iit mains 2015 set a
DESCRIPTION
This is a IIT mains Q paper.TRANSCRIPT
Time : 3 hrs. M.M. : 360
Regd. Office : Aakash Tower, Plot No.-4, Sec-11, MLU, Dwarka, New Delhi-110075
Ph.: 011-47623456 Fax : 011-47623472
JEE (MAIN)-2015
Important Instructions :
1. The test is of 3 hours duration.
2. The Test Booklet consists of 90 questions. The maximum marks are 360.
3. There are three parts in the question paper A, B, C consisting of Physics, Chemistry and
Mathematics having 30 questions in each part of equal weightage. Each question is allotted 4 (four)
marks for each correct response.
4. Candidates will be awarded marks as stated above in Instructions No. 3 for correct response of each
question. ¼ (one-fourth) marks will be deducted for indicating incorrect response of each question.
No deduction from the total score will be made if no response is indicated for an item in the answer
sheet.
5. There is only one correct response for each question. Filling up more than one response in each
question will be treated as wrong response and marks for wrong response will be deducted accordingly
as per instruction 4 above.
6. Use Blue/Black Ball Point Pen only for writing particulars/marking responses on Side-1 and Side-2
of the Answer Sheet. Use of pencil is strictly prohibited.
7. No candidate is allowed to carry any textual material, printed or written, bits of papers, pager, mobile
phone, any electronic device, etc. except the Admit Card inside the examination room/hall.
8. The CODE for this Booklet is A. Make sure that the CODE printed on Side-2 of the Answer Sheet
and also tally the serial number of the Test Booklet and Answer Sheet are the same as that on this
booklet. In case of discrepancy, the candidate should immediately report the matter to the Invigilator
for replacement of both the Test Booklet and the Answer Sheet.
(Physics, Chemistry and Mathematics)
A
Test Booklet Code
JEE (MAIN)-2015
2
1. Two stones are thrown up simultaneously from the
edge of a cliff 240 m high with initial speed of
10 m/s and 40 m/s respectively. Which of the
following graph best represents the time variation of
relative position of the second stone with respect to
the first?
(Assume stones do not rebound after hitting the
ground and neglect air resistance, take g = 10 m/s2)
(The figures are schematic and not drawn to scale)
(1)
(y2 – y
1) m
240
8t (s)
12t
(2)
(y2 – y
1) m
240
t (s)12
(3)
(y2 – y
1) m
240
8t (s)
12
(4)
(y2 – y
1) m
240
8t (s)
12
2. The period of oscillation of a simple pendulum is
2L
Tg
. Measured value of L is 20.0 cm known
to 1 mm accuracy and time for 100 oscillations of
the pendulum is found to be 90 s using a wrist
watch of 1 s resolution. The accuracy in the
determination of g is
(1) 2% (2) 3%
(3) 1% (4) 5%
PART–A : PHYSICS
1. fdlh 240 m Å¡ph pksVh ds ,d fdukjs ls] nks iRFkjksa dks,dlkFk Åij dh vksj isaQdk x;k gS] budh izkjafHkd pkyØe'k% 10 m/s rFkk 40 m/s gS] rks] fuEukafdr esa ls dkSulkxzkiQ (vkys[k) igys iRFkj ds lkis{k nwljs iRFkj dh fLFkfrds le; fopj.k (ifjorZu) dks lokZfèkd lgh n'kkZrk gS\
(eku yhft, fd] iRFkj tehu ls Vdjkus ds i'pkr Åijdh vksj ugha mNyrs gSa rFkk ok;q dk izfrjksèk ux.; gS]fn;k gS g = 10 m/s2)
(;gk¡ xzkiQ dsoy O;oLFkk vkjs[k gSa vkSj Ldsy ds vuqlkjugha gSa)
(1)
(y2 – y
1) m
240
8t (s)
12t
(2)
(y2 – y
1) m
240
t (s)12
(3)
(y2 – y
1) m
240
8t (s)
12
(4)
(y2 – y
1) m
240
8t (s)
12
2. fdlh ljy yksyd dk vkorZ] 2 LT
g gSA L dk
ekfir eku 20.0 cm gS] ftldh ;FkkFkZrk 1 mm gSA bl yksydds 100 nksyuksa dk le; 90 s gS] ftls 1 s foHksnu dh?kM+h ls ukik x;k gSA rks] g ds fuèkkZj.k esa ;FkkFkZrk gksxh %(1) 2% (2) 3%
(3) 1% (4) 5%
3
JEE (MAIN)-2015
3. A BF
Given in the figure are two blocks A and B of
weight 20 N and 100 N, respectively. These are
being pressed against a wall by a force F as shown.
If the coefficient of friction between the blocks is 0.1
and between block B and the wall is 0.15, the
frictional force applied by the wall on block B is
(1) 100 N (2) 80 N
(3) 120 N (4) 150 N
4. A particle of mass m moving in the x direction with
speed 2v is hit by another particle of mass 2m
moving in the y direction wth speed v. If the
collision is perfectly inelastic, the percentage loss in
the energy during the collision is close to
(1) 44% (2) 50%
(3) 56% (4) 62%
5. Distance of the centre of mass of a solid uniform
cone from its vertex is z0. If the radius of its base is
R and its height is h then z0 is equal to
(1)
2
4
h
R(2)
3
4
h
(3)5
8
h(4)
23
8
h
R
6. From a solid sphere of mass M and radius R a cube
of maximum possible volume is cut. Moment of
inertia of cube about an axis passing through its
center and perpendicular to one of its faces is
(1)
2
32 2
MR
(2)
2
16 2
MR
(3)
24
9 3
MR
(4)
24
3 3
MR
7. From a solid sphere of mass M and radius R, a
spherical portion of radius 2
R is removed, as
shown in the figure. Taking gravitational potential
V = 0 at r = , the potential at the centre of the
cavity thus formed is (G = gravitational constant)
(1)2
GM
R(2)
GMR
(3)23
GM
R(4)
2GMR
3. A BF
;gk¡ vkjs[k esa nks CykWd (xqVds) A vkSj B n'kkZ;s x;s gSaftuds Hkkj Øe'k% 20 N rFkk 100 N gSaA bUgsa] ,d cy F
}kjk fdlh nhokj ij nck;k tk jgk gSA ;fn ?k"kZ.k xq.kkaddk eku] A rFkk B ds chp 0.1 rFkk B vkSj nhokj ds chp0.15 gS rks] nhokj }kjk CykWd B ij yxk cy gksxk %(1) 100 N (2) 80 N
(3) 120 N (4) 150 N
4. x–fn'kk esa 2v pky ls pyrs gq, m æO;eku ds ,d d.kls] y–fn'kk esa v osx ls pyrk gqvk 2m æO;eku dk ,dd.k] Vdjkrk gSA ;fn ;g la?kV~V (VDdj) iw.kZr% vizR;kLFkgS rks] VDdj ds nkSjku ÅtkZ dk {k; (gkfu) gksxh%(1) 44% (2) 50%
(3) 56% (4) 62%
5. fdlh ,dleku Bksl 'kadq ds nzO;eku dsUæ dh mlds 'kh"kZ lsnwjh z
0 gSA ;fn 'kadq ds vkèkkj dh f=kT;k R rFkk 'kadq dh Å¡pkbZ
h gks rks z0 dk eku fuEukafdr esa ls fdlds cjkcj gksxk\
(1)
2
4
h
R(2)
3
4
h
(3)5
8
h(4)
23
8
h
R
6. fdlh Bksl xksys dk nzO;eku M rFkk bldh f=kT;k R gSA blesals vfèkdre laHko vk;ru dk ,d D;wc (?ku) dkV fy;ktkrk gSA bl D;wc dk tM+Ro vk?kw.kZ fdruk gksxk] ;fn]bldh ?kw.kZu&v{k] blds dsUnz ls gksdj xqtjrh gS rFkk bldsfdlh ,d iQyd ds yEcor~ gS\
(1)
2
32 2
MR
(2)
2
16 2
MR
(3)
24
9 3
MR
(4)
24
3 3
MR
7. ,d Bksl xksys dk nzO;eku M rFkk f=kT;k R gSA blls 2
R
f=kT;k dk ,d xksyh; Hkkx] vkjs[k esa n'kkZ;s x;s vuqlkjdkV fy;k tkrk gSA r = (vuUr) ij xq#Roh; foHkods eku V dks 'kwU; (V = 0) ekurs gq,] bl izdkj cusdksVj (dSfoVh) ds dsUnz ij] xq#Roh; foHko dk eku gksxk%
(G = xq#Roh; fLFkjk¡d gS)
(1)2
GM
R(2)
GMR
(3)23
GM
R(4)
2GMR
JEE (MAIN)-2015
4
8. A pendulum made of a uniform wire of cross-
sectional area A has time period T. When an
additional mass M is added to its bob, the time
period changes to TM
. If the Young's modulus of the
material of the wire is Y then 1
Y is equal to
(g = gravitational acceleration)
(1)
⎡ ⎤⎛ ⎞ ⎢ ⎥⎜ ⎟⎝ ⎠⎢ ⎥⎣ ⎦
2
1M
T A
T Mg (2)
⎡ ⎤⎛ ⎞ ⎢ ⎥⎜ ⎟⎝ ⎠⎢ ⎥⎣ ⎦
2
1M
MgT
T A
(3)
⎡ ⎤⎛ ⎞⎢ ⎥⎜ ⎟⎝ ⎠⎢ ⎥⎣ ⎦
2
1M
T A
T Mg (4)
⎡ ⎤⎛ ⎞⎢ ⎥ ⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦
2
1
M
T A
T Mg
9. Consider a spherical shell of radius R at
temperature T. The black body radiation inside it
can be considered as an ideal gas of photons with
internal energy per unit volume 4U
u TV
and
pressure ⎛ ⎞ ⎜ ⎟⎝ ⎠
1
3
UP
V
. If the shell now undergoes an
adiabatic expansion the relation between T and R is
(1) T e–R
(2) T e–3R
(3)1
TR
(4) 3
1T
R
10. A solid body of constant heat capacity 1 J/°C is
being heated by keeping it in contact with reservoirs
in two ways :
(i) Sequentially keeping in contact with 2
reservoirs such that each reservoir supplies
same amount of heat.
