Embed Size (px)
Citation preview
HALLTICKETNUMBER
? 5 o L) o t q 3(To be filled in by the Candidate) tr
I(LET
l,llr
BOO CODE
4.
INSTRUCTIONS TO THE CANDIDATES(Read the Instructions carefully before Answering)
Separate Optical Mark Reader (OMR) Answer Sheet is suppliedto you along with Question Paper
Booklet. Please read and follow the insfructions on the OMRAnswer Sheet for marking the responses
and also the required data.
Candidates should write the Hall Ticket Number only in the space provided on this page and on the
OMRAnswer Sheet. Do not wdte the Hall ticket number any',vhere else.
Immediately on opening the Question Paper Booklet by tearing offthe paper seal, please
check for (i) The same booklet code (NBlClD) on each page, (ii) Serial number of the
Questions (I-160), (iii) The number ofpages and (iv) Correct Printing. In case ofany defect,please report to the invigilator and ask for replacement with the same booklet code within five minutes
from the commencement ofthe test.
Electronic gadgets like Cell Phone, Pager, Calculator, Electonic watches and MathematicaVlog Tables
are not permitted into the examination hall. .
Darken the appropriate circles of 1, 2, 3 or 4 in the OMRAnswer sheet corresponding to correct orthe most appropriate answer to the concemed question number in the sheet. Darkening ofmore than
one circle against any question automatically gets invalidated.
Rough work should be done only in the space provided for this purpose in the Question Paper Booklet.
Once the candidate enters the Examination Hall, heishe shall not be permitted to leave the Hall till the
end ofthe Examination.
Ensure that the Invigilator puts his,4rer signature in the space provided on Question Paper Booklet and
the OMRAnswer Sheet. Candidate should sign in the space provided on the OMR Answer Sheet and
filled in applicarion form.
The candidate should write the Question Paper Booklet number, OMRAnswer Sheet number, sign inthe space provided inthe Nominal Rolls and affix the left hand thumb impression in the nominal rolls and
filled in application form.
Rehrm the OMR Answer Sheet to the Invigilator before leaving the examination haIl. Failure to retumthe OMR Answer Sheet is liable for criminal action. The Question Paper Booklet shall be taken out bythe candidate and should be preserved till the declaration ofresults.
Filled-in application form shall be submitted to the Invigilator in the examination ha1l. In case of11.
SC/ST candidates attested copy ofCaste Certificate should also be enclosed along with filled-inapplication form.
This Booklet consists of 51 Pages for 160 Questions + 2 Pagesof Rough Work + 1 Title Page i.e. Total 64 Pages.
5.
6.
7.
8.
9.
10.
Signature of the Invigilator
82016-A
Time: 3 Hours
Instructions:
(i) Each question c arries one mark.
6E 6dJ5.> e.d 5rd:2, Socn.
(ii) Choose the correct or most appropriate answer from the given options to the following
questions and darken, with blue,&lack ball point pen the corresponding digit 1' 2,3 or 4
in the circle peftaining to the qubstion number concerned in the OMR Answer Sheet,
separately supplied to you.
a,{:5 a,}5 6s 6dJ$ e55a:65 a"isd Soo3cs S5:'o"55cc$o J5o15'e oeo S:"SoS
eroB 1, 2, 3 dS 4 Sdurr aa;S OMR $5:'o"5 5r.65r:ef 6d;So SoaoOo,.)S $opgde){":0355o ar:"/arS o'e5 }occoc5 =o5o3 65&rflo3 Co55d5c.
MATHEMATICS
1. The domain ofthe function /(x):
f(,)= eetu 6r$cD)O 1€i6da])
(1) {0, 1,2, 3, ...} (2) {t,2,3,...} (3) (0,-) (4) {0,1}
trMarks : 160
o96.5 x!
2. If f (x): lx-l1 + lx-21 +lx-31,2<x<3, then/is
(1) an onto function but not one-one
(2) one-one function but not onto
(3) a bijection
(4) neither one-one nor onto
/(x): lx-l| + lx-21 + lx-31,2<x<3 erood, er556c /(1) e"5 $o(S 6;00$5rr, s'& erd555:: rel:
(2) e"5 er355 $docdr$rr, rC So(Q5r s'6:
(3) e.5 a5r{:eo 6erc$$J
(4) er3555:c s"6o, $o({;1r: s-6:
Rough Work
E 2016 3-A
!
t
I
3 ' I[t;t1::*"sitive
integer which divides (n+16) (n+17) (n+18) (n+l9),for all positive
erel 6SXyqos.erc n e>6r, (n+16) (n+17) (n+18) (n+19) So a_Eod ds6 65 {rq;S5r:(1) 6 Q) 24 (3) 28 G) 20
4. rf a, b, c are distinct positive rear numbers, then the value ortne a.t.rr-,irunt /il.
b
c
a
(3) (4\ >0
bcl
" ol',,bl
a, b, c e>tiASJ 65 -r, ..^.^^.^.-* jl
,nt".ru, j:
,l,l,l
0
AqdSfu ob:S6 ioc5
(1) <0 (2) >0
5. Ifnl; n2, ,r3 as w elr as y t,,yz, ys.are in geometric progression with the same .or,,* *athenthepoints (*vil,(*iyj,14,yl1are JdruE uullrrrr
( 1) vertices ofan equilateral triangle(2) vertices ofa right angled triangle(3 ) vertices of a right angled isosceles triangle(4) collinear
xt, x2, x3 5oEc6:: y1,y2,y3 e.r: a.t So"Xo$6o ryo ,$eo@6oc ercr:d, $t. yt),(jr2,,.r2),(x3,y3) 0o6:gu:
( I ) $5oo"Sr:L@a$a &{Sr:e::
(2) eroar $ea t8e;$a g{irq:(3) ooa:$eo 55o85a"$u Leaba B{S::oc
(a) $dgo$"q>
Rough Work
82016 4-A
I
fs-rc;;llczl
6. The equations x-y+22=4
5x+Y++z=b
x+y+z=lhave
(1) unique solution
(3) no soluiion
--ttt-)z-A
3x+y+42=6
x+ y+ z=l S5:SdeaS::e>So
(1) lES $65 6o{.Doa
(3) $65 6066 .
(2) infinitely many solutions
(4) two solqtions
(2) es5oei &d5eDodr-o)
(4) Bodc d'65ococo-or:
7 . The locus of the point representing the complex numberz for which
l, +zl2 *1, *zl2 =rs is
(1) a circle
(3) a straight line
(2) aparabola
(4) an ellipse
(2) e.5 5o"Socd:o
( 4\ a,S 6d 5re5oiO Q,'J
l, +zl2 -1, -zl2 =Ls egoloEoc*, $o8$ so+g z $o bc",)od ooc!$ o3r:$2, oo6: 56o
(1) e.s 51{o
(3) e"5 Sdcr6q)
(1+ l;20168.
0_,.,zo-1" =
(r) -2i (2) 2i (3) 2 (4) -2
,wrw
82016 5-A
Io tr
is
9. ttlzrl=t,lzrl=z,lr,l=: una lgzrzr+42r4+2241:12,thenthevalueof lrr+rr+4lis
lrtl=t,lrrl=z'lr:l=3 Soocsr: lgzrzr+42r4+ 224l=12 ero:d, lz1
+r, +r,l o-52,
(1) 3 (2) 4 (3) 8 (4) 2
10. If l,zr,zr,...,zn r arethenth roots of unity, then (1-21) $-z)... 1l-zn_):
l, zr,22, ..1 zn_tor 5SS5:: dr56 n 5 f>"e:"e:o::d, (1-21) 1t-22) ... (l-zni:(1) 0 (2) n-l (3) n (4) I
^ ^211. Ift2.*,* =\24.13)
^ ^2 ^
,ro*r,'-(uJl)'^ -'
(1) +Fq(2) r{; (3) + (4) +
12. The product and sum of the roots of the equation 1x21 - S1x| - 24 : O are respectirell'
1x21 -S|x| -24:O crso S5:S66a5! dr:56 Srro5>:e: ogsr: 5ooo5r ar:giS: 5d:5n
-2, thenx:
eso::d, erbya6: x:
(r) -64,0 (2) 14, s (3) s,-24 (4) 0,72
13
nt2
13
5
t4
13. The number ofreal roots ofthe equation x5 + 3x3 + 4x + 30:0 is
,5 + 3r3 + 4x + 30:0 epSo S5cSdeo"eg 6o a.$^5 5r:"o-o Sopg
(1) 1 (2) 2 (3) 3 (4) 5
Rough Work
82016 6-A
If the coefficients of the equation whose roots are k tim.es the roots of the equation
r 1, I Ix'+-x' - - x+ ^ =0. are integers then a possible value ofk is4 16 144
.r 1r I 1,' ,.r'--x r--^ -0 S5o5deao d:cS; S::.ero {r:4 16 r44
$5c(deao o3r:56 t$sos.o: xgr$bo+5er epqr:6, k 3, 5OS
(1) 3 (2) t2 (3) e
k BUD 65J Sr:.er"e.:5o 5Ofl5
e"5 $e)rs
(4) 4
15. The sum of all 4-digit numbers rhat can be formed using rhe digits 2, 3, 4, 5, 6 withoutrepetition. is
2,3,4,5,6ero3e5o {$o"53e3o s-6:oa" 6i-,,,i:.for,5n" Sr}S er&1 4-eooBo bopger 3:r{o
(1) 533820 (2) s32280 (3) s33280 (4) s32380
i6. if a setA has 5 elements, then the numtrer of ways of selecting two subsets p and e fromAsuch that P and Q are mutually disjoirr.r, is
S$rS A ef 5 S::.es.orod, P So0r:5:r Q w SdS;6o io5::qodogece3:n- A Soo& tso6:
6S$Soe6e>J R Q o$ Jodc$rfC,i CSSr:o Sopg
(1) 64 , (2) 128 (3) 243 (4) 72e
17. The coefficient ofx4 in the r.:xpansion of (1 -, +x2 -*3)4 is
(l - x + x2 - x3)a aqoea*f, ,a o,rs2, r{:ea5$o
(1) 3l (i:,) 30 (3) 2s (4) -14
Rough Work
E 2016 7-A 10
P,"
18. If the middle term in r*he expansion of (1 + x;2' is the greatest term, then x lies in the
interval
11 + x;2'a::S2, s{6soef'C Sodgf6o r(0$66o eso$d, x6od epodd5::
( n n+1)il) I .,-l
\n+l n )(3) (n1, n)
(n+l n \t__1\L) | n 'n+t)
(4) (n-1, n)
19. To find the coefficient of xa in the expansion
" (, -#, - D , the interval in s'hich the
expansion is valid. is
rr d::$ c$6sae5"s xa
t-. ''t\t.. I\ (, r
JJ
-
LtllJi(x-2)(x-1)
3x& xattso,r&155o{,5o'e8, es S{6ea Ee>:alOD erd:g eo66o
(l) -2 <x< co
(3) -l <x< 1
(.2)
(4)
--<x<-22-ao<r<oo
20. If (r+tan a) (l+tan 4c:):2.".(r,#),then o :
( l+tan cr) ( 1 +tan 4o) : r, ".(0,#)eoor:6.
