UPSEE 2020 Question Paper 1

MM MM

MM PAPER-1 àíZnwpñVH$m H«$‘m§H$ àíZnwpñVH$m H$moS> MM
MM MM
AA
Question Booklet Sr. No.
AZwH«$‘m§H$ / Roll No.
MM MM
MM Q. Booklet Code
MM
CÎma-erQ> H«$‘m§H$ / OMR Answer Sheet No.
MM MM
MM MM
MM KmofUm : / Declaration : MM
MM ‘¢Zo n¥îR> g§»¶m 1 na {X¶o J¶o {ZX}em| H$mo n‹T>H$a g‘P {b¶m h¡& narjm Ho$ÝÐmܶj H$s ‘moha MM
I have read and understood the instructions given on page No. 1 Seal of Superintendent of Examination Centre
MM MM
MM MM
MM narjmWu H$m hñVmja /Signature of Candidate MM
(AmdoXZ nÌ Ho$ AwZgma /as signed in application) H$j {ZarjH$ Ho$ hñVmja /Signature of the Invigilator
MM MM
narjmWu H$m Zm‘/
Name of Candidate :

narjmWu H$mo {X¶o n¡amJ«m’$ H$s ZH$b ñd¶§ H$s hñV{b{n ‘| ZrMo {X¶o J¶o [a³V ñWmZ na ZH$b (H$m°nr) H$aZr h¡&
""Amn ghr ì¶dgm¶ ‘| h¢, ¶h Amn V^r OmZ|Jo O~ : Amn H$m‘ na OmZo Ho$ {bE qM{VV h¢, Amn {Z˶ AnZm H$m‘ g~go AÀN>m H$aZm MmhVo h¢, Am¡a Amn AnZo H$m¶© Ho$
‘hËd H$mo g‘PVo h¢&'' AWdm / OR
To be copied by the candidate in your own handwriting in the space given below for this purpose is compulsory.
‘‘You will know you are in the right profession when : you wake anxious to go to work, you want to do your best daily, and you know your work is
important.”

* Bg n¥îR> H$m D$nar AmYm ^mJ H$mQ>Zo Ho$ ~mX drjH$ Bgo N>mÌ H$s OMR sheet Ho$ gmW gwa{jV aIo&
* After cutting half upper part of this page, invigilator preserve it along with student’s OMR sheet.

 
nwpñVH$m ‘| ‘wIn¥îR> g{hV n¥îR>m| H$s g§»¶m g‘¶ 3 K§Q>o A§H$ / Marks nwpñVH$m ‘| àíZm| H$s g§»¶m
No. of Pages in Booklet including title
36 Time 3 Hours 600 No. of Questions in Booklet
150

PAPER-1 àíZnwpñVH$m H«$‘m§H$/ Question Booklet Sr. No.

AZwH«$‘m§H$ / Roll No.
H$j {ZarjH$ Ho$ hñVmja /Signature of the Invigilator
àíZnwpñVH$m H$moS>
narjmWu H$m Zm‘/
Name of Candidate : AA
Q. Booklet Code
narjm{W©¶m| Ho$ {bE {ZX}e /INSTRUCTIONS TO CANDIDATE
Aä¶{W©¶m| hoVw Amdí¶H$ {ZX}e : Instructions for the Candidate :
1. Amo.E‘.Ama. CÎma n{ÌH$m ‘| Jmobm| VWm g^r à{dpîQ>¶m| H$mo ^aZo Ho$ {bE Ho$db 1. Use BLUE or BLACK BALL POINT PEN only for all entries and for filling
Zrbo ¶m H$mbo ~mb ßdmB§Q> noZ H$m hr Cn¶moJ H$a|& the bubbles in the OMR Answer Sheet.
2. SECURITY SEAL ImobZo Ho$ nhbo Aä¶Wu AnZm Zm‘, AZwH«$‘m§H$ (A§H$m| 2. Before opening the SECURITY SEAL of the question booklet, write your
Name, Roll Number (In figures), and OMR Answer-sheet Number in the
‘|) Ed§ Amo.E‘.Ama. CÎma-erQ> H$m H«$‘m§H$ Bg àíZ-nwpñVH$m Ho$ D$na {X¶o J¶o space provided at the top of the Question Booklet. Non-compliance
ñWmZ na {bI|& ¶{X do Bg {ZX}e H$m nmbZ Zht H$a|Jo Vmo CZH$s CÎma-erQ> H$m of these instructions would mean that the Answer Sheet can not be
‘yë¶m§H$Z Zhr hmo gHo$Jm VWm Eogo Aä¶Wu A¶mo½¶ Kmo{fV hmo Om¶|Jo& evaluated leading the disqualification of the candidate.
3. à˶oH$ àíZ Mma A§H$m| H$m h¡& {Og àíZ H$m CÎma Zht {X¶m J¶m h¡, Cg na H$moB© 3. Each question carries FOUR marks. No marks will be awarded for
A§H$ Zht {X¶m Om¶oJm& JbV CÎma na A§H$ Zht H$mQ>m OmEJm& unattempted questions. There is no negative marking on wrong answer.
4. Each multiple choice questions has only one correct answer and marks
4. g^r ~hþ{dH$ënr¶ àíZm| ‘| EH$ hr {dH$ën ghr h¡, {Ogna A§H$ Xo¶ hmoJm& shall be awarded for correct answer.
5. JUH$, bm°J Q>o{~b, ‘mo~mBb ’$moZ, Bbo³Q´>m°{ZH$ CnH$aU VWm ñbmBS> ê$b Am{X 5. Use of calculator, log table, mobile phones, any electronic gadget and
H$m à¶moJ d{O©V h¡& slide rule etc. is strictly prohibited.
6. Aä¶Wu H$mo narjm H$j N>moS>Zo H$s AZw‘{V narjm Ad{Y H$s g‘mpßV na hr Xr 6. Candidate will be allowed to leave the examination hall at the end of
Om¶oJr& examination time period only.
7. ¶{X {H$gr Aä¶Wu Ho$ nmg nwñVH|$ ¶m Aݶ {b{IV ¶m N>nr gm‘J«r, {Oggo do 7. If a candidate is found in possession of books or any other printed or
ghm¶Vm bo gH$Vo/gH$Vr h¢, nm¶r Om¶oJr, Vmo Cgo A¶mo½¶ Kmo{fV H$a {X¶m Om written material from which he/she might derive assistance, he/she is
gH$Vm h¡& Bgr àH$ma, ¶{X H$moB© Aä¶Wu {H$gr ^r àH$ma H$s ghm¶Vm {H$gr ^r liable to be treated as disqualified. Similarly, if a candidate is found
ómoV go XoVm ¶m boVm (¶m XoZo H$m ¶m boZo H$m à¶mg H$aVm) hþAm nm¶m Om¶oJm, giving or obtaining (or attempting to give or obtain) assistance from any
source, he/she is liable to be disqualified.
Vmo Cgo ^r A¶mo½¶ Kmo{fV {H$¶m Om gH$Vm h¡&
8. {H$gr ^r ^«‘ H$s Xem ‘| àíZ-nwpñVH$m Ho$ A§J«oOr A§e H$mo hr ghr d A§{V‘ 8. English version of questions paper is to be considered as authentic and
‘mZm Om¶oJm& final to resolve any ambiguity.
9. OMR sheet Bg Paper Ho$ ^rVa h¡ VWm Bgo ~mha {ZH$mbm Om gH$Vm h¡ naÝVw 9. OMR sheet is placed within this paper and can be taken out from this
Paper H$s grb Ho$db nona ewé hmoZo Ho$ g‘¶ na hr Imobm Om¶oJm& paper but seal of paper must be opened only at the start of paper.

MM
MM
MM
MM
MM
MM
MM
MM
MM
MM
MM
MM
MM PAPER-1
Physics : Q. 1 to Q. 50
Chemistry : Q. 51 to Q. 100
Mathematics : Q. 101 to Q. 150

PHYSICS / ^m¡{VH$emó

001. Which of the following expression has a 001. {ZåZm§{H$V ‘o {H$g 춧OH$ H$m {d‘r¶ gyÌ Xÿgam|
dimensional formula different from others? go {^Þ h¡?
1 2
(A)  !0 E (∈0 permitivity of free space, E: 1 2
2 (A)  !0 E (∈0 {Zdm©V H$s {dÚwVerbVm,
electric field ) 2
E: d¡X²¶wV joÌ)
(B) hv (h : Plancks constant, v : frequency)
(B) hv (h : ßbm§H$ {Z¶Vm§H$, v : Amd¥{V)
(C) ρgh (ρ: density, g: acceleration due to
gravity, h: height) (C) ρgh (ρ: KZËd, g: JwéËdr¶ ËdaU, h: C±MmB©)
1 2 1 2
(D)  ρv (ρ: density, v: velocity) (D) ρv (ρ: KZËd, v: doJ)
2 2

002. The acceleration (a) of an object varies as 002. EH$ dñVw H$m ËdaU (a) CgHo$ doJ (v) Ho$ nXm|
a function of its velocity (v) as a = m v ‘o a = m v h¡ Ohm± λ EH$ pñWam§H$ h¡& ¶{X
where λ is a constant. If at t=0, v=0, then the t=0 na v=0 hmo, Vmo g‘¶ (t) Ho$ nXm| ‘o doJ
velocity as a function of time (t) is given as
3 2 3 1
{X¶m OmVm h¡:
(A) m t (B) mt 3 2 3 1
4 4 (A) m t (B) mt
4 4
1 2 2 1 2
(C) m t (D) m t 1 2 2 1 2
4 4 (C) m t (D) m t
4 4

1-AA ] [2] [ Contd...

MM
MM
MM
003. A car starts from rest to cover distance 'd' on 003. {dam‘mdñWm go MbH$a EH$ H$ma EH$ g‹S>H$ na MM
a road where the coefficient of friction between MM
'd' Xÿar V¶ H$aVr h¡ Ohm§ g‹S>H$ Am¡a Q>m¶amo Ho$
the road and the tyres is µ. The minimum MM
‘ܶ Kf©U JwUm§H$ µ h¡& ݶyZV‘ g‘¶, {Og‘o MM
time in which car can cover this distance is
H$ma ¶h Xÿar V¶ H$a gH$Vr h¡, g‘mZwnmVr hmoJm: MM
proportional to
(A) µ (B) µ–1 MM
(A) µ (B) µ–1
1 1 MM
(C) n 2
1
(D) n- 2
1
(C) n 2 (D) n- 2 MM
MM
004. A 1.5 m tall girl standing at a distance of 004. 1.5 ‘rQ>a b§~r b‹S>H$s Omo 5 ‘rQ>a D$§Mr EH$ MM
15 m from a fence 5 m high throws a stone MhmaXrdmar go 15 ‘rQ>a Xÿa I‹S>r h¡, MhmaXrdmar
of mass 0.25 Kg at an angle of 450 to the H$s Amoa 0.25 {H$J«m H$m EH$ nËWa j¡{VO go
horizontal. The minimum velocity of the stone 450 H$moU na ’|$H$Vr h¡& nËWa H$m ݶyZV‘ doJ,
to be thrown to fly over the fence is {Oggo dh MhmaXrdmar Ho$ D$na go JwOa OmE, h¡:
(A) 9.8 m/s (B) 10.2 m/s (A) 9.8 ‘r/goH|$S> (B) 10.2 ‘r/goH|$S>
(C) 13.8 m/s (D) 19.6 m/s
(C) 13.8 ‘r/goH|$S> (D) 19.6 ‘r/goH|$S>

005. A body of mass M in the form of an inclined 005. 450 PwH$md H$moU dmbo ZV g‘Vb Ho$ AmH$ma H$s
plane with a 450 angle of inclination lies on 'M' Ð춑mZ H$s EH$ dñVw j¡{VO Vb na pñWV h¡&
a horizontal plane. A ball of mass 'm' moving
'v0' doJ go j¡{VO {Xem ‘o J{Verb m Ð춑mZ
horizontally with velocity 'v0' collides with
H$s EH$ J|X ZV g‘Vb go Q>H$amVr h¡& Q>¸$a Ho$
the inclined plane. After the impact the ball
bounces vertically upwards and the inclined
nümV J|X CÜdm©Ya D$na H$s Amoa CN>b OmVr h¡
plane begins to slide without friction along VWm ZV g‘Vb j¡{VO Vb na {~Zm Kf©U Ho$
the horizontal plane. The velocity of the ball {’$gbZo bJVr h¡& Q>¸$a Ho$ nümV CÜdm©Ya J{V
after the collision in its vertical travel is ‘o J|X H$m doJ h¡:

m m
M M
0 0
45 45
mv0 Mv0 mv0 Mv0
(A) (B) (A) M
(B)
m
M m

M-m M-m M-m M-m
(C) v0 (D) v0 (C) v0 (D) v0
M m M m

1-AA ] [3] [ P.T.O.