(ii) Sequentially keeping in contact with 8
reservoirs such that each reservoir supplies
same amount of heat.
In both the cases body is brought from initial
temperature 100°C to final temperature 200°C.
Entropy change of the body in the two cases
respectively is
(1) ln 2, 4ln 2
(2) ln 2, ln 2
(3) ln 2, 2ln 2
(4) 2ln 2, 8ln 2
8. fdlh ,dleku rkj dh vuqizLFk dkV dk {ks=kiQy 'A' gSA
blls cuk;s x;s ,d yksyd dk vkorZdky T gSA bl yksyd
ds xksyd ls ,d vfrfjDr M nzO;eku tksM+ nsus ls yksyd
dk vkorZdky ifjofrZr gksdj TM gks tkrk gSA ;fn bl rkj
ds inkFkZ dk ;ax xq.kkad 'Y' gks rks 1
Y dk eku gksxk%
(g = xq#Roh; Roj.k)
(1)
⎡ ⎤⎛ ⎞ ⎢ ⎥⎜ ⎟⎝ ⎠⎢ ⎥⎣ ⎦
2
1M
T A
T Mg (2)
⎡ ⎤⎛ ⎞ ⎢ ⎥⎜ ⎟⎝ ⎠⎢ ⎥⎣ ⎦
2
1M
MgT
T A
(3)
⎡ ⎤⎛ ⎞⎢ ⎥⎜ ⎟⎝ ⎠⎢ ⎥⎣ ⎦
2
1M
T A
T Mg (4)
⎡ ⎤⎛ ⎞⎢ ⎥ ⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦
2
1
M
T A
T Mg
9. fdlh xksyh; dks'k ('kSy) dh f=kT;k R gS vkSj bldk rki
T gSA blds Hkhrj Ñf".kdk fofdj.kksa dks iQksVkWuksa dh ,d
,slh vkn'kZ xSl ekuk tk ldrk gS ftldh izfr bdkbZ
vk;ru vkUrfjd Åtk Z ] 4Uu T
V rFk k n kc]
⎛ ⎞ ⎜ ⎟⎝ ⎠
1
3
Up
V gSA ;fn bl dks'k esa #n~èkks"e izlkj gks rks] T
rFkk R ds chp lacaèk gksxk %
(1) T e–R
(2) T e–3R
(3)1
TR
(4) 3
1T
R
10. ,d Bksl fiaM (oLrq) dh fLFkj Å"ek /kfjrk 1 J/°C gSA bldks
Å"edksa (Å"ek HkaMkjksa) ds lEidZ esa j[kdj fuEu nks izdkj
ls xeZ fd;k tkrk gS]
(i) vuqØfed :i ls 2 Å"edksa ds lEidZ esa bl izdkj
j[kdj fd izR;sd Å"ed leku ek=kk esa Å"ek nsrk gS]
(ii) vuqØfed :i ls 8 Å"edksa ds lEidZ esa bl izdkj
j[kdj fd izR;sd Å"ed leku ek=kk esa Å"ek nsrk gS]
nksuksa fLFkfr;ksa esa fiaM dk izkjafHkd rki 100°C rFkk vfUre
rki 200°C gSA rks] bu nks fLFkfr;ksa esa fiaM dh ,UVªkWih esa
ifjorZu gksxk] Øe'k%
(1) ln 2, 4ln 2
(2) ln 2, ln 2
(3) ln 2, 2ln 2
(4) 2ln 2, 8ln 2
5
JEE (MAIN)-2015
11. Consider an ideal gas confined in an isolated closed
chamber. As the gas undergoes an adiabatic
expansion, the average time of collision between
molecules increases as Vq, where V is the volume of
the gas. The value of q is
⎛ ⎞ ⎜ ⎟
⎝ ⎠
P
v
C
C
(1) 3 5
6(2)
3 5
6
(3) 12
(4) 12
12. For a simple pendulum, a graph is plotted between
its kinetic energy (KE) and potential energy (PE)
against its displacement d. Which one of the
following represents these correctly?
(Graphs are schematic and not drawn to scale)
(1)
E
KE
d
PE
(2)
E
KEd
PE
(3)
E KE
d
PE
(4)
E
PE
KE
13. A train is moving on a straight track with speed
20 ms–1. It is blowing its whistle at the frequency of
1000 Hz. The percentage change in the frequency
heard by a person standing near the track as the
train passes him is (speed of sound = 320 ms–1)
close to
(1) 6% (2) 12%
(3) 18% (4) 24%
11. ,d vkn'kZ xSl fdlh cUn (laor)] fo;qDr (foyfxr) d{kesa lhfer (j[kh) gSA bl xSl esa #n~èkks"e izlkj gksus ij] bldsv.k qvk s a ds chp VDdj dk vk Slr dky (le;)
qV ds vuqlkj c<+ tkrk gS] tgk¡ V xSl dk vk;ru gSArks q dk eku gksxk %
⎛ ⎞ ⎜ ⎟
⎝ ⎠
P
v
C
C
(1) 3 5
6(2)
3 5
6
(3) 12
(4) 12
12. fdlh ljy yksyd ds fy;s] mlds foLFkkiu d rFkk mldhxfrt ÅtkZ ds chp vkSj foLFkkiu d rFkk mldh fLFkfrtÅtkZ ds chp xzkiQ [khaps x;s gSaA fuEukafdr esa ls dkSu lkxzkiQ (vkys[k) lgh gS\
(;gk¡ xzkiQ dsoy O;oLFkk vkjs[k gSa vkSj Ldsy ds vuqlkjugha gSa)
(1)
E
KE
d
PE
(2)
E
KEd
PE
(3)
E KE
d
PE
(4)
E
PE
KE
13. ,d Vªsu (jsyxkM+h) lhèkh iVfj;ksa ij 20 ms–1 dh pky lsxfr dj jgh gSA bldh lhVh dh èofu dh vko`fÙk1000 Hz gSA ;fn èofu dh ok;q esa pky 320 ms–1 gks rks]iVfj;ksa ds fudV [kM+s O;fDr ds ikl ls Vªsu ds xqtjusij] ml O;fDr }kjk lquh xbZ lhVh dh èofu dh vko`fÙkesa izfr'kr ifjorZu gksxk yxHkx :
(1) 6% (2) 12%
(3) 18% (4) 24%
JEE (MAIN)-2015
6
14. A long cylindrical shell carries positive surface
charge in the upper half and negative surface
charge – in the lower half. The electric field lines
around the cylinder will look like figure given in
(figures are schematic and not drawn to scale)
(1)
++++
++
––––
–
–
–
–
(2)
+++
+++
––––
––––
(3) +++ +
++
––––
––––
(4)
15. A uniformly charged solid sphere of radius R has
potential V0
(measured with respect to ) on its
surface. For this sphere the equipotential surfaces
with potentials 0 0 0 0
3 5 3, , and
2 4 4 4
V V V V have radius
R1, R
2, R
3 and R
4 respectively. Then
(1) R1
= 0 and R2 > (R
4 – R
3)
(2) R1 0 and (R
2 – R
1) > (R
4 – R
3)
(3) R1
= 0 and R2 < (R
4 – R
3)
(4) 2R < R
4
16. In the given circuit, charge Q2 on the 2 F capacitor
changes as C is varied from 1 F to 3 F. Q2 as a
function of C is given properly by : (Figures are
drawn schematically and are not to scale)
1 F
2 FC
E
14. fdlh yEcs csyukdkj dks'k ds Åijh Hkkx esa èkukRed i"Bvkos'k rFkk fupys Hkkx esa ½.kkRed i`"B vkos'k – gSaAbl csyu (flfyUMj) ds pkjksa vksj fo|qr {ks=k&js[kk;sa] ;gk¡n'kkZ;s x;s vkjs[kksa esa ls fdl vkjs[k ds leku gksaxhA
(;g vkjs[k dsoy O;oLFkk vkjs[k gS vkSj Ldsy ds vuqlkjugha gS)
(1)
++++
++
––––
–
–
–
–
(2)
(3)
+++ +
++
––––
––––
(4)
15. R f=kT;k ds fdlh ,dleku vkosf'kr Bksl xksys ds i`"Bdk foHko V
