2019 Apr Jee-Main Q P K S · 2019-04-15 · PHYSICS 1. A particle of ... A transformer consisting of 300 turns in the primary and 150 turns in the secondary gives output power of

2019_Apr_Jee-Main Question Paper_Key & Solutions

2019_Jee-Main Question Paper_Key & Solutions

Sri Chaitanya IIT Academy # 304, Kasetty Hegihts, Ayappa Society, Madhapur, Hyderabad – 500081

www. srichaitanya.net, [email protected]

PHYSICS 1. A particle of mass m is moving along a trajectory given by 0 1cosx x a t

0 2siny y b t The torque,acting on the particle about the origin, at t=0 is :

1) 20 1my a k

2) 20 0 1m x b y a k

3) 2 2

0 2 0 1ˆm x bw y aw k 4) Zero

Ans. 1

Sol. o 1 o 2r x a cos t i y b sin t j ; at t=0 o or x a i y j

2 2

2 2

d x d yˆ â i jdt dt

2 21 1 2 2

ˆr a cos t i b sin t j ; at t=0 2

1â a i

T r F m r a

2o 1

ˆm y a k

oˆˆmy a ik

2. A stationary source emits sound waves of frequency 500Hz. Two observers moving along a line passing through the source detect sound to be of frequencies 480 Hz ad 530Hz. Their respective speeds are,in ms-1

(given speed of sound =300 m/s) 1) 12, 18 2) 8,18 3) 16, 14 4) 12,16 Ans. 1

Sol. o300 V480 500

300

oV24 1

25 300 oV 1

300 25 oV =12 o300 V

530 500300

oV53 1

50 300

oV 3

300 50

0V 18 Hence Velocities -12,18

3. n moles of an ideal gas with constant volume heat capacity Cv undergo an isobraric expansion by certain volume . The ratio of the work done in the process, to the heat supplied is :

1) 4

v

nRC nR

2) v

nRC nR

3) v

nRC nR

4) 4

v

nRC nR

Ans. 2

Sol. n=moles cv=neat capacity

2 1

v 2 1

P v vC t P v v

v

nRC nR

4. One Plano-convex and one plane of-concave lens of same radius of Curvature ‘R’ but of different materials are joined side by side as shown in the figure . If refractive index of the material of 1 is 1 and that of 2 is 2 ,then the focal length of the combination is

1

21

2




1) 1 22

R 2) 1 2

2R 3) 1 22

R

4) 1 2

R

Ans. 4

Sol. Diagram 2 11F R

1 2

Rf

5. In a photoelectric effect experiment the threshold wavelength of the is 380nm. If the wavelength of indent is 260nm, the maximum kinetic energy of emitted electrons

will be: given E{in ev}= 1237innm

1) 1.5 eV 2) 15.1 eV 3) 3.0 eV 4) 4.5 eV Ans. 1

Sol. No

hc hc K.E

hc hc K.E260 380

1240 1240K.E260 380

= 4.8 3.2 =1.5ev

6. The electric field of a plane electromagnetic wave is given by 0 cos cosE E i kz t

The corresponding magnetic field :B is then givenby

1) 0 sin CosEB k kz tC

2) 0 sin cosEB j kz tC

3) 0 sin sinEB j kz tC

4) 0 cos sinEB j kz tC

Ans. 3

Sol. oE Ê i cos kz t cos kz t2

oB ˆB j cos kz t cos kz t2

oB ˆB jsin kz sin t2

7. A transformer consisting of 300 turns in the primary and 150 turns in the secondary gives output power of 2.2kw. if the current in the secondary coil is 10A, then the input voltage and current in the primary Coil are:

1) 440 V and 5A 2) 440 V and 20 A 3) 220 V and 10A 4) 220 V and 20A 1) 748J 2) 700J 3) 374J 4) 350J Ans. 1

Sol. Np=300 Ns=150 o s s sV 2.2kw V .I V 220V p sP

s s p

V INN V I

s sp

V II 5ANlp

p sNpN V 440vNs

8. A cylinder with fixed capacity of 67.2lit contains helium gas at STP. The amount of heat needed to raise the temperature of the gas by 200C is : [Given that R=8.31J