MM
MM
MM
MM 006. A body can rotate in a vertical plane at the 006. EH$ dñVw L b§~mB© H$s EH$ S>moar Ho$ {gao na
MM end of a string of length L. The horizontal D$Üdm©Ya Vb ‘o Ky‘ gH$Vr h¡& CƒV‘ pñW{V
MM velocity imparted to the body in its highest
MM ‘o dñVw H$mo {X¶m J¶m j¡{VO doJ, ¶{X ݶyZV‘
position, so that the tension in the string at pñW{V ‘o S>moar ‘o VZmd dñVw Ho$ ^ma H$m Xg
MM
MM the lowermost position is ten times the weight JwZm h¡, hmoJm:
MM of the body, will be
MM
MM (A) 13gL (B) 6gL
(A) 13gL (B) 6gL
MM (C) 5gL (D) gL
(C) 5gL (D) gL

007. An empty container is put on the pan of a 007. EH$ Imbr ~V©Z EH$ ^m¡{VH$ Vwbm Ho$ nb‹S>o ‘o
physical balance and the scale is adjusted to aIm h¡ VWm BgHo$ n¡‘mZo H$mo eyݶ na g‘m¶mo{OV
zero. Small identical balls of mass 10 g each H$a {X¶m J¶m h¡& à˶oH$ 10 J«m‘ Ð춑mZ H$s
are dropped into the container from rest from EH$g‘mZ J|Xo {dam‘mdñWm go 4.9 ‘rQ>a H$s D$§MmB©
height 4.9 m at a constant rate of 100 balls per go 100 J|Xo à{V goH§$S> H$s Xa go ~V©Z ‘o {JamB©
second. If the collision between each ball and OmVr h¡& ¶{X à˶oH$ J|X Am¡a ~V©Z Ho$ ‘ܶ g§KÅ>
container is completely inelastic, the reading of nyU©V… Aà˶mñW hmo Vmo 5 goH§$S> Ho$ ~mX Vwbm
the balance after 5 second will be H$m nmR>çm§H$ hmoJm:
(A) 1 Kg (B) 2 Kg (A) 1 {H$J«m (B) 2 {H$J«m
(C) 5 Kg (D) 6 Kg (C) 5 {H$J«m (D) 6 {H$J«m

008. A ball of mass 'm' lying on a frictionless surface
008. EH$ Kf©Ua{hV g‘Vb gVh na pñWV 'm' Ð춑mZ
is attached to the two elastic springs of force
H$s EH$ J|X 'k' ~b {Z¶Vm§H$ H$s Xmo à˶mñW
constant 'k' as shown in the figure. The other
two ends of the spring are connected to rigid
pñà§Jm| go {MÌmZwgma Ow‹S>r h¡& pñà§J Ho$ Xÿgao Xmo
wall. The ball can perform simple harmonic {gao Ñ‹T> Xrdmb go Ow‹S>o h¡& J|X j¡{VO {Xem ‘o
motion horizontally. The ratio of the velocity gab AmdV©J{V H$a gH$Vr h¡& gmå¶mdñWm go
of the ball at positions equal to one half and Am¶m‘ Ho$ AmYo Am¡a EH$ {VhmB© pñW{V¶m| na J|X
one third of amplitude from the equilibrium Ho$ doJ H$m AZwnmV hmoJm:
position will be
m
k k
m
k k

2 3
(A) (B)
2 3 3 2
(A) (B)
3 2
2 3 3
3 3 (C) (D)
2 3 4 2
(C) (D)
3 4 2

1-AA ] [4] [ Contd...

MM
MM
MM
009. The angular velocity of earth rotation, at which 009. n¥Ïdr KyU©Z H$m H$moUr¶ doJ, {Og na ^y‘ܶ aoIm MM
the bodies at the equator become weightless, na dñVwE§ ^mahrZ hmo OmVr h¡, h¡: (n¥Ïdr H$s MM
is (Radius of earth = 6400 Km) {ÌÁ¶m = 6400 {H$‘r) MM
(A) 800 /sec (A) 800 à{V goH§$S>
MM
(B) 1.25 /sec (B) 1.25 à{V goH§$S>
MM
(C) 1.25 × 10–2 /sec (C) 1.25 × 10-2 à{V goH§$S>
MM
MM
(D) 1.25 × 10–3 /sec (D) 1.25 × 10-3 à{V goH§$S>
MM
MM
010. A metal rod of Young’s modulus 1.5 × 1010 010. 1.5 x 1010 N/m2 ¶§J à˶mñWVm JwUm§H$ H$s EH$ MM
N/m2 undergoes an elastic strain of 0.06%. The YmVw H$s N>‹S> 0.06% à˶mñW {dH¥$V hmoVr h¡&
energy stored per unit volume of the rod is N>‹S> Ho$ à{V EH$m§H$ Am¶VZ ‘o g§{MV D$Om© h¡
(A) 900 J/m3 (B) 1800 J/m3 (A) 900 Oyb/‘r3 (B) 1800 Oyb/‘r3
(C) 2700 J/m3 (D) 5400 J/m3 (C) 2700 Oyb/‘r3 (D) 5400 Oyb/‘r3

011. A piece of ice containing a piece of iron inside
011. EH$ bmoho Ho$ Qw>H$‹S>o H$mo A§Xa aŠIo ~’©$ H$m Qw>H$‹S>m
it is floating on water in a container. When
EH$ ~V©Z ‘o nmZr Ho$ D$na V¡a ahm h¡& O~ ~’©$
ice melts completely, the level of water in the
nyU©V… {nKb OmVr h¡ Vmo ~V©Z ‘o nmZr H$m ñVa
container will
(A) ~‹T>oJm
(A) Increase
(B) Decrease (B) KQ>oJm
(C) Remain unchanged (C) An[ad{V©V ahoJm
(D) Become zero (D) eyݶ hmo OmEJm

012. A uniform circular disc of mass 'M' and radius 012. 'M' Ð춑mZ Ed§ 'R' {ÌÁ¶m H$s EH$ EH$g‘mZ
'R' is rotating in a horizontal plane about an Jmob MH$Vr j¡{VO Vb ‘o AnZo Ð춑mZ H|$Ð go
axis passing through its centre of mass and JwOaZo dmbr VWm Vb Ho$ bå~dV Aj Ho$ n[aV…
perpendicular to its plane with an angular ω H$moUr¶ doJ go Ky‘ ahr h¡& Cgr {ÌÁ¶m VWm
velocity ω. Another disc of same radius but (M/2) Ð춑mZ H$s EH$ Xÿgar MH$Vr H$mo nhbr
mass (M/2) is placed gently on the first disc. MH$Vr Ho$ D$na gmdYmZr go aI {X¶m OmVm h¡&
The angular velocity of the system now is A~ {ZH$m¶ H$m H$moUr¶ doJ h¡:
3 2 3 2
(A) ~ (B) ~ (A) ~ (B) ~
2 3 2 3
1 1
(C) ~ (D) ω (C) ~ (D) ω
3 3
013. The period of a simple pendulum hanging from
013. EH$ pñWa Jm‹S>r H$s N>V go bQ>H$Vo EH$ gab
the ceiling of a stationary cart is T0. When the
cart rolls without friction down the inclined
bmobH$ H$m AmdV©H$mb T0 h¡& O~ ¶h Jm‹S>r θ
plane with angle of inclination θ, the period PwH$md H$moU Ho$ ZV g‘Vb go {~Zm Kf©U Ho$
of oscillation ZrMo bwT>H$Vr h¡, Vmo XmobZ H$m AmdV©H$mb
(A) increases (A) ~T> OmVm h¡
(B) decreases (B) KQ> OmVm h¡
(C) remains unchanged (C) An[ad{V©V ahVm h¡
(D) becomes infinity
(D) AZ§V hmo OmVm h¡&

1-AA ] [5] [ P.T.O.

MM
MM
MM
MM 014. Four identical rings of radius R and mass M 014. M Ð춑mZ VWm R {ÌÁ¶m Ho$ Mma EH$g‘mZ db¶m|
MM are placed at the corner of a square in x-y H$mo x-y Vb ‘o EH$ dJ© Ho$ H$moZmo na Bg àH$ma
MM plane such that each ring touches the two
MM aIm OmVm h¡ {H$ à˶oH$ db¶ Xmo db¶m| H$mo
rings tangentially. The moment of inertia of
MM ñne©aoIr¶ Ny>Vm h¡& dJ© Ho$ H|$Ð go JwOaVo z-Aj
this system about z-axis passing through the
MM centre of the square is
Ho$ n[aV… Bg {ZH$m¶ H$m O‹S>Ëd AmKyU© h¡:
MM (A) 8 MR2 (B) 7 MR2 (A) 8 MR2 (B) 7 MR2
MM (C) 6 MR2 (D) 4 MR2 (C) 6 MR2 (D) 4 MR2
MM
MM 015. A police car moving at 5.4 Km/Hr sounds 015. 5.4 {H$‘r/K§Q>m H$s Mmb go J{Verb EH$ nw{bg
siren emitting frequency of 550 Hz which is H$ma go CËg{O©V 550 hQ²O© Amd¥{V H$s gmBaZ
reflected back from a stationary object some H$s Üd{Z H$ma go Hw$N> Xÿar AmJo pñWV EH$ pñWa
distance ahead of the car. The number of beats dñVw go nrN>o H$s Amoa namd{V©V hmo OmVr h¡& H$ma
heard per second by an observer sitting in the ‘o ~¡R>o EH$ àojH$ Ûmam gwZo à{V goH§$S> {dñn§Xm|
car is (Assume velocity of sound in air= 330 H$s g§»¶m h¡: (‘mZ br{O¶o {H$ hdm ‘o Üd{Z
m/sec) H$m doJ = 330 ‘r/go)
(A) 4 (B) 5 (A) 4 (B) 5
(C) 6 (D) 0 (C) 6 (D) 0

016. A uniform string of mass M and length L is 016. M Ð춑mZ Am¡a L bå~mB© H$s EH$ EH$g‘mZ añgr
hanging from the ceiling. If a transverse wave N>V go bQ>H$ ahr h¡& ¶{X añgr H$s bå~mB© Ho$
travels along the length of the string, then the n[aV… EH$ AZwàñW Va§J MbVr h¡, Vmo BgH$s
time taken by it to travel the whole length is nyar bå~mB© MbZo ‘o bJm g‘¶ h¡:
L 2L L 2L
(A) (B) (A) g
(B)
g
g g
3L 4L 3L 4L
(C) (D) (C) (D)
g g g g

017. In an organ pipe open at one and closed at 017. EH$ AmJ©Z Z{bH$m, Omo EH$ {gao na Iwbr VWm
the other end, two successive harmonics have Xÿgao {gao na ~§X h¡, H$s H«${‘H$ g§ZmXr Amd¥{V¶m§
frequencies 560 Hz and 720 Hz. The length 560 hQ²O© VWm 720 hQ²O© h¡& AmJ©Z Z{bH$m H$s
of the pipe is (Assume the velocity of sound bå~mB© h¡: (‘mZ br{O¶o {H$ hdm ‘o Üd{Z H$m
in air =330 m/sec) doJ = 330 ‘r/go)
(A) 20.6 cm (B) 41.25 cm (A) 20.6 go‘r (B) 41.25 go‘r
(C) 103.13 cm (D) 206.25 cm (C) 103.13 go‘r (D) 206.25 go‘r

018. The equation of the displacement of a wave 018. EH$ Va§J Ho$ {dñWmnZ H$m g‘rH$aU y (go‘r ‘o)
is y (in cm) = 10 ^ 3 sin 2rt + cos 2rt h . The =10 ^ 3 sin 2rt + cos 2rt h h¡& Va§J H$m Am¶m‘
amplitude of the wave is h¡:
(A) 10 cm (B) 17.3 cm (A) 10 go‘r (B) 17.3 go‘r
(C) 20 cm (D) 40 cm (C) 20 go‘r (D) 40 go‘r

1-AA ] [6] [ Contd...

MM
MM
MM
019. 200 gram of ice at -10 0C is mixed with 019. EH$ H¡$bmoar‘rQ>a ‘o -10 0C H$s 200 J«m‘ ~’©$ MM
200 gram of water at 6 0C in a calorimeter. H$mo 6 0C Ho$ 200 J«m‘ Ob ‘o {‘bm¶m OmVm MM
If the specific heat of ice and water are 0.5 h¡& ¶{X ~’©$ Am¡a Ob H$s {d{eï> D$î‘m¶o H«$‘e… MM
and 1.0 cal/gm 0C respectively and the latent 0.5 Am¡a 1.0 H¡$bmoar/J«m‘ 0C hmo VWm ~’©$ MM
heat of ice is 80 cal/gm, the temperature of H$s JbZ H$s Jwá D$î‘m 80 H¡$bmoar/J«m‘ h¡, Vmo MM
the mixture in thermal equilibrium is D$î‘r¶ gmå¶ ‘o {‘lU H$m Vmn h¡: MM
(A) 0 0C (B) -2 0C (A) 0 0C (B) -2 0C MM
0 (D) 6 0C
(C) -10 C (C) -10 0C (D) 6 0C MM
MM
020. An ideal gas having pressure P, volume V 020. EH$ AmXe© J¡g, {OgH$m Xm~ P, Am¶VZ V VWm MM
and temperature T is allowed to expand Vmn T h¡, H$mo éÕmoî‘V… {dñVm[aV {H$¶m OmVm h¡
adiabatically until its volume becomes 4V {H$ CgH$m Am¶VZ 4V hmo OmVm h¡ Am¡a Vmn {JaH$a
while its temperature falls to T/2. The adiabatic T/2 hmo OmVm h¡& J¡g H$m éÕmoî‘ KmVm§H$ h¡:
exponent of the gas is
(A) 1.66 (B) 1.50
(A) 1.66 (B) 1.50
(C) 1.40 (D) 1.33
(C) 1.40 (D) 1.33