0 gS (ds lkis{k ekik x;k)A bl xksys ds fy;s]
0 0 0 03 5 3
, , 2 4 4 4
V V V VrFkk foHkoksa okys lefoHkoh i`"Bksa dh
f=kT;k;sa] Øe'k% R1, R
2, R
3 rFkk R
4 gSaA rks]
(1) R1
= 0 rFkk R2 > (R
4 – R
3)
(2) R1 0 rFkk (R
2 – R
1) > (R
4 – R
3)
(3) R1
= 0 rFkk R2 < (R
4 – R
3)
(4) 2R < R
4
16. fn;s x;s ifjiFk esa] C ds eku ds 1F ls 3F ifjofrZr gksusls] 2F laèkkfj=k ij vkos'k Q
2 esa ifjorZu gksrk gSA 'C' ds iQyu
ds :i esa Q2 dks dkSu lk vkys[k lgh n'kkZrk gS\ (vkys[k
dsoy O;oLFkk vkjs[k gSa vkSj Ldsy ds vuqlkj ugha gSaA)
1 F
2 FC
E
7
JEE (MAIN)-2015
(1)
Q2
C1 F 3 F
Charge
(2)
Q2
C1 F 3 F
Charge
(3)
Q2
C1 F 3 F
Charge
(4)
Q2
C1 F 3 F
Charge
17. When 5 V potential difference is applied across a
wire of length 0.1 m, the drift speed of electrons is
2.5 × 10–4 ms–1. If the electron density in the wire is
8 × 1028 m–3, the resistivity of the material is close to
(1) 1.6 × 10–8 m (2) 1.6 × 10–7 m
(3) 1.6 × 10–6 m (4) 1.6 × 10–5 m
18. In the circuit shown, the current in the 1 resistor
is
9 V1
2 P
6 V
3 3 Q
(1) 1.3 A, from P to Q
(2) 0 A
(3) 0.13 A, from Q to P
(4) 0.13 A, from P to Q
19. Two coaxial solenoids of different radii carry
current I in the same direction. Let ���
1F be the
magnetic force on the inner solenoid due to the
outer one and ���
2F be the magnetic force on the outer
solenoid due to the inner one. Then
(1)���
1F =
���
2F = 0
(2)���
1F is radially inwards and
���
2F is radially
outwards
(3)���
1F is radially inwards and
���
2F = 0
(4)���
1F is radially outwards and
���
2F = 0
(1)
Q2
C1 F
3 F
vkos'k
(2)
Q2
C1 F 3 F
vkos'k
(3)
Q2
C1 F 3 F
vkos'k
(4)
Q2
C1 F 3 F
vkos'k
17. 0.1 m yacs fdlh rkj ds fljksa ds chp 5 V foHkokarj vkjksfirdjus ls bysDVªkWuksa dh viokg pky 2.5 × 10–4 ms–1 gksrhgSA ;fn bl rkj esa bysDVªkWu ?kuRo 8 × 1028 m–3 gks rks]bl ds inkFkZ dh izfrjksèkdrk gksxh] yxHkx%
(1) 1.6 × 10–8 m (2) 1.6 × 10–7 m
(3) 1.6 × 10–6 m (4) 1.6 × 10–5 m
18. n'kkZ;s x;s ifjiFk esa 1 izfrjksèkd ls izokfgr èkkjk gksxh%
9 V1
2 P
6 V
3 3 Q
(1) 1.3 A, P ls Q dh vksj
(2) 0 A
(3) 0.13 A, Q ls P dh vksj
(4) 0.13 A, P ls Q dh vksj
19. nks lek{kh ifjukfydkvksa esa] izR;sd ls I èkkjk ,d gh fn'kkesa izokfgr gks jgh gSA ;fn] ckgjh ifjukfydk ds dkj.k]
Hkhrjh ifjukfydk ij pqEcdh; cy ���
1F rFkk Hkhrjh ifjukfydk
ds dkj.k] ckgjh ifjukfydk ij pqEcdh; cy ���
2F gks rks %
(1)���
1F =
���
2F = 0
(2)���
1F Hkhrj dh vksj o vjh; (f=kT;) gS rFkk
���
2F ckgj
dh vksj o vjh; gSA
(3)���
1F Hkhrj dh vksj o vjh; gS rFkk
���
2F = 0 gSA
(4)���
1F ckgj dh vksj o vjh; gS rFkk
���
2F = 0 gSA
JEE (MAIN)-2015
8
20. Two long current carrying thin wires, both with
current I, are held by insulating threads of length L
and are in equilibrium as shown in the figure, with
threads making an angle with the vertical. If wires
have mass per unit length then the value of I is
(g = gravitational acceleration)
I I
L
(1)
0
sin
cos
gL
(2)
0
2 sincos
gL
(3)
0
2 tangL
(4)
0
tangL
21. A rectangular loop of sides 10 cm and 5 cm carrying
a current I of 12 A is placed in different orientations
as shown in the figures below:
(a)
z
BI I
I
I
y
x
(b)
z
B
I
I
y
xI
I
(c)
z
I
y
x
B
I
I
I
(d)
z
B
I
I
y
xI
I
20. nks irys yEcs rkjksa esa izR;sd ls I èkkjk izokfgr gks jgh gSAbUgsa L yEckbZ ds fo|qrjksèkh èkkxksa ls yVdk;k x;k gSA buèkkxksa esa izR;sd ds }kjk ÅèokZèkj fn'kk ls dks.k cukus dhfLFkfr esa] ;s nksuksa rkj lkE;koLFkk esa jgrs gSaA ;fn bu rkjksadh izfr bdkbZ yEckbZ nzO;eku gS rFkk g xq#Roh; Roj.kgS rks] I dk eku gksxk %
I I
L
(1)
0
sin
cos
gL
(2)
0
2 sincos
gL
(3)
0
2 tangL
(4)
0
tangL
21. 10 cm rFkk 5 cm Hkqtkvksa ds ,d vk;rkdkj ywi (ik'k)ls ,d fo|qr èkkjk] I = 12 A, izokfgr gks jgh gSA bl ik'kdks vkjs[k esa n'kkZ;s x;s vuqlkj fofHkUu vfHkfoU;klksa(fLFkfr;ksa) esa j[kk x;k gSA
(a)
z
BI I
I
I
y
x
(b)
z
B
I
I
y
xI
I
(c)
z
I
y
x
B
I
I
I
(d)
z
B
I
I
y
xI
I
9
JEE (MAIN)-2015
If there is a uniform magnetic field of 0.3 T in the
positive z direction, in which orientations the loop
would be in (i) stable equilibrium and (ii) unstable
equilibrium?
(1) (a) and (b), respectively
(2) (a) and (c), respectively
(3) (b) and (d), respectively
(4) (b) and (c), respectively
22. An inductor (L = 0.03 H) and a resistor (R = 0.15
k) are connected in series to a battery of 15 V EMF
in a circuit shown below. The key K1 has been kept
closed for a long time. Then at t = 0, K1 is opened
and key K2 is closed simultaneously. At
t = 1 ms, the current in the circuit will be 5( 150)e
K2
K1
15 V
0.15 k0.03 H
(1) 100 mA (2) 67 mA
(3) 6.7 mA (4) 0.67 mA
23. A red LED emits light at 0.1 watt uniformly around
it. The amplitude of the electric field of the light at
a distance of 1 m from the diode is
(1) 1.73 V/m (2) 2.45 V/m
(3) 5.48 V/m (4) 7.75 V/m
24. Monochromatic light is incident on a glass prism of
angle A. If the refractive index of the material of the
prism is , a ray, incident at an angle , on the face
AB would get transmitted through the face AC of the
prism provided.
