8/18/2019 Mathematics Objective Questions Part 15
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w w
w . e x a
m r a c e
. c o m
cS. t;.
p
. 2D0
7
I ol ICI
MATHEMATICS
r
J
Let
X=
l u • n
IS
a
po
s
ili1
·e mteger. n.s
50}
,
If A -
ln
e
:<
,n
is
evcrnf
and.
B= fue X:n mu tuploof7J , then what is
the number
of
elemen
ts
in
lhe smallest
su
bset of
cQn
t
ntning
bo
th
A
and B?
~ 28
b. 2 1
c. 32
d. 35
2 Let A
=
[t
e N.
Il and l are
rela tn•
el)
pcimel and
B = 1t.: N. t s
241
. Wtmtis lhe
numbe
r
of
elements in
A("' B
I
a. [()
b. H
c. 7
cL 4
3
t.et
7, c o s : r + f 1 t / and
A=
rz
u e
NJ which
011e
of
the
follo\\1li
J;
is correct
n. A
is
1101
a
linim
set
b. A contams
12
non-real comple'
n
umbe
rs
o. The
number of
elements in A 1S
16
d.
A con tains no mlegers
1 Which
ooe of
the fo llou
ing is correct? The
e q n ~ 221ox
1
(2Ml
' { 2 6 1 ~ ~
u
Has
no
mull
1ple roots
.
b, Has
one
rea l
ro
ot.
c. as no non-real
roots
,
d. Has
no
integral roots
5.
\Vl\a
t
is
the sum of the roots
of
the equnnon
((•-2 )
H}(tN
-3f >=l)'/
n. 5
b. JO
0.
l3
d. 18
6 Let rn be positive intege
r,
m ~ l . If
, ~ ,
...
_
8/18/2019 Mathematics Objective Questions Part 15
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w . e x a
m r a c e
. c o m
11.
~
u m i t l e r the group
(R•
R• t, where<
R*=R-10} illld
ro.
b) • (c,d
) (ac,
bc - d)
\Vhnt an. th•
id
entity element nnd the
in,,._,., of
(n,
b) resp<
-c
tive ly'l
a.
(l.O)
nnd(a
1
.b n
1
l
b. (
0.
J) rutd
(a
1
• ba
1
1
c. (0. l) nnd (o
1
• •
bn
·t)
d
(1
.
U)
ond
(al.
·
b
'
1)
l3
.
Wh
lc
h one
of foll
QIIlng.
•Ui
tetnenls is
euttet:t'
a
..
AbclU.n groups _may ha
vt.: u o u - ~ a b c - l i n n
subgroups.
b. N011-abclfan groups may have abelian
c.
Cyclic
gtQU
Jl"
ma
y havg non•eycJic
;, ubgJ
'O
UilS·
d. Noq-.:yclic gmups C311MI ho1e C)'ll
lic
sub gro ul -
14. U:t
o - = - ( 1 , 3 , 5 .
) 1 2 . .
Wh.tl
the
s m o
e c ~ l
11ositive int
eger
n. •uci•
that
ri =
rs ?
n. 3
b. 5
the nUtllber of
lnwrtibel ulcm.,uts
un
ttr nutltiplfcallon
In
R'
l
1 l
b
. It
c. u
1
d. (n.'2 ] whcrt:H l. 1lte brnckct
.l
lmctiou
19. If Q. R.
C
ore rcspoc tivdy lh t litlds of
rational numbcf>l , rc•l
n u m b c ~
3nd m
nnrnbers,
which
cme
of
tl)
e fo
ll
owing
olg*ruicSl{\lttur"s ill nvt yeciqr p : t c ~
n,
R ClVe
r
th
e field Q.
h Rov
erthdi
eld R,
"· CJ over
lh• tiold R.
•I
(' Qver the fie
ld
C,
20. Let "' = (
3. 2.
·
1)
. y
=
(2,
4,
1). z = (4, \),
ond
11 10.
-1
, ·3) be vectors in R:\. il rtill
1
cclot p a c e \Vl•i
c
li on of tho
fo
ll
o11 iog Is
correct?
o. 2't z
\v y
t
z -- w
b.
2x
y
z .
y
.. ._
2z
•
w
c.
:t •z • w.2. Cty z.
d
. y
f
2z \ \T X
z_
21.
lf
V
rool
vector
spoc.:
of m> pp ings
from
R
to
R, : ( f ~ V I r t · x ) : f ( . ' < ) l and
V,= -{ f « V I f.