021. If the Wien’s constant b=0.3 cm-K, then 021. ¶{X drZ {Z¶Vm§H$ b=0.3 go‘r-K, Vmo 6000 A0
the temperature of the sun having maximum Va§JX¡Ü¶© na A{YH$V‘ Vrd«Vm Ho$ {d{H$aU dmbo
intensity of radiation at 6000 A0 wavelength is gy¶© H$m Vmn h¡:
(A) 2000 K (B) 5000 K (A) 2000 K (B) 5000 K
(C) 6000 K (D) 7000 K (C) 6000 K (D) 7000 K

022. A Carnot engine works between 7270C and 022. EH$ H$moZm}Q> B§OZ 7270C Am¡a 270C Ho$ ‘ܶ
270C. The efficiency of the engine is H$m¶© H$aVm h¡& B§OZ H$s XjVm h¡:
(A) 30 % (B) 70 % (A) 30% (B) 70 %
(C) 96 % (D) 100 % (C) 96% (D) 100 %

023. The entropy remains constant in 023. EÝQ´>m°nr {Z¶V ahVr h¡
(A) A cyclic process (A) EH$ MH«$s¶ àH«$‘ ‘|
(B) An isobaric process (B) EH$ g‘Xm~r àH«$‘ ‘|
(C) EH$ g‘Vmnr àH«$‘ ‘|
(C) An isothermal process
(D) An adiabatic process (D) EH$ éÕmoî‘ àH«$‘ ‘|

024. Two identically charged spherical balls of mass 024. 'm' Ð춑mZ H$s Xmo EH$g‘mZ Amdo{eV Jmobr¶
'm' are suspended by strings of length l each J|Xo l bå~mB© H$s apñg¶m| Ûmam EH$ hr {~ÝXþ go
from the same point. At the point of suspension, bQ>H$mB© J¶r h¢& {Zbå~Z {~ÝXþ na, g‘mZ Amdoe
there is a third ball of same charge. The charge H$s EH$ Vrgar J|X h¡& gmå¶mdñWm ‘o apñg¶m| Ho$
of the balls for the angle between the strings ‘ܶ H$moU 900 hmoZo Ho$ {bE J|Xm| na Amdoe h¡:
in equilibrium position being 900 is
2
2
(A) 8rf0 l mg
(A) 8rf0 l mg
2
2
(B) 16rf0 l mg
(B) 16rf0 l mg
2
2
(C) 4rf0 l mg
(C) 4rf0 l mg
(D) 16rf0 mg
(D) 16rf0 mg

1-AA ] [7] [ P.T.O.

MM
MM
MM
MM 025. The circuit shown in the figure has four 025. {MÌ ‘o àX{e©V n[anW ‘o d¡ÚwVdmhH$ ~b E VWm
MM batteries of emf E and internal resistance 'r', Am§V[aH$ à{VamoY 'r' H$s Mma ~¡Q>ar, Xmo à{VamoY
MM two resistances R each and a parallel plate
capacitor with plates of length l and the à˶oH$ R VWm EH$ l bå~mB© H$s ßboQ>mo Ed§ CZHo$
MM distance between them as 'd'. An electron ~rM Xÿar 'd' dmbm g‘m§Va ßboQ> g§Ym[aÌ h¡& EH$
MM having charge 'e' enters the capacitor plates at BboŠQ´>m°Z ßboQ>mo Ho$ g‘mÝVa 'v' doJ go g§Ym[aÌ
MM velocity 'v' parallel to the plates. The angle to Ho$ A§Xa àdoe H$aVm h¡& BboŠQ´>m°Z Ho$ g§Ym[aÌ Ho$
MM the plates with which the electron come out ~mha AmZo na ßboQ>mo go ~Zm H$moU h¡:
of the capacitor is E E
MM E E

MM r r
r r

MM R R
R R

r r
r r

E E
E E
-1 2eEl
-1 2eEl (A) tan c 2m
(A) tan c 2m mdv
mdv
-1 2eEl
-1 2eEl (B) tan c 2m
(B) tan c 2m m ^2R + 4r h dv
m ^2R + 4r h dv
-1 4eEl
-1 4eEl (C) tan c 2m
(C) tan c 2m mdv
mdv
(D) 00 (D) 00

026. A battery of EMF 4V and internal resistance 026. 4V d¡ÚwVdmhH$ ~b VWm 1 Amo‘ Am§V[aH$ à{VamoY
1 Ohm is connected with three 45 Ohms H$s EH$ ~¡Q>ar {MÌmZwgma d¡ÚwV n[anW ‘o VrZ 45
resistances, a voltmeter and an ammeter in the
electrical circuit as shown in the figure. The Amo‘ à{VamoYm|, EH$ dmoëQ>‘rQ>a VWm EH$ A‘rQ>a go
reading of the voltmeter and ammeter are Ow‹S>r h¡& dmoëQ>‘rQ>a VWm A‘rQ>a H$m nmR>çm§H$ h¡:
V V

45 45 45 45 45 45

4V 4V

A A

1 1

(A) 11.25 V, 0.25 A (A) 11.25 V, 0.25 A
(B) 3.75 V, 0.25 A (B) 3.75 V, 0.25 A
(C) 1.32 V, 0.03 A (C) 1.32 V, 0.03 A
(D) 3.06 V, 0.94 A (D) 3.06 V, 0.94 A

027. The filament of an electric kettle is made up 027. EH$ d¡ÚwV Ho$Vbr H$m {µ’$bm‘|Q> g‘mZ à{VamoYm|
of three sections of equal resistances. These Ho$ VrZ ^mJm| go {‘bH$a ~Zm h¡& ¶o g^r ^mJ
sections are connected in parallel and the water g‘m§Va H«$‘ ‘o Ow‹S>o h¡ VWm nmZr 9 {‘ZQ> ‘o
begins to boil in 9 minutes. If these resistances C~bZm àmaå^ H$a XoVm h¡& ¶{X BZ à{VamoYm| H$mo
are connected in series, then the time taken by loUrH«$‘ ‘o Omo‹S> Xo, Vmo g‘mZ Ð춑mZ Ho$ nmZr
the same mass of water in the kettle to boil is H$mo Ho$Vbr ‘o C~bZo ‘o bJm g‘¶ h¡:
(A) 1 minute (B) 9 minute (A) 1 {‘ZQ> (B) 9 {‘ZQ
(C) 27 minutes (D) 81 minutes (C) 27 {‘ZQ> (D) 81 {‘ZQ>

1-AA ] [8] [ Contd...

MM
MM
MM
028. Two conducting spheres A and B of radii 028. 1 go‘r Am¡a 2 go‘r {ÌÁ¶m Ho$ Xmo Mm{bV Jmobo MM
1 cm and 2 cm carrying charge 5 × 10–8 A Am¡a B {OZ na H«$‘e… 5 × 10-8 Hy$bm‘ MM
C and 1 x 10–7 C respectively are kept far and 1 × 10-7 Hy$bm‘ Amdoe h¡, EH$ Xÿgao go MM
apart. If the spheres are joined by a conducting Xÿar na aIo h¡& ¶{X BZ Jmobm| H$mo EH$ MmbH$ MM
wire, then Vma Ûmam Omo‹S> Xo, Vmo MM
(A) Amdoe A go B H$s Amoa àdm{hV hmoJm& MM
(A) Charge will flow from A to B
(B) Amdoe B go A H$s Amoa àdm{hV hmoJm& MM
(B) Charge will flow from B to A (C) A Am¡a B Ho$ ‘ܶ H$moB© Amdoe àdm{hV
(C) No charge will flow between A and B
MM
Zht hmoJm&
(D) Charge may flow on either side (D) Amdoe {H$gr ^r {Xem ‘o àdm{hV hmo gH$Vm
MM
h¡&
MM
029. A piece of platinum and germanium are heated 029. EH$ ßbo{Q>Z‘ VWm Oa‘o{Z¶‘ Ho$ Qw>H$‹S>o H$mo H$‘ao
above the room temperature, then the resistance Ho$ Vmn go D$na Ja‘ {H$¶m OmVm h¡ Vmo Vmn Ho$
of gmW
(A) Germanium will increase while platinum (A) Oa‘o{Z¶‘ H$m à{VamoY ~T>oJm O~{H$ ßbo{Q>Z‘
will decrease with temperature H$m à{VamoY KQ>oJm&
(B) Platinum will increase while germanium (B) ßbo{Q>Z‘ H$m à{VamoY ~T>oJm O~{H$ Oa‘o{Z¶‘
will decrease with temperature H$m à{VamoY KQ>oJm&
(C) Both platinum and germanium will (C) XmoZm| ßbo{Q>Z‘ VWm Oa‘o{Z¶‘ H$m à{VamoY
increase with temperature ~T>oJm&
(D) Both platinum and germanium will (D) XmoZm| ßbo{Q>Z‘ VWm Oa‘o{Z¶‘ H$m à{VamoY
decrease with temperature KQ>oJm&

030. The ratio of electrostatic force F e and 030. EH$Xÿgao go r Xÿar na pñWV EH$ àmoQ>mZ Am¡a EH$
gravitational force Fg acting between a proton BboŠQ´>m°Z Ho$ ‘ܶ H$m¶©H$mar d¡ÚwVñW¡{VH$ ~b VWm
and an electron distant r from each other is JwéËdmH$f©U ~b H$m AZwnmV hmoJm bJ^J
approximately (A) 1019 (B) 1029
(A) 1019 (B) 1029
(C) 1039 (D) 1049
(C) 1039 (D) 1049

031. An electron is moving in a circular orbit of 031. EH$ BboŠQ´>mZ° ω H$moUr¶ doJ go r {ÌÁ¶m Ho$ d¥ÎmmH$ma
radius r with angular velocity ω. The magnetic nW na J{Verb h¡& BgHo$ H|$Ð na Mw§~H$s¶ joÌ
field at its centre will be hmoJm:
n0 ~e n ~e
(A) 0 (B) (A) 0 (B)
0
4rr 4rr
2 n0 ~e 2
n0 ~e n0 ~ e n0 ~ e
(C) (D) (C) (D)
4r r 4r r
032. In an ammeter, 0.2 % of the main current 032. EH$ A‘rQ>a ‘o ‘w»¶ Ymam H$m 0.2 % ^mJ
flows from the coil of the galvanometer. If Ymam‘mnr H$s Hw§$S>br go JwOaVm h¡& ¶{X Ymam‘mnr
the resistance of the coil of galvanometer is H$s Hw§$S>br H$m à{VamoY G hmo Vmo A‘rQ>a H$m
G, then the resistance of the ammeter will be à{VamoY hmoJm:
G G
(A) (B) G G
499 500 (A) (B)
499 500
500 G 499 G 500 G 499 G
(C) (D) (C) (D)
499 500 499 500

1-AA ] [9] [ P.T.O.

MM
MM
MM
MM 033. A long straight conductor carrying current I and 033. I Ymamdmhr EH$ b§~m grYm MmbH$ Vma VWm a
MM a square frame of side a are in the same plane ^wOm H$m EH$ dJm©H$ma ’«o$‘ {MÌmZwgma EH$ hr
MM as shown in the figure. This frame moves with Vb ‘| h¢& ¶h ’«o$‘ Xm¶t Amoa H$mo EH$ {Z¶V
MM a constant velocity v right side. The induced v doJ go MbVm h¡& ’«o$‘ ‘o ào[aV {dÚwV dmhH$
MM emf in the frame will be proportional to
MM r
~b g‘mZwnmVr hmoJm:
r
MM
MM I
I
MM
MM
a
a
1 1
(A) (B) (A)
1
(B)
1
^2r - ah2 ^2r + ah2 ^2r - ah2 ^2r + ah2
1 1
(C) (D) 2 (C)
1
(D)
1
^2r - ah^2r + ah r ^2r - ah^2r + ah 2
r

034. The angle of dip at a place is 300. If horizontal 034. {H$gr ñWmZ na Z{V H$moU 300 h¡& ¶{X n¥Ïdr Ho$
component of earth’s magnetic field is H, the Mw§~H$s¶ joÌ H$m j¡{VO KQ>H$ H h¡, Vmo gånyU©
total field intensity is joÌ H$s Vrd«Vm h¡:
H 2H H 2H
(A) (B) (A) (B)
2 3 2 3

(C) H 2 (D) H 3 (C) H 2 (D) H 3

035. The magnetic susceptibility is positive and 035. Mwå~H$s¶ YmaUerbVm YZmË‘H$ Am¡a H$‘ hmoVr h¡:
small for a (A) à{VMw§~H$s¶ nXmW© ‘|
(A) Diamagnetic substance
(B) AZwMw§~H$s¶ nXmW© ‘|
(B) Paramagnetic substance
(C) bm¡hMw§~H$s¶ nXmW© ‘|
(C) Ferromagnetic substance
(D) AMw§~H$s¶ nXmW© ‘|
(D) Nonmagnetic substance

036. The phenomenon of propagation of light in an 036. EH$ àH$m{eH$ VÝVw go àH$me n[aJ‘Z H$s KQ>Zm
optical fiber is due to H$m H$maU h¡:
(A) Interference of light (A) àH$me H$m ì¶{VH$aU
(B) Diffraction of light (B) àH$me H$m {ddV©Z
(C) Polarization of light (C) àH$me H$m YwdU
(D) Total internal reflection of light (D) àH$me H$m nyU© Am§V[aH$ namdV©Z

1-AA ] [ 10 ] [ Contd...

