /sec
r:. 16m /st JI
a. L2m ~ e c
Let x.
y.
.:
1.
the
$Ct of ntegC1's. C o n s i ~ c : t
the
following
slllteme
nt
with
regard to
some
propcnies associated
wflh
the 1:
I. c:ither
x
=;· or
x<
y or
x )'
2 X < y X
-t
z
y
't'
:;t,
X )'
.,.Y
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c.
Jr
>
I
>p•
d,
p
">r
34. Let l he eq onplex nomber s
11tiAf
ying 7? -
;: + I
=
t lfn
is
not a mulliple o f 3 . 1hen
the vnlue of is
a. 2
b. - 2
c..
I)
d. - 1
35
,
l f 4
w. ll>:
.ue th
e cub.:
o o ~ of
unity .
t h q ~ l h o will"
•>f
· IP
1
)
6
is
12
b. 32
c. 64
(1 128
36. Tite oumbcr of rw l t i o n ( ~
uf th
e
CI
Jilitti
lln liZ 2- 0
•• l
b. 2
1 , 3
iJ
. non e of lhe C
37, C
on
s ider
th
o followmg
t a t c
m c n l i
/ls.cr1ion (A): 11' " i
nt
eg•r iN
divWblc lty 2 ond 3, them
it
i• h l ~ I t ~
(l
Rcasort(R): Jf
:r prn;i livc i
nt
eger
i• i v i ~
by tv.·o positive intcgcB. Dum i1 divisible
by
thdo
·produ
cL
O ~ e
stat ements
Uolh A
•nd
R are but R l• not a
~ , ; m : c t l a n n t i
of A
b. 3oth A and .R are true
but
R Li
not
a
CQn·ect e.sp Bnotion ofA
e. A
is
l.nll:l but R I ; f•lllc:
d. A
is fo)}e l>Ul
R
is lrUc
38. f in o •cmiuar tltc numbor of p•rticip311l i
in l i n d £ngUsb a nd Mathematics "' 6d,
84
and 108 re,;pootively, then Ut.:
minimum number
o
fruoms
n:
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7.
5(1
.
51 .
c.
1
28
d.
nona of the
nbovc
Let :\ rond B ba two sets llitvlns Sco
mt
Mn
~ l e m e n t s 'the oumber of alemenli
common
lo
ond
IJ vA,.
4. 0
b 5-:
c,.
2
tl. nOlle tlf the alluvc
[[ ~
be • ••1 wilb u
e l ~ t m : n i S
. whore u. i
,.
;my
futilu cntd
in:tl flUm
bcr.
then lha
c:trdinalnumher of ts
o w e r ~ e l
Pi:\, )
is
n.
:zn·l
b. 2
11
C..
2 u
t l
d. non e ofihe
nbove
T
e
t 'R be • reln
t
.ion In the of integer. I ,
Jdincd b.)' R h ilr • :tnd b both
~ t o t
neither
cw.;n
nor
odtl..
Tl
u:
n R
j$
n
rc:ll
i. ..'
e)(
number
"- 'Inc set uf n 1 J n · 7 ~ r o Tl:lridue . l n ~ S t i S
mod ulo o m p
i t c
~ i t i v e
intcgo:l'
ut
wilb
r
csp
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d. M=
57.
Lee
A
be
nn n n
mnlTil.from
che••Cof re.1l
num bers and A=:.3A A GJ
=
0
\Vhere1 is n : n
uni
t mS
tri
x
T .-\'
1
o x i s L • then
n. A
1
=
A-1
h. A
=
A
T
.:.. A = 3A- 61
d, A '
1
-
(A'-3A t
4J)
•
;
SS
Lee
A= t
o a
nd 1 be
3 ·3
unit
0 -1
mnlli <
rn
nkof i -A is
•- 0
b. I
c.. 2
d. 3
59.
t f
A:
:]
t.ltcn A{n
dj
A)
eq
uo
ts
a [ u ,:,]
b.
[ ~ ~
': ]
:
[:
'• :o]
d
.None of
Ow
abo
ve
60
It 3x+
2y
+
z.
=O
+ 4y + z = cl
2 . ~ +
y -
4
>: = C
be
a
OJ'S
Iem
of
eq
ua
tions.
then
n. ills
in
c{l
nsiscent
h.
ic
h•• vnl) ch
e triv
i.l
so
lucio
n
K = 0 .
y: O,t.= O
c. .it
c:w. be
red oo..:
d
co a single
equocion
~ n d
so a sQiution dotS not L .'(ist
d.
u,
e
dcremoinaot of
lbe
mo lri.x Qf
.
.Jt:
ffi
c:
ie
nLi
i.
?. :r
o
61.