: < ) - f l ~ ) } .
l
hon
which one
of
l h ~
following
i.s
Cf)m:cl?
IS. Nelther V
1
God V, h a Sltbsapce of V.
b. V
1
i.•
n
a c c
o f
V. hu
t.
V:
;., not G
Rl:>,
apa
ce
ofV
.
c.
V
1
' no
t
o
s
ub
s
pa
ce of
V.
hut
\1
1
;
,,
suln pact:
orv.
d.
Botl• Vt
and v:
ace
subs5t>ces .,rv.
22. l.el F[xI he the
rin
g or pOI)'nu rnial. m One>
variab le
J(
11\'Cl' O li'c:Jd F wilh Ue
rc
la
li
8/18/2019 Mathematics Objective Questions Part 15
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. c o m
23. Which nne of
th
e
fo llowing i•
co•
1'e
ct 7 l he
st:t S
= {a
~ ih, c
+
ul} L• o b
asi
s
tb
•·
th
e
v J J u
c
nvcrR
to
'
a. e ~
b. ad +be - 0
R by T(x,y,?.)=(y
iJ 2)'
1
I l.
b, 2
c. 1
d.
()
29
Comider Lh e vcctor•
pn
ce C uwr R und lot
T C C be n linenr r t r u ~ f n
n n r o t i o n
given
by 1'(z) = 1 . fh en w
hi
ch one
1.1f
the
fo
lluwing is
cotre
8/18/2019 Mathematics Objective Questions Part 15
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w w
w . e x a
m r a c e
. c o m
given
by
xu -
2
b
Yl • - 3h)
=
:o b
p:tt: unply
e
;1
cb
oibet.
\VItal
is ibe angl
co
between
tl1
e
tw
o
drawn from ( L 0) to
tl1c
eurvo: y - 4:t
OJ
3. 30°
b.
4 '"
)
c.
60•
d.
< 0
•
I f ~
cu·
de
ami lhe
reewugubr hypel'bola xy
c
meet in f-our poi.nt8 lt - t
3
and
4 th..:u
what ;, t
1
t
1
(3t.. equal to?
:1
I
b. - J
"- 2
d. 2
l
fP. Q. A.
B
lire\
I, 2, 5), (·2.
1.3).(4
,
-1
.
2)
,
(2. I, respect
ive ly
. then
wha t
ill
lh
e
projt:
8/18/2019 Mathematics Objective Questions Part 15
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w w
w . e x a
m r a c e
. c o m
~ " b
c'
=- . - . are
non coplonar.
Jnbcl
Which one
of
th" fo
ll
owins L Orrcct?
u. S
1
impli
es S1
b u t ~ docs
nOl
imply S
t,
I),
s ,
d
oe;;
n
ot
im11ly St hut
S1
mpli ts s,.
.::. S, implies S, and lh impliCll S,,
d. 5
1
docs
M l
imt ly
St
and
S
1
dn
os
lUI
imply
s.
\Vhnt is the
vol
um
e of
the
lctrahetlron witlt
vurticcsat(O, U
O).(L 1.1), 2 Ll):tnd
( L
2, I)?
• . 1/6
b, 113
c.
1
:
47
. I f
r ••ti;>lies the e q u ; l l i ~ n
f
i ~ 2 j L
) =
i - t <
then
for
an
y
.Cll
lar
m.
what is
;
l l j
to•
a. i-m(i-2)+ k)
h. j 1m(1.zj' k)
:
k
· mti +
l]-k)
d. i- k+m(lT 2+- k)
48. For the triangle OB('. one '""""" 0
i•
the
or
igin l\nd the position vector.. of
Ute
o
Ut
8/18/2019 Mathematics Objective Questions Part 15
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w . e x a
m r a c e
. c o m
5
3.
>< < -lorx " 6
. - 2
c;
~
6
o
d s i
.\ B
c D
b.
4
2
]
3
c.
3 1
2 4
d. 3
2
1
4
c.
4 1 ?
3
f
.t.
2b 0 0. ih
8/18/2019 Mathematics Objective Questions Part 15
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w w
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m r a c e
. c o m
b, 12 n
c. Sn
d.
