iit mains 2015 set a

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



(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



(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


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 fofHkÂ 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



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

iit mains 2015 set a

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