MM
MM
MM
037. The resolving power of a microscope can be 037. EH$ g§¶wº$ gyú‘Xeu H$s {d^oXZ j‘Vm ~‹T>mB© Om MM
MM
increased by gH$Vr h¡: MM
(A) Increasing diameter of objective lens (A) A{^Ñí¶H$ b|g H$m ì¶mg ~‹T>m H$a MM
(B) Increasing diameter of eye lens
MM
(B) Zo{ÌH$m b|g H$m ì¶mg ~‹T>m H$a
MM
(C) Increasing wavelength of light used (C) à¶wº$ àH$me H$s Va§JX¡Ü¶© ~‹T>m H$a MM
(D) decreasing wavelength of light used (D) à¶wº$ àH$me H$s Va§JX¡Ü¶© KQ>m H$a MM
MM
MM
038. The convex side of a plano-convex lens of 038. EH$ {deof àH$ma H$m AdVb Xn©U àmá H$aZo Ho$
radius of curvature 60 cm and refractive index
{bE 60 go‘r d«H$Vm {ÌÁ¶m VWm 1.5 AndV©Zm§H$
1.5 is silver plated to obtain a special type of
Ho$ EH$ g‘Vb-CÎmb b|g Ho$ CÎmb {gao na Mm±Xr
concave mirror. The focal length of the mirror
M‹T>m Xr OmVr h¡& Bg Xn©U H$s ’$moH$g Xÿar h¡:
is
(A) 60 cm (B) 30 cm
(A) 60 cm (B) 30 cm
(C) 24 cm (D) 20 cm
(C) 24 cm (D) 20 cm

039. A monochromatic beam of light of wavelength 039. 600 Z¡Zmo‘rQ>a Va§JX¡Ü¶© H$m EH$daUr¶ àH$me nw§O
600 nm in vacuum enters a medium of {Zdm©V go 4/3 AndV©Zm§H$ Ho$ ‘mܶ‘ ‘o àdoe
refractive index (4/3). Its wavelength and H$aVm h¡& BgH$s Va§JX¡Ü¶© Am¡a Amd¥{V Bg ‘mܶ‘
frequency in the medium will be ‘o hmoJr:
(A) 450 nm, 5 × 1014 Hz (A) 450 Z¡Zmo‘rQ>a, 5 × 1014 hQ²O©
14
(B) 600 nm, 5 × 1014 Hz (B) 600 Z¡Zmo‘rQ>a, 5 × 10 hQ²O©
(C) 800 nm, 3.8 × 1014 Hz (C) 800 Z¡Zmo‘rQ>a, 3.8 × 1014 hQ²O©
(D) 450 nm, 6.7 × 1014 Hz (D) 450 Z¡Zmo‘rQ>a, 6.7 × 1014 hQ²O©

040. A thin mica sheet of refractive index 040. 6000 A0 Va§JX¡Ü¶© Ho$ EH$daUr¶ àH$me nw§O H$m
1.4 is used to cover one slit of Young’s Cn¶moJ H$aHo$ à{Vnm{XV ¶§J {Û-pñbQ> à¶moJ H$s
double slit experiment being performed using EH$ pñbQ> H$mo 1.4 AndV©Zm§H$ H$s nVbr ‘mBH$m
monochromatic beam of light of wavelength erQ> go ‹T>H$ {X¶m OmVm h¡& ¶{X Ho$ÝÐr¶ {~ÝXþ na
6000 A0. If at the central point is now found
A~ nm±Mdt Xrá q’«$O àmá hmoVr h¡ Vmo ‘mBH$m
the fifth bright fringe, the thickness of the
erQ> H$s ‘moQ>mB© h¡
mica sheet is
(A) 4.2 ‘mB©H«$mZ (B) 6.0 ‘mB©H«$mZ
(A) 4.2 micron (B) 6.0 micron
(C) 7.5 ‘mB©H«$mZ (D) 8.4 ‘mB©H«$mZ
(C) 7.5 micron (D) 8.4 micron

1-AA ] [ 11 ] [ P.T.O.

MM
MM
MM
MM 041. An unpolarized light wave is incident from air 041. EH$ AY«w{dV àH$me Va§J hdm go H$m±M H$s gVh
MM
on a glass surface at the Brewster angle. The na ~«yñQ>a H$moU na Amn{VV h¡& namd{V©V Am¡a
MM
MM angle between the reflected and the refracted And{V©V Va§Jmo Ho$ ‘ܶ H$moU h¡:
MM wave is (A) 00 (B) 450
MM
MM (A) 00 (B) 450 (C) 900 (D) 1200
MM (C) 900 (D) 1200
MM
MM
042. A prism of angle of prism 600 has angle of 042. 600 {àÁ‘ H$moU dmbo {àÁ‘ H$m ݶyZV‘ {dMbZ
minimum deviation 400. The angle of incidence H$moU 400 h¡& Bg pñW{V ‘o AmnVZ H$moU h¡:
in this position is (A) 300 (B) 500
(A) 300 (B) 500 (C) 600 (D) 1000
(C) 600 (D) 1000

043. If the common-base current gain of a transistor 043. EH$ Q´>m§{OñQ>a H$m C^¶{Zð>-AmYma Ymam bm^ 0.96
is 0.96, then its common-emitter current gain h¡, Vmo BgH$m C^¶{Zð>-CËgO©H$ Ymam bm^ hmoJm:
will be (A) 2 (B) 20
(A) 2 (B) 20 (C) 24 (D) 48
(C) 24 (D) 48

044. The work function of a metal is 2.0 eV. The 044. EH$ YmVw H$m H$m¶© ’$bZ 2.0 BboŠQ´>m°Z dmoëQ> h¡&
stopping potential for the light of wavelength 4000 A0 Va§JX¡Ü¶© Ho$ àH$me Ho$ {bE g§ñVãY
4000 A0 will be {d^d hmoJm:
(A) 5.1 V (B) 3.1 V (A) 5.1 dmoëQ> (B) 3.1 dmoëQ>
(C) 2.0 V (D) 1.1 V (C) 2.0 dmoëQ> (D) 1.1 dmoëQ>

045. A 1 milliwatt laser source is emitting light of 045. EH$ 1 {‘brdmQ> boOa òmoV 555 Z¡Zmo‘rQ>a àH$me
wavelength 555 nm. The number of photons H$m CËgO©Z H$a ahm h¡& à{V goH§$S> CËg{O©V
emitted per second are approximately (Planck’s ’$moQ>moZm| H$s g§»¶m hmoJr bJ^J (ßbm§H$ {Z¶Vm§H$
constant = 6.6 × 10–34 m2 Kg/s) = 6.6 × 10–34 ‘r2 {H$J«m/goH§$S>)
(A) 107 (B) 1011 (A) 107 (B) 1011
(C) 1015 (D) 1018 (C) 1015 (D) 1018

1-AA ] [ 12 ] [ Contd...

MM
MM
MM
046. If V be the accelerating voltage of the tube, 046. ¶{X V Q>çy~ H$m Ëd[aV {d^d hmo Vmo CËnÞ gVV MM
the maximum frequency of continuous x-rays
MM
EŠg-{H$aUm| H$s A{YH$V‘ Amd¥{V, V na {Z^©a MM
produced depends on V as H$aVr h¡: MM
(A) V2 (B) V (A) V2 (B) V MM
(C) V1/2 (D) V–1 (C) V1/2 (D) V–1
MM
MM
MM
047. Hydrogen atoms in its ground state are excited 047. {ZåZV‘ AdñWm ‘o pñWV hmBS´>moOZ na‘mUwAmo H$mo MM
by monochromatic radiation of photon energy ’$moQ>moZ D$Om© 12.8 BboŠQ´>m°Z dmoëQ> Ho$ EH$daUr¶ MM
{d{H$aU Ûmam CÎmo{OV {H$¶m OmVm h¡& ¶{X hmBS´>moOZ
12.8 eV. If the ionization potential of hydrogen
na‘mUw H$m Am¶ZZ {d^d 13.6 Bbo³Q´>mZ dmoëQ>
atom is 13.6 eV, the number of spectral lines h¡ Vmo ~moha {gÕmÝV Ho$ AZwgma CËg{O©V ñnoŠQ´>‘
emitted according to Bohr theory will be bmBZm| H$s g§»¶m hmoJr:
(A) 6 (B) 4 (A) 6 (B) 4
(C) 3 (D) 1 (C) 3 (D) 1

048. The half life of a radioactive substance is 7.5 048. EH$ ao{S>¶moEpŠQ>d nXmW© H$s AÕ©Am¶w 7.5 goH§$S>
seconds. The fraction of substance left after h¡& EH$ {‘ZQ> Ho$ nümV nXmW© H$m ~Mm hþAm ^mJ
one minute is h¡:
(A) 1/16 (B) 1/64 (A) 1/16 (B) 1/64
(C) 1/128 (D) 1/256 (C) 1/128 (D) 1/256

049. The output equation of the logical circuit shown 049. {MÌ ‘o àX{e©V bm°{OH$ n[anW H$m {ZJ©V g‘rH$aU
in figure is h¡:
A A

y y
B B

C C

(A) Y= (A+B)BC (B) Y = AB+(B+C)
(A) Y= (A+B)BC (B) Y = AB+(B+C)
(C) Y= A+B+C (D) Y=ABC
(C) Y= A+B+C (D) Y = ABC

050. The number of atoms in the lower and upper 050. EH$ nXmW© Ho$ {ZåZ Am¡a Cƒ D$Om© ñVam| ‘o
energy states of a material are N1 and N2 na‘mUwAmo H$s g§»¶m H«$‘e… N1 Am¡a N2 h¡& BZ
respectively. For population inversion between
Xmo ñVam| Ho$ ‘ܶ OZg§»¶m ì¶wËH«$‘U Ho$ {bE
these two levels
(A) N2 = N1 (B) N2 > N1 (A) N2 = N1 (B) N2 > N 1
(C) N2 < N1 (D) N2 = 0 (C) N2 < N1 (D) N2 = 0

1-AA ] [ 13 ] [ P.T.O.

MM
MM
MM
MM CHEMISTRY / agm¶Zemó
MM
MM 051. Which one of the following will be most 051. {ZåZ{b{IV ‘| go H$m¡Z EH$ jmar¶ ObAnKQ>Z
MM reactive for alkaline hydrolysis
MM Ho$ à{V gdm©{YH$ {H«$¶merb h¡&
MM (A) CH3 - CH2 - CH2 - CH - COOH
|
MM Br (A)> CH3 - CH2 - CH2 - CH - COOH
MM |
(B) CH3 - CH2 - CH - CH - COOH Br
MM |
(B) CH3 - CH2 - CH - CH - COOH
MM Br |
Br
(C) CH3 - CH - CH2 - Ch2 - COOH
| (C) CH3 - CH - CH2 - CH2 - COOH
Br |
Br
(D) Br - CH2 - CH2 - CH2 - CH2 - COOH (D) Br - CH2 - CH2 - CH2 - CH2 - COOH

052. The most suitable reagent for the conversion 052. ‘o{Wb ~oÝOmoEQ> go ~opÝOb EëH$mohm°b àmá H$aZo
of methylbenzoate to be benzyalcohol is Ho$ {bE g~go Cn¶wº$ A{^H$‘©H$ h¡
(A) H2/Pd-C (B) LiAlH4 (A)> H2/Pd-C (B) LiAlH4
(C) NaBH4 (D) Li/NH3 (l) (C) NaBH4 (D) Li/NH3 (l)

053.   
Which one can be synthesized by Wurtz reaction 053. dwQ>©O A{^{H«$¶m Ûmam {H$gH$mo g§íbo{fV {H$¶m Om
(A) Toluene (B) alkyle halide gH$Vm h¡&
(C) alkane (D) alkene (A) Q>m°byB©Z> (B) EobH$mBb hobmBS>
(C) EobHo$Z (D) EobH$sZ

054. Which one of the following made through 054. {ZåZ{b{IV ‘¡ go {H$gH$mo g§KZZ ~hþbH$sH$aU
condensation polymerization. Ûmam ~Zm¶m OmVm h¡&
(A) Teflon (B) bakelite (A) Q>o’$bm°Z> (B) ~oHo$bmBQ>
(C) Polythene (D) Acrilan (C) nm°brWrZ (D) EoH«$mBboZ

055. Which one of the following has hexagonal 055. {ZåZ{b{IV ‘| go H$m¡Z fQ>H$moUr¶ {H«$ñQ>b g§aMZm
crystal structure aIVm h¡&
(A) BaSO4 (B) CdS (A) BaSO4> (B) CdS
(C) SnO2 (D) Na2SO4 ⋅ 10H2O (C) SnO2 (D) Na2SO4 ⋅ 10H2O

1-AA ] [ 14 ] [ Contd...