er$y,5o cr :
E1'(1) 20 Q) 30
tfE(3) 40 (4)
60
Rough Work
ry*ryh/ .:^ $ 6
*.{dA wE 2016 8-A
-\l
f^s-rc;;l
lczl2t. 1r.o, a=fffi , then one ofthe values *,*(i) *
- cosd-cos B - (0\cOS d =______r_ cro!e9, tanl _
|I-cosacosP \ 2 )oi::S6 a,5 Ser:S
(2) tana tart.L
(4) tm2 L rlnz
tr
(1)
(3)
0acot i- tan -22
Batan.:- cot -22
!_2
22. The value ofthe expression
I + sin2a
I
t,
1S
( 3r a\)cotl
-+- | |
( 2 2))
(3r a\)cotl
-+- ll
l? ))l- /)
1
r.-( d--sln 2d I cot- +4[2
r. - ( d--sln 2al cot-+4[2
(2)
(4)
cos(2a -2n\tan( " -lI)\ ,, \ 4/
I + sin2a
cos(2a-2r)tan("-+)SSTSSD d>56 $euS
.2sln d
(l) 0
.1d(3) sm"-
Rough Work
F 12016 9-A
\*
^o
1
23. If ;stnf/,cosdandtand are in geometric pr.ogression, then the solution set of 0is
lsin(/,cosd soocrr:
(1) 2n"r(%)
(3) "ft+(-\"(%)
tandel foea@6ef +od, 0d.:c56 +65 S$rS
zn" x("/,1\/ )J
",*(%)
(2)
(4)
24. IIx=sin(2ran-r z;anoy=5;n[lt-,1], tr.,.n- \2 3)',
x=sin(2tan-r 2) boocuD y=rin[]tun-, ]l*ola, *r3o,- (2 3)
(1) x>y (2) x:y (3) x:0:y (4) x <y
25. If cos/z (x)=1, then cosZ (3x):
cosh(x|=1 ero::6, erbye6: cosZ (3x) &er5
6t(1)
t6
63(2\
16(3) (4)
6l63
65
L6
Rough Work
10 -AE 2016
26 tn LABC.,r,=o"(t')*^l.r=o"(7)"^i *d,=nn(A;)'-i'
then(x+y+z):
^ABC er. *=ranf
B-c)tun!.,=r*(' o'l,un{ *u* ,="^(l:l)*nl''-\ IJ'-"2''*'( z )'-" z-------- \ 2.) 2
eror:6, (x+y+z)Ser:S
(1) xy z (2) -xy z (3) 2xyz (4)
2'7. In LABC" if the sides a, b, c are in geometric progression and the largest angle exceeds
1
- x! z2',
the smallest angle by 60', then cos B :
IBC 1@+na5re$S qfasr: oc a, D, c,{:eo@6ef 6o6,
60o e.po::d, cos B :
./13 + I 1-J3
es 184ba 606, Se6 $ea"o 655::
JE-t(4)(1) (2) (3) 1
28. rna LABCiTp!=e0o, then."'-'[#) isequalto
LABC E V.=90" eeorrd. cos-rt'-+-l =
\r2+\ )
(1) 9oo (2) 3oo (3) 60" (4) 45"
Rough Work
F.2016 1l-A
,.r$$
/w
{-
(2) 2x -y:5(4\ )v+z=\
tr29. The cartesian equation ofthe plane whose vector equation is
y -(l+ )'- p)7+Q* )")i+Q-22+2@E,where ), p are scalars, is
,{ . po e.ratrd56yd: 7 =( I t ) - 117 + 12 _ )1j + e _ 2 I +272) k er$ K>aa" 65:Sd6oSDS)
5On5. eJo$c o3::56 s"$"oc6:S i5:sdsosn
(i) 2x + y:5r?) )v _".-\
30. For three vectors p, q and r, if i 4F + 4Q and 2T = p _3q, then
( I ) lrl.Zlql and v.q have the same direcrion
(2) lrl>Zl|l andT,Q have opposite directions
l-l ^ t-r(r, l"l<2lSl and, r.g have opposite direcrions
(4) ltl>ZlOl and v,Q haverhe samedirection
5::.ctu S8del: p, A XoOctu r o6o, F=3p+4A SoEotu 2V_F_3q
(1) lrl.zlql sooosx r,A e>J z.t adet-6ouror>
(2) lrlrZl|l saocsD r,1 er sge!5Q (sEsds) Edef 6or.r"or>
(3) lrl.zlAl xDocdx r,7 o: 5gd5$ (sge6s) Edd 6o9ro:>
(4) lrl>zl|l sooctu r,A o e.€ E{ef 6oe.r.o:>
erS3ctu
Rough Work
E 2016 t2-A
\=
tf a=27 +37 -sE,i=ni +nj +128 and ax6=0,then(nt,n):
a =ZT + Zj - SE, i : ni + nj + I 2k soootu A x b -- 0 ero::6, (m, r) :
( -24 36\e) [;.;J
( 24 36\(4)
[;,;]
( -zq -to\n) [;.;J( z+ -ze\(3) [;.;.]
so"s, (a,a)=izo'
(2) 7
*o.ra, l+a+:rl a*s
(3) 13 (4) 12
lz . tt a.t ,e are non-zero vectors such th ut (a ,6)re =Lltllela , c La and 0 is the angle ,t
between the vectors b ,c then sin 0 =
1a";)"e=ll'llela , a La so.ur, 6,a o 5o6g$o5r gerd:ge;tl: a,6,e *e{r3Edd
$adoc 6od, er$36r sin 6 =
t l.t(.2) (3) (4)(i)
2
l,5
3
1
3
32. rr lal=:, le l=a and the angle between a and $ is 120", then l+a +Z6lis equal to
lal=z,16l=+
(1) 2s
Rough Work
82016.o\
,s\(
{r
13-A
34. If a(axp)+b(pxy)+c(yxa)=0 andatleastoneofthescalarsa, b, cisnon-zero,then
the vectors a,p.V are
(2) non coplanar
(4) mutuallyperpendicular
a(axp)-61pxy)+c(yxa)=O Soo:, a. b. cepade.:ef SbSo a,dc3 drd5ddo oo::d,
-;-oJodeD a,lr. r/ e.))
(i) parallel
(3) coplanar
(1) Siroe5d5,::o.>
(3) $e50cdre))
(2) ep60c6:.oc
(4) Sd536o e>oaorr c6.:cotr"o::
35. If the mean of 10 observations is 50 and the sum of the squares of the deviations ofthe observations from the mean is 250, then the coefficient of variation of thoseobservations is
10 50&o5.: $dE5oo 50 Soooi! SdESoo Soo0 ;:,ij irjoo.o Sgo a::g[o 250 u,oo6,
es 603er5e> irje.:S 6:eo5o
(1) 25 {
to (3) 10 (4) 5
36. The variance ofthe first 50 even natural numbers is
tscrde 50 SB Si:.a $opge i$S
(1)833
4(2) 833 (3) 437 (4)
437
4
WCI
!r- #t\ \ "l/t. / ^.*. _v'1 o$brt
' / , )i7 u,Eq,-,-, l'€ld
".'*L' "frAr:/ 14-A'u/"'r", -l-s' I
..al- r-"r - l-t- t\#lq
82016
\p\i
tr
3j . 3 out of6 vertices ofa regular hexagon are chosen at a time at random. The probability that
the triangle formed with these three vertices is an equilateral triangle, is
e.5 $5oXrc6:;e oir$2, 6 &oloef 3 Sqe:So c5r63Q;5om e"t&o Jottuso16' e: 5:s'60
Sqe,:A bdld 1&4bao e"5 $5oa'5r: 1SAbaS:: s"6e; $osr'5E6'
(1) (2) (3) (4)
3g. A speaks truth in 75% of the cases and B in 80% of the cases. Then the probability that their
statements about an incident do not match, is
75% $odoloef A$65o 5:"i.:-6o"6o, 80% $o5o1oef B 5e55o 5:'eJ'6o"6:' a"5 $ofubs
t$0o.1 a"ct Et:J Sf)c6o SdS36o Sd8od So+"5E6.
(1) (2) (3) (4)
If the mean and variance of a binomial distribution are 4 and 2 respectively, then the
probability of2 successes ofthat binomial variate,( is
e.5 6556 SqIaSo dr66 5o6g5oo Soocd:: ;l$So: 56$m 4,2 coor:d, es 6556"5oo'3
X d>56 3o6: $6ode.: Soa'SEd
1
^
1
10I5
1
2
5
12
7
3
20
7
20
t
I2
2t9(2) 256
7
64(3)
3t
256(4)
Rough Work
.0\-
J
r,2016 ls -A
\$fu'
(1)
40. In a ci{z 10 accidents take place in a span of 50 days. Assuming that the number ofaccidents follow the Poisson distribution, the probabilif that three or more accidents
occur in a day, is
e.S $6doef 50 6*alo 5g56ef
Serao'S; erSoSo Qo65oSod,
5oa"$5d
(1) L'-ilr,^=0,
(3) ,-i"-i!r,rol,
10 $5.:"o"o $oq5$Qor. g55:.o"o Soqpg e,S $o::asS
e.(6 6"a,et' 3 do" esou5 dod J$;5 S5ro"er: adi{r{e.:
q: ) "k(2) l" ! .s"=o.z
x
3 -) .k
(4) l" ,! ,s'=o.zk=o Kl
4 1 . Equation of the locus of the centroid of the triangle whose vertices are (a cos &, a sin k),
(b sin k, -b cos fr) and (1, 0), where fr is a parameter, is
fe"S $o"ic& coor:55y6c, (a cos k, a sin fr), (b sink,-b cos ft) 5ooo5r: (1, 0) o5o 3o3o:n"
r{e.: q&e;f:a €o16a.5o d::S5 &o6o $6 $5:5deoo
(1) (l1x)2 + 9f -- a2 + bz
(3) (3x+1)2 + (3y12: o2 a 6z
(2) (3x-t)2+%?:zl+zf
(4) (3x+l)2 + 13y)2 : zl + 3b2
Rough Work
f.20t6 16-A
fEt c"d;'l
lczl42. Ifthe coordinate axes arc rotated through an angle I about the origin, then the transformed
6
equation of .1fr *2 -4ty+",f1 y2 =o is
tr
Suo ooc$$sdoo f Seooe cdr55 eog"o5o GJfoEao db5O6J , Jl *2 -qry+.,f1 y2 =o
d::62, Cu"$o6d5u AoOS 65:$deao
(1) Jl y2 +xy=s
(3) Jl y'-*y=o
43. Ifthelinesx+3y-9:0,4x+by):0,and2x-y4:0areconcur:rent,thentheequationofthe line passing through the point (b, 0) and concurrent with the given lines, is
x+3y-9 : 0, 4x+by) : 0 5roc6r 2x*y4 : 0 -6q:w er$oige.:o:rd, (0, 0) ao5:6
nloa'#dr., 5gi dq)erd eo$oi4io erotg 6+ $Srsdeoo
(1) 2x+y+10:0(3) x-y+5:0
(2) tz - y2 =0
(4) Jl y2 -zry=s
(2) 4x *7y + 20:0(4) x- 4y + 5:0 f
44. The midpoint of the line segment joining the centroid and the orthocentre of the triangle
whose vertices are (a, b)., (a, c) and (d, c), is
(a, b),(a.c), (d c) e.:So 8o3er:rr r{o 1&4bao dr 56 3o164"$o 5oB c6:: ooa€o6ro5o (0+o
derq:o6o dr(2, 5:6g ao5o6.
u) (5a+d.b+5c) frl (9:4.y-)[6 6) \6 6)
(3) (o, c) (4) (0, 0)
Rough Work
820t6 t7-A rSIt']
,\"r\l
45. The distance from the origin to the image of (i, i) with respect to the line x+y+5 :0 is
$r"e.: &o6$ 5oo6, x+y+5:0d+ 63{5 (1, 1)Ao6rO oa::S6 @eaoa-&S .{e) 6rdo.