B C
A
(1) ⎡ ⎤⎛ ⎞⎛ ⎞ ⎢ ⎥⎜ ⎟⎜ ⎟⎢ ⎥⎝ ⎠⎝ ⎠⎣ ⎦
1 1 1sin sin sinA
(2) ⎡ ⎤⎛ ⎞⎛ ⎞ ⎢ ⎥⎜ ⎟⎜ ⎟⎢ ⎥⎝ ⎠⎝ ⎠⎣ ⎦
1 1 1sin sin sinA
(3) ⎡ ⎤⎛ ⎞⎛ ⎞ ⎢ ⎥⎜ ⎟⎜ ⎟⎢ ⎥⎝ ⎠⎝ ⎠⎣ ⎦
1 1 1cos sin sinA
(4) ⎡ ⎤⎛ ⎞⎛ ⎞ ⎢ ⎥⎜ ⎟⎜ ⎟⎢ ⎥⎝ ⎠⎝ ⎠⎣ ⎦
1 1 1cos sin sinA
;fn ogk¡ 0.3 T rhozrk dk dksbZ ,dleku pqEcdh; {ks=k]èkukRed z fn'kk esa fo|eku gS rks] n'kkZ;s x;s fdl vfHkfoU;klesa] ;g ik'k (ywi) (i) LFkk;h larqyu rFkk (ii) vLFkk;h larqyuesa] gksxk\
(1) Øe'k% (a) rFkk (b) esa
(2) Øe'k% (a) rFkk (c) esa
(3) Øe'k% (b) rFkk (d) esa
(4) Øe'k% (b) rFkk (c) esa
22. n'kkZ;s x;s ifjiFk esa] ,d izsjd (L = 0.03 H) rFkk ,dizfrjksèkd (R = 0.15 k) fdlh 15 V fo|qr okgd cy(bZ-,e-,iQ) dh cSVjh ls tqM+s gSaA dqath K
1 dks cgqr le;
rd cUn j[kk x;k gSA blds i'pkr~ le; t = 0 ij] K1
dks [kksy dj lkFk gh lkFk] K2 dks cUn fd;k tkrk gSA
le; t = 1 ms ij] ifjiFk esa fo|qr èkkjk gksxh % 5( 150)e
K2
K1
15V
0.15 k0.03H
(1) 100 mA (2) 67 mA
(3) 6.7 mA (4) 0.67 mA
23. ,d yky jax dk ,y-bZ-Mh- (izdk'k mRltZd Mk;ksM) 0.1 okVij] ,dleku izdk'k mRlftZr djrk gSA Mk;ksM ls 1 m nwjh ij]bl izdk'k ds fo|qr {ks=k dk vk;ke gksxk %(1) 1.73 V/m (2) 2.45 V/m
(3) 5.48 V/m (4) 7.75 V/m
24. dk¡p ds fdlh fizTe dk dks.k 'A' gSA bl ij ,do.khZ izdk'kvkifrr gksrk gSA ;fn] fizTe ds inkFkZ dk viorZukad gSrks] fizTe ds AB iQyd ij] dks.k vkifrr izdk'k dhfdj.k] fizTe ds iQyd AC ls ikjxr gksxh ;fn %
B C
A
(1) ⎡ ⎤⎛ ⎞⎛ ⎞ ⎢ ⎥⎜ ⎟⎜ ⎟⎢ ⎥⎝ ⎠⎝ ⎠⎣ ⎦
1 1 1sin sin sinA
(2) ⎡ ⎤⎛ ⎞⎛ ⎞ ⎢ ⎥⎜ ⎟⎜ ⎟⎢ ⎥⎝ ⎠⎝ ⎠⎣ ⎦
1 1 1sin sin sinA
(3) ⎡ ⎤⎛ ⎞⎛ ⎞ ⎢ ⎥⎜ ⎟⎜ ⎟⎢ ⎥⎝ ⎠⎝ ⎠⎣ ⎦
1 1 1cos sin sinA
(4) ⎡ ⎤⎛ ⎞⎛ ⎞ ⎢ ⎥⎜ ⎟⎜ ⎟⎢ ⎥⎝ ⎠⎝ ⎠⎣ ⎦
1 1 1cos sin sinA
JEE (MAIN)-2015
10
25. On a hot summer night, the refractive index of air is
smallest near the ground and increases with height
form the ground. When a light beam is directed
horizontally, the Huygen's principle leads us to
conclude that as it travels, the light beam
(1) Becomes narrower
(2) Goes horizontally without any deflection
(3) Bends downwards
(4) Bends upwards
26. Assuming human pupil to have a radius of 0.25 cm
and a comfortable viewing distance of 25 cm, the
minimum separation between two objects that
human eye can resolve at 500 nm wavelength is
(1) 1 m
(2) 30 m
(3) 100 m
(4) 300 m
27. As an electron makes a transition from an excited
state to the ground state of a hydrogen-like atom/ion
(1) Its kinetic energy increases but potential energy
and total energy decrease
(2) Kinetic energy, potential energy and total energy
decrease
(3) Kinetic energy decreases, potential energy
increases but total energy remains same
(4) Kinetic energy and total energy decrease but
potential energy increases
28. Match List-I (Fundamental Experiment) with List-II
(its conclusion) and select the correct option from
the choices given below the list:
(A) Franck-Hertz (i) Particle nature
experiment of light
List -I List-II
(B) Photo-electric (ii) Discrete energyexperiment levels of atom
(C) Davison-Germer (iii) Wave nature ofexperiment electron
(iv) Structure ofatom
(1) (A) - (i) (B) - (iv) (C) - (iii)
(2) (A) - (ii) (B) - (iv) (C) - (iii)
(3) (A) - (ii) (B) - (i) (C) - (iii)
(4) (A) - (iv) (B) - (iii) (C) - (ii)
25. xzh"e ½rq dh xeZ jkf=k esa] Hkw&ry ds fudV] ok;q dkviorZukad U;wure gksrk gS vkSj Hkw&ry ls Å¡pkbZ ds lkFkc<+rk tkrk gSA ;fn] dksbZ izdk'k&fdj.k&iqat {kSfrt fn'kkesa tk jgk gks rks] gkbxsUl ds fl¼kUr ls ;g ifj.kke izkIrgksrk gS fd] pyrs gq, izdk'k&fdj.k iaqt %
(1) ladqfpr (ladh.kZ) gks tk;sxkA
(2) fcuk fo{ksfir gq,] {kSfrt fn'kk esa pyrk jgsxkA
(3) uhps dh vksj >qd tk;sxkA
(4) Åij dh vksj >qd tk;sxkA
26. ;fn ekuo us=k dh iqryh dh f=kT;k 0.25 cm, vkSj Li"Vlqfoèkk tud ns[kus dh nwjh 25 cm gks rks] 500 nm rjaxnSè;Zds izdk'k esa] nks oLrqvksa ds chp fdruh U;wure nwjh rdekuo us=k mu nksuksa ds chp foHksnu dj ldsxk\
(1) 1 m
(2) 30 m
(3) 100 m
(4) 300 m
27. tc dksbZ bysDVªkWu] gkbMªkstu tSls ijek.kq@vk;u dh mÙksftrvoLFkk ls U;wure ÅtkZ voLFkk esa laØe.k djrk gS rksmldh%
(1) xfrt ÅtkZ esa of¼ rFkk fLFkfrt ÅtkZ rFkk dqy ÅtkZesa deh gksrh gSA
(2) xfrt ÅtkZ] fLFkfrt ÅtkZ rFkk dqy ÅtkZ esa dehgks tkrh gSA
(3) xfrt ÅtkZ de gksrh gS] fLFkfrt ÅtkZ c<+rh gS vkSjdqy ÅtkZ ogh jgrh gSA
(4) xfrt ÅtkZ o dqy ÅtkZ de gks tkrh gSa fdUrq]fLFkfrt ÅtkZ c<+ tkrh gSA
28. lwph&I (ewy iz;ksx) dk lwph&II (mlds ifj.kke) ds lkFklqesyu (eSp) dhft;s vkSj fuEukafdr fodYiksa esa ls lghfodYi dk p;u dhft;s %
(A) (i)
lwph lwphizsaQd gV~Zl iz;ksx izdk'k dh df.kdk
izÑfr
-I -II
(B) (ii)
(C) (iii)
(iv)
izdk'k fo|qr iz;ksx v.kq ds fofoDr ÅtkZ Lrj
Msohlu teZj iz;ksx bysDVªkWu dh rjax izÑfrijek.kq dh lajpuk
(1) (A) - (i) (B) - (iv) (C) - (iii)
(2) (A) - (ii) (B) - (iv) (C) - (iii)
(3) (A) - (ii) (B) - (i) (C) - (iii)
(4) (A) - (iv) (B) - (iii) (C) - (ii)
11
JEE (MAIN)-2015
29. A signal of 5 kHz frequency is amplitude modulated
on a carrier wave of frequency 2 MHz. The
frequencies of the resultant signal is/are
(1) 2 MHz only
(2) 2005 kHz and 1995 kHz
(3) 2005 kHz, 2000 kHz and 1995 kHz
(4) 2000 kHz and 1995 kHz
30. An LCR circuit is equivalent to a damped
pendulum. In an LCR circuit the capacitor is
charged to Q0 and then connected to the L and R as
shown below :
R
C
L
If a student plots graphs of the square of maximum
charge 2
MaxQ on the capacitor with time (t) for two
different values L1 and L
2 (L
1 > L
2) of L then which
of the following represents this graph correctly?
(Plots are schematic and not drawn to scale)
(1)
L1
L2
t
Q2
Max
(2)
L2
L1
t
Q2
Max
(3)
L1
L2
t
Q2
Max
(4)
t
Q2
Max
Q0 (For both and )L L
1 2
29. 5 kHz vkofÙk ds fdlh ladsr (flXuy) dk 2 MHz vkofÙkdh okgd rjax ij vk;ke ekWMqyu fd;k x;k gSA rks] ifj.kkehflXuy (ladsr) dh vkofÙk gksxh %
(1) 2 MHz dsoy
(2) 2005 kHz rFkk 1995 kHz
(3) 2005 kHz, 2000 kHz rFkk 1995 kHz
(4) 2000 kHz rFkk 1995 kHz
30. LCR (,y-lh-vkj) ifjiFk fdlh voeafnr yksyd ds rqY;gksrk gSA fdlh LCR ifjiFk esa laèkkfj=k dks Q
0 rd vkosf'kr
fd;k x;k gS] vkSj fiQj bls vkjs[k esa n'kkZ;s x;s vuqlkj L
o R ls tksM+k x;k gSA
R
C
L
;fn ,d fo|kFkhZ L ds] nks fofHkUu ekuksa] L1 rFkk L
2 (L
1 >
L2) ds fy;s] le; t rFkk laèkkfj=k ij vfèkdre vkos'k ds
oxZ 2
MaxQ ds chp nks xzkiQ cukrk gS rks fuEukafdr esa ls
dkSu lk xzkiQ lgh gS\ (IykWV dsoy O;oLFkk IykWV gSa rFkkLdsy ds vuqlkj ugha gSa)
(1)
L1
L2
t
Q2
Max
(2)
L2
L1
t
Q2
Max
(3)
L1
L2
t
Q2
Max
(4)
t
Q2
Max
Q0 ( )L L
1 2 vkSj nksuksa ds fy,
JEE (MAIN)-2015
12
31. The molecular formula of a commercial resin used
for exchanging ions in water softening is
C8H
7SO
3Na (mol. wt. 206). What would be the
maximum uptake of Ca2+ ions by the resin when
expressed in mole per gram resin?