MM
MM
MM
056. Which of the following is anti ferromagnetic. 056. {ZåZ{b{IV ‘| go H$m¡Z à{V bmoh Mwå~H$s¶ h¡& MM
MM
(A) H2O (B) CrO2 (A) H2O (B) CrO2 MM
(C) MnO (D) MgFe2O4 (C) MnO (D) MgFe2O4 MM
MM
MM
057. Synthesis of amonia is represented by the 057. A‘mo{Z¶m H$m {Z‘m©U {ZåZ A{^{H«$¶m Ûmam Xem©¶m MM
following reaction. J¶m h¡& MM
MM
N2(g) + 3H2(g) → 2NH3(g) N2(g) + 3H2(g) → 2NH3(g) MM
∆rH°= –91.8KJ mol–1 ∆rH°= –91.8KJ mol–1
What will be enthalpy of decomposition of A{^{H«$¶m Ho$ AZwgma NH3 Ho$ {dKQ>Z Ho$ {b¶o
ammonia according to reaction. A{^{H«$¶m H$s EÝW¡ënr ³¶m hmoJr?
2NH3(g) → N2 + 3H2(g) ; ∆rH° = ? 2NH3(g) → N2 + 3H2(g) ; ∆rH° = ?
(A) – 91.8 kJ mol–1 (B) + 91.8 kJ mol–1 (A) – 91.8 kJ mol–1> (B) + 91.8 kJ mol–1
(C) – 45.9 kJ mol–1 (D) + 45.9 kJ mol–1 (C) – 45.9 kJ mol–1 (D) + 45.9 kJ mol–1

058. What will be the pH of ⋅ 001M Ba(OH)2 solution 058. ⋅ 001M Ba(OH)2 {db¶ZHo$ pH H$m ‘mZ hmoJm&
(A) 2.0 (B) 8.4 (A) 2.0> (B) 8.4
(C) 11.3 (D) 2.7 (C) 11.3 (D) 2.7

059. Which of the following aqueous solution must 059. {ZåZ ‘| go {H$g Obr¶ {db¶Z H$m gdm©{YH$
have the highest boiling point. ³dWZm§H$ hmoZm Mm{hE
(A) 1.0 M NaOH (A) 1.0 M NaOH>
(B) 1.0 M Na2SO4 (B) 1.0 M Na2SO4
(C) 1.0 M NH4 NO3 (C) 1.0 M NH4 NO3
(D) 1.0 M KNO3 (D) 1.0 M KNO3

060. Which of the following is the correct for 060. {ZåZ{b{IV ‘| H$m¡Z ~T>Vo ~§YH«$‘m| H$m ghr H«$‘
increasing bond order. hmoJm
+ - 2-
(A) O2 2 O2 2 O2 2 O2 +
(A) O2 2 O2 2 O2 2 O2
- 2-
+ - 2-
(B) O2 1 O2 1 O2 1 O2 +
(B) O2 1 O2 1 O2 1 O2
- 2-

(C) O2 = O2, O2 2 O2
+ - 2-
(C) O2 = O2, O2 2 O2
+ - 2-
+ - 2-
(D) O2 1 O2 2 O2 1 O2 +
(D) O2 1 O2 2 O2 1 O2
- 2-

1-AA ] [ 15 ] [ P.T.O.

MM
MM
MM
MM 061. Two particles A and B are in motion. If the 061. Xmo H$U A Ed§ B J{V H$a aho h¢, ¶{X H$U
MM
wavelength associated with particle A in motion A go g§¶mo{OV Va§JX¡Ü¶© H$m ‘mZ 5 × 10–8 m
MM
MM is 5 × 10–8 m. What will be the wavelength h¡ Vmo H$U B go g§¶mo{OV Va§J X¡Ü¶© H$m ‘mZ
MM associated with particle B if the momentum is
MM ³¶m hmoJm O~ {H$ H$U B H$m g§doJ H$U A
MM half than that of A. Ho$ Vwë¶ AmYm h¡&
MM (A) 5 × 10–8 m (B) 10 × 10–8 m (A) 5 × 10–8 m> (B) 10 × 10–8 m
MM
(C) 2.5 × 10–8 m (D) 0.2 × 10–8 m (C) 2.5 × 10–8 m (D) 0.2 × 10–8 m
MM

062. The radius of which of the following orbits 062. {ZåZ{b{IV ‘| go {H$gHo$ H$j H$s {ÌÁ¶m H$m ‘mZ
is same as that of the first Bohr's orbit of hmBS´>moOZ na‘mUw Ho$ àW‘ ~moha H$j H$s {ÌÁ¶m
H atom? Ho$ ~am~a hmoJm
(A) He+ (n=2) (B) Li2+ (n=2) (A) He+ (n=2)> (B) Li2+ (n=2)
(C) Li2+ (n=3) (D) Be3+ (n=2) (C) Li2+ (n=3) (D) Be3+ (n=2)

063. Which of the following substances is serving 063. {ZåZ ‘| go H$m¡Z gm nXmW© {ZåZ{b{IV A{^{H«$¶m
as a reducing agent in the following reaction? ‘| AnMm¶H$ H$s Vah H$m¶© H$aoJm?
2-
14H+ +  Cr2 O 7 + 3Ni → 2Cr3+ + 7H2O + 3Ni2+ 2-
14H+ +  Cr2 O 7 + 3Ni → 2Cr3+ + 7H2O + 3Ni2+
(A) H2O (B) Ni (A) H2O$> (B) Ni
2-
(C) H+ (D) Cr2 O2-
7 (C) H+ (D) Cr2 O 7

064. Which is the strongest acid? 064. {ZåZ ‘| g~go à~b Aåb hmoJm&
(A) H(ClO)O2 (B) H(ClO)O3 (A) H(ClO)O2 (B) H(ClO)O3
(C) H(ClO)O (D) H(ClO) (C) H(ClO)O (D) H(ClO)

065. IUPAC name of compound 065. {X¶o J¶o ¶m¡{JH$ H$m IUPAC Zm‘ hmoJm
O CH3 O CH3
N is is
C CH3 C N
CH3

(A) N, N - dimethyl cyclopropan carboxamide (A) N, N - S>mB©‘o{Wb gmB³bmoàmonoZ H$m~m}³gmo‘mBS>
(B) N - methyl cyclopropanamide (B) N - ‘o{Wb gmB³bmoàmonoZ‘mBS>
(C) Cyclopropianomide (C) gmB³bmoàmonoZmo‘mBS>
(D) None of the above (D) D$n¶w³V© ‘| H$moB© Zhr

1-AA ] [ 16 ] [ Contd...

MM
MM
MM
066. Which of the following reaction is not correct. 066. {ZåZ{b{IV ‘| go H$m¡Z gr A{^{H«$¶m ghr Zht  h¡ MM
- + 2+ 3+
MM
(A) MnO4 + 8H + 5Fe " 5Fe + -
A) MnO4 8H + +
+ 2+
5Fe " 5Fe
3+
+ MM
Mn
2+
+ 4H2 O 2+
Mn + 4H2 O MM
(B) 2MnO2 + 4KOH + O2 → 4KMnO4 + 2H2O
MM
(B) 2MnO2 + 4KOH + O2 → 4KMnO4 + 2H2O
MM
(C) 2Na2CrO4 + 2H+ → Na2Cr2O7 + 2Na+ + H2O (C) 2Na2CrO4 + 2H+ → Na2Cr2O7 + 2Na+ + H2O MM
MM
(D) K2Cr2O7 + 7H2SO4+ 6KI → 4K2SO4+ (D) K2Cr2O7 + 7H2SO4+ 6KI → 4K2SO4+ MM
MM
Cr2(SO4)3+ 3I2 + 7H2O Cr2(SO4)3+ 3I2 + 7H2O

067. Which of the following compound will give 067. {ZåZ ‘| go H$m¡Z-gm ¶m¡{JH$ ~«mo‘rZ Ob Ho$ gmW
tribromo derivative when treated with bromine CnM[aV H$aZo na Q´>mB~«mo‘mo ì¶wËnÞ XoJm?
CH3
water. CH2DH
CH3
CH2OH
(A) (B)
(A) (B) OH
OH CH3
CH3 CH3
CH3 OH
OH (C) (D)
(C) (D)
OH
OH

068. If E°Cu2+| Cu = 0.34V and E°Ag+|Ag = 0.80V, 068. ¶{X E°Cu2+| Cu = 0.34V Ed§ E°Ag+|Ag = 0.80V.
what is the emf of the cell {ZåZ g¡b H$m {dÚwVdmVH$ ~b 298 K na hmoJm
Cu|Cu2+ (0.01M) || Ag+(0.01M)|Ag Cu|Cu2+ (0.01M) || Ag+(0.01M)|Ag

at 298 K? (A) 0.40V (B) 0.46 V

(A) 0.40V (B) 0.46 V (C) 0.50 V (D) 0.52 V

(C) 0.50 V (D) 0.52 V

069. The dark purple colours of KMnO4 is due to 069. KMnO4 H$m Jham ~¢JZr a§J {H$go H$maU hmoJm
(A) d - d transition (A) d - d g§H«$‘U>

(B) Ligand field transition (B) {bJ|S> joÌ g§H«$‘U

(C) Charge transfer transition (C) Amdoe ñWmÝVaU g§H«$‘U

(D) σ– π+ transition (D) σ – π+ g§H«$‘U

1-AA ] [ 17 ] [ P.T.O.

MM
MM
MM
MM 070. The number of σ and π bonds between two 070. CaC2 ‘| Xmo H$m~©Z na‘mUw Ho$ ‘ܶ σ Ed§ π
MM
carbon atoms in CaC2 is ~ÝYm| H$s g§»¶m hmoJr
MM
MM (A) Three σ bonds and no π bonds (A) VrZ σ ~ÝY Am¡a H$moB© π ~ÝY Zht>
MM (B) Two π bonds and one σ bond (B) Xmo π ~ÝY Am¡a EH$ σ ~ÝY
MM
MM (C) Two σ bonds and one π bond (C) Xmo σ ~ÝY Am¡a EH$ π ~ÝY
MM (D) One π bond and one σ bond (D) EH$ π ~ÝY Am¡a EH$ σ ~ÝY
MM
MM
071. Which one of the following is the weakest 071. {ZåZ ‘| go H$m¡Z gm Xþ~©bV‘ bwBg jma h¡
Lewis base? -
(A) CH3 > (B) NH2
-

- -
(A) CH3 (B) NH2 (C) OH– (D) F–
(C) OH– (D) F–

072. Which of the following cations will be have 072. Amg}{ZH$ gë’$mBS> gm°b Ho$ {b¶o {ZåZ{b{IV ‘|
minimum flocculation value for arsenic sulphide go H$m¡Z gm YZm¶Z ݶyZV‘ D$U©Z ‘mZ aIVm h¡&
sol? (A) Na+ (B) Mg2+
(A) Na+ (B) Mg2+ (C) Ca2+ (D) Al3+
(C) Ca2+ (D) Al3+

x
073. In the plot of log
m
vs log P for an adsorption, 073. A{YemofU AmaoI ‘| log mx vs log P go EH$
a straight line inclined at an angle of θ =14.04o grYr aoIm àmá hmoVr h¡ Omo {H$ x-Aj Ho$ gmnoj
to the x-axis was obtained. The 'n' value for H$moU θ =14.04o na PwH$s h¡. A{YemofU àH«$‘
this adsorption process is (tan 14.04o = 0.25) ‘| 'n' H$m ‘mZ hmoJm (tan 14.04o = 0.25)
(A) 5 (B) 8 (A) 5 (B) 8
(C) 4 (D) 2 (C) 4 (D) 2

074. Extra pure N2 can be obtained by heating 074. {H$gH$mo J‘© H$aZo na gdm©{YH$ ewÕ N2 H$mo àmá
(A) NH3 with CuO (B) NH4 NO3 {H$¶m Om gH$Vm h¡&
(A) NH3 g§J CuO (B) NH4 NO3
(C) (NH4)2 Cr2O7 (D) Ba (N3)2
(C) (NH4)2 Cr2O7 (D) Ba (N3)2

1-AA ] [ 18 ] [ Contd...

MM
MM
MM
075. Which of the following exhibits square 075. {ZåZ go H$m¡Z dJm©H$ma {nao{‘S>b Á¶m{‘{V àX{e©V MM
MM
pyramidal geometry? H$aVm h¡. MM
(A) XeF6 (B) XeO3 (A) XeF6 (B) XeO3 MM
(C) BrF5 (D) XeF4
MM
(C) BrF5 (D) XeF4
MM
MM
076. Which one amongst the following exhibit 076. {ZåZ{b{IV ‘| go H$m¡Z Á¶m{‘Vr¶ g‘md¶dVm MM
MM
geometrical isomerism àX{e©V H$aVm h¡& MM
(A) 8CoIII ^NH3h5 BrB SO 4 (A) 8CoIII ^NH3h5 BrB SO 4 >
(B) 6Co ^EDTA h@ (B) 6Co ^EDTA h@
III -1 III -1

(C) 6Cr ^SCN h6@ (C) 6Cr ^SCN h6@
III 3- 3-
III

(D) 8PtIII ^NH3h2 Cl2B (D) 8PtIII ^NH3h2 Cl2B

077. The carbocation formed in SN1 reaction of 077. EopëH$b h¡bmBS> H$s SN1 A{^{H«$¶m Ho$ ‘§X nX
alkyl halide in the slow stop is ‘| àmá H$m~©YZm¶Z hmoVm h¡
(A) SP3 - hybridised (B) SP2 - hybridised (A) SP3 - g§H$[aV (B) SP2 - g§H$[aV
(C) SP - hybridised (D) SP3d - hybridised (C) SP - g§H$[aV (D) SP3d - g§H$[aV

078. Which of the following compounds is 078. AmoOmoZ naV Ho$ jaU Ho$ {b¶o {ZåZ ‘| H$m¡Z gm
responsible for depletion of Ozone layer? ¶m¡{JH$ CÎmaXm¶r h¡
(A) Freon (B) Chloroform (A) {’«$Am°Z (B) ³bmoamo’$m‘©
(C) D.D.T (D) Iodoform (C) S>r.S>r.Q>r (D) Am¶moS>mo’$m°‘©

079. The chemical reation 079. {ZåZ amgm¶{ZH$ A{^{H«$¶m ³¶m H$hbmVr h¡
CHO
CO, HCl CHO
CO, HCl
Anhyd AlCl3 /CuCl
ew$$îH$ AlCl3 /CuCl
is known as
(A) JoQ>a‘Z A{^{H«$¶m
(A) Gatterman reaction
> (B) {Q>eoZH$mo A{^{H«$¶m
(B) Tischenko reaction
(C) Gatterman - Koch reaction (C) JoQ>a‘Z - H$moe A{^{H«$¶m
(D) Frankland reaction (D) ’«o$ÝH$boÝS> A{^{H«$¶m

1-AA ] [ 19 ] [ P.T.O.