(1) iJi (2) 3J, (3) 6.tD (4) 4J,
46. The equation of the pair of lines joining the origin to the points of intersection ofr'-y' - 9 and x+y - 3. is
,2+l :9, x+y:3 e:
O::S5 S5:56eoo
(1) l+ Q-i2:e(3) x2 -y2 =9
po65 Oodc$o5o 5::"e.: Ooc5:$6: 5o5n- 56; Sdf6qr"o5Dd6o
47 . The orthocentre of the triangle formed by the lines x+y : 1 and 2f -xy4x2 : 0 is
x+y - | SoBoJr f-xy-6x2 - 06perd 5O3do gOelao ob:56 e.:oarBo@o.
(3) (3 +) (4) (i +)
48. Let L be the line joining the origin to the point of intersection ofthe lines represented by
2x' - 3xy - 2y' + llx + 5y : 0. If L is perpendicular to the line lu, + y + 3 : 0, then k :
2x2-3xy-Zf + 10x+5y:0d S:.ao,Joddpei eo65 OoSo{5o, baro aod:gd
5er:5n" 5i3 Sdf6e)5o Lerso$o6.6 L$6f6q:, la t y+3:03 erooon- a.od, i:
(1) (2) (3) -1 (4)
(2) (3+y)2 + y2:g
(4) 'y:o
(q +\(1) l;,; l
\J J,/
IJ
-12
1
2
(z z\e) [r.r.,J
Rough Work
82016 l8 -A
49. A circie .s: 0 with radius r[ touchesthelinex+y-z:0at(1, 1). Thenthe lengthofthe
tangent drawn from the point (1,2) to S:0 is
]J a"g+$on'r{er S:0eri a,( 53{o, $dd6p x +y-z:0So (1, 1) 5{ SPaQSla'
erfydo (1,2)Ao6:$ SooB S:09 4fl5 53d16a: +66.
50. The normdl drawn at P (-1, 2) on the circle x2 + 1? -zx -2y -3 = 0 meets the circle at
another point p. Then the coordinates of Q are
*''y'-2x-2y -3-0eri S;giop P(-1.2)ao5:6 56 A'rs eoQooao, es 53Ec;5c6*
aodo$ Q 5{ Ser:Q5;a. eo$do 0 d::Si, Od:'Ss"o:
(2) (-3,0)
(4) (*2,0)
51. If the lines to +2y-4:0 and 5x-2y-4:0 are conjugate with respect to the circle
*2 + 1? -2t -2y + 1 : o, then *:
* * y' - 2x - 2y+ i : 0 51{o 51{g,
$oc6::n"goor:d. er636c i :
(1) 0
(3) 2
kx + 2y - 4 -- O5o0c5x 5x - 2y - 4 : 06pe:)
(2) J'(4) 2
(1) 1
(3) J1
(2) I
(4) 3
(1) (3,0)
(3) (2,0)ri
Rough Work
E 2016e
J
\N
19 -A
r
52. The angle behveen the tangents drawn from the origin to the circle x2+y2+4y4y+4 : 0 is
5::"o sod:g $o& x2+y2+4x4y+4:0 SSqsB AaS s36p6+o SodSSmo
,(5 \(l) tan 'l l
\1J./
, (tz\(3) tan 'i _ |
\5/
_/ < \(2t ,*-
[;.,J
,/13\(4\ ,-'[r,
53. Iftheanglebetweenthecirclesx2 +f -zr-4y+c:0and,x2+1?-4x-2y+4-}is60",then r is equal ro
*2 +y2 -2*-4y + c:0 Soocdr *2 +y2 -4*-2y+4 = 0esd SJqer Jodg rfe.: $eoo 60o
elo::5{6c, c:
(1)31.6 6r.6
(2)2
9t\6
2
7 xJi(3) (4)
Rough Work
F,2016 20-A
54 A circle S cuts three circles
,2+1?-4* 2y+4:0,
,2-y2-2x-4y-l-0,andx2 +y2 +4x+2y+ 1:0 orthogonaiiy. Then the radius of Sis
y2+y2-4x-2y+4 0.
*2+1?-2*-4y+ 1:0,
r'-y'-4x+2! t I = 0 epd 5x"60 53gi5r:o5o. 539:o
d::56 a"ge$o
(2)5nlal\1,, ! t
Bl-ltt
Sooe.:on" +o&Q516 er{6: S
(4)(3)6I
!s5ot'-!z
5 5. The distance betlveen the veftex and the focus of the parabola x2 - 2* + 3y - 2 = O is
,2 -2, + 3y -2:0 So-$oc6:o ar55 36,$r: SoocdoJ o'A o 5o6g cSrdo
(1) (2) 14
!5
I(3) ,5(4) =o
56. If @r, ! ) and (xr, !2) are the end points of a focal chord of the panbola 1? : 5x, then
4xrxrt Y, Yr:y2 : 5x 5o.Seosoo
erSy6:4x, x2+!1lz
(1) 2s
j-*, e"d o.0e.g ero"Jgsodc$oo (xy !), (x2, yr) eoocod,
(2) s (3) 0 (4) :4
RoughWork
2t-AF.2016
57. The distance between the focii ofthe ellipse x : 3 cos 0, y: 4 .in 91,
x:3 cos 0,y:4 sin 0eo3 6$ 53gio o3162, o"41:er Sogg 5:.6o
(r) 2J1
(3) Jt
(2) iJ,
(4) iJl
58. The equations ofthe latus recta ofthe ellipse 9x2 +2r? -36x+ 50y- 164:0 are
O* + ZS1? - 36x + 50y - 164: 0 C Sr,)od 5S53g[o d::52, o.&oooSr:e.: $55dea.oJ
(1) x-4:0,x+2:0
(3) x+ 6:0,x-2:0
(2) t-6=0,x+2:0
(4) x+4:0,x+5:0
59. The values of m for which the line y : mx 't 2 becomes a tangent to the hyperbola
4x2 -9y2 - 36 it
lxz -Sf :36 era 5o.5eo5>cB, Sdf6p y: rzx + 2 53dp6+ s.Sa-sB rn dr56 sq:Serc
't-lit2l +-
J
4J'(4) +-J
)fi) +-
J
8(3) rt
Rough Work
82016 22-A
..\
tr60. The harmonic conjugate of (2,3.4) with respect to the points (3, -2,2), (6, -fi , a) is
(3, -2,2). (6, -17, -4) ao6:go a;{g, (2, 3, 4) o:::65 ir.o:6g6 6ocdr:r{6 aoc5:g
(i) (::i)
(3) [-'*.:.:)\ 5 4 5i
(2) []!._r.1)\5 s)
(ts _ -4)(4) I -.-
).- |(s 5 )
(2) (3) (4) 13
1
3
ql
r[,,1,
62. If the plane 56x + 4y + 9z:2016 meets the coordinate axes inA, B, c thenthe centroid ofthe triangle l-BC is
e"5 6oo 56x + 4y + 9z : 2016, Sd:.Jg'o5o A, B, C &o5oge: o $o(3qloo, ABC
q8&ao d:r55 3og!a.So
(r) (t2,168,224)
( 't'tt \(3) I i2. i68. -"', I
\ 3i
(2) (12,
(4) (,,,
158, tt2)
-168,+'l))
61. If a line makes ang^les a, p, y and 6 with the four diagonals of a cube, then the value ofsin2a + sin20 + sin2 y - 51n25 15
a,5 dq:, e.5 fuSo dr:S6 o.q)Jt$ so"e)ef a, fl 7, 6$eo"er: d!,
sin2a+ sin? B + tinzy+ sin25 a>s6 c.lS
4(l) ;J
Rough Work
n^q,^"iy'e"
o-\ /r--/-\ /'1 \\
"sYf-V,Y'^i r ,J P-->.1-li '\€82016 -N.! /
,
"*r) $
,
23-A
SFzs .,ry5op,*" 1V "-;/i
(.'.Y./\_,/ I
t s.t c"d"l
lczl63. The value(s) ofx for which the function
[l-* , x<1
,r(r)=](t-xX2-n), 1< x<2t^[3-, , x>2
fails to be continuous is (are)
(1) 1
(3) 3
(2)
(4)
2
All real numbers
2
.&J
)(2- *)
1-xI
/(x)=l(1-xl.3-,
eetu pJ)cDJo
(i) 1
(3) 3
it}5ro
6' *3' -2* +r2x
(log"2)logn3
log"6
, )c <l
,l<x<.2, x>2
eod:g x &::56 Ser5(o:)
(2)
(4) a"{55oq:ger:
64. Ltx-+0
(1)
/?)