(1)1
103(2)
1
206
(3)2
309(4)
1
412
32. Sodium metal crystallizes in a body centred cubic
lattice with a unit cell edge of 4.29 Å. The radius of
sodium atom is approximately
(1) 1.86 Å (2) 3.22 Å
(3) 5.72 Å (4) 0.93 Å
33. Which of the following is the energy of a possible
excited state of hydrogen?
(1) +13.6 eV (2) –6.8 eV
(3) –3.4 eV (4) +6.8 eV
34. The intermolecular interaction that is dependent on
the inverse cube of distance between the molecules
is
(1) Ion-ion interaction (2) Ion-dipole interaction
(3) London force (4) Hydrogen bond
35. The following reaction is performed at 298 K.
2NO(g) + O2(g) ��⇀↽�� 2NO
2(g)
The standard free energy of formation of NO(g) is
86.6 kJ/mol at 298 K. What is the standard free
energy of formation of NO2(g) at 298 K?
(Kp = 1.6 × 1012)
(1) R(298) ln(1.6 × 1012) – 86600
(2) 86600 + R(298) ln(1.6 × 1012)
(3)
121.6 10
86600R 298
ln
(4) 120.5 2 86,600 R 298 1.6 10ln⎡ ⎤ ⎣ ⎦
36. The vapour pressure of acetone at 20°C is 185 torr.
When 1.2 g of a non-volatile substance was
dissolved in 100 g of acetone at 20°C, its vapour
pressure was 183 torr. The molar mass (g mol–1) of
the substance is
(1) 32 (2) 64
(3) 128 (4) 488
PART–B : CHEMISTRY
31. ,d okf.kT; jsft+u dk vkf.od lw=k C8H
7SO
3Na gS
(vkf.od Hkkj = 206) bl jsft+u dh Ca2+ vk;u dhvfèkdre varxzZg.k {kerk (eksy izfr xzke jsft+u) D;k gS\
(1)1
103(2)
1
206
(3)2
309(4)
1
412
32. lksfM;e /krq ,d var%dsfUnzr ?kuh; tkyd esa fØLVfyr gksrkgS ftlds dksj dh yackbZ 4.29Å gSA lksfM;e ijek.kq dh f=kT;kyxHkx gS :
(1) 1.86 Å (2) 3.22 Å
(3) 5.72 Å (4) 0.93 Å
33. fuEufyf[kr esa ls gkbZMªkstu dh laHko mÙksftr voLFkk dhmQtkZ dkSulh gS\
(1) +13.6 eV (2) –6.8 eV
(3) –3.4 eV (4) +6.8 eV
34. og varjk&v.kqd vU;ksU; fØ;k tks v.kqvksa ds chp dh nwjhds izfrykse ?ku ij fuHkZj gS] gS :
(1) vk;u&vk;u vU;ksU; (2) vk;u&f}/zqo vU;ksU;
(3) yaMu cy (4) gkbZMªkstu ca/d
35. fuEufyf[kr vfHkfØ;k dks 298 K ij fd;k x;kA
2NO(g) + O2(g) ��⇀↽�� 2NO
2(g)
298 K ij NO(g) ds laHkou dh ekud eqDr mQtkZ86.6 kJ/mol gSA 298 K ij NO
2(g) dh ekud eqDr
mQtkZ D;k gS\(Kp = 1.6 × 1012)
(1) R(298) ln(1.6 × 1012) – 86600
(2) 86600 + R(298) ln(1.6 × 1012)
(3)
121.6 10
86600R 298
ln
(4) 120.5 2 86,600 R 298 1.6 10ln⎡ ⎤ ⎣ ⎦
36. 20°C ij ,sflVksu dh ok"i nkc 185 torr gSA tc 20°C
ij] 1.2 g vok"i'khy inkFkZ dks 100 g ,sflVksu esa ?kksykx;k] rc ok"i nkc 183 torr gks x;kA bl inkFkZ dk eksyjnzO;eku (g mol–1 esa) gS :
(1) 32 (2) 64
(3) 128 (4) 488
13
JEE (MAIN)-2015
37. The standard Gibbs energy change at 300 K for the
reaction 2A ���⇀↽��� B + C is 2494.2 J. At a given time,
the composition of the reaction mixture is
1 1A , B 2 and C
2 2. The reaction proceeds
in the : [R = 8.314 J/K/mol, e = 2.718]
(1) Forward direction because Q > KC
(2) Reverse direction because Q > KC
(3) Forward direction because Q < KC
(4) Reverse direction because Q < KC
38. Two faraday of electricity is passed through a
solution of CuSO4. The mass of copper deposited at
the cathode is (at. mass of Cu = 63.5 amu)
(1) 0 g (2) 63.5 g
(3) 2 g (4) 127 g
39. Higher order (>3) reactions are rare due to
(1) Low probability of simultaneous collision of all
the reacting species
(2) Increase in entropy and activation energy as
more molecules are involved
(3) Shifting of equilibrium towards reactants due to
elastic collisions
(4) Loss of active species on collision
40. 3 g of activated charcoal was added to 50 mL of
acetic acid solution (0.06N) in a flask. After an hour
it was filtered and the strength of the filtrate was
found to be 0.042 N. The amount of acetic acid
adsorbed (per gram of charcoal) is
(1) 18 mg (2) 36 mg
(3) 42 mg (4) 54 mg
41. The ionic radii (in Å) of N3–, O2– and F– are
respectively
(1) 1.36, 1.40 and 1.71 (2) 1.36, 1.71 and 1.40
(3) 1.71, 1.40 and 1.36 (4) 1.71, 1.36 and 1.40
42. In the context of the Hall-Heroult process for the
extraction of Al, which of the following statement is
false?
(1) CO and CO2 are produced in this process
(2) Al2O
3 is mixed with CaF
2 which lowers the
melting point of the mixture and brings
conductivity
(3) Al3+ is reduced at the cathode to form Al
(4) Na3AlF
6 serves as the electrolyte
37. 300 K ij vfHkfØ;k 2A ���⇀↽��� B + C dh ekud fxCt+
mQtkZ 2494.2 J gSA fn, x, le; esa vfHkfØ;k feJ.k dk
l a ? kVu 1 1A , B 2 C
2 2vkSj g SA vfH k fØ;k
vxzflr gksrh gS : [R = 8.314 J/K/mol, e = 2.718]
(1) vxz fn'kk esa D;ksafd Q > KC
(2) foijhr fn'kk esa D;ksafd Q > KC
(3) vxz fn'kk esa D;ksafd Q < KC
(4) foijhr fn'kk eas D;ksafd Q < KC
38. CuSO4 ds ,d foy;u esa] nks iQSjkMs fo|qr izokfgr dh
xbZA dSFkksM ij fu{ksfir rkacs dk nzO;eku gS :
(Cu dk ijekf.od nzO;eku = 63.5 amu)
(1) 0 g (2) 63.5 g
(3) 2 g (4) 127 g
39. mPp dksfV vfHkfØ;k (>3) nqyZHk gS D;ksafd :
(1) izfrfØ;k esa lHkh iztkfr;ksa ds ,d lkFk VDdj dhlaHkkouk de gksrh gSA
(2) vf/d v.kqvksa ds 'kkfey gkssus ls ,aVªkih vkSj lafØ;.kmQtkZ esa of¼ gksrh gSA
(3) ykspnkj Vdjko ds dkj.k vfHkdkjdksa dh fn'kk esa lkE;dk LFkkukarj.k gksrk gSA
(4) Vdjko ls lfØ; Lih'kht+ dk {k; gksrk gSA
40. ,d ÝykLd esa 0.06N ,flfVd vEy ds 50 mL foy;uesa 3 g lfØ;r~ dk"B dks;yk feyk;k x;kA ,d ?kaVs dsi'pkr~ mls Nkuk x;k vkSj fuL;an dh izcyrk 0.042 N
ikbZ xbZA vf/'kksf"kr ,flfVd vEy dh ek=kk (dk"B&dks;ykds izfr xzke ij) gS:
(1) 18 mg (2) 36 mg
(3) 42 mg (4) 54 mg
41. N3–, O2– rFkk F– dh vk;fud f=kT;k;sa (Å esa) Øe'k% gSa :
(1) 1.36, 1.40 rFkk 1.71 (2) 1.36, 1.71 rFkk 1.40
(3) 1.71, 1.40 rFkk 1.36 (4) 1.71, 1.36 rFkk 1.40
42. gkWy&gsjkWYV izØe ls ,syqfefu;e ds fu"d"kZ.k ds lanHkZ esadkSu lk dFku xyrxyrxyrxyrxyr gS\
(1) bl izØe esa CO rFkk CO2 dk mRiknu gksrk gSA
(2) CaF2 dks Al
2O
3 esa feykus ij feJ.k dk xyukad de
gksrk gS vkSj mlesa pkydrk vkrh gSA
(3) dSFkksM ij Al3+ vipf;r gks dj Al cukrk gSA
(4) Na3AlF
6 fo|qr vi?kV~; dk dke djrk gSA
JEE (MAIN)-2015
14
43. From the following statement regarding H2O
2,
choose the incorrect statement
(1) It can act only as an oxidizing agent
(2) It decomposes on exposure to light
(3) It has to be stored in plastic or wax lined glass
bottles in dark.