MM
MM
MM
MM 080. When acetone is treated with dilute alkali, the 080. O~ EgrQ>moZ H$s A{^{H«$¶m VZw jma Ho$ gmW
MM
product obtained is H$am¶r OmVr h¡ àmá CËnmX hmoJm&
MM
MM (A) Mesitylene (B) Mesityl oxide (A) ‘ogrQ>mBbrZ> (B) ‘ogrQ>mBb Am°³gmBS>
MM (C) Paraldheyde (D) Phorone (C) noamEëS>rhmBS> (D) ’$moamoZ
MM
MM
MM 081. A metal present in insulin is 081. BÝgw{bZ ‘o§ CnpñWV YmVw h¡
MM
(A) aluminium (B) zinc (A) Eë¶w{‘{Z¶‘> (B) qOH$
MM
(C) iron (D) copper (C) Am¶aZ (D) H$m°na

082. Which of the following amino acid is not 082. {ZåZ ‘| go H$m¡Z gm A‘rZmo Aåb àH$mer¶ g{H«$¶
optically active Zht h¡&
(A) lactic acid (B) serine (A) bo³Q>rH$ Aåb> (B) {gamBZ
(C) alanine (D) glycine (C) EboZmBZ (D) ½bmB{gZ

083. Time required for 100% completion of a zero 083. eyݶ H$moQ>r A{^{H«$¶m Ho$ 100% nyU© hmoZo Ho$
order reaction is {b¶o Amdí¶H$ g‘¶ h¡
a a
(A) ak (B) (A) ak (B)
2k 2k
a 2k a 2k
(C) (D) (C) (D)
k a k a

084. The final product formed in this reaction is 084. Xr J¶r A{^{H«$¶m H$m A§{V‘ CËnmX hmoJm
CH3
KMn O4 /KOH H3 O+ CH3
(A) (B) KMn O4 /KOH H3 O+
(A) (B)
CHO COOK
CHO COOK
(A) (B)
(A) (B)

CH2OH COOH
CH2OH COOH
(C) (D)
(C) (D)

1-AA ] [ 20 ] [ Contd...

MM
MM
MM
085. Lassaigne's test for the detection of nitrogen 085. ZmBQ´>moOZ Ho$ {ZYm©aU Ho$ {bE b¡gmZo narjU ‘| MM
MM
fails in Ag’$b h¡ MM
(A) H2N – CO – NHNH2 • HCl (A) H2N – CO – NHNH2 HCl •
MM
MM
(B) NH2 – NH2 • HCl > (B) NH2 – NH2 HCl •
MM
(C) NH2 CO NH2 (C) NH2 CO NH2
MM
MM
(D) C6H5 – NH - NH2 HCl (D) C6H5 – NH - NH2 HCl MM
MM
086. The self indicating silicagel impregnated with 086. H$mo~mëQ> ³bmoamBS> Ûmam ^[aV ñdV: gyMH$ {g{bH$m
cobalt chloride turns pink on absorbing moisture O¡b dmVmdaU H$s Z‘r Ademo{fV H$a Jwbm~r hmoVm
and becomes blue on heating. The pink and h¡ VWm J‘© H$aZo Ho$ níMmV² Zrbm hmo OmVm h¡&
blue colours are repectively due to Jwbm~r Ed§ Zrbm a§J H«$‘e: {H$gHo$ H$maU hmoJm&
(A) [Co (H2O)6]2+ and [CoCl4]2- (A) [Co (H2O)6]2+ and [CoCl4]2-

(B) [Co (H2O)6]2+ and Co2O3 (B) [Co (H2O)6]2+ and Co2O3

(C) [Co (H2O)6]2+ and [Co(H2O)6]3+ (C) [Co (H2O)6]2+ and [Co(H2O)6]3+

(D) Co2+ and Co3+ (D) Co2+ and Co3+

087. Which of the following complex ions has the 087. {ZåZ{b{IV ‘| go H$m¡Z gm g§Hw$b Am¶Z A{YH$V‘
highest magnetic moment Mwå~H$s¶ AmKyU© aIVm h¡&
(A) [Cr (NH3)6]3+ (B) [Fe (CN)6]3– (A) [Cr (NH3)6]3+$> (B) [Fe (CN)6]3–

(C) [Fe (CN)6]4– (D) [Zn (NH3)6]2+ (C) [Fe (CN)6]4– (D) [Zn (NH3)6]2+

088. Which of the following compounds is most 088. {ZåZ{b{IV ‘| go H$m¡Z ¶m¡{JH$ Zm{^H$ñZohr ¶moJmË‘H$
reactive towards nucleophilic A{^{H«$¶m Ho$ à{V g~go A{YH$ {H«$¶merb h¡&
(A) CH3CHO (B) PhCOCH3 (A) CH3CHO (B) PhCOCH3
(C) PhCOPh (D) CH3COCH3 (C) PhCOPh (D) CH3COCH3

1-AA ] [ 21 ] [ P.T.O.

MM
MM
MM
MM 089. In the cannizzaro reaction given below 089. ZrMo Xr J¶r H¡${ZOmam| A{^{H«$¶m H$o {b¶o Yr‘m
MM -
2 PhCHO → PhCH2OH + PhCO2 , the slowest nX h¡&
MM
MM step is 2 PhCHO → PhCH2OH + PhCO2
-

MM (A) the attack of OH– at the carbonyl group
MM (A) H$m~m}{Zb g‘yh na OH– H$m AmH«$‘U>
MM (B) the transfer of hydride to the carbonyl (B) H$m~m}{Zb g‘yh na hmBS´>mBS> Am¶Z H$m
MM group ñWmZmÝVaU
MM (C) the obstruction of proton from the
MM (C) H$m~m}{³g{bH$ Aåb go àmoQ>moZ H$m {ZH$bZm
carboxylic acid (D) PhCH2 OH H$m {dàmoQ>moZrH$aU
(D) the deprotonation of PhCH2 OH

090. Which of the following fcc structures contains 090. {ZåZ{b{IV ‘| go H$m¡Z gr fcc g§aMZm EH$mÝV[aV
cations in the alternate tetrahedral voids MVwî’$bH$s¶ [a{º$¶m| ‘| YZm¶Z aIVr h¡&
(A) Na2O (B) ZnS (A) Na2O (B) ZnS
(C) CaF2 (D) CaO (C) CaF2 (D) CaO

091. In soap industry, glycerol can be sepeated from 091. gm~wZ CÚmoJ ‘| ñn|Q> bmB© ‘| go {¾{gam°b H$m
spent lye using the technique. n¥W³H$sH$aU H$aZo hoVy H$m¡Z gr {d{Y à¶moJ ‘|
(A) differential extraction br OmVr h¡&
(B) distillation under reduced pressure (A) {d^oXr {ZîH$f©U
(C) filteration (B) H$‘ Xm~ na AmgdZ
(D) chromatographic sepesation (C) emoYZ
(D) H«$mo‘oQmoJ«m{’$H$ n¥W³H$aU

092. 0.532g of chloroplatinate of an organic base 092. H$m~© { ZH$ jma (AUw ^ ma 244) H$m 0.532 g
(mol wt. 244) gave 0.195 g of platinum on ³bmoamoßboQ>rZoQ> XhZ Ho$ níMmV 0.195g ßboQ>rZ‘
ignition. The number of nitrogen atoms per XoVm h¡& jma Ho$ à{V AUw ‘| ZmBQ´>moOZ na‘mUwAm|
molecule of base is H$s g§»¶m h¡
(A) 1 (0ne) (B) 2 (two) (A) 1 (EH$)> (B) 2 (Xmo)
(C) 3 (three) (D) 4 (four) (C) 3 (VrZ) (D) 4 (Mma)

1-AA ] [ 22 ] [ Contd...

MM
MM
MM
093. The standard emf of a glavanic cell involving 093. 250c Vmn na EH$ ½moëdo{ZH$ g¡b H$m ‘mZH$ MM
MM
cell reaction with n=2 is found to be 0.295V at {dÚwVdmhH$ ~b 0.295 V nm¶m J¶m O~{H$ g¡b MM
250c. The equilibrium constant of the reaction A{^{H«$¶m ‘| n H$m ‘mZ 2 h¡& Bg A{^{H«$¶m Ho$ MM
MM
would be. {b¶o gmå¶mdñWm pñWam§H$ hmoJm& MM
(A) 2.0 x 1011 (B) 4.0 x 1012 (A) 2.0 x 10 >11 (B) 4.0 x 10 12 MM
MM
(C) 1.0 x 102 (D) 1.0 x 1010 (C) 1.0 x 102 (D) 1.0 x 1010
MM
MM
094. A reaction occurs spontaneously if 094. ñdV: A{^{H«$¶m hmoVr h¡ ¶{X
(A) T∆S < ∆H and both ∆H and ∆S are +ve (A) T
 ∆S < ∆H VWm XmoZm| ∆H d ∆S KZmË‘H$ h¢
> (B) T
 ∆S > ∆H VWm XmoZm| ∆H d ∆S KZmË‘H$ h¢
(B) T∆S > ∆H and both ∆H and ∆S are +ve
(C) T
 ∆S = ∆H VWm XmoZm| ∆H d ∆S KZmË‘H$ h¢
(C) T∆S = ∆H and both ∆H and ∆S are +ve
(D) T
 ∆S > ∆H VWm ∆H KZmË‘H$ d ∆S
(D) T∆S > ∆H and ∆H is +ve and ∆S is –ve
F$UmË‘H$ h¢

-
095. The conjugate acid of NH2 is
- 095. NH2 H$m g§¶wp½‘V Aåb h¡
(A) N2H4> (B) NH4+
(A) N2H4 (B) NH4+
(C) NH2OH (D) NH3
(C) NH2OH (D) NH3

096. If the density of CH3OH is 0.793 KgL–1, 096. ¶{X ‘oWoZm°b H$m KZËd 0.793 {H$J«m / {bQ>a h¡
what is the volume of methanol is needed for Vmo 0.25 ‘moba ‘oWoZm°b Ho$ 2.5 {bQ>a {db¶Z
making 2.5 L of its 0.25 M solution? Ho$ {b¶o Amdí¶H$ ‘oWoZm°b H$m Am¶VZ hmoJm&
(A) 20.2 ml (B) 50.4 ml (A) 20.2 ml$> (B) 50.4 ml

(C) 25.2 ml (D) 10.0 ml (C) 25.2 ml (D) 10.0 ml

097. Among the following the aromatic compound 097. {ZåZ ‘| go H$m¡Z Eoamo‘o{Q>H$ ¶m¡{JH$ h¡&
is (A) (B)
+ +
(A) (B)
+ +
(C) (D)
–
(C) (D)
–

1-AA ] [ 23 ] [ P.T.O.

MM
MM
MM
MM 098. Only two isomeric monochloro derivatives are 098. {H$gHo$ {bE Ho$db Xmo EH$b ³bmoamo g‘md¶dr
MM
possible for ì¶wáÞ gå^d h¡&
MM
MM (A) n-butane (A) n-ã¶yQ>oZ>
MM (B) 2, 4-dimethyl pentane (B) 2, 4-S>mB©‘o{Wb noÝQ>oZ
MM
MM (C) benzene (C) ~oÝOrZ
MM (D) 2 - methyl butane (D) 2 - ‘o{Wb ã¶yQ>oZ
MM
MM
099. Major pollutant in Jet plane emission is 099. OoQ> ßboZ CËg{O©V à‘wI àXÿfH$ h¡
(A) SO2 (B) CFC (A) SO2> (B) CFC
(C) CO (D) CCl4 (C) CO (D) CCl4

100. Galvanised iron is 100. ½m¡ëdZrH¥$V bmohm hmoVm h¡
(A) an alloy of iron with gallium (A) Am¶aZ Ho$ gmW J¡{b¶‘H$m {‘l YmVw
(B) iron used in a glavanometer > (B) EH$ J¡ëdoZmo‘rQ>a ‘| à¶wº$ Am¶aZ
(C) iron coated with zinc (C) qOH$ Amd[aV bmohm
(D) an alloy of iron with zinc (D) Am¶aZ Ho$ gmW qOH$ H$m {‘l YmVw

1-AA ] [ 24 ] [ Contd...