Gn
o7
. Jr
u l l - : f . r l -
xl ' then whot
•
••
68.
i&p equn l t
o?
a. 2n
b.
I l l
C..
l-i
tt
d.
W h ~ t 1S 1 1 ~
area
of the region b o u n d ~
t
he curve 2y - - l y'
•nd he
l ·n.'l.is
'J
a. 12
514$
uph
b. 4 unit
c..
3 uni
t
d.. 2 ~ / U sq
un11
. x -
y•
G9.
\Vha11s t h e ~
e o h
1
.-yJt"-y'
7 l.
h ln v
1- In'"
b
1- lny
I
r lny
"-
- + loy
l+lny
d.
1 · loy
I lny
s3n
COS.X
rf f C ~ < ) - (I - 1 u where I
p p· p·
constaut.. Ute:n ' ' bal
i5
Ute
val
ue of ~ {f(x))
nt x : O']
p
b.
p • p'
c. p - p·
d.
[ndepcndent of
p
71
. Whot ore
Ute
order and cl" 9"'e respective )
ol
' the
dilferentiaJ l CjUOt
tO
n nf
t
he f.1mi lv of
u r v e ~ ~ :
J c b < +
where
c ; , ·an
;trhitr:u- · conslanrl
n. I, 1
b 1, 2
c.
I.
3
d. '2, I
7
ul
Ill
72.
\VJ1ot is the
oofutiou o
lh
e
73
.
d-)
dv
ditlerentiat eqnotion - .
-2
- · " " ~ Y "'"·
d,
·
~ ~ .
.
with tho< g
ivc1
1 conditimu ) (tl) - 0 ond
y
O)
= 1?
11.
V= i
•
CmiX
b y ~
c.
o o s x
-
. .
d. y :S fn :<
Wh31 iii lhc o l u t i o n of
equa tion
(1• e' )dx•e
'(
l
••
X y e ~ " '
= ~
h. Y t-Xe
:tJ
c
1 .
X J fi'f C
d.
n < J n ~
11f th
esc
Ute differential
~ \ y e
,.
74, 1'hc
smgulor
$(llu
t
1o
n
or
lhe
dinerenlial
cquat
ioll
y pll +
f1p)
will bo QblJJined b)•
elirniunting p
between
he equation ) :
l' p)
and wl ich
one
of
the 19
11nwing
U l l . • o n
df
tt.
J t + - - 1 1
dp
dv
elf
b. - · -
• t
-
dp dp
c. dy - p
d.
Jy
8/18/2019 Mathematics Objective Questions Part 15
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. c o m
76.
Whol
arc
the urthogonal trajectories or
d•
e al A s lh,,l Ue new centre
or
grovi ly
d i
\ll de.
median
through A
in
til e mt lo 3 :
47
•.
'4
b. 3g
1 ,
d.
S&
82 Two p h e r c s of radti 6 m 3 em •ro finnly
uniled.
11•o two e o an: to lid
3nd
of
lll
e
same mnt,.,.;al.
What
i
;.
the
d
is
tnnce of the
centtc or
of l1e wlwl•
bo
dy lrom
lhe
centre nf 11c la•·ser
' J ' l h c u
a,
I
em
b. 1cou
t:..
~ t u
d. -1
· ~ n
83.
U
h . < > a n g l
of
friction
IS
:t.
lh
cn w
ho
I is
Ue
ycntcsl
hcigbl nl wlticll iU I
Q tes
t
inside • hollow sphereofrnd
i\J$
a7
::t t s
i n
).
b. o(l cos1..)
c. trul ?..
d. •0 - liiJl.).l
14
. B
1\
w poinl$ A and
B
hn
ve
velociti
el<
u1
nod u1
ns
shc111n ill
he
f i g u
obl)
ve, lf AB= d, whal U c 11ng
ular
of A n:
JatiVQ 111
11'1
3.
< > : ; ~ L )l d
b. tu
1
co• .l
; u
•O>
8/18/2019 Mathematics Objective Questions Part 15
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. c o m
SS
1'wo
p ; ~ r t i c l
ure projected v c r G c a l l ~
UpWaT
i
l<
Jrum a
pfaee
:ll
an tnlC Vaf
of 2
socottds. I f
Utt .Gn H
1
and
n situultaooousty, tblltl whkb ouu of tltu
foUowing
;.
con:cct
?
a. .pi;=(
. j t { .