1 1mol k ] 1) 748J 2) 700J 3) 374J 4) 350J Ans. 1

Sol. 67.2 A7STP n= =nCV 7 = 3R3 202

9 3.14 =748




9. Two radioactive materials A and B have decay constants10 and ,respectively . If initially they have the same number of nuclei, then the ratio of the number of nuclei, then the ratio of the number of nuclei of A to that of B will be 1/e after a time

1) 19

2) 111

3) 110

4) 1110

Ans. 1

Sol. 10 tA oN N e t

B oN N e 9 tA

B

N 1eN e

9 t 1 1t9

10. In the given circuit,an ideal voltmeter connected across the 10 resistance reads 2V. The internal resistance r, of each cell is

1) 0.5 2) 0 3) 1.5 4) 1 Ans. 1

Sol. ABV 2 110i 2 11i5

215i 2 22i

15 1 2

1i i3

1 2 1 1 23 2r i i 10i 2 i i 0

2 2r13 3

1 2r3 3

1r 0.52

11. A ray of light AO in vacuum is incident on a glass slab at angle 600 and refracted at angle 300 along OB as shown in the figure.The optical path length of light ray from A to B is:

1) 2a+2b 2) 2 3 2ba

3) 223ba 4) 22

3ba

Ans. 1

Sol. Optical length=AO+OB o2

A sin 30 y90

AO 2ab 3cos30

OB 2

2bOB3

OA+OB=2a+ 2b3




12. A current of 5A passes through a copper conductor (resistivity= 81.7 10 )m radius of cross section 5mm.Find the mobility of the charges if their drift velocity is

31.1 10 / .m s 1) 21.8 / .m Vs 2) 21.5 / .m Vs 3) 21.0 / .m Vs 4) 21.3 / .m Vs Ans. 3

Sol. i=neA(vd) j E ineAVd

ne vd E Mobility= vdE

i.e vd p EeAvd

3 6 1

8

221.1 10 10 10vd A 7ip 5 1.7 10

=

1 2s

11 22 5 10 1m / V17 7

13. Figure shows charge (q) versus voltage (v) graph for series and parallel combination of two given capacitors . The capacitances are :

1) 50 30F and F 2) 60 40F and F 3) 40 10F and F 4) 20 30F and F Ans. 3 Sol. N

14. The value of acceleration due to gravity at Earth‘s surface is 9.8ms-2 . The altitude above its surface at which the acceleration due to gravity decreases to 4.9 ms-2, is close to (Radius of earth = 66.4 10 .m )

1) 66.4 10 .m 2) 61.6 10 .m 3) 62.6 10 .m 4) 69.0 10 .m Ans. 3

Sol. a vc 1 280 C C 1 2

1 2

C C8C C

400=(C1 C2)Options of (a) satisfy

15. Two wires A&B are carrying currents 1 2&I I as shown in the figure . the separation between them is d . A third wire C carrying a current I is to be kept parallel to them at a distance x from A such that the net force acting on it is Zero . The possible values of x are:




1) 2 2

1 2 1 2

I Ix d and x dI I I I

2) 1 2

1 2 1 2


3) 1

1 2( )I dx

I I

4)

1 2

1 2 1 2


Ans. 3

Sol. DiagramFl

=

0 1 o 2I I I I

2 dx 2 x d

1 2x d I x I 1 2 1x I I dI 1

1 2

dIxI I

If 2 1I I

DiagramFl

=

o 1I I

2 x

=

o 2I I2 d x

1 2I x d I / x 1

2 1

I dxI I

1

1 2

IdxI I

16. In a meter bridge experiment the circuit diagram and the corresponding observation table are shown in figure .

Which of the readings is inconsistent ? 1) 4 2) 3 3) 1 4) 2 Ans. 1

Sol. We know that in meter bridge R xl 100 l

a) R=1000, l=60 1000 x 2x 1000 666

60 40 3

b) R=100, l=13 100 x 87x 100 66613 87 13

c) 10 x 89.5x 10 6661.5 89.5 1.5

d) 1 x x 991 99

Option ‘d’ is odd one So it is incontinent

17. An npn transistor operates as a common emitter amplifier , with a power gain of 60dB. The input circuit resistance is 100 and the output load resitance is 10K . The common emitter current gain is :

1) 410 2) 60 3) 210 4) 26 10 Ans. 3

Sol. 60db=100Log L

1

RR

6 L

x

R10R

4

6 1010100

410

18. A massage signal of frequency 100MHz and peak voltage 100V is used to execute amplitude modulation on a carrier wave of frequency 300GHz and peak voltage 400 V . The modulation index and difference between the two side band frequencies are