MM
MM
MM
MATHEMATICS / J{UV
MM
MM
101. Sn denotes the sum of n terms of an AP, whose 101. Sn EH$ Eogr g‘mÝVa loUr Ho$ n nXm| Ho$ ¶moJ H$mo {Zé{nV MM
first term is a. If the common difference
MM
H$aVm h¡. {OgH$m àW‘ nX a h¡& ¶{X Bg loUr H$m MM
d = Sn– k Sn–1 + Sn–2, then k is equal to gmd© AÝVa d = Sn– k Sn–1 + Sn–2, V~ k ~am~a h¡… MM
(A) 2 (B) 3 (A) 2 (B) 3
MM
MM
(C) 5 (D) 7 (C) 5 (D) 7 MM
MM
102. If Z1 and Z2 are two complex numbers such 102. ¶{X Z1 VWm Z2 Xmo Eogr g{‘l g§»¶mE§ h¡, {H$
that |Z1| = |Z2| and arg (Z1) + arg (Z2) = π, |Z1| = |Z2| VWm arg (Z1) + arg (Z2) = π, V~
then Z1 is equal to Z1 ~am~a h¡…
(A) 2Z2 (B) Z2 (A) 2Z2 (B) Z2
(C) –Z2 (D) None of these (C) –Z2 (D) BZ‘| go H$moB© Zht

103. If Z1, Z2 and Z3 represent the vertices of an 103. ¶{X Z1, Z2 VWm Z3 {H$gr g‘~mhþ {Ì^wO Ho$ erfm] H$mo
equilateral triangle such that |Z1| = |Z2| = |Z3|, Bg àH$ma {Zé[nV H$aVo h¢ {H$ |Z1| = |Z2| = |Z3|,
then V~
(A) Z1 + Z2 = Z3 (B) Z1 + Z2 + Z3 = 0 (A) Z1 + Z2 = Z3 (B) Z1 + Z2 + Z3 = 0
(C) Z1 Z2 = Z3 (D) Z1 – Z2 = Z3 – Z2 (C) Z1 Z2 = Z3 (D) Z1 – Z2 = Z3 – Z2

104. If the equation x2 + 2x + 3 = 0 and ax2 + bx + c = 0, 104. ¶{X g‘rH$aU x2 + 2x + 3 = 0 VWm ax2 + bx + c= 0,
a, b, c ∈ R, have a common root, then a:b:c is a, b, c ∈ R, Ho$ EH$ ‘yb g‘mZ h¡, V~ a:b:c h¡…
(A) 3 : 2 : 1 (B) 1:3:2 (A) 3 : 2 : 1 (B) 1:3:2
(C) 3 : 1 : 2 (D) 1:2:3 (C) 3 : 1 : 2 (D) 1:2:3

1 1 1 1 1 1
105. If a, b, c are in GP and a x = b y = c z , then 105. ¶{X a, b, c JwUmoÝVa loUr ‘| h¡ VWm a x = b y = c z ,
x, y, z are in V~ x, y, z h¢
(A) AP (B) GP (A) g‘mÝVa loUr ‘| (B) JwUmoÝVa loUr ‘|
(C) HP (D) None of these (C) hamË‘H$ loUr ‘| (D) BZ‘| go H$moB© Zht

1-AA ] [ 25 ] [ P.T.O.

MM
MM
MM
MM 106. If p, q, r and s are positive real numbers such 106. ¶{X p, q, r VWm s Bg àH$ma H$s KZmË‘H$ dmñVm{dH$
MM
that p + q + r + s = 2, then M = (p + q) g§»¶mE§ h¡ {H p + q + r + s = 2, V~ M = (p + q) (r + s)
MM
MM (r + s) satisfies the relation, when gå~ÝY V~ g§Vwï> hmoJm, O~
MM (A) 0 < M < 1 (B) 1 < M < 2 (A) 0 < M < 1 (B) 1 < M < 2
MM
MM (C) 2 < M < 3 (D) 3 < M < 4 (C) 2 < M < 3 (D) 3 < M < 4
MM
MM 2
2
2
4
2
6

MM 107. The sum of the infinite series
2 4 6
107. AZÝV loUr 2! + 4! + 6! + --- H$m ¶moJ
2 2 2
2! + 4! + 6! + --- is h¡…
2 4
e +1 e +1 2
e +1 e +1
4
(A) 2 (B) 2 (A) (B)
2e 2 2e
2

2 2 2 2
(e - 1) (e + 1) 2
(e - 1)
2
(e + 1)
2 2
(C) 2 (D) 2 (C) (D)
2e 2e 2e
2
2e
2

108. If n is a positive integer, then n3 + 2n is divisible 108. ¶{X n EH$ KZmË‘H$ nyUmªH$ h¡, V~ n3 + 2n ^mÁ¶
by hmoJm
(A) 2 (B) 6 (A) 2 go> (B) 6 go>
(C) 15 (D) 3 (C) 15 go> (D) 3 go>

109. If a and b are the coefficients of xr and xn–r 109. ¶{X a VWm b H«$‘e… (1 + x)n Ho$ {dñVma ‘| xr VWm
respectively in the expansion of (1 + x)n, then xn–r Ho$ JwUm§H$ h¡, V~
(A) a = b (B) a + b = n2 (A) a = b (B) a + b = n2
(C) a = nb (D) a – b = n (C) a = nb (D) a – b = n

110. If A = = G and I is the unit matrix of order 110. ¶{X A = = G VWm I 2 × 2 H$mo[Q> H$s EH$H$
2 -1 2 -1
-1 2 -1 2
2 × 2, then A2 equals to Amì¶yh (unit matrix) h¡, V~ A2 ~am~a h¡
(A) 4A – 3I (B) 3A – 4I (A) 4A – 3I (B) 3A – 4I
(C) A – I (D) A + I (C) A – I (D) A + I

111. The value of λ, such that the system of equations 111. g‘rH$aUm| Ho$ {ZH$m¶ x – 2y + z = –4, 2x – y + 2z = 2
x – 2y + z = –4, 2x – y + 2z = 2 and x + y + λz = 4 has VWm x + y + λz = 4 H$m H$moB© hb Zht h¡ V~ λ
no solutions, is h¡…
(A) 0 (B) 1 (A) 0 (B) 1
(C) ≠1 (D) 3 (C) ≠1 (D) 3

1-AA ] [ 26 ] [ Contd...

MM
MM
MM
112. If α, b and ϒ are the roots of the equation 112. ¶{X α, b VWm ϒ g‘rH$aU x3 + px + q = 0 Ho$ ‘yb
MM
MM
x3 + px + q = 0, then the value of the determinant
a b Y MM
a b Y h¢, V~ {ZYm©aH$ b Y a H$m ‘mZ h¡… MM
b Y a is Y a b MM
Y a b MM
(A) 0 (B) 2 MM
(A) 0 (B) 2
(C) –2 (D) 1 MM
(C) –2 (D) 1 MM
MM
113. If n(U) = 700, n(A) = 200, n(B) = 300 and 113. ¶{X n(U) = 700, n(A) = 200, n(B) = 300 VWm

n(A ∩ B) = 100, then n(A1 ∩ B1) is equal to n(A ∩ B) = 100, V~ n(A1 ∩ B1) ~am~a h¡…
(A) 300 (B) 350 (A) 300 (B) 350

(C) 400 (D) 500 (C) 400 (D) 500

114. Which of the following statement is not correct 114. gå~ÝY R Omo {H$ a R b, O~ {H$ (if and only if)

for the relation R defined by a R b, if and only if b, a go EH$ {H$bmo‘rQ>a Ho$ AÝXa ahVm h¡, go n[a^m{fV

b lives within one kilometer from a? h¡& V~ {ZåZ ‘| go H$m¡Z gm H$WZ Ag˶ h¡…
(A) R is reflexive (A) R ñdVwë¶ gå~ÝY h¡

(B) R is symmetric (B) R g‘{‘V gå~ÝY h¡

(C) R is not anti-symmetric (C) R n«{V-g‘{‘V gå~ÝY Zht h¡

(D) None of these (D) BZ‘| go H$moB© Zht

-
115. Let f : R → R be a function defined by 115. ¶{X ’$bZ f : R → R Omo {H$ f (x) = xx - m
n
,
x-m Ohm± m ≠ n go n[a‘m{fV h¡, V~
f (x) = , where m ≠ n, then
x-n
(A) f EH¡$H$ Am¡a AmÀN>mXH$ ’$bZ h¡
(A) f is one-one and onto
(B) f EH¡$H$ Am¡a AmÀN>mXH$ Zht ’$bZ h¡
(B) f is one-one and not onto
(C) f ~hþEH$ Am¡a AmÀN>mXH$ ’$bZ h¡
(C) f is many one and onto (D) f ~hþEH$ Am¡a AmÝV[aH$ AmÀN>mXH$ ’$bZ h¡

(D) f is many one and into

1-AA ] [ 27 ] [ P.T.O.

MM
MM
MM
MM 116. The value of (tan10° + tan35°) + tan10° tan35° is 116. (tan10° + tan35°) + tan10° tan35° H$m ‘mZ h¡…
MM 1 1
(A) 0 (B) (A) 0 (B)
MM 2 2
MM (C) –1 (D) 1 (C) –1 (D) 1
MM
MM 4xy 4xy
MM 117. Sec2 θ = 2 is true, if 117. Sec2 θ = 2 g˶ h¡, ¶{X
(x + y) (x + y)
MM (A) x + y ≠ 0 (B) x = y, x ≠ 0 (A) x + y ≠ 0 (B) x = y, x ≠ 0
MM (C) x = y x ≠ 0, y = 0
(C) x = y (D) x ≠ 0, y = 0 (D)
MM

118. The minimum value of 9 tan2 θ + 4cot2 θ is 118. 9 tan2 θ + 4cot2 θ H$m ݶyZV‘ ‘mZ h¡…
(A) 13 (B) 9 (A) 13 (B) 9
(C) 6 (D) 12 (C) 6 (D) 12

r r
119. In ∆ABC, if ∠A= 2 , then cos2 B + cos2 c equals 119. {Ì^wO ∆ABC ‘|, ¶{X ∠A= 2 , V~ cos2 B + cos2 c
~am~a h¡…
(A) –2 (B) –1
(A) –2 (B) –1
(C) 1 (D) 0 (C) 1 (D) 0

Cos A Cos B Cos C
120. In ∆ABC, if a = b = c and a = 2, 120. {Ì^wO ∆ABC ‘|, ¶{X Cosa A = Cosb B = Cosc C
then area of triangle ∆ABC is VWm a = 2, V~ {Ì^wO ∆ABC H$m job’$b h¡…
(A) 2 sq. unit (B) 2 sq. unit (A) 2 dJ© BH$mB© (B) 2 dJ© BH$mB©
(C) 3 sq. unit (D) 3 sq. unit (C) 3 dJ© BH$mB© (D) 3 dJ© BH$mB©

121. The solution set of the equation sin–1 x  = 2 tan–1 x 121. g‘rH$aU sin–1 x  = 2 tan–1 x H$m hb-g‘yh h¡
is (A) {1, 2} (B) {–1, 2}
(A) {1, 2} (B) {–1, 2} 1
(C) {–1, 1, 0} (D) {1, 2 , 0}
1
(C) {–1, 1, 0} (D) {1, 2 , 0}

122. The angle between the lines 3 x + y = 1 and 122. aoImAm| 3 x + y = 1 VWm x + 3 y = 1 Ho$ ~rM
x+ 3 y = 1 is H$m H$moU h¡…
(A) 30° (B) 60° (A) 30° (B) 60°
(C) 90° (D) 45° (C) 90° (D) 45°

1-AA ] [ 28 ] [ Contd...

MM
MM
MM
123. A straight line through the point A(3,4) is such 123. {~ÝXþ A(3,4) go JwOaZo dmbr EH$ gab aoIm Bg àH$ma MM
MM
that its intercept between the axes is bisected h¡ {H$ Ajm| Ho$ ~rM H$m BgH$m A§V…IÊS (intercept)> MM
at A. Its equation is {~ÝXþ A na {Û^m{OV hmoVm h¡& Bg aoIm H$m g‘rH$aU h¡… MM
(A) 4x + 3y = 24 (B) 3x + 4y = 25 (A) 4x + 3y = 24 (B) 3x + 4y = 25 MM
MM
(C) x + y = 7 (D) 3x – 4y = –7 (C) x + y = 7 (D) 3x – 4y = –7 MM
MM
124. What is the length of an equilateral triangle
4
124. d¥Îm x2 + y2 = 3 ‘| CËH$sU© g‘~mhþ {Ì^wO Ho$ MM
4
MM
inscribed in the circle x2 + y2 = 3 ? ^wOm H$s bå~mB© ³¶m h¡?
(A) 2 units (B) 3 units (A) 2 BH$mB©> (B) 3 BH$mB©>

(C) 4 units (D) 5 units (C) 4 BH$mB©> (D) 5 BH$mB©>

125. The condition for a line y = 2x + c to touch 125. aoIm y = 2x + c VWm d¥Îm x2 + y2 = 16 Ho$ ñne©

the circle x2 + y2 = 16 is H$aZo H$m à{V~ÝY h¡…
(A) c = 10 (B) c2 = 80 (A) c = 10 (B) c2 = 80

(C) c = 12 (D) c2 = 64 (C) c = 12 (D) c2 = 64

126. If a parabola has the origin as its focus and 126. ¶{X EH$ nadb¶ {OgH$s Zm{^ (focus) ‘wb{~ÝXw h¡

the line x = 2 as the directrix. Then, the vertex VWm aoIm x = 2 {Z¶Vm (directrix) h¡& V~ nadb¶
of the parabola is at H$m erf© (vertex) h¡…
(A) (2, 0) (B) (0, 2) (A) (2, 0) (B) (0, 2)

(C) (1, 0) (D) (0, 1) (C) (1, 0) (D) (0, 1)

2
x
2
y
127. The length of the major axis of the ellipse 127. ¶{X XrK©dÎ¥ m 2 + 2 = 1 Ho$ XrK©Aj (major axis)
2
a b
x
2
y H$s bå~mB© CgH$s bKwAj (minor axis) H$s bå~mB© go
2 + 2 = 1 is three time the length of
a b
minor axis, then its eccentricity is VrZ JwZr h¡, V~ CgH$s {dHo$ÝÐVm (eccentricity) h¡…
1 1 1 1
(A) 3 (B) (A) 3 (B)
3 3

2 2 2 2 2 2
(C) (D) (C) 3 (D) 3
3 3

1-AA ] [ 29 ] [ P.T.O.