,fi8)
h.
foL
-t
./H
./2i
)
e; m ~ -
:.zs
d. JH I I i
l
86. A rarticte or unit mass 1S U1)05tmined to
move in a smooth clrcul3.r pAth ul' ,ndim> a
witlt
ronsi.Ont spoerojection
. Whllt L'
U1o
greatest
hct
gbt (h) a l l ~
inctl
tlunug ~ 1 0 paih uf Ihe
pfojtctilu 7
v•r
rgRJ])
. h = - 1-
.,
1 -
-lg
v•
b + ~ J I J
=
l f J
89
.
~ 1 .
92
9nl lll
A paniole Is executing s
impl
e ham.onic
motion and its
tli splncetnent Irotn i ts
mean
position
S
giv n
.,.<
~ c a s { r u . k ) . .
wh r
l denotes the Urn.: and n,
n.
k at (< pasili""
con•tants.
Und
er
w
hat
co
ndilion
wi
ll
th
e
speed oflbe por1itle be m a x i m u m
a. t
=l2p+
l)lr :n. tl befug,an mtegor
n
t
=('lp+l)
ni
Zn
- (1; n)
p
1ein8 :m
integer
c.
1"
(2
p • 1 an
' a} r
being
:t11
integer
d.
t
p1r/ n (k n
).
p bcmg :uuntcgcr
A. portkle who,e w ~ i g h t OJJ
IJ1
d
s u r f • ~
of
the earth is \V. falls to the surfoce of t l ~
earth
fmm
a
heigh
Xll13llo
th
e
dinmeter
2R
of tlte e.1rth. What is the work dnoe by U1e
eatth
••
iltlJ'Ol
8/18/2019 Mathematics Objective Questions Part 15
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w . e x a
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. c o m
Comment l : f
'
(i ,
J)
is the product matnx
AB
of
o
rd
er m •
p.
Wltnt is
X
in the obovc
l g o r i t h m
a. C'(i. j) I A(i, k
)"B(
k,J)
b. C Lj) r
A(l.
k)• B(J,k
J
c.
A(t,k
)•
B(l;.j)
d,
C ' ( t . j ) ~
A(i
,J) •B(t.J)
94.
What
is tltc decimal
equ
iv
alent
of
t
ile
hexacl
ecimo
I numbc:r FF ?
.•. 225
b.
u
255
d 256
95
W
Wch ouc of tlt
cnllcd
"eo
inciden
ce
deteo1 l
••
OR gotc
b.
NAND
l-
''
""
NOT
gato
d. AND ga te
96. Let n ::.3.n be odd.
A.S>I rtiou (A):
For
01uy 1-l, ..
.
"n l i f
u,,c..,
..,a
,,
""'
the
t
tlol.s of the
cqu•tiotl
x" ~ - :IJ then
(I
1 «, '(l
1.
.
. I
Rt•asun (R.)
:
l f 11
,
rt,
ore the m1•1Jri'th.:
cq u:itiun.•, .,.• - '< - I : ) , ant
io
n
nr
A
b.
Botlt
A and R a r ~
indh
dduo lly true bul
R iR tc
n . , e t
Cl
nnatiun
nrA
c.
A ls
tru but
R
i >
f:ilie
d.
. U s
fal c bu t R iu.ruc.
9 8.
Asse
rti
on
(A):
Tho
l\mc6on f (>.) - - - is
1
lxl
nm difforcntiabl" 111 s
=
0,
Rt•
uson {R)
t
lsi
nnd hcnQc; (J
I lX)
i . ~
n-wlue to c m the gc
ncm
l so lution
• · BoUt /1 .end R .ere individu•lly
true
und
R
iR
the
~ o i 1 ' < ' C t explonnlion orA
b. Hoth A Md R ore
d
a l l v
~ bul
R '" he
.:om;ct
eXp
lanation
of
A
c: A is true bul R til be
d. A is fnl lc
bLLl
R
is
'" '
""
10(). Assertion
(A)
:
r·05 •
- oolxdx
' ,,
Rea•on (R) : 'Tho inlcgr:md i$ on oven
functio .
"' Jloth A and R nre individually true
nod
R the .:ot
we
t l o n 1 1 t i orA
b. Bot.h A :md R ure
md
ividunltv true but
R
r. lbc .:orrect cxplnnnlion
of
A
tl.
A
i•
true
but
-a [
fn
L