1) 84;2 10 Hz 2) 80.25;2 10 Hz 3) 84;1 10 Hz 4) 80.25;1 10 Hz




Ans. 2

Sol. Modulation index= 100v 0.25400v

Diff= 7m2 2 10 Hz

19. A uniformly charged ring of radius 3a and total charge q is placed in xy-plane centred at orign. A point charge q is moving towards the ring along the z-axis and has speed 4vat z a The minimum value of v such that it crosses the origin is:

1) 1/22

0

2 215 4

qm a

2) 1/22

0

2 115 4

qm a

3) 1/22

0

2 15 4

qm a

4) 1/22

0

2 415 4

qm a

Ans. 1

Sol. Diagram E av to plane /ring=

32 2 2

kqr

2 r

Total workdone by electric field=change in KE

0 22 02

131 2 24a

2kq 2dn 1 1mv4 mv2 22 2 r

2

0 2

324a

kq 3 1kq dt 2 232 t 1

2

=-kq2o

2 4a

1ey =

2

2 2

1 1kqa 3a x 3a

2 1 1kq3a 5a

20. A proton,an electron, and a Helium nucleus, have the same energy. they are in circular orbits in a plane due to magnetic field perpendicular to the plane. Let

,p e Her r and r be their respective radii, then, 1) e p Her r r 2) e p Her r r 3) e p Her r r 4) e p Her r r Ans. 4

Sol.

mv rqB

22 2

e e p p me He1 1 1m v k m v m V2 2 2

e1Vm

emVq

He2k ' k '2

p

1k ' k '1

e k" k ' e p Her r r

21. The ratio of surface tensions of mercury and water is given to be 7.5 while the ratio of their densities is 13.6. Their contact angles, with glass, are close to 1350 and 00 respectively. it is observed that mercury gets depressed by an amount h in a capillary tube of radius r1 , while water rises by the same amount h in a capillary tube of radius r2 ,the ratio, (r1/ r2) is then close to:

1) 4/5 2) 2/5 3) 2/3 4) 3/5 Ans. 2

Sol. 2

Hg Hg

H O water

T P7.5 13.6

T P For a Capillar tube

22 RTcos R hgP 2Tcos Rpgh

2

oH O

Hg 2

Hg 1350 0

1 cos H O 12

2

Hg1 z

2 Hg H O 2

2T Cos Hgr PH oghr P gh 2T Cos H o

2

2 2

H OHg Hg

H o Hg H O

PT CosT P Cos

1 17.5

13.6 2

=25




22. a moving Coil galvanometer allows a full scale current 10-4 A.A series resistance of2- M is required to convert the above galvanometer into a voltmeter of range 0-5V.

Therefore the value of shunt resistance required to convert the above galvanometer in to ammeter of range 0-10mA is :

1) 100 2) 10 3) 500 4) 200 Ans. 4

Sol. 410 RG RS maxV i max/ RG RS 4 35 10 RG 2 10

4 3

G5 10 R 2 10 348 10 RG

i max RG RSI

RS

4

3 10 RG R10 10

R

23. A ball is thrown upward with an initial velocity V0 from the surface of the earth. the motion of the ball is affected by a drag force equal to m 2V ( where m is mass of the ball v is its instaneous velocity and is a constant) . Time taken by the ball to rise to its zenith is :

1) 10

1 sin vgg

2) 01 ln 1 v

gg

3) 10

1 tan vgg

4) 10

1 2tan2

vgg

Ans. 3

Sol. Fnetng-mrv2=ma-(g+ev2)=dvdt

2

2

dvgdtr1 vg

rg

2 2

2

g d rdv sec dx gdt secr gr sec

g

t

0 0

ddtrg

0

v01 rt tan v]

grg

o

1 rt 0 / tan vgrg

o

1 rt tan vgrg

24. A thin disc of mass M and radius R has mass per unit area ( )r =kr2 where r is the

distance from its center . Its moment of inertia about an axis going through its centre of mass and perpendicular to its plane is :

1) 2

3MR 2)

223

MR 3) 2

2MR 4)

2

6MR

Ans. 2

Sol. 2I dmr 2 2I 2 x dx kx x 52 k x dx

r6

0

x2 k6

6R2 k6

62 kR 4

6 4

=22mR

3




25. Given below in the left column are different modes of communication using the kinds of waves given in the right column .