MM
MM
MM
MM 128. The length of the tangent from point (5, 1) to 128. {~ÝXþ (5, 1) go d¥Îm x2 + y2 + 6x – 4y – 3 = 0
MM
the circle x2 + y2 + 6x – 4y – 3 = 0 is na ñne© aoIm H$s bå~mB© h¡…
MM
MM (A) 81 (B) 29 (A) 81 (B) 29
MM (C) 7 (D) 21 (C) 7 (D) 21
MM
MM m
MM 129. lim x -- 1 is equal to
n 129. lim
m
x -1
~am~a h¡…
x"1 x 1 n
x"1 x - 1
MM
n m n m
MM (A) m (B) n (A) m (B) n
2m 2n 2m 2n
(C) n (D) m (C) (D)
n m

xf (2) - 2f (x) xf (2) - 2f (x)
130. If f (2) = 4 and f1 (2) = 1, then lim 130. ¶{X  f (2) = 4 VWm  f1 (2) =1,  V~ lim
x"2 x-2 x"2 x-2
is equal to ~am~a h¡…
(A) –2 (B) 1 (A) –2 (B) 1
(C) 2 (D) –1 (C) 2 (D) –1

d d
131. If x is measured in degree, then dx (cos x) is 131. g{X x H$s Zmn {S>J«r ‘| hmo, Vmo dx (cos x) ~am~a
equal to h¡…
180 180
(A) –sin x (B) r sin x (A) –sin x (B) r sin x
r r
(C) – 180 sin x (D) sin x (C) – 180 sin x (D) sin x

x +1 x -1 dy x -1
132. If y = sec–1 d n + sin–1 d n x +1 dy
x -1 x + 1 then dx 132. ¶{X  y = sec–1d n+ sin–1d n
x + 1 ,  V~ dx
x -1
is equal to ~am~a h¡…
1 1
(A) 0 (B) (A) 0 (B)
x +1 x +1
(C) 1 (D) x -1 (C) 1 (D) x -1

133. The minimum value of 2x + 3y, when xy = 6 is 133. O~ xy = 6 hmo Vmo 2x + 3y H$m ݶyZV‘ ‘mZ h¡…
(A) 9 (B) 12 (A) 9 (B) 12
(C) 8 (D) 6 (C) 8 (D) 6

1-AA ] [ 30 ] [ Contd...

MM
MM
MM
134. The point (0, 5) is closer to the curve x2 = 2y at 134. {~ÝXþ (0, 5), dH«$ x2 = 2y Ho$ H$ar~ hmoJm {~ÝXþ MM
MM
(A) ^ 2 , 0 h (B) (0, 0) (A) ^ 2 , 0 h go (B) (0, 0) go MM
(C) ^2, 2h (D) None of these (C) ^2, 2 h go (D) BZ‘| go H$moB© Zht MM
MM
MM
# 11 +- tan
2
x
# 11 +- tan
2
135. dx is equal to x
tan x
2 135.
tan x
dx ~am~a h¡…
2 MM
1 - tan x
MM
(A) log ` + j+ c 1 - tan x
1 tan x (A) log ` +
1 tan x
j+ c MM
MM
1 + tan x 1 + tan x
(B) log ` - j+ c (B) log ` - j+ c
1 tan x 1 tan x

(C)
1
` 1 - tan x j
2 log 1 + tan x + c (C)
1
` 1 - tan x j
2 log 1 + tan x + c

(D)
1
` 1 + tan x j
2 log 1 - tan x + c (D)
1
` 1 + tan x j
2 log 1 - tan x + c

136. Integral of f (x) = 1 + x with respect to x2, is H$m x2 Ho$ gmnoj g‘mH$bZ h¡…
2
136. f (x) =
2
1+x
3
2
2 . (1 + x )
2 3
2
2 . (1 + x )
2
(A) 3 x + c (A) + c
3 x
2 3
(B) 3 x (1 + x 2) 2 + c
(B)
2
x (1
3
+ x 2) 2 + c
3
2 3
(C) 3 (1 + x 2) 2 + c
(C)
2
(1
3
+ x 2) 2 + c
3
(D) None of these (D) BZ‘| go H$moB© Zht

# x - 5 dx is equal to
8
137. # x - 5 dx ~am~a h¡…
8

0 137.
0
(A) 17 (B) 9 (A) 17 (B) 9
(C) 12 (D) 18 (C) 12 (D) 18

138. The area enclosed by the curves y = x3 and y = x 138. dH«$m| y = x3 VWm y = x go {Kao hþEo joÌ H$m joÌ’$b
is h¡…
5 5
(A) 3 sq. unit (B) 4 sq. unit (A)
5
(B)
5
3 dJ© BH$mB© 4 dJ© BH$mB©
5 5
(C) 12 sq. unit (D) 8 sq. unit (C)
5
(D)
5
12 dJ© BH$mB© 8 dJ© BH$mB©

1-AA ] [ 31 ] [ P.T.O.

MM
MM
MM
MM dy ax + h dy ax + h
MM 139. The solution of dx = by + k represents a 139. dx =
by + k
H$m hb nadb¶ {Zé{nV H$aoJm,
MM parabola, when O~
MM
(A) a = b = 0 (B) a = 1, b = 2 (A) a = b = 0 (B) a = 1, b = 2
MM
MM (C) a = 0, b ≠ 0 (D) a = 2, b = 1 (C) a = 0, b ≠ 0 (D) a = 2, b = 1
MM
MM
MM 140. The differential equation of all non-vertical 140. EH$ Vb na g^r aoImAm|, Omo bå~dV Zhr h¢
MM lines in a plane is H$m AdH$bV g‘rH$aU h¡…
2 2
d y 2
d x d y 2
d x
(A) 2 = 0 (B) 2 = 0 (A) 2 = 0 (B) 2 = 0
dx dy dx dy
dy dx dy dx
(C) dx = 0 (D) dy = 0 (C) dx = 0 (D) dy = 0

141. A and B stand in a ring along with 10 other 141. A VWm B 10 Aݶ ì¶p³V¶m| Ho$ gmW EH$ Koao ‘| IS>o
persons. If the arrangement is at random, then h¢& ¶{X ì¶dñWm H«$‘ a{hV H$s JB© hmo, Vmo A Am¡a B
the probability that there are exactly 3 persons Ho$ ~rM ‘| ¶WmW©V … (exactly) 3 ì¶p³VAm| Ho$ hmoZo H$s
between A and B, is àm{¶H$Vm h¡…
1 2 1 2
(A) 11 (B) 11 (A) 11 (B) 11
3 4 3 4
(C) 11 (D) 11 (C) 11 (D) 11

142. The probability that the same number appears 142. VrZ nmem| H$mo EH$ gmW CN>mbZo na VmZm| nmem| na
on throwing three dice simultaneously, is EH$ hr g§»¶m àH$Q> hmoZo H$s àm{¶H$Vm h¡…
1 5 1 5
(A) 36 (B) 36 (A) 36 (B) 36
3 4 3 4
(C) 36 (D) 13 (C) 36 (D) 13

5
143. For any two events A and B, if P(A∪B) = 6 , 143. {H$Ýhr Xmo KQ>ZmAm| A VWm B Ho$ {b¶o, ¶{X P(A∪B) =
1 1 5 1 1
P(A∩B) = 3 , P(B)= 2 , then P(A) is 6 , P(A∩B) = 3 , P(B)= 2 hmo, Vmo P(A) ~am~a h¡…
1 2 1 2
(A) 2 (B) 3 (A) 2 (B) 3
1 1
(C) 3 (D) None of these (C) 3 (D) BZ‘| go H$moB© Zht

1-AA ] [ 32 ] [ Contd...

MM
MM
MM
MM
144. The position vector of P and Q are respectively a 144. P Am¡ a Q Ho $ pñW{V g{Xe H« $ ‘e… a   V Wm
MM
and b . If R is a point on PQ such that PR = 5PQ, b   {Zé{nV h¢& ¶{X H$moB© {~ÝXþ R aoIm PQ na Bg MM
then the position vector of R is àH$ma h¡ {H$ PR = 5PQ, V~ R H$m pñW{V g{Xe h¡… MM
MM
(A) 5 b – 4 a (B) 5b + 4a (A) 5 b – 4 a (B) 5 b + 4 a MM
(C) 4 b – 5 a (D) 4b + 5a (C) 4 b – 5 a (D) 4 b + 5 a MM
MM
MM
145. If a . ( b × c ) = 0, then the correct statement is 145. ¶{X a . ( b × c ) = 0, V~ g˶ H$WZ h¡- MM
(A) Out of a , b , c any two vectors are parallel (A) $ a , b , c ‘| H$moB© Xmo g{Xe g‘mZmÝVa h¡.
(B) a , b , c are coplaner (B) a , b , c EH$ hr Vb ‘| h¢  
(C) any two are equal among a , b , c (C) a , b , c ‘| H$moB© Xmo ~am~a h¢
(D) None of these (D) BZ‘| go H$moB© Zht

146. If at, bt, ct are unit vectors satisfying 146. ¶{X at, bt, ct
Eo g o BH$mB© g{Xe h¢ Omo {H$
at - 3 bt + ct = 0, then the angle between the at - 3 bt + ct = 0 H$mo g§Vïw > H$aVo h¡, V~ g{Xe at VWm
vectors at and ct is ct Ho$ ~rM H$m H$moU h¡…
r r r r
(A) 4 (B) 3 (A) (B)
4 3
r r r r
(C) 6 (D) 2 (C) (D)
6 2

147. The resultant of two forces A and B is of 147. Xmo ~bm| A Am¡a B Ho$ n[aUm‘r H$m n[a‘mU A h¡&
magnitude A. If the force A is doubled, B ¶{X ~b A H$mo XþJZm H$a {X¶m Om¶ VWm ~b B
remaining the same, then the angle between H$mo Z ~Xbm Om¶ V~ Z¶o n[aUm‘r VWm B ~b Ho$
new resultant and the force B is ~rM H$m H$moU hmoJm
(A) 30° (B) 45° (A) 30° (B) 45°
(C) 90° (D) 60° (C) 90° (D) 60°

1-AA ] [ 33 ] [ P.T.O.

MM
MM
MM
MM 148. A point particle moves along a straight line such
148. EH$ {~ÝXþ H$U EH$ gab aoIm ‘| x = Ho$ AZwgma
t
MM
that x = t , where t is time. The ratio of
MM J{V H$a ahm h¡, Ohm± t g‘¶ h¡& V~ H$U Ho$ ËdaU
MM acceleration to cube of velocity is
H$m doJ Ho$ KZ Ho$ gmW AZwnmV hmoJm…
MM (A) –1 (B) –2
MM (A) –1 (B) –2
MM (C) –3 (D) None of these
(C) –3 (D) BZ‘| go H$moB© Zht
MM
MM 149. The centre of gravity of a rod of length L whose
MM 149. EH$ N>S> {OgH$s bå~mB© L h¡, BgH$m aoIr¶ Ð춑mZ
linear mass density varies as the square of the
KZËd BgHo$ EH$ {gao go Xÿar Ho$ dJ© Ho$ AZwgma ~Xb ahm
distance from one end is at
h¡& Bg N>S> H$m Jwê$Ëd Ho$ÝÐ BgHo {gao go {Z½Z na hmoJm-
L 3L
(A) 3 (B) L 3L
5 (A) 3 (B) 5
2L 3L
(C) 5 (D) 2L 3L
4 (C) 5 (D) 4

150. The equation of displacement of a particle is
150. EH$ H$U H$m {dñWmnZ g‘rH$aU x (t) = 5t2  –  7t  +  3
x (t) = 5t2  –  7t  +  3. The acceleration at the moment
h¡& O~ BgH$m doJ 5 m/sec hmo OmVm h¡ Cg jU
when its velocity becomes 5 m/sec is
ËdaU hmoJm-
(A) 3 m/sec2 (B) 8 m/sec2
(A) 3 m/sec2 (B) 8 m/sec2
(C) 7 m/sec2 (D) 10 m/sec2
(C) 7 m/sec2 (D) 10 m/sec2

1-AA ] [ 34 ] [ Contd...

MM
MM
SPACE FOR ROUGH WORK / H$ÀMo H$m‘ Ho$ {b¶o OJh MM
MM
MM
MM
MM
MM
MM
MM
MM
MM
MM

1-AA ] [ 35 ] [ P.T.O.

MM MM
MM MM
MM SPACE FOR ROUGH WORK / H$ÀMo H$m‘ Ho$ {b¶o OJh MM
MM MM
MM MM
MM MM
MM MM
MM MM
MM MM
MM MM
MM MM
MM MM
MM MM

1-AA ] [ 36 ]