If
x
an
dy
are real numbers, lhen
wh1c
h
une
of Uoe follow
in
&
s
a
l\\ayst
ruc?
n.
lx-
Y s
)(
1- lyl
b.
1
<
-
Y
IX
fr IY
c l:
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70.
d.
1-los .
x•·····
A
rod 26
m c t ~ r s long leans ag•lnst •
l ' e r t i c wall. The fool
of
the rod
dritl n
c S.,
2- .[ i
cl ,
Su =
:n
73. 1f
• CUI'\ e
io
rleGncd
by
I he J):ir>IIICidc C()
ordinnl x 1J
' z
I)
I
I':
lien -
1s
equal to
r'«
01
"
u v
211
-
v
1
It
,
2uv
7;
76.
77.
78.
79.
7 or9
3 u ~ -. v
e.
2uv
d
11'
- 3v
1
21l
( '
u
=f{y
+ ch;) + ¢(y - dx) , then
a.
f
b
21
¢.
tan
r
d.
sin f
C n n ~ i d c r
the
totln'' in
g
Sl:llcm¢nls
witlt
rugu.rd
to t
be
curve y - 3 (x-2)"
~ < t l i o o A):
t2.
3) is • point of
inflcxion.
p.
Re'ISon
(R)
; - al(2, 3 )
dl:
) f heJc ~ ~ I e m e n
Is
a. Both A
nnd
R are
tru
e nnd R
U
lhc
corre:<
ploootioo o[
A
c. ,-\ tru" b u t ~ is f•bc
d. A
is faille
but R
is
IJiJe
IIJn r-·
--
- - . . . . , . . ; - , - : - +
. . -
,,t 1 n
equal-o
••
1
II
h. 0
c.
r
'I
d.
>
l
..
.
. .
a.. X
: - i ~
XCOS X ..,.. 0 ) ~ - X Sm "
b. x + -
x
CllS
x
c.
,.L
.c _ . .., ....
} 2
)
a. Nouc oftlte above
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80
.
Sl .
84.
85
.
86.
b. . .r.
c. e
d.
00 /t
,. t '•
f ''"
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92.
93
.
95.
a.
y;= :<
h, = ~ . : ;
. '
c.
y - x- -
2:<
J.
y
; ~ ? . s
1l10 singul•rso
lution of
p- log1Jl
l .
·y).i•
;L y X ( logx - J)
1-. y ; x l lgx - .1
c. )
- Jog x
- I
d y •
X
. og X
hc differential equation IJf U
ld
fomily of
r
am
bol3
foci
:11
lh
e r•ng1n
and
axlJ
:
li
onJ the
,.;
-
mcis is
a,
>{ rly)' 2r,2- J'
=
I
clx
d.>:
(
ell'J
t
.
,,.
-< -
.. 4 - - - -0
. dt dr
c.
>
fy
)'
.
2xl d;· _ " _ II
r l . ~
t/.,
d. > y )' -
2."
rJy .,. y
-II
dx d.v
Let (v· C)
1
Cx be the prinutjvc
of
the
d i f f e r ; , cq11111ion
"{d) ) ; .
J dy
)-1- 0 he numb,.,. of
d.>: l d.>:
intcgt•l
.:l
urves which will l ass 111roUJ b ( I.
2 ) 1 ~
.l
One
b. Two
~ hree
d. Four
"l11e sol of orlhogo
uo
l trajectories to •
f,1 ntily of curves whose diffarential
equation 9(
r.61. : ~
)=
Oi•
lil
und
b)
1
the
dtirercnt equotion
"•
I J . r d r ) -
rfO
b.
r . I J cUIJ
0
,,,
c. (r.O.-r
) -
d. [
r
.
-; ~ )=
0
9 o
r9
96, Tite .
so
lution of ilie differential .;qu>.lion
tl Y •
y =
) satisl'i'ing the y(Ol
dx
·
=
l 1{ ..) 2 is
•• 2
a. wsx 12sin K
b. ""·'
x
' .sio
x
e. 2cos x t-
si
n x
d.
t t o , ~
X < XI
91.
e"'(C
1
cos ../3x +C, sin
../3
x)
c , e " "
is tbe
generalso
lllli(
IU
al
iou
+
S D 16)) : 0 is given 1
y
a. C
1
olx• t::e'""+Cjo"• C,,,-•
>; c (' ,,,
b. ~
, J ~ •l
1+ 1Jc.
c, (Ca-c,x)cos 2.x
C . . . x ) ~
2 . ~
d. (C ,
.-
C
,x
)
cosh
2x
+
(CJ
+C.)sinh
2"
??. The general solutjon
of
d }'
s m <
b. ~ c C,c '·3cos
c. )=
C
1
c''+C
1
?'-Jx 8in x
d. - r C - 3 c o ~ X - Hin X
Ill()
. Tite
S