A. Optical Fibre communication P. Ultra sound B. Radar Q. Infrared light C. Sonar R . Microwaves D. Mobile phones S. radiowaves From the options given below , find the most appropriate match between entries in

the left and the right column. 1) A-Q B-S, C-P, D-R 2) A-S B-Q, C-R, D-P 3) A-R B-P, C-S, D-Q 4) A-Q B-S, C-R, D-P Ans. 1 Sol. Optical Fibre Communication: Infrared light Radar: Radio waves Sonar:

Ultra Sound Mobile phones: micro waves Mode of communication 26. In an experiment , the resistance of a material is plotted as a function of

temperature ( in some range) .As shown in the figure , It is a straight line

one may conclude that:

1) 2 2

0/0

TTR T R e 2) 2 2

0 /0

T TR T R e 3) 02

RR TT

4) 2 2

0/0

TTR T R e

Ans. 2

Sol. In 2

R T KRlo T

R(T)=

2oR e k / T

27. A 3 325 10 m volume cylinder is field with 1 mol O2 gas room temperature (300k) The molicular diameter of O2,and its root mean square speed , are found to be 0.3 nm and 200m/s, respectively.what is the average collision rate (per second) for an O2 Molecule?

1) 12~ 10 2) 13~ 10 3) 10~ 10 4) 11~ 10 Ans. 1

Sol. Molecular density= A3

N25 10

Diameter=0.3nm Vrms=200ms-1 2d dx n

22nNA d v collisionrate

V

=2.9×109≈1010




28. Two Coaxial discs , having moments of inertia I1and 1

2I are rotating with respective

angular velocity 11 2

and

,about their common axis.They are brought in contact

with each other and thereafter they rotate with a common angular velocity . If fE

and iE `, are the final and initial total energies,then f iE E is

1) 2

1 1

12I

`2) 2

1 1

6I 3)

21 1

24I

4) 21 1

38

I Ans. 3

Sol.

21 2ra

1 2

I I12 I I

29. Two Particles , of masses M and 2M moving , as shown,with speeds of 10m/s and 5m/s , collied elastically at the origin. After the collision , they move along the indicated directions with speeds 1 2v and v ,respectively , The value of 1 2v and v are

nearly:

1) 3.2m/s and 12.6 m/s 2) 6.5m/s and 3.2 m/s 3) 3.2m/s and 6.3 m/s 4) 6.5m/s and 6.3 m/s Ans. 4 Sol. X-axis o om 10 cos30 2m 5 cos 45 o o

2 1m v cos 45 2m v cos30

2

1V3 10 310 2v

2 22 2

21

v105 3 v 32 2

…….(1)

Y-Axis o om 10 sin 30 2m 5 sin 45 o o2 1m v sin 45 2M sin 30 v

2

1v10 10 v

2 2 2

…….(2) Solve 1 & 2 V1=6.5m/s; V2=6.3m/s

30. The displacement of a damped harmonic oscillator is given by 0.1 c s 10tx t e o t Here t it is in seconds.The time taken for its amplitude of vibration to drop to half of

its initial value is close to: 1) 27s 2) 13s 3) 7s 4) 4s Ans. 3

Sol. Here A=Ae-0.1t 0.1too

A A e2

20.1t 1n 0.693 7s

0.1




CHEMISTRY 31. The major producer of the following reaction is

1) 3 2 2CH CH CH CH NH 2) 3 2CH CH CH CH

OH

3) 3 2 2 2CH CHCH CH NH

O H

O

4) 3 2 2CH CHCH CH NHCHO

OH

Ans. 4

Sol. 3 2 2 2 3 2 2CH CH CH CH NH H C OH CH CH CH CH NH C H

OH OH OH O

32. Major products of the following of the reaction are

Ans. 1 Sol. Aldehydes locking α – Hydrogen give cross cannizaro reaction. HCHO acts as hydride donor because it gives less sterically hindered tetrahedral

Intermediat 33. Which of the following is a condensation polymer? 1) Buna-S 2) Teflon 3) Nylon 6,6 4) Neoprene Ans. 3 Sol. . Nylon 6,6,- is a conclusion polymer of 2 2 6 2( )NH CH NH & Adinic Acid 34. Ethylamine 2 5 2C H NH can be obtained from N-ethyiphthalimide on treatment with

: 1) CaH2 2) H2O 3) NaBH4 4) NH2NH2 Ans. 4




Sol. 35. A process will be spontaneous at all temperatures if : 1) 0 0H and S 2) 0 0H and S 3) 0 0H and S 4) 0 0H and S Ans. 2

Sol.