(2)
(4)
1og" 5
0
Rough Work
82016 24-A
^. f,'+bx+c x<l65. D.fin" "lt")=1 . . Iff(x) isdifferentiableatx: l.then16-c,)-
[x , x>l
po$c$o I (x) il
('tlx'+bx+c . xcl
tG)=1[x , x>l
rr &d5r)go. x : 1 5{ /(x) er56o$cd:o ero::d, eo$y6o (b - c) :
(1) -2 (2) 0 (3) I (4) 2
66. If x : a is a root of multiplicity two of a polynomial equation/(r) : 0, then
x = a epi8 e"5 oJro$6 $556eoo /(x) :0 6::52, Boc6&6 es5;e!Sodo5 Sr>e:o eror:d,
(1) f'(a):f"(a):o(3) f'(a)+0+f"(a)
(2) "f" (a):f(a)=0
@) "f (a):f' ("):0;f" (a) + 0
[:67. lf y:log2(og2x), tnenff :
y =logz(log2 x) ero>d, eo$Jcb
log"2ttt
x loge x
dy_dx
(3) (xlog" x)logu2
(2)log,(2x)'
1
(4) *(tog2*)2
noug\$rx!/
t.EAtidF
NNU
25 -A
I
L' '-
68. The angle of intersection between the cuwesy2 + 12 = o2 nD
y2 + x2 : r2.,E so"s, *2 -f : o2.e SgS::o 5o6g de>
E(1) ;J
1t(2) i7t(3) -'o
and x2 -1? : o2,it
$65 $eoo
E(4\
12
69. If A > O, B > O and A + B -- f , then the maximum value of t an A tan B is
A>0,8> 0 So8ctrD A+B--
1
6
E
3eoo::d, er$yc{: tan I tan B dr56 6Of Seu$
I(3) , (4) J1(1)
1(2) ;l
7 0. The equation of the common tangent drawn to the curves y2 : g;s and r7 : -1 i,y2 :8x 5o0c6.:r xy : -1 epi 51s.e.:6: A,tS 650&& fpdpdq> o3:.:S1 S5:ddeao
(l) y:2x+ I
(3) y:x+2(2) 2y:x+6(4) 3y:8x+2
71. Suppose/(x) : x (x+3) (x1), x el-t, 41. Then a value
/'(c): 10 is
"f (*):x(x+3)(x)),x e[-1,4] er5osoo"o. (-1,\ ef f,(c):
&ooS
(1) 2 (2) t2
(3) 3
of c in (-1, 4) satisfi,ing
10,$ er&5dd coi:r66 e,5
(4)
.7
,
Rough Work
\
E 2016 26-A
5-t
72. rc l'3 "s' ar=j-(f {r1)*",then/(x):
5r
[*3 ns' dr=1;(71x1)+c erood. ersycic/(x):'5*
*3 3xz 6x 6
55',5',5*52x3-l5ll+3ox*6
(2)
(4)
(1)
(3)
-'l -)) -'l)-x--)-x"+)-x-o
53x3-7sxz+3ox-6
73. dx=(xz +2x+2)2
x +t(1)
x2 +2x+2
x +z(2)
2(x2 +2x+2)
*2 -z(3)
4(xz +2x+2)
1(;r+1)+c
-1,un '(x I )+c2
*ior-'(x+1)+c
1
--tan2
2(x -1\ 1 't ,1\ --^ a+-tan '(x+ l)+c(+''
62 +2x +2) 2
(C is an arbitrary constant)
(C e"S o5r51a;S "Edo"a)
Rough Work
82016 27-A
74. tf J
log(a2 + x2)dx=h(x)+c, then /z (x) =
!log1o2 + x2)dx=h(x)-c epo::d, er$ydo /r (x) :
(l) xlog(o2 * r'1*r*r'(|)
(2) x2log1a2-r'1-r-rtun'(])
(3) xlog{a2 + *2)-2* ,rr*u'(I)
(4) x2 log{a2 + 121+2* - * r^t(*)
I
75. Forx > o, ir J(toer)5 a=
'[,](rogr)s + a(togx)a +c(togx)3 + D(tosx)2 + E(logx)+ F] + constant.
thenA+B+C+D+E+F:
x>os. lloz*1s ar=
, [,]
(rog r)s + B ( log x)a + C (tog r)3 + D (\og x\2 + E(rog x) + ir] + ""r6o"a
ero::d, eobyd:l + B + C + D + E + F -(t) -44 (2) -42 (3) -40 *36(4)
Rough Work
82016 28-A
--2 8a376. Thearea included betu een the parabola y=L andthecurve / - ---;---:-- - is
4a (x" +4a")
8a35:0oir: v=' ^^ ests' (x' + 4a'1
g aDc& '6'53 tsa-ogo
(1)
(3)
Sqs"e3 5o{
,( ^ 8)a I ztt-- |
\, 3/
,( ^ 4)a I ltT-- |
I 3)
2x
- bo-bocDr S
4a
/ .)\o2l 2, +11( 3/
"( 4\a I lt+- |\. 3l
(2)
(4)
77. By the definition ofthe definite integral, the value of
0fl6 SSr6erSo &d5,55o
ri*(-L*-"--[Jr2-l "lrr-22
\_,11
l. . l-
t!n'-(n-r)' )
(1) It
lt(3) n
(2)
(4)
ft
2
1t
6
Rough Work
E 2016 29-A
a
u*(-L*++ +
"*-[ Jn2 _ I ,ln2 _22
r-fs*rcoa;l
lczl tr,/( ,z \
-/4 I x+- |
i8 I lr*;V*-%l )
8tr ^13
zxJj +t iJ2
1t
,l;o{J(1) (1\ (3) (4)
79. The solurion ol'the ditterential eouation h, y'\*(, - r*n-r v)dy-^---'-----r--""..\ - / [ )dx
esses $tusd.o (t+12)-(r-n""
(1) x etan rY :tan-t y * c
(3) 2x etan 'Y = shan
'Y - g
(C is an arbitrary constant)
(C e"5 cdr6;a;S i;do"a)
-r ,) dv
.)a*
(2)
(4)
IS
6 dr56 &dS
y g2tan 'y : e-lan 'y + c
x2 gtar, ly : 4g2tan-ty I 6
ii
80. The solution of the differential equation (Zx - + t, + \ ff+ (x - 2y + 1) = O 6
er55e$ $tusd.o (2*-4y+s)fi+@-zy+1)=0 arrsU +Os
(1) log ((2x4y)+3) : xly+6(3) tog [2(x1y)+5]: 2(x+y)+c
(c is an arbitrary constant)
(c e"5 o5r53'lp5 Qdo"a)
(2) tog [2(2x4y)+31 : 2(x-2y)+c
(4) log l4(x-2y)+sl : 4(x+2y)+c
Rough Work
82016 30 -A
fs*rc;;llczlPHYSICS
81. Match the list - I with list - II
A) Boltzmann constant
B) Coeflicient of viscosity
C) Water equivalent
D) Coefficient of thermal conductivity
6a 13oS 5Q5-l So 5€5-II "f a.l5d#c5r:.
3€6-I
D
D
trD
rV)
List - II
MLOTO
MrlT-l
MLT-3K*I
ML2T-2K-l
A)
B)
c)
D)
ef eI 5;5 3o"o6oeEa
Q,1te" t$eoso
Sti e6o"go6o
6* r'rr5d5
5(35 - II
MLO TO
ML-lT-l
MLT-3K1
}y'rL2T1K-l
r)
D
trI)
M
I
r$eo5o
The correct match in the following is
qSoE a'tSef 685 ad
(1) A-III; B-I; C-II;D-IV
(3) AJV; B-II;CJ; DJII
(2) AJII; B-II; C-I; D-IV
(4) AJV;B-I; CJI; D-III
Rough Work
82016 3l -A
,,,]i
82. Two trains, which are moving along different tracks in opposite directions are put on the same
track by mistake. On noticing the mistake, when the trains are 300 m apart the drivers start
slowing dou,n the trains. The graphs given below show decrease in their velocities as function
oftime. The separation betrveen the trains when both have stopped is
aoctu $Q5; $tgo 5>6 SE&AS Edet' ScdrseQ5laod* pdpSo $dlulS e"3 $c{e, 5D6So
&So6o5o"rd:. a.c3 u565$o 6 Sfrcdrcl (3:-or3, esc 300 m J6oeJ '451$3do pdp
dn"oSo e5flo5i.:o @doOoa-6. a"c3 3n'oeJ e5tf6e.: s'o 653:cscon'i{er 6a 18oO gr$o:
f:r&Qo"lor:. 6 Bodo pdp ao"5o "goe dd:S.:53$3c6: a"t3 5o65,alrdo
10 rG)
(1) 120m (2) 20m (3) 60 m (4) 280 m
83. Apoint object moves along an arc of a circle of radius'R'. Its velocity depends upon the
distance covered'S' as V:KJS where 'K' is a constant. If '0' is the angle between the
total acceleration and tangential acceleration, then
a"5 Ooa$6r$ SQO 'n'a"g&{o r{o e"S 53qs-6 o'5o 3oa6 @c6:"e5Qoa. cr$ 3t1o, erE
-25t r 0:-R
@o5re8oa5 drdo 'S' 5:d V:K\6 n- ego'd5&58. e52,6 K er5oSa "go'o5o. ar{o
65deo"CB 5ooctu S3o"; e556ea"eS 5o6g $oo '0'ero:cd
(1) tan9: (2) tar9: (3) tand: S
(4),2RS
2R
S
R
Rough Work
82016 32-A
-
t
84. A body projected from the ground reaches a point 'X' in its path after 3 seconds and from
there it reaches the ground after furlher 6 seconds. The v^ertical distance of the point'X'
from the ground is (acceleration due to gravity : 10 ms-2)
d:.1: 5oo& S${o dctua:eS a,5 sQb 6"e Sr'foef0 'X' eri ao6o65o 3 -i':S5ooef
dosa. e9 &od:$ Soo& 66:a"d 6 =o5soer$o dr"3rc dE5.5' qir"so 5oo& 'X'aodc$
o:r:S6 Je{ (t$Cu65 65deao : 10 ms-2)
(1) 30m (2) 60m (3) 80 m (4) 90 m
85. A pafticle of mass 'm' is suspended from a ceiling through a sffing of iength 'I.'. If the
particle moves in a horizontal circle ofradius 'r' as shown in the figure, then the speed of
the particle is
e.5 }SSS 5oo& 'L' +6$ SOn5 o-dod 'm'g555o'a r{e.: a,5 SeaoSo G3er66}6. SiJoe,
(4) s
t$."o$ l6on" (eao 'r'a"g&$o 6o $Aa $5:"odd 5;{o Eoo& rfOQod es Ssoo ddo
(r ) r (2) sl,
(3) 'le?
Rough \llrork
E 2016 33-A
tr86' A parlicle is placed at rest inside a hollow hemisphere of radius ,R,.
The co-efficient of
(2) i,-# l*\ -/
3R
8
87. A 1 kg ball moving with a speed of 6 ms-1 collides head-on with a 0.5 kg balr moving in the
, opposite direction with a speed of 9 ms-l. If the co-efficient ofrestitution i, ], m.
"n.ro,lost in the collision is
6 ms I SA.f 6c6r"€S{\SJ I kg ao& SEs6s E,re, 9 ms-l 56g .Joe{ 0.5 kg aoe3.f
5::q:-5rS cs&6r6o aOB:Sa. q5e-g5frS ,{r.S" +
ero:cd eo&{rrdoef d$S$o
(1) 303.4l (2) 66.7 J (3) . 33.3 J (4) 67.8l
Rough Work
82016 34 _ A
friction befween the parlicle and the hemisphere is F= rf,. The maximum height upto
lvhich the parlicle can remain stationarv is
'R'4"5&$5r: SORS eS*oJ er{6"do efso a,5 Sea'l& Ao,bo "ge3d 6oa,6. Seo.&S,
er6iffe'e3 SodS {o{ea r{rEo5o p:# epo::d Seao $o,boftsef +odrlo ,{06 Jee
Rfl)
2
l;(3t '" R
2
tr88. A ball is thrown vertically down Aom a height of 40 m from the ground with an initial
1'dvelocity 'v'. The ball hits the ground. loses , of its total mechanical energy and rebounds
back to the same height. If the acceleration due to gravity is 10ms-2, the value of 'v' ii
?iltuS 40 m J63 SooB a,6 oo8 'v' etO ld5!8 CQeo{n" 13od5o iSda656. a:o&
Id:.S:C e.S, tu:{o c5:"o1&5 A$ef
1S 5oe6 $efJo:: 5ods. erd J.{$5u dSsA. rtd:d5
"J5deoo 10 ms-2 ero"rd 'v' dl66 iero5
(l) 5 ms-r
(3) 15 ms-l
(2)
(4)
89. Three identical uniform thin metal rods form the three sides of an equilateral triangle. Ifthe moment of inertia ofthe system ofthese three rods about an axis passing through the
centroid of the triangle and perpeirdicular to the plane ofthe triangle is 'n' times the moment
of inertia ofone rod separately about an axis passing through the centre of the rod and
perpendicular to its length, the value of 'n' is
Sr:'cb $d565r5 b56e $SJc etfr{ 6Qu: a"5 $Soa"Xrr: 1&4$ao dr:56 5x"6o 4brocn-
5O;aSe. 1&4!a e5o.s3 eooofi- o'c Soqdqlo ,{:oa" d$ er$o 56on' 6a S::"dc SQe.:
SgSf a::56 a6e55 pi:-5oSo e.5 d{ s&n" a51Sy6o o"e }6$6: eoaon' 6o0u o"c
5o{g Ooen$ /uoo" #$ er$o $don- 6od a6e55 gn5os'cB 'n'BeD esorrd 'n'$ocS
10 msl
20 ms-l
(2) 6
(4) 12
(1) 3
(3) e
Rough Work
['2016 35-A
90.