(4) It has to be kept away from dust
44. Which one of the following alkaline earth metal
sulphates has its hydration enthalpy greater than
its lattice enthalpy?
(1) CaSO4
(2) BeSO4
(3) BaSO4
(4) SrSO4
45. Which among the following is the most reactive?
(1) Cl2
(2) Br2
(3) I2
(4) ICl
46. Match the catalysts to the correct processes :
Catalyst Process
a. TiCl3
(i) Wacker process
b. PdCl2
(ii) Ziegler-Natta
polymerization
c. CuCl2
(iii) Contact process
d. V2O
5(iv) Deacon's process
(1) a(iii), b(ii), c(iv), d(i)
(2) a(ii), b(i), c(iv), d(iii)
(3) a(ii), b(iii), c(iv), d(i)
(4) a(iii), b(i), c(ii), d(iv)
47. Which one has the highest boiling point?
(1) He (2) Ne
(3) Kr (4) Xe
48. The number of geometric isomers that can exist for
square planar [Pt(Cl)(py)(NH3)(NH
2OH)]+ is
(py = pyridine)
(1) 2 (2) 3
(3) 4 (4) 6
49. The color of KMnO4 is due to
(1) M L charge transfer transition
(2) d - d transition
(3) L M charge transfer transition
(4) - * transition
43. H2O
2 ds lanHkZ esa] fuEufyf[kr dFkuksa esa ls xyrxyrxyrxyrxyr dFku pqfu,
(1) ;g dsoy vkWDlhdkjd gS
(2) izdk'k esa bldk vi?kVu gksrk gS
(3) bls IykfLVd ;k eksevVs dkap cksryksa esa va/sjs esa laxzfgr
fd;k tkrk gS
(4) bls /wy ls nwj j[kuk pkfg,
44. fuEufyf[kr esa ls dkSu ls {kkjh; e`nk /krq lYiQsV dh
ty;kstu ,sUFkkYih mlds tkyd ,sUFkkYih ls vf/d gS\
(1) CaSO4
(2) BeSO4
(3) BaSO4
(4) SrSO4
45. fuEufyf[kr esa ls dkSu lokZf/d vfHkfØ;k'khy gS\
(1) Cl2
(2) Br2
(3) I2
(4) ICl
46. fn;s x, mRiszjdksa dks lgh izØe ds lkFk lqesfyr djsa
mRizsjdmRizsjdmRizsjdmRizsjdmRizsjd izØeizØeizØeizØeizØe
a. TiCl3
(i) okWdj izØe
b. PbCl2
(ii) RlhXyj&uêðk
cgqydhdj.k
c. CuCl2
(iii) laLi'kZ izØe
d. V2O
5(iv) Mhdu izØe
(1) a(iii), b(ii), c(iv), d(i)
(2) a(ii), b(i), c(iv), d(iii)
(3) a(ii), b(iii), c(iv), d(i)
(4) a(iii), b(i), c(ii), d(iv)
47. fuEufyf[kr esa ls lokZf/d DoFkukad fdldk gS\
(1) He (2) Ne
(3) Kr (4) Xe
48. ox Z leryh; [Pt (Cl) (py) (NH3)(NH
2OH)]+
(py = pyridine) ds T;kferh; leko;fo;ksa dh la[;k gS :
(1) 2 (2) 3
(3) 4 (4) 6
49. KMnO4 ds jax dk dkj.k gS
(1) M L vkos'k LFkkukarj.k laØe.k
(2) d - d laØe.k
(3) L M vkos'k LFkkukarj.k laØe.k
(4) - * laØe.k
15
JEE (MAIN)-2015
50. Assertion : Nitrogen and Oxygen are the main
components in the atmosphere but these
do not react to form oxides of nitrogen.
Reason : The reaction between nitrogen and
oxygen requires high temperature.
(1) Both assertion and reason are correct, and the
reason is the correct explanation for the
assertion
(2) Both assertion and reason are correct, but the
reason is not the correct explanation for the
assertion
(3) The assertion is incorrect, but the reason is
correct
(4) Both the assertion and reason are incorrect
51. In Carius method of estimation of halogens, 250 mg
of an organic compound gave 141 mg of AgBr. The
percentage of bromine in the compound is (At. mass
Ag = 108; Br = 80)
(1) 24 (2) 36
(3) 48 (4) 60
52. Which of the following compounds will exhibit
geometrical isomerism?
(1) 1 - Phenyl - 2 - butene
(2) 3 - Phenyl - 1 - butene
(3) 2 - Phenyl - 1 - butene
(4) 1, 1 - Diphenyl - 1 propane
53. Which compound would give 5-keto-2-methyl
hexanal upon ozonolysis?
(1)
CH3
CH3
(2)
CH3
CH3
(3)
CH3
CH3
(4)
CH3
H3C
54. The synthesis of alkyl fluorides is best
accomplished by
(1) Free radical fluorination
(2) Sandmeyer's reaction
(3) Finkelstein reaction
(4) Swarts reaction
50. vfHkdFkuvfHkdFkuvfHkdFkuvfHkdFkuvfHkdFku : ukbVªkstu vkSj vkWDlhtu okrkoj.k ds eq[;?kVd gSa ijUrq ;g fØ;k djds ukbVªkstu dsvkWDlkbM ugha cukrsA
rdZrdZrdZrdZrdZ : ukbVªkstu vkSj vkWDlhtu ds chp vfHkfØ;k dsfy, mPp rki dh vko';drk gS
(1) vfHkdFku vkSj rdZ nksuksa lgh gSa vkSj rdZ vfHkdFkudk lgh Li"Vhdj.k gSA
(2) vfHkdFku vkSj rdZ nksuksa lgh gSa ijUrq rdZ vfHkdFkudk lgh Li"Vhdj.k ugha gSA
(3) vfHkdFku xyr gS ijUrq rdZ lgh gSA
(4) vfHkdFku o rdZ nksuksa xyr gSaA
51. gSykstu ds vkdyu dh dSfjvl fof/ esa 250 mg dkcZfud;kSfxd 141 mg AgBr nsrk gSA ;kSfxd esa czksehu dhizfr'krrk gSS :
(ijekf.od nzO;eku Ag = 108; Br = 80)
(1) 24 (2) 36
(3) 48 (4) 60
52. fuEufyf[kr esa ls dkSu lk ;kSfxd T;kferh; leko;orkn'kkZrk gS\
(1) 1 - iQsfuy - 2 - C;wVhu
(2) 3 - iQsfuy - 1 - C;wVhu
(3) 2 - iQsfuy - 1 - C;wVhu
(4) 1, 1 - MkbZiQsfuy - 1 izksisu
53. vkst+ksuksfyfll djus ij dkSulk ;kSfxd 5-dhVks-2-esfFkygSDlkuSy nsrk gS\
(1)
CH3
CH3
(2)
CH3
CH3
(3)
CH3
CH3
(4)
CH3
H3C
54. vYdkby ÝyksjkbM ds la'ys"k.k ds fy, lcls csgrjhu fofèk gS
(1) eqDr ewyd Ýyksfjus'ku
(2) lSUMek;j vfHkfØ;k
(3) fiQadyLVkbu vfHkfØ;k
(4) LokVZl vfHkfØ;k
JEE (MAIN)-2015
16
55. In the following sequence of reactions :
4 2 2
4
KMnO SOCl H /Pd
BaSOToluene A B C,
the product C is
(1) C6H
5COOH (2) C
6H
5CH
3
(3) C6H
5CH
2OH (4) C
6H
5CHO
56. In the reaction
CH3
NH2
NaNO /HCl2
0-5°CD
CuCN/KCN
E + N2 ,
the product E is
(1)
COOH
CH3
(2) HC3
CH3
(3)
CN
CH3
(4)
CH3
57. Which polymer is used in the manufacture of paints
and lacquers?
(1) Bakelite (2) Glyptal
(3) Polypropene (4) Poly vinyl chloride
58. Which of the vitamins given below is water soluble?
(1) Vitamin C (2) Vitamin D
(3) Vitamin E (4) Vitamin K
59. Which of the following compounds is not an
antacid?
(1) Aluminium Hydroxide
(2) Cimetidine
(3) Phenelzine
(4) Ranitidine
60. Which of the following compounds is not colored
yellow?