G H T Sve

ve ve

0H 0S

36. Amylopectin is composed of 1) cosD glu e C1-C4 and C2-C6 linkages 2) cosD glu e C1-C4 and C1-C6 linkages 3) cosD glu e C1-C4 and C1-C6 linkages 4) cosD glu e C1-C4 and C2-C6 linkages Ans. 3 Sol. Fact Based 37. At 300k and 1 atmospheric pressure 10ml of a hydrocarbon required 55mL of O2

for complete combustion and 40mL of CO2 is formed. The formula of the hydrocarbon is:

1) 4 6C H 2) 4 7C H CI 3) 4 8C H 4) 4 10C H Ans. 1

Sol. 2 2 2 10 55

2 4yy yCxh O xCO H O x

10 40 4 5.5 5.5 44 4y yx x x 1.5 6

4y y

38. A gas undergoes physical adsorption on a surface and follows the given freundlich

adsorption isotherm equation 0.5x kpm Adosrption of the gas increases with:

1) increase in P and decrease in T 2) Decrease in P and decrease in T 3) Increase in P and Increase in T 4) Decrease in P and Increase in T Ans. 1

Sol. . rate of physical adsorption 1Temp

Pr essure

39. The correct order of catenation is 1) Si Sn C Ge 2) C Sn Si Ge 3) Ge Sn Si C 4) C Si Ge C Ans. 4




Sol. Syn gas is used in production (CO+H2) of methanol 40. The isoelectronic set of ions is : 1) 2,Li Na O and F 2) 3 2,N O F and Na 3) 2,F Li Na and Mg 4) 3 2 2,N Li Mg and O Ans. 2 Sol. All are having 10e-

41. A baclerial infection in an initial wound grows N0(t)= 0N exp(t), where the time t is in

hours A dose of antibiotic, taken orally , needs 1 hour to reach the wound. Once it

reaches there , the bacterial Population goes down as 25dN NHdt

What will be the plot of 0N VsN

t after 1 hour

Ans. 1 Sol. Initially, till t=1hr.

0 ( )exp sin .ktN e J onentially decrea gN

After t=1 Hr.

1 1

12

211

11

1 15 5 5 51

1 5

NN t

N N

dN dN NN dt t tdt N N N

NLinear NN

42. The species that can have a trams-isomer (en=ethane-1,2-diamine,ox=oxalate) 1) 2

[ ]Cr en ox 2) 222

[ ]Pr en Cl 3) 2[ ]Zn en Cl 4) 2[ ]Pt en Cl Ans. 2

Sol. 43. The increasing order of the reactivity of the following compounds towards

electrophilic aromatic substitution reactions is :

1) III<I<II 2)III<II<I 3) I<III<II 4)II<I<III




Ans. 1 Sol. Rate of electroplate aromatic substitution reaction depends on electron density in

benzene ring. So it is increased by electron donating group. 44. During the change of O2 to O2

- ,the incoming electron goes to the orbital: 1) * 2 xP 2) 2 xP 3) * 2 zP 4) 2 yP Ans. 1 Sol. For O2 HOMO 2Px

is incompletely filled. So incoming C- goes to 2Px

45. The major product of the following reaction is :

Ans. 4

Sol.

3 3 3 3 3 2 3 3 2 3CH C CH CH CH C CH CH CH C CH CH CH C CH CH

3CH 3CH

OCHH Br1( )SN

3CH

H

( ) ( )H Shift3CH

( )

3CH OH

46. Consider the hydrated ions of Ti2+ ,v2+ Ti3+ and Sc3+ The correct order of their spin-

only magnetic moments is :

1. 3 2 23Ti Ti Sc v 2) 2 2 33V Ti Ti Sc

3) 3 3 2 2Sc Ti Ti V 4) 3 23 2Sc Ti V Ti Ans. 3

Sol.