(1) a*b (2)
a ---)b-a
(3)
<_-b a-b
(4)
91 . A particle is executing simple harmonic motion with an amplitude of 2 m. The difference
inthe magnitudes of its maximum accelelation and ma,rimum velocif is 4. The time period
of its oscillation and its velocity when it is I m away from the mean position are respectively.
e,5 Sgao 2 m 5o$5 SosJse, Sdd iro"ei65 rJoSS:: dcSNi$sJ8. dEf 65deafr: scocdr>
r{of di{sao Sos}easle Sodg 55e"g$5:: 4. ero::d 5o55Sr:e.: d::66 essg[s s"os::
5ooc6> es Seoo 5:"6g$o6 {5o 5oo& 1m d:"6od 45153d: SdSDer> 56Sn'
(2) L', 4'!i ^'-l(1) 2s, 2rE ms-l
aa(3) a s, 2J3 ms-' (4)
I
ms'/.L
- s. 4J3l
trTwo smooth and similar right angled prisms ale aranged on a smooth horizontal plane as
shown in the figure. The lower prism has a mass '3'times the upper prism. The prisms are
held in an initial position as shown and are then released. As the upper prism touches the
horizontal plane. the distance moved by the Iowerprism.is
Bo6: SoS;C 2.3 6@ e.:oe:$ea l8eifors-6 5Qs-o5: Su:oef rJr"o5d.>on" 5o51& $@a
S5:"odd 6oop erSooX&. $oa $QdS:: dr$2, 1655o"4 p S$So oj>:52, @$5o'aB
3 atJJ 6516. SJJ6eJn- itds"o: 5t:oef t5r"o5 $o-eret' 6.51S. ! 5Q$o $ea $SroeJd
elo-03 o"€ef$ $oa $$5o @cdrg3oas c5:"6o
<- b ----)
Rough Work
F.2016 36 -A
(1)r
' -l2Gm
f-s*rcoa;l
lczl92. Two bodies olmasses 'miand '9m' are placed at a distance'r'. The gravitational potential ar
a point on the line joining them, where gravitational field is zero, is
(G is universal gravitational constant)
'm' 5o0o5:c '9m' g55go-d:o: de.: 3o6: sQ{e.:$o 'r' d:"doef '6o;"d>. ;i3&. 5o:$
, 6df6e)-"r r$CDd5!L6o {r5gSoo$g Ao6$ Sf; &d:el5 }8{c6e5 Jo:S
(G erda Cd5 rtfue55 "6o"o5o)
^ -l4Gm -16Gm
-8Gm(3)r
(4)r
93. When aloadof80N is suspended from a string, its length is 101 mm. Ifaloadof 100 N is
suspended, its length is 102 mm. Ifa load of 160 N is suspended from it, then length ofthe
string is (Assume the area ofcross-section unchanged)
e.5 do1& 5oo& 80 N o a:-o.&; @e66"o55ydc o"& &dg 10i mm. erd "5o1eS
100 N
a-o.Q @o-66tu5S95: 6"e +60 i02 rnm. 6o1st 160 N a.o-sJ @e:.66"o$iyd: es
6o1S &d$ (6o1S er6;$6 Ba.ogoef 5rd:Sd6SoSSoSr:)
(1) 15.5 cm (2) 13.5 cm (3) 16.5 cm (4) 10.5 cm
- 94. A sphere ofmaterial ofrelative density 8 has a concentric spherical cavity andjust sinks in
water. If the radius ofthe sphere is 2 cm, then the volume of the cavity is
, &*rS &o$6 8 6o So$fr*So bS €o@S 6*e-s.d $icdoso sOE 6o& 5{3eJ So,'r- S!&ESa.
6"do ob56 a"g&$o 2 cm ero::d SdJ6o obrS& fu5 SBSreao
76.79.82.88"(l) T.r- (2) T.*- (3) T.*' (4) T.*-
Rough Work
I
82016 37-A
tr95 A hunter fired a metallic bullet of mass'mr kg from a gun towards an obstacle and it just
melts when it is stopped by the obstacle. The initial temperature of the bullet is 300 K. Iflthi of heat is absorbed by the obstacle, then the minimum velocity of the bullet is
[Melting point of bullet: 600 K;
Specific heat of bullet:0.03 cal gl 'C-1,
Latent heat of fusion of bullet: 6 cal 5ll
e.6 3i.:n"6r err)e 5oo& 'm'kg g555o"a 6o efir.{ rud0I5o er$d6o pOS.: =o03o"6o.
ruO055o ep$6'6o er3:55y6:, erd01 iyQn- 50E56. a:cO05 AO 6*6"5 300 K. es56"6o
1
75 Soei: '6rte; s-ileoo d6o5.:od ertrJb a>OeS dr:S6 SSf dt{o
[aDoui @5qJ55 $5o :600 K,
aroeS saff$S:: :0.03 cal t-l o6-1,
aDOu5 @5qJ55 r$q65. :6 cal g 1l
(1) 410 ms-r
(3) 460 ms-1
(2)
(4)
260 ms-l
310 ms-l
Rough Work
82016 38-A
Eii
96. 'M'. kg of water at't'oC is divided into two parts so that one part
converted into ice at OoC would release enough heat to vapourise the other
ol *us i,r'
'm'1<g@Sgo'a 6o e"5
equal to
[Specific heat of water: 1 cal g I 'C-1,
Latent heat of fusion ofice:80 cal g l,
Latent heat ofsteam:540 cal g 1l
t' "C 56 rfo 'M'kg Stic do6o q:'n'errr pdet ero6od
720640
e,:.t{o OoC
&6: d e:
by25%,
36%
5{ do Sooi$m 5r0, Bo65 er66r5o e.:-tc5afSSo 3o8or5:dr5: SofA t
mdbSa. eoo::d , a*S
t$d ea**s], : I cal gr oC 1,
Soodc 65ds$ 6rq*5r. : 80 cal g l,
er6qd55 drq*S. :540 cal 8ll720-t 640+t
(1) 640 - t (2) (3) (4)
97. A diatomic gas (y: 1.4) does 300 J work when it is expanded isobarically.'
the gas in this process is
2.5 a5$d5rso:S a"c6r:$ (y: 1.4) S5o 565 4"5$r5o aqa5S36)
66"6:ef a"o5::d16o ero6dc6:er&5 +go
(l) 1050 J (2) 950 J (3) 600 J (4)
98. When the absolute temperature ofthe source of a Camot heat engine is
its efficiency increases by 80%. The new efficiency ofthe engine is
a"5 s"6) 6$c6:o16o dr:52, a55o SdSo a'q6650 25% =oort5S56: 656 80%
=o0ir56. cScolelo ArSl 1S{ 6{el
(r) t2% (2) 24% (3) 48% (4)
RoughWork
*ll:
,*r
82016 39-A
a
99. A cylinder of fixed capacity 67 .2litres contains helium gas at STp. The amount of heatneeded to rise the temperature of the gas in the cylinder by 20 .C
is (R: 8.3 1 J mol-lK 1;
67.2 OeJ6 "Bd {oSfoSr.o 6o bOod6d STP 56 u.r"Oc$co a"cdr:g 5oa5o. ?:Ood6ef
r{e.: ;o5r$ 6*({650 20 "C -oot5:r.:6r er5$6A:5 6*dg (R: 8.31 J mol-lK-l)(1) 748 t (2) 374 J (3) 1000 J (4) s00 J
100. For a certain organ pipe, three successive resonance fiequencies are observed at425,595 and765 Hz, respectively. The length ofthe pipe is
(speed of sound in air : 340 ms l)
a,5 eso"S f,'(:"C8, 5r:.c6: ep5oo,5 *S:Xgo-go$o 5dc6n 425,595 ioocdl 765HzSg
i{So$oa"c!. erord nqo }66 (n"Oef 65CBr1o :340 ms-l)
(1) 0.5 m (2) 1m (3) 1.5 m (4) 2m
101 . A student holds a tuning fork oscillating at 170 Hz. He walks towards a wall at a constantspeed of2 ms ' . The beat lrequency ob_served by the student between the tuning fork and its
echo is (Velociry of sound - 342 ms t)
e,5 So"6Q 170 Hz $$ 5o3:Q51 d;e doa"s1 Sq5oe6J. esd6o 2 *r-l qO S&ef e,S
n-5EO 56Qo)dr. d;e5oes.C3 Soocdrr 6"& 1;5S6503 SodE ao"EB r15o0o,)S C(:3od5
i'S:g5go (65c di{o 342 ms-l)
(1) 2.sHz (2) 3Hz (3) tHz (4) 2Hz
102. An infinitely long rod lies along the axis of a concave mirror of focal length'f '. The nearerend of the rod is at a distance u, (u > f) from the mirror. It's image will have a length
er5ouJic$ $5$i{o e.6 $Qe 'f 'o'q55oe5doi{o e.6 Jgt:-s.d dd;eo er{o Boo& .aoa"d:. SQ
o3,r:56 S5:3 ')5d, 6d3eoo 5oo6 u (u > f) 6r6oef 6od o"0 $&Ooao &69
82016 40-A
il
(1) u+f (2) u-f (r, u+f (4)u-ff2f2
I 03. In Young's double slit experimenl. red light ofwavelength 6000 A is used and the n1h brighr
fringe is obtained at a point 'P' on the screen. Keeping the same setting, the source of lightis replaced by green light ofwavetength 5000 A and now (n+l)th bright fringe is obtained at
the point P on the screen. The value of 'n' is
cSoo6 aocc ISOS $o3c"r(oet' 6000 A d6or(dd*5o .r(o'JCud; s-o&& o"6, 6dbJd
'P' Aoc5:$ 5{ n 5 ao:d: SeSC L:U;fa"O. (dri{ er5oo55o S>.d>J dc$:6!o@- eoer.f,
-6otl, s-o8 a5s-e1 5000 A "SOoXp6go
r{o er6oS'5; s-o8 a55od SrO36d*g,
6d$d P aod:g 5( (n+1) 5 Bo,{: f{ 5d36oa. n aws
(1) 4 (2) 5 (3) 6
104. Two charges each of charge + 10 pc are kept on Y-axis at y : -a and y : +a
respectively. Another point charge -20 pc is placed at the origin and given a
small displacement x (x<<a) along X-axis. The force acting on the point charge is
/L a.rd u arein rnetres-
I gr l09Nm2 c-2 I
| 4r €o )
a,S5d6t^3 + 10 pc egJ.to do Bodo egJa"oSc Y-er{o=o y: -a SoOoJoo
!: +a 5{ 6.or5a:65e. -20 prc esJdo rler a"( 0o6o erJa'C1 Scc.o0o6og 5{6o0 X-er{o BooB 55o; $Sldodo x (x<<a) 5o SOEot)S o"Si: S&d+o aoo
(,\I x 5:oo5:: a Secdef . ' -9.109 Nr-rr2 c-2 |
\. - '4ne6 )
(1) fNa-
(2) *- (3) $N (4) $N
(4) 3
Rough Work
4t-AE 2016
trcharges, each 2 pC lie at the vertices ofa right angled triangle as shown in
. Forces on the charge at B due to the charges at A and C respectively are F 1 and
F2. The angle between their resultant force and F2 is
e"s2,52,e3 2 pC 6e: Sd5SSrSpS eg3a"oc 5C.:oet' '5r5e;&5
ooa:$ea 181bao Sr:.ere.: 5{
6r)*. B ${ rlo'egdds::a ASooosD C 5{ r{o es3d$:o $o5 aosr:er:
5oEc6x F2. 6a a:o5.>:o 60.5 a:q:'CB F2 S 5o6g 6o $o5r:
105.