(1) Zn2[Fe(CN)
6]
(2) K3[Co(NO
2)6]
(3) (NH4)3[As (Mo
3O
10)4]
(4) BaCrO4
55. fn, x, vfHkfØ;k vuqØe esa mRikn C gS :
4 2 2
4
KMnO SOCl H /Pd
BaSOToluene A B C,
(1) C6H
5COOH (2) C
6H
5CH
3
(3) C6H
5CH
2OH (4) C
6H
5CHO
56. fn, x, vfHkfØ;k esa mRikn E gS
CH3
NH2
NaNO /HCl2
0-5°CD
CuCN/KCN
E + N2 ,
(1)
COOH
CH3
(2) HC3
CH3
(3)
CN
CH3
(4)
CH3
57. fdl cgqyd dk mi;ksx izysi vkSj izyk{k cukus esa gksrk gS\
(1) csdsykbV (2) fXyIVky
(3) ikWfyizksihu (4) ikWfy okbfuy DyksjkbM
58. fuEufyf[kr foVkfeuksa esa ty esa foys; gksus okyk gS :
(1) foVkfeu C (2) foVkfeu D
(3) foVkfeu E (4) foVkfeu K
59. fuEufyf[kr esa ls dkSulk ;kSfxd izfrvEy ughaughaughaughaugha gS\
(1) ,syqfefu;e gkbMªkDlkbM
(2) flesfVMhu
(3) fiQufYtu
(4) jSfufVMhu
60. fn, x, ;kSfxdksa esa dkSuls ;kSfxd dk jax ihyk ughaughaughaughaugha gS\
(1) Zn2[Fe(CN)
6]
(2) K3[Co(NO
2)6]
(3) (NH4)3[As(Mo
3O
10)4]
(4) BaCrO4
17
JEE (MAIN)-2015
61. Let A and B be two sets containing four and two
elements respectively. Then the number of subsets of
the set A × B, each having at least three elements is
(1) 219 (2) 256
(3) 275 (4) 510
62. A complex number z is said to be unimodular if
|z| = 1. Suppose z1 and z
2 are complex numbers
such that 1 2
1 2
2
2
z z
z z
is unimodular and z2 is not
unimodular. Then the point z1 lies on a
(1) Straight line parallel to x-axis
(2) Straight line parallel to y-axis
(3) Circle of radius 2
(4) Circle of radius 2
63. Let and be the roots of equation x2 – 6x – 2 = 0.
If an = n – n, for n 1, then the value of
10 8
9
– 2
2
a a
a
is equal to
(1) 6 (2) –6
(3) 3 (4) –3
64. If A =
⎡ ⎤⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦
1 2 2
2 1 2
2a b
is a matrix satisfying the
equation AAT = 9I, where I is 3 × 3 identity matrix,
then the ordered pair (a, b) is equal to
(1) (2, –1) (2) (–2, 1)
(3) (2, 1) (4) (–2, –1)
65. The set of all values of for which the system of
linear equations
2x1 – 2x
2 + x
3 = x
1
2x1 – 3x
2 + 2x
3 = x
2
–x1 + 2x
2 = x
3
has a non-trivial solution
(1) Is an empty set
(2) Is a singleton
(3) Contains two elements
(4) Contains more than two elements
PART–C : MATHEMATICS
61. ekuk A rFkk B nks leqPp; gSa ftuesa Øe'k% pkj rFkk nksvo;o gSa] rks leqPp; A × B ds mu mileqPp;ksa dh la[;k]ftuesa izR;sd esa de ls de rhu vo;o gSa] gS
(1) 219 (3) 256
(2) 275 (4) 510
62. ,d lfEeJ la[;k z ,dekikadh dgykrh gS ;fn |z| = 1
gSA ekuk z1 rFkk z
2 ,slh lfEeJ la[;k,¡ gSa fd
1 2
1 2
2
2
z z
z z
,dekikadh gS rFkk z2 ,dekikadh ugha gS] rks fcUnq z
1
fLFkr gS
(1) x-v{k ds lekarj ,d js[kk ijA
(2) y-v{k ds lekarj ,d js[kk ijA
(3) 2 f=kT;k okys oÙk ijA
(4) 2 f=kT;k okys oÙk ijA
63. ekuk rFkk f}?kkr lehdj.k x2 – 6x – 2 = 0 ds ewy gSaA
;fn n 1 ds fy,] an = n – n gS] rks
10 8
9
– 2
2
a a
a dk
eku gS
(1) 6 (2) –6
(3) 3 (4) –3
64. ;fn A =
⎡ ⎤⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦
1 2 2
2 1 2
2a b
,d ,slk vkO;wg gS tks vkO;wg
lehdj.k AAT = 9I, dks larq"V djrk gS] tgk¡ I, 3 × 3 dkrRled vkO;wg gS] rks Øfer ;qXe (a, b) dk eku gS
(1) (2, –1) (2) (–2, 1)
(3) (2, 1) (4) (–2, –1)
65. ds lHkh ekuksa dk leqPp;] ftuds fy, jSf[kd lehdj.kfudk;
2x1 – 2x
2 + x
3 = x
1
2x1 – 3x
2 + 2x
3 = x
2
–x1 + 2x
2 = x
3
dk ,d vrqPN gy gS]
(1) ,d fjDr leqPp; gSA
(2) ,d ,dy leqPp; gSA
(3) esa nks vo;o gSa
(4) esa nks ls vf/d vo;o gSaA
JEE (MAIN)-2015
18
66. The number of integers greater than 6,000 that can
be formed, using the digits 3, 5, 6, 7 and 8, without
repetition, is
(1) 216 (2) 192
(3) 120 (4) 72
67. The sum of coefficients of integral powers of x in
the binomial expansion of 50
1 2 x is
(1) 501(3 1)
2(2)
501(3 )
2
(3) 501(3 1)
2(4) 501
(2 1)2
68. If m is the A.M. of two distinct real numbers l and
n (l, n > 1) and G1, G
2 and G
3 are three geometric
means between l and n, then 4 4 4
1 2 32G G G equals.
(1) 4 l2mn (2) 4 lm2n
(3) 4 lmn2 (4) 4 l2m2n2
69. The sum of first 9 terms of the series
3 3 3 3 3 31 1 2 1 2 3
........1 1 3 1 3 5
is
(1) 71 (2) 96
(3) 142 (4) 192
70.
0
1 cos2 3 coslim
tan 4x
x x
x x
is equal to
(1) 4 (2) 3
(3) 2 (4)1
2
71. If the function.
⎧ ⎪ ⎨ ⎪⎩
1 , 0 3( )
2 , 3 5
k x xg x
mx x
is differentiable, the value of k + m is
(1) 2 (2)16
5
(3)10
3(4) 4
72. The normal to the curve, x2 + 2xy – 3y2 = 0 at (1,1)
(1) Does not meet the curve again
(2) Meets the curve again in the second quadrant
(3) Meets the curve again in the third quadrant
(4) Meets the curve again in the fourth quadrant
66. vadksa 3, 5, 6, 7 rFkk 8 ds iz;ksx ls] fcuk nksgjk;s] cuus okys6,000 ls cM+s iw.kk±dksa dh la[;k gS
(1) 216 (2) 192
(3) 120 (4) 72
67. 50
1 2 x ds f}in izlkj esa x dh iw.kk±dh; ?kkrksa ds
xq.kkadksa dk ;ksx gS
(1) 501(3 1)
2(2)
501(3 )
2
(3) 501(3 1)
2(4) 501
(2 1)2
68. ;fn nks fofHk okLrfod la[;kvksa l rFkk n (l, n > 1) dklekarj ekè; (A.M.) m gS vkSj l rFkk n ds chp rhu xq.kksÙkj
ekè; (G.M.) G1, G
2 rFkk G
3 gS a] rk s 4 4 4
1 2 32G G G
cjkcj gS(1) 4 l2mn (2) 4 lm2n
(3) 4 lmn2 (4) 4 l2m2n2
69. Js.kh
3 3 3 3 3 31 1 2 1 2 3
........1 1 3 1 3 5
ds izFke 9 inksa
dk ;ksx gS(1) 71 (2) 96
(3) 142 (4) 192
70.