4m
o\:t16)'(
BL
tan(2) '
(s)1.7.1
20v
30v
60v
o
30 cm
),iV,n'r
(4) 9u-r-(2) (3)(1 4u* 'r-
E, ?1016 42 - A
,/re\ ,(t\(3) *' '[;J (4) ,* '[r)
C
(1)
106. The figure shows equipotential surfaces concentric at'O'. The magnitude of electric field
at a distaince 'r' meters from 'O' is
5bo ,5o6o 'O'!:5 to6Son" 6er $5o $cl{c6:5 6e.:-oJ i>:"flo,5a&5&. 'O' 5:o& 'r' fuod
d,:.doef sc5:55 {@ ie.::S
fs*rc;;llczl
107. Aregion contains auniform electric field E:1f Oi+:Oj; Vm-I. A and B are two points in
the field at (1,2,0) m and (2, 1,3) m respectively. The work done when a charge of0.8 C
moves from A to B in a parabolic path is
e,5 glo65oo60 b56e s6oE5$1"5 &p5.! E:ttOir:Oj; Vml. ASooos, Be.qdaod)
Ooci$oo es {@od Scu$n" (1, 2. 0) m sooctu 12, I. 3) m 5{
A 5oo& B 3 5o'5oc6: S:"foef SAOSOdT a0E6 50
(1) 8J (2) 80 J (3) 40 J
108. When a long straight uniform rod is connected across an ideal cell, the drift velocity ofelectrons in it is v. If a uniform hole is made along the axis of the rod and the same battery
is used, then the drift velocity of electrons becomes
tr
+514. 0.8 C esBd5r:
(4) 16 J
(1) v
s51c +dps b66s
(2) >v (3) <v
o"n SQC es6d; {oure; SObSOdJ,
(4) zero
ccefc JolgSoo @'g 56 v.
es 5ft ergo aoeJ& b56& do6re; S"o, Sodo erd o'gt:6& 4"6d, a{6 SQd Je.:1g$oe>
t.[ sa
(1) v (2) >v (3) <v (4) soSJ
109. In a meter bridge experiment, when a nichrome wire is in the right gap. the balancing lengrh
is 60 cm. When the nichrome wire is uniformly stretched to increase its length by 20%o and
again connected in the right gap, the new balancing length is nearly
Sreau: pg 65d:.rloef S\re EO q:'9.f a.g e$$ &rl5o Sob566 Soc5:e5 *66 60 cm.
a1$5: &6 &6650 20% -ocu65dr: 5S6en" &.{6tu Sode Su&pO w'$ef So3:d, 1sg1
$o6;o5 *66 $o5rd:n"
(3) 51cm(l) 6l cm (2) 31cm (4) 41cm
Rough Work
E,2016 43 -A
( s.'tc-d. l
lczl110. A loop of flexible conducting wire lies in a magnetic field of 2.0 T with its plane
perpendicular to the held. The length of the wire is I m. When a current of 1.1 A is passed
through the loop. it opens into a circle, then the tension developed in the wire is
e.5 +A &6 5e-:c6:o d::6; doo 2.0 T ec$:i1od tl6od ooaon- '608' ee &dld$ 1 m'
o"C o"5o. 1.1A sd:gd 5ob5 eg6 S;qs'dorr Sr'ESa. er$Sd: es &det' 56Jdo 'JSS"'
(1) 0.1s N
(3) 0.3s N
(2) 0.25 N
(4) 0.45 N
11 1. A charge q is spread uniformly over an isolated ring of radius'R'. The ring is rotated about
its natural axis with an angular velocity '<o'. Magnetic dipole moment of the ring is
Ra"g+$sr: do b(6s Eor{:=o qer3d5:.:5g6e.i" SdtJar&sa. ooa{: eJs Sr'a er$o 56on-
co feScUc 365D6" g55oeoo d!, o'0 erc$ci1oe5 S5635 pr5o6o
ot,lR2 qoR qo(l ) + Qt ? (3) qoR2 (4)
2R
112. A magnetic dipole of moment 2.5 Amz is free to rotate about a vertical axis passing
through its centre. It is released from East-West direction. Its kinetic energy at the moment
it takes North-South position is (B,1 : 3 x 10-5 t).
2.5 Am2 La"SogS) t{o a,5 erc6:i1od 456$5:.: o"e Sodg Oocb$ t{:oa" 3te{:51 &Qcer:dl
er{o 5don" *5'5;n" g55ootu 8o6r{od:. gi 6563a"&1 etu63-6d5od Ad 5oo& $dode)
drg, 6{d-6$ea EdSo d65odr, o-e r{sd$ (BH:3x10-5 T)
(1) s0 rrJ (2) 100 pJ (3) 175 pJ (4) 751t1
Rough Work
E 2016 44-A
113. A branch of a circuit is shown in the figure. If current is decreasing at the
trrate of
i03 As-l, the potential difference between A and B is
e,6 Se.:oj:oefo e,S q'n'&J $iJod ':$'"'10'6' sf::55 654"s-5r:
l* ffnflmr .BI g'nH
103 Asl .s'5J$ eJqer,
(4) 2v4V
(3) 10 V
114. The natural frequency ofanLC circuit is l25kHz.Whenthe capacitor is totally filledwith
a dielectric matlrial, the natural frequency decreases by 25 kHz. Dielectric constant ofthe
material is nearlY
LCSoc6c SXra #5:{55o l25ld1z.3}'"rb65o o'd6 So"$o"f {vQn'cob553dc $*ra
*5:{55,oef0 e5K;5o 25 kHz 6'66 b6'g 6'65 tuo"odo $c5rd:n"
(1) 3.33 (2) 2.t2 (3) 1.s6 (4) 1.e 1
I 1 5. choose the correct sequence ofthe radiation sources in increasing order ofthe wavelength
of electromagnetic waves produced by them '
( 1) X-ray tube, Magnetron valve, Radio active source, Sodium lamp
(2) Radio active source, X-ray tube, Sodium 1amp, Magqetron valve
(3) X-ray tube, Magtetron valve, Sodium lamp, Radio active source
(4) Magnetron valve, Sodium lamp, X-ray tube, Radio active source
66odp$5o i:oi 155ooef a,l;$ Sc$56c6:i1o6 ssdeo aSs"o 535 $5:"s; Jot$s$o5r'
(1) X-SdEoo'do, tuS{t-S o"do, B&a:' a'E&g es550, Rr&cd:o 65o
(2) AAd:,A"OgS a55o, X-Sdeao"do, ff&c6:o 66o, tu5t[e;-S o"do
(3) X-Bdeocdo, 5:"5r[t:'5 o-do, d'6c$co 6tro, 6&d)'4"065 a55o
(4) 5J".$r'5 o"do, RF&c6:o 63o, X-Sdeao"So, d&Aro"OgS a55o
RoughWork
-eod, ASoscSr: B o Xr:6g &6{cSce5 dc"
A
(1) 1v
24, 7A
(2) sv
E 201645 -A
f--s-i c,"d" I
lczli 16. A photo sensitive metallic surface emits electrons when X-rays of wavelength'1,' fall on it.
The de Broglie wavelength of the emitted electrons is Q.{eglect the work function of the
surface, m is mass of the electron. h-Planck's constant, c-velocity oflight)
'1,' 6dodd$go SOES X-Sdeo.o: e.5 ilUf ef*r{ .5oo-o $e5$do JeLESoe.6qdo
ado,{:e6co8. 6g0d Je.:qg5oo A1e:-o$ SdodA$5o (6oo $e653rc6r01 e$g0ot5:S::,
m Je.:qg5o 1d55o-4, h - $oS fio.o6o, c - s-o8 3do)
E^" th r0) r/ * \2t {r_.
ffi; ,Gi(3) { r,i e) {;
117 . An electron in a hydrogen atom undergoes a transition from a higher energy levei to a '
lowerenergy level. The incorrect statement of the following is
( I ) Kinetic energy of the electron increases
(2) Velocity ofthe electron increases
( 3 ) Angular momentum of the electron remains conslant
(4) Wavelength of de-Broglie wave associated with the motion of electron decreases
e"5 ir1d"a5 bd5rso$eJfe JotgSo erOS{$ Sor: 5oo& ero;d$ Qo:rS 6o155oeoo Bo658.
5a lBoA @5#o.e.:ef SEo3rSA s"oa
(1) Jo1g5o dead! =.:tl:tu5o
12) Jo1g5o 3i1o =":d:t{:$o
(3) Jerqg5o SeBc6 @s5dtlo "66on" *odb$o
(4) Jo1g5o #ero'&t es5oao6 &gro$ 6dor{o o3::56 eJdoi{p$5o e5ifSo.
Rough Work
82016 46-A
1 i 8. The radius of germanium (Ge) nuclide is measured to be twice the radius of lRe ' The
number of nucleons in Ge will be
e660c6:o (Ge) Sr"r:5 ;:"5&$o,
'6od 5:'5So5:"Soe.: $oer5
(1) 72
(3) 74
119. For a common-emitter traflsistor amplifier, the cunent gain is 60. If the emitter current is
]ne a"g+gaS ao6o 4d.15;6s $o5o&54' Ge d
(2) 73
(4) 7s
51Q 60. aqd ec$gd So"*ro 6.6 mA ePo:6
(2) 0.108mA
(4) 0.343 mA
120. lf arransmining antenna ofheight l05m is placed on a hill. then its coverage area is
e.5 so6} 105 m Jelrlo p5}d esoao";so a.oas$3d:, el8 +oser: elo6o#i{er 3a.o5o
6.6 mA then.its base current is
65D&a '6gd $:-c;$6 s{s"sB @o"rr
es6"d ec$gd @o"Xro
(1) 6.492m4
(3) 4.208 mA
(1) 4224k$r2
(3) 6400Wn2
(2) 3264kri2
(4) 4864 km2
R0ugh Work
E 201647-A
trCHEM I STRY
121, In which ofthe following, the product of uncerlainity in velocity and uncertainity in position
of a micro particle of mass 'm' is not less than
'm' 655go"Ai{o S:"foSeoo of,r56 lr{oefe er&A;e!65o, S5oefe er&A;6e55oo o3o Cu:$
rSoB a-Eef d$d,ur 6$r,5 s.6o
h(4) -xm+7t
-3n(1) h'-m
h()\ _\ m1n
h1(3) . ^-+,Im
122. An element has [Ar] 3d1 configuration in its +2 oxidation state. Its position in theperiodic table is
(1) period-3,group-3
(3) period-4. group-3
+2 es835dea Q&ef e,S 5::"e.:s.$3 [Ar] 3d1
5r:.o5o o3::66 $5o
(1) 6doc6r5-3, (lO-3
(3) 50c$5-4, ({J"O-3
(2) period-3, group-7
(4) period-3, group-9
JolgS io"g$o 6$;6. er5g5 $eflSef es
5ocs:E-3,6:.0-7
bocsrS-3, dr6-9
(2)
(4)
123. Inwhich ofthe following molecules allbond lengths are not equal?
poE ereo$eref er$; a:o{ Pggo: SSrSorr dCa 5a?
(1) SFo (2) PCr5 (3) BCl3 (4) CCr4
Rough Work
E.2016 48-A
124. In which of the following molecules maximum number of lone pairs is present on the
central atom?
13oB ereo:$e;ef 3o@d 56$rea:$ 5:5 r{o$ Soa5ef e'otc0 Jertg5 aobo: 65JA b8?
(1) NH: (2) Ito (3) c1F: (4) XeF2
125. which one of the following is the kinetic energy of a gaseous mixture containing 3 g of
hydrogen and 80 g ofoxygen at temperature T(K) ?
TG) 6qdd 5( 3 gl1@"45, 80 g essJas r{o a's a"ojc':
;:.e3et' !)a?
(1) 3RT (2) 6Rr (3) 4RT
So@5oo d:c52, dead$ lBoE
(4) 8RT
|26.A,B,CandDarefourdifferentgaseswithcriticaltempe1atures304.i,154.3,405.5and126.0 K respectively. While cooling the gas which gets liquified first is
A, B, C, D erd o'o:& &5; a"osr:$o Soa{ tffdejo: $6:i>n" 304'1' 154'3' 405'5
5oOc6D 126.0 K r5oodt$5i9e5: B::6c'rn" 65qJ55o Aod a"cdrb
(4) c(2) A
l2.T.4omlofxMKMnoasolutionisrequiredtoIeactcompletelywith200mlof0.02M
oxalic acid solution in acidic medium' The value of x iS
200 sJ.O. 0.02 M esrgos eQ p"Ssao$ fQn- $65 8o6t.r&3 40 ic'oo 'x M KMnOa
1o"$oo, esS3 65o$oef eSSd5o$otuoa' 6a rl65ef 4 ser:S
(1) 0.04 (2) 0.01 (3) 0.03 (4) 0.02
(i) B (3) D
Rough Work
E 201649-A
tr128. Giventhat
. C,"r -Or,o, -+ COr,-\; AH'- -xkJ
2CO,.1 +021"1 + 2CO,r") '41Jo = -ykJ. \S,,
The enthalpy of formation ofCO will be
A/uS afl;S $556ea-e.:5o er{ CO d::56 $oiiro JoqrOS Cer:b
C 14o1 + 021o"; -+ CO2 1;.1 i AH' = -x kJ
2CO1p-1 +021-) -+ 2CO2(,,) 6g" = -ykJ
v-2x v -2x(1) -3 Q) -, (3)2t- y
129. At 400 K, in a 1.0L vessel N2Oa is allowed to attain equilibrium
NrOr,"., + 2NOr,-,-\ E,r
At equilibrium the total presswe is 600 mm Hg, when 20% of N2oa is dissociated. The Kovalue for the reaction is
400 K56 1.0 OtJ6 )1e5e$ N2Oaq3oa S5oe"ftes $oaSB
N2Oa16";* 2NO2(a")
20%N2O4S{ocrso ioasigdo $;ne."g@ S{ uglo SaSo 600 eJ.5) 6SJ$J6o ee .5dS
do56 K, &er:S
(1) 50 (2) 100 (3) 1s0 (4) 200
Rough Work
82016 50 -A
x- y2
(4)
130. In which of the following salts only cationic hydrolysis is involved?
13oB o5eo-oef b o5eoo, €Sero Seccdr5 aosdi)eo-$S et'56e6o6?
(1) cH3cooNH4
(3) NH4C1
(2) CH3COONa
(4) Na2SOa
131. Calgon is
s'er5 er5o56
(1) Na2lIPOa
(3) Na6P6O1s
(2) Na3POa
(4) NaH2PO4
132. Consider the following statements.
I) Cs+ ion is more highly hydrated than other alkali metal ions
tr) Among the alkali metals, only lithium forms a stable nitride by direct combination
with nitrogen
Among alkali metals Li, Na, K, Rb, the metal, Rb has the highest metting point
Among alkali metals Li, Na, K, Rb only Li forms peroxide when heated with oxygen
SSdeae.rSo 503OoJo&.
Cs+ epoXrS ael6 y6 ef*r esc6:'5er 5oB er66on'l1@il5 aoel:So
g.d ef*fe.:ef OQo5oo 5>653: 3on- ppfase gertu "g6p5 pg5$o
m)
M13o6
D
tr)
m)
M
drbSo
(3) III (4) rv
Li, Na, K, Rb, 9,6 efr$e.:et' Rb 5o esOS 165{$5 S5o '6o&5o
Li, Na, K, Rb g"d ef*rod Li $"@fu esB;a5ef 3ed"o$66: =oo"B35$o 1636'5c5o
The corect statement is
5ri., $ps ssdeo ba?
(1) r (2) II
Rough Work
E 2016 51 -A
1 3 3. Asserlion (A) : AlCl3 exists as a dimer through halogen bridged bonds.
Reason (R) : Alcl3 gets stability by accepting electrons from the bridged halogen.( i ) Both (A) and (R) are true and (R) is the corect explanation of (A)(2) Both (A) and (R) are true but (R) is not the correct explanation of (A)(3 ) (A ) is true. but (R) is nor rue(4) (A) is nor rrue. bur (R) is true
Ca;e5o (A): {fefas a"de ao6.oef AlCl3 psoarp .6o6:5o.
s"6eao (R): a-d6 *fefa5 Soo& Je.:q5er5c b55oots:c.r SoS AICI3fide-5c1 *o6:io.(1) (A) 5oo cs.:r (R) w ao6:. sBSs SoBc6) (A) 60 (R) SBS csdeo
(2) (A) Sooctu (R) e.r: Ao6:" $BSS s.s (A) SD (R) $BS ssdeo s"dr
. (3) (A) sps8 s-c (R) $B56 s.c$
(4) (A) $358 s-d: s.c (R) SpS6
134. Which of the following causes
"Blue baby syndrome"
(1) High concentration of lead in drinking water
(2) High concentration of sulphates in drinking water
(3) High concentration ofnitrates in drinking water
(4) High concentration of copper in drinking water
lBoB a-&ef SOA€ R o@,Sr(Blue baby syndrome) So SOnod$S6 bA?
1o"d$u3ef 65 es6S n"66ef 6o6otc be$
1o"i SOef 6d;tr:oc es05 n 66et 6odot: Se.:S
1e"d St3ef E@u"* ep05 n"6"JeJ 6o6:tr SoS
1e"i $eef s.i:6 er0d n-6eJef *.ocfub SoS
(1)
(2)
(3)
(4)
Rough Work
82016 52-A
135. Which of the following belongs to the homologous series of C5H3O2N?
6 $oB a"Oet' C5H8O2N o3oS2, S5oa"e5 €e'3S tso65s 5A?
(1) c6H10o3N (2) C#8O2N2 (3) C6H10O2N2 (4) c6Hr0o2N
136. In Dumas method, 0.3 g of an organic compound gave 45 mL of nitrogen at STP. The
percentage ol nitrogen is
6;"5515 66se56 0.3 gr. o 5d;5 53rgd5o STP 56 45 mL o F$'sSfD arQloa' 3Ps{aS
a"6o Jo6?
(1) t6.e (2) 18.7 (3) 23.2 (4) 2e.6
137. TheIIIPACnameof
(CHi)2 CH-{H-CH-{H-CH-{H {H3 is
I
CzHs
(1) 2,7 -dtmethYl -3, 5-nonadiene
12) 2. 7-dimethyl -2-ethylheptadiene
(3) 2-methyl-7-ethy1 - 3, 5-octadiene
g/ t,1-dierethyl-6-ethyl-2, 4-heptadiene
(CH3)2 CH-CH:CH-CH:CH-CH-CH3 d!g2, IllPACrod:
I
CzHs
(l) 2. 7-8tuP5-3, 5-,$o"P65
(2) 2, 7-E5rp5-2-ePes-.r{P6s
(3) 2-tupe5-7-aPe5-3, 5-es6P65
(4) 1, 1-p5:Fes-6-ePe5-2, 4-="r{F65
Rough Work
F.20t6 53 -A
tr138. Match the following.
LIST-I
(magnetic property)
A) Ferromagnetic
B) Anti lerro magnetic
C) Ferri magnetic
D) Para magnetic
LIST-II
(substahce)
1) 02
2) CrOz
3) MnO
4) Fe3O4
5) cdk
565 - II, €.)
(ro"{o)
1) 02
2) CrOz
3) MnO
4) Fe3Oa
5) C6Ir6
qSoA a"d3&
$€s-r
(eectudtoir 6O&o)
A) -o16" ero5:iXoe5e55o
B) cdrod3 =oLderc6ciXo6el5o
C) -+16 erc6cilodeS5o
D) )o" erc6:iXoe!65o
The correct answer is
$0do5 $5>o"5o
ABCD(1)3 2 4 I
(2)2 3 4 1
(3)1 3 s 4
(4)4 2 3 s
a65dt5:5::.