0
1 cos2 3 coslim
tan 4x
x x
x x
cjkcj gS
(1) 4 (2) 3
(3) 2 (4)1
2
71. ;fn iQyu
⎧ ⎪ ⎨ ⎪⎩
1 , 0 3( )
2 , 3 5
k x xg x
mx x
vodyuh; gS] rks k + m dk eku gS
(1) 2 (2)16
5
(3)10
3(4) 4
72. oØ x2 + 2xy – 3y2 = 0 ds fcUnq (1,1) ij vfHkyEc
(1) oØ dks nksckjk ugha feyrk
(2) oØ dks nksckjk f}rh; prqFkk±'k esa feyrk gS
(3) oØ dks nksckjk rrh; prqFkk±'k esa feyrk gS
(4) oØ dks nksckjk prqFkZ prqFkk±'k esa feyrk gS
19
JEE (MAIN)-2015
73. Let f(x) be a polynomial of degree four having extreme
values at x = 1 and x = 2. If
⎡ ⎤ ⎢ ⎥⎣ ⎦20
( )lim 1 3x
f x
x, then
f(2) is equal to
(1) –8 (2) –4
(3) 0 (4) 4
74. The integral
∫ 2 4 3/4( 1)
dx
x x equals
(1)⎛ ⎞
⎜ ⎟⎝ ⎠
1
4 4
4
1x
c
x
(2) 1
4 4( 1)x c
(3) 1
4 4( 1)x c (4)⎛ ⎞
⎜ ⎟⎝ ⎠
1
4 4
4
1x
c
x
75. The integral ∫
4 2
2 2
2
log
log log(36 – 12 )
xdx
x x x is equal
to
(1) 2 (2) 4
(3) 1 (4) 6
76. The area (in sq. units) of the region described by
{(x, y) : y2 2x and y 4x – 1} is
(1)7
32(2)
5
64
(3)15
64(4)
9
32
77. Let y(x) be the solution of the differential equation
log 2 log , ( 1).dy
x x y x x xdx
Then y(e) is equal to
(1) e (2) 0
(3) 2 (4) 2e
78. The number of points, having both co-ordinates as
integers, that lie in the interior of the triangle with
vertices (0, 0), (0, 41) and (41, 0), is
(1) 901 (2) 861
(3) 820 (4) 780
79. Locus of the image of the point (2, 3) in the line
(2x – 3y + 4) + k(x – 2y + 3) = 0, k R, is a
(1) Straight line parallel to x-axis
(2) Straight line parallel to y-axis
(3) Circle of radius 2
(4) Circle of radius 3
73. ekuk f(x) ?kkr 4 dk ,d cgqin gS ftlds x = 1 rFkk
x = 2 ij pje eku gSaA ;fn
⎡ ⎤ ⎢ ⎥⎣ ⎦20
( )lim 1 3x
f x
x gS] rks f(2)
cjkcj gS
(1) –8 (2) –4
(3) 0 (4) 4
74. lekdy
∫ 2 4 3/4( 1)
dx
x x cjkcj gS
(1)⎛ ⎞
⎜ ⎟⎝ ⎠
1
4 4
4
1x
c
x
(2) 1
4 4( 1)x c
(3) 1
4 4( 1)x c (4)⎛ ⎞
⎜ ⎟⎝ ⎠
1
4 4
4
1x
c
x
75. lekdy ∫
4 2
2 2
2
log
log log(36 – 12 )
xdx
x x x cjkcj gS
(1) 2 (2) 4
(3) 1 (4) 6
76. {(x, y) : y2 2x rFkk y 4x – 1} }kjk ifjHkkf"kr {ks=k dk{ks=kiQy (oxZ bdkb;ksa) esa gS
(1)7
32(2)
5
64
(3)15
64(4)
9
32
77. ekuk vody lehdj.k
log 2 log , ( 1)dy
x x y x x xdx
dk gy y(x) gS] rks
y(e) cjkcj gS
(1) e (2) 0
(3) 2 (4) 2e
78. f=kHkqt] ftlds 'kh"kZ (0, 0), (0, 41) rFkk (41, 0) gSa] dsvkUrfjd Hkkx esa fLFkr mu fcUnqvksa dh la[;k ftuds nksuskafunsZ'kkad iw.kk±d gSa] gS
(1) 901 (2) 861
(3) 820 (4) 780
79. fcUnq (2, 3) ds js[kk (2x – 3y + 4) + k(x – 2y + 3) = 0,
k R esa izfrfcac dk fcUnqiFk ,d
(1) x-v{k ds lekarj js[kk gSaA
(2) y-v{k ds lekarj js[kk gSaA
(3) 2 f=kT;k dk oÙk gSA
(4) 3 f=kT;k dk oÙk gSA
JEE (MAIN)-2015
20
80. The number of common tangents to the circles
x2 + y2 – 4x – 6y – 12 = 0 and
x2 + y2 + 6x + 18y + 26 = 0, is
(1) 1 (2) 2
(3) 3 (4) 4
81. The area (in sq. units) of the quadrilateral formed by
the tangents at the end points of the latera recta to
the ellipse 22
19 5
yx, is
(1)27
4(2) 18
(3)27
2(4) 27
82. Let O be the vertex and Q be any point on the
parabola, x2 = 8y. If the point P divides the line
segment OQ internally in the ratio 1 : 3, then the
locus of P is
(1) 2x y (2) 2
y x
(3) 22y x (4) 2
2x y
83. The distance of the point (1, 0, 2) from the point of
intersection of the line 12 2
3 4 12
yx z and the
plane x – y + z = 16, is
(1) 2 14 (2) 8
(3) 3 21 (4) 13
84. The equation of the plane containing the line
2x – 5y + z = 3; x + y + 4z = 5, and parallel to the
plane, x + 3y + 6z = 1, is
(1) 2 6 12 13x y z (2) 3 6 7x y z
(3) 3 6 7x y z (4) 2 6 12 13x y z
85. Let �
� �
, and a b c be three non-zero vectors such that
no two of them are collinear and
� �
� � � �1( ) | || |
3a b c b c a . If is the angle between
vectors �
b and �
c , then a value of sin is
(1)2 2
3(2)
2
3
(3)2
3(4)
2 3
3
80. o`Ùkksa x2 + y2 – 4x – 6y – 12 = 0 rFkkx2 + y2 + 6x + 18y + 26 = 0 dh mHk;fu"B Li'kZ js[kkvksadh la[;k gS
(1) 1 (2) 2
(3) 3 (4) 4
81. nh?kZo`Ùk 22
19 5
yx ds ukfHkyEcksa ds fljksa ij [khaph xbZ
Li'kZ js[kkvksa }kjk fufeZr prqHkqZt dk {ks=kiQy (oxZ bdkb;ksaesa) gSa
(1)27
4(2) 18
(3)27
2(4) 27
82. ekuk ijoy; x2 = 8y dk 'kh"kZ O rFkk ml ij dksbZ fcUnqQ gSA ;fn fcUnq P] js[kk[kaM OQ dks 1 : 3 ds vkarfjdvuqikr esa ck¡Vrk gS] rks P dk fcUnqiFk gS %
(1) 2x y (2) 2
y x
(3) 22y x (4) 2
2x y
83. js[kk 12 2
3 4 12
yx z rFkk lery x – y + z = 16
ds izfrPNsn fcUnq dh] fcUnq (1, 0, 2) ls nwjh gS
(1) 2 14 (2) 8
(3) 3 21 (4) 13
84. js[kk 2x – 5y + z = 3; x + y + 4z = 5 dks varfoZ"V djusokys lery] tks lery x + 3y + 6z = 1 ds lekarj gSa]dk lehdj.k gS
(1) 2 6 12 13x y z
(2) 3 6 7x y z
(3) 3 6 7x y z
(4) 2 6 12 13x y z
85. ekuk rFkk�
� �
,a b c rhu 'kwU;srj ,sls lfn'k gSa fd muesa ls
dksbZ nks lajs[k ugha gSa rFkk � �
� � � �1( ) | || |
3a b c b c a gSA ;fn
lfn'kksa �
b rFkk �c ds chp dk dks.k gS] rks sin dk ,d
eku gS
(1)2 2
3(2)
2
3
(3)2
3(4)
2 3
3
21
JEE (MAIN)-2015
86. If 12 identical balls are to be placed in 3 identical
boxes, then the probability that one the boxes
contains exactly 3 balls is
(1)⎛ ⎞⎜ ⎟⎝ ⎠
1155 2
3 3(2)
⎛ ⎞⎜ ⎟⎝ ⎠
102
553
(3)⎛ ⎞⎜ ⎟⎝ ⎠
121
2203
(4)⎛ ⎞⎜ ⎟⎝ ⎠
111
223
87. The mean of the data set comprising of 16
observations is 16. If one of the observation valued
16 is deleted and three new observations valued 3,
4 and 5 are added to the data, then the mean of the
resultant data, is
(1) 16.8 (2) 16.0
(3) 15.8 (4) 14.0
88. If the angles of elevation of the top of a tower from
three collinear points A, B and C, on a line leading
to the foot of the tower, are 30º, 45º and 60º
respectively, then the ratio, AB : BC, is
(1) 3 : 1 (2) 3 : 2
(3) 1 : 3 (4) 2 : 3
89. Let ⎛ ⎞ ⎜ ⎟⎝ ⎠1 1 1
2
2tan tan tan
1
xy x
x
where 1| |
3x . Then a value of y is
(1)
3
2
3
1 3
x x
x
(2)
3
2
3
1 3
x x
x
(3)
3
2
3
1 3
x x
x
(4)
3
2
3
1 3
x x
x
90. The negation of ~ s (~ r s) is equivalent to
(1) s ~ r (2) s (r ~ s)
(3) s (r ~ s) (4) s r
� � �
86. ;fn 12 ,d tSlh xsans] 3 ,d tSls cDlksa esa j[kh tkrh gSa]rks buesa ls ,d cDls esa Bhd 3 xsansa gksus dh izkf;drk gS
(1)⎛ ⎞⎜ ⎟⎝ ⎠
1155 2
3 3(2)
⎛ ⎞⎜ ⎟⎝ ⎠
102
553
(3)⎛ ⎞⎜ ⎟⎝ ⎠
121
2203
(4)⎛ ⎞⎜ ⎟⎝ ⎠
111
223
87. 16 izs{k.kksa okys vk¡dM+ksa dk ekè; 16 gSA;fn ,d izs{k.k ftldkeku 16 gS] dks gVk dj] 3 u;s izs{k.k ftuds eku 3, 4 rFkk5 gSa] vk¡dM+ksa esa feyk fn;s tkrs gSa] rks u;s vk¡dM+ksa dkekè; gS(1) 16.8 (2) 16.0
(3) 15.8 (4) 14.0
88. rhu lajs[k fcUnqvksa A, B rFkk C, ,d ,slh js[kk ij fLFkr gSatks ,d ehukj ds ikn dh fn'kk esa ys tkrh gS] ls ,dehukj ds f'k[kj ds mÂ;u dks.k Øe'k% 30º, 45º rFkk 60º
gSa] rks AB : BC dk vuqikr gS
(1) 3 : 1 (2) 3 : 2
(3) 1 : 3 (4) 2 : 3
89. ekuk ⎛ ⎞ ⎜ ⎟⎝ ⎠1 1 1
2
2tan tan tan
1
xy x
x
tgk¡ 1| |
3x gS] rks y dk ,d eku gS
(1)
3
2
3
1 3
x x
x
(2)
3
2
3
1 3
x x
x
(3)
3
2
3
1 3
x x
x
(4)
3
2
3
1 3
x x
x
90. ~ s (~ r s) dk fu"ks/ lerqY; gS(1) s ~ r (2) s (r ~ s)
(3) s (r ~ s) (4) s r