Rough Work
54 -A820t6
fs*-t c"d. I
lczl13g. The vapour pressures ofpure benzene and toluene are 160 and 60 mm Hg respectively. The
mole fraction ofbenzene in vapour phase in contact with equimolar soiution ofbenzene
and loluene is
668od5,d:$tv05oa-irri:6o'o:56c5mi60,60mmHgn-'*o';or:'55)!5a;"er5
n'66ertloAodS,tyosegr5eoouf,rc6::@5fet'5o562roet'5ododS3r'e5q:-t{o
D oc5
(1) 0.073 (2) 0.027 (3) 0.27 (4) 0.'73
140. 6 g ofa non volatile, non electrolyte X dissolved in 100 g ofwater freezes at -{'93'C' The
molar mass of X in g mol l is (K1of H2O: 1'86 K kg mol-l)
6 g era"i5&o, eoe5o55 e?fu -":o'$o Xc 100 g SuSef Son bdJ6'15 g:'Seao -0'93'C 5f;
6DSqJ55o tsoa5a. X drlsl, aroi 6s5oa g mol l e:d (H2O $ Kr: 1'86 K kg mol l)
(1) 60 (2) 140 (3) 180 (4) r20
141. The products obtained at the cathode and anode respectively during the electrolysis of
aqueous K2SO4 solution using platinum electrodes are
Jd3$o JoS65o'6i:drEort K2SOaaogrSo'eJ 36E6$a€oo ao"o$$6: s'6'5' eg'$6ce:
5{ 5o;d bo'qo: 56(>n-
(1) oz,Hz Q) Hr,Oz (3) H2,SO2 (4) K'SO2
142. The slope ofthe graph drawn between /n k and 1/T as perArrhenius equation gives the value
(R: gas constant, Eu:Activation energy)
ee*cc$r5 65:56eao esQ-6on" /n k 6o 1iT 5c A'rS 6p"5tcoef a-oc so:55o (r:")od6
(R: a"ctu$o"oSo, Er: aQaS d$)
R(1) ELa
(2) ?D
(3) E-R
(4) E^
Rough Work
E 20165s-A
143. Which is not the correct statement in respect of chemisorption?( 1 ) Highly specific adsorption (2) Iueversible adsorption(3) Multilayered adsorption (4) High enthalpy ofadsorption
d&c6)5 .erQ66i1eao GSo&5J{15)S! Soaoeort 13oA Ssdeooef bA SOo3JSA s"6j?
(1) es6565 $a$e55o 5OR5 eo0aaileao (2) es85dd ca66ifieao
(3) a:iru*6o erQfXreao (4) ered Jo6"O3 ere#J1eoo
144. Which of the following is carbonate ore?
(1) Cuprite (2) Siderite (3) Zincite (4) Bauxite
6 18oE a"&ef s,A;3i^:,: O"itu6 5S?
( l) 5.:5@5 (2t todpr.t (3) *osd (4) a.Bpes
145. Which one of the.follou,ing statements is not correct?
( 1) 03 is used as germicide
(2) In 03, O O bond length is identical with that of molecular oxygen' (3) 05 isanoxidisingagent
(4) The shape of 03 molecule is angular
, 6oA Ssdeooe-f 5E So5358 s"dt?
(1) 03 5o 18
Cc Soif0n" df of,J.no6J6
(2) Oj ef O-O arod p$o. es3"la5 ersa:g ,od p$Joe f5:.Som 6o65>(3) 03 e"g eegJ6de8
(4) 03 eoeo$Su $eEcUl ess-do 6o6o5o
146. Which of the following reactions does not take place?
13oB r.5d5e-re)f a6.(CA bB?
(1) Fr+2Cl -+2F- +Ct, (2) Br2+2I- -+2Br- +1,
(3) ct, +2Br- -+ 2cl- +Br2 (4) Ctr+2F -+ 2Cl- +F,
Rough Work
s6 -A82016
trt s"tc"d. I
lczl147. Which ofthe following statements regarding sulphur is not correct?
(1) At about 1000K, it mainly consists of 52 molecules
(2) The oxidation state ofsulphur is never less than +4 in its compounds
(3) 52 molecule is Paramagnetic
(4) Rhombic sulphur is readily soluble in C52
5 e,:r65o EoBS r8oE i5deoeeit bA $OdcSE s"6?
o"o"6 1000K 5{ o"Cd Sr:pgon- 52eoeoc$o.> 6odc5o.
a"d3 Sfugdo'oef $e.:;6+4 e8";6deo fi@ SoE 6$2,5 er8";Sdea QeO Srrto$6o.
52 erea:$So Jo" erc$cilo6 66go 6odc5o
o-oDS Se.:r6 CS.,Sodo Sv0n' 5d:1u5o.
(1)
(2)
(3)
(4)
148. Which of the following reactions does not involve, liberation of bxygen?
rSoE ,56ee.reJ eg3raS5o Sdr6e dc6CE b6?!U
(1) XeF4 +H2O -+
(3) XeF, + H2O ->
(2) XeFa + O2F2 ->
(4) XeF6 + H2O -+
149. Select the correct IUPAC name ol [Co(NH3 )s(COi )]Cl
( 1) Penta ammonia carbonate cobalt QII) chloride
(2) Pentammine carbonate cobalt chloride
(3) Pentammine carbonato cobalt (II) chloride
(4) Cobalt ([I) pentammine carbonate chloride
[ColNur;riCO:)]C1 5oa5o o3-r:56 sEs IUPAC?)650 tuQo6o8
(1) =oot:. eoar6&c$r s"o)Bu5 $a"f (III) {pE(2) =ooe.:" JpS s"6';3e5 ea"e[ ffiE(3) =oor"r JpS s"aldof sa-s [II) frE(4) Se.:"S GII) -ood:' J&5 s"o)Bef s"a6
Rough Work
82016 57-A
tr150. Which of the following characteristics of the transition metals is associated with their
catalytic activiry?
(i) Colour ofhydrated ions
(2) Diamagneticbehaviour
(3) Paramagneticbehaviour
(4) Variable oxidation states
5o5g[5 ef*re> 13oB er0o'Se36 6o'6oef 4"€3 6.q6365 9o6$r $oaoOoASB bE?
lI@65 coc6:.5e.: doiJ:
6o5r erc6:i1oe5 $5a:.5o
)o" ercd:Qo6 $5e:-5o
Dfr"rd crgJgdea "E&e::
(1)
(2)
(3)
(4)
l
1 5 1 . Observe the following polymers
t
PHBV
(A)
Nylon 2-nylon 6
(B)
Glyptal
(c)
nle5
(c)
(3) (D)
Bakelite
(D)
Biodegradable polymer(s) from the above is/are
13oA )O5o5o5o 58&0ot5:51
PT{BV JelJ l-JeJ-J O
(A) (B)
=o a'(3ef d555SJe, )O5o5(er)
(1) (c) (2) (A),(B)
2]Se)CJ
(D)
(4) (c), (D)
Rough Work
82016 58-A
fs.tc"d. I
[il tri 52. Observe the following statements
i) Sucrose has glYcosidic linkage
ii) Cellulose is present in both plants and animals
iii) Lactose contains D-galactose and D-glucose units
6a lSoB c$6soe:$o $o&OotS:S::
i) 5cr$5eJ E$=o&S aod5r5;6
ii) -oo:5ef€ a::S2roef5o Sooc$J 8oe$6od5o 'ao0::o6
iiD o'S6ef D-n"er{€ SDocS$ D-6*Sd c$::"Stq t51$
The correct statements are
$Odo5 S5doo:
(2) (i), (iD
(4) (i), (iii)
153. Identi$, the antioxidant used in foods
( I ) Aspartame
(3) Ortho-sulPhobenzimide
e*f d Scrgerd '6$oirEodc c$:'ot3
(1) ersJQs:
(3) e:d-$dr BodQ:6(;lq/
Sodium benzoate
Butylated hydroxY toluene
r{:Qo '5c
5:>
ir"&oJco Ao#d:U5
?:lgpd65 -o'1c8;0f05
(2)
(4)
e835deBS
(2)
(4)
RoughWork
82016 59 -A
trn4. A:
tlrru., cH3cr--!sghe-
This reaclion is known as
(l) Wurlz-Fittigreaction
(3) Fittig reaction
. cH3
+2NaCl
(2) Wurtz reaction
(4) Friedei-craftsreaction
CX"' +2Na+cH3cl $& dd65 > Ctrt''
5a rX6g5o SSooUrd:?
(1) aS€ - 3:SF rrdS
(3) 3:€5 *oS
+2NaCl
(2) *f,F 156g
(4) ti)65-E"EJ #dE
155. What is Z in the following sequence of reactions?
2-methyl-2-bromo propane ;fu X--lz9-+z
6 go8 r5o"ggSooef Z b8?
2-tupe5 2-1tr3:. r&1,s ;J$il x Hzo >Z
(1) propane
(3) 2-methylpropane
(1) @*os
(3) 2-5:pe5 6fo5
(2) 2-methylpropene
(4) 2-methyl butane
(2) 2-tuEd L&5s
(4) 2-5cAd arSd5
Rough Work
60-A82016
I
156. In which ofthe following reactions the product is not correct?
(1) CHTCHO-!418a"+CH3CH2OH
(3; cu,cH2cHo-rffir.* cH3cH2cH3
(4) cH3cH2cHo--Iy44-+cH3cH2cooH
5a q3oa S6ge.:ef deef 13c6:'a555) $oS)Ss s"do?
(2) CH3COCH3 -j+ CH3-CH-CH3
OH
(1)
(2)
(3)
(4)
cH3cHo --!4!q4-+ cH3cH2oH
CH3COCH3 +#+ CH3-CH- CH 3
OH
cn rcHrcuo 1ffi[ffi" ral cH3cH2cH j
cH3cH2cHo --51994--+ cH 3 cH2cooH
E 2016 61 -A
I57. Identi$' the name of the following reaction
(x.t"--sexu-A H:o , CI,-t*
(I) Gatlerman - Koch reaclion
(3) Stephen reaction
qSoA rJdg 6o56 +oct5o /uQo{S:r
(2) Gatterman reaction
(4) Etard reaction
(1-t''--sexu-A H:o* , CX-"'o
f l) n-c.:55o5 - $'5 .J6ee)
(3) "E=os sos
(2) n"er55o5 156g
(a) au:'f 'Jdg
15 8.
cH3oH--!ql+o rcN n" ""i86' ,g
(1) CH3CH2OH
(3) CH3COOH
(2) CH3CHO
(4) HOCH2{F{2OH
Rough Work
82016 62-A
tr
159. The order ofbasic strength ofthe following in aqueous solution is
ao 6l5eooef $oE a'c3 g'd a:e.:'e.:165oo
C6H5NH2 (CH3)3N NH3
t2(1) 4> l>5>3>2
(3) 5> 4>2>3> I
J
(2)
(4)
cH3NH2
4
2>5>4>3>l
4>3>5>2>l
(cH3)2NH
5
1 60. Yellow dye can be prepared by a coupling reaction of benzene diazonium chloride in acid
medium with X. Identifu X from the following
5$o6 dolu doasoso essoc$J"ssoet EodS Ao5:#&c6:o 5'45'66 X So o$Jd96dsa 'J6E
o"5o' e5cdrd:dcdc5t5:15o. poB a't3d X 5o /uQot5:$:>
(1) Aniline
(3) Cumene '
(1) es&05
(3) 6rg5:s
(2) Phenol
(4) Benzene
(2) &o"e5
(4) aod5
Rough Work
-l CH)ov(]5<''c*'n()\
Cdqta*- ')
f.2016 63-A