3 0 2 2 3 1 2 3,3 ,3 ,3 ,3SC d Ti d Ti d V d

47. Three complexes 23 5

[ ]CoCI NH I 33 25

[ ]Co NH H O II and 33 6

[ ]Co NH III absorb light in the visible region . the correct order of the wavelength of lightabsorbed by them is : 1) (II)>(I)>(III) 2) (III)>(I)>(II) 3) (I)>(II)>(III) 4) (III)>(II)>(I) Ans. 3

Sol. More S.F.L, more is absorption, so Nabs frequency.

III>II>I

III<II<I




48. Consider the following table

Gas a/(kPa dm6 mol-1) b/(dm3mol-1

A. 642.32 0.05196

B. 155.21 0.04136

C. 431.91 0.05196

D. 155.21 0.4382

And b are vander walls contants . The correct statement a Bout the gases is :

1. Gas A will occupy than gas D c Compressible than gas D Gas C will Occupy more

volume than

2) gas A gas B will be more compressible than gas D Gas C will Occupy Lesser

volume than

3) Gas A gas B will be more compressible than gas D Gas C will Occupy Lesser

volume than

4) Gas A: gas B will be lesser Compressble than gasD Ans. 2

Sol. Compressibility a 1b

A is having higher intermolecular forces of attraction and hence occupies less

volume.

49. Increasing rate of 1NS reaction in the following compounds is :

1) (B)<(A)<(C)<(D) 2) (A)<(B)<(D)<(C)

3) (B)<(A)<(D)<(C) 4) (A)<(B)<(C)<(D) Ans. 1 Sol. Rate of SN1 reaction depends on stability of corbocation




50. The major product of the following reaction is :

Ans. 4

Sol. in acidic medium Based on structure it may following SN1 (or) SN2 pathway.

51. The alloy used in the contruction of aircrafts is :

1) Mg-A1 2) Mg-Mn 3) Mg-Zn 4)Mg-Sn

Ans. 1

Sol. Due alumin alloy (Mg-Al) is used in manufacturing of aircrafts

52. The graphbetween 2 and r(radial diatance) is shown beow . This represents

1) 2s orbital 2) 2p orbital 3) 3s orbital 4 1s orbital Ans. 1

Sol. No.of radial nodes=1 n-l-1=1 n-l=2 l=0n=22s l=1n=33p

53. The oxoacid of sulphur that does not contain bond between sulphur atoms is :

1) 2 2 3H S O 2) 2 2 7H S O 3) 2 4 6H S O 4) 2 2 4H S O

Ans. 2




Sol.

HO S O S OH

O

O O

O

No S-S bond 54. The principle of Column Chromatography is 1) Capillary action 2) Differential absorption of the substances on the solid phase 3) Differential absorption of the substances on the phase 4) Gravation forc Ans. 3 Sol. Column Chromatography is based on difference in adsorption tendany of different

substances in stationary phase.

55. At room temperature a dilute solution of urea is prepared by dissolving 0.60g of

urea in 360g of water . If the vapour pressure of pure water at this temperature is

35mmHg , Lowering of vapour pressure will be (molar mass of urea =60g mol-1 )

1) 0.28mmHg 2) 0.031 mmHg 3) 0.027Hg 4) 0.017mmHg

Ans. 4

Sol.

2

2

3

3

0.6 360 0.010.01 20 0.5 1060 18 20 0.1

0.5 10 0.175

urea H O urea

OP H O

x x x

xp mmofhg

56. The synonym for water gas when used in the production of methanol is : 1) Laughing gas 2) syngas 3) fuel gas 4) natural gas Ans. 2 Sol. Syn gas is used in production (CO+H2) of methanol. 57. Consider the following statements a) The pH of a mixture containing 400mL of 0.1M H2SO4 and 400 mLof 0.1M

NaOH will be approximately 1.3 b) Ionic product of water is temperature dependent

C) A monobasic acid with Ka=10-5 has a pH=5. The degree of dissociation of this acid is 50% d) The Le Chatelier’s Principle is not applicable to common-ion effect

The correct statements are

1) b and c 2) a,b and d 3) a,b, and c 4) a and b




Ans. 3

Sol.

2 4H SO NaOH

H 2OH H O

I=400x0.1 400x0.1 =80meq =40meq

F= 40meq 0 2 1040 1 1log log log 13

800 20 20H pH

58. Consider the statement S1 snd S2: S1: Conductivity always increases with decreases in the concentraction of electrolyte

S2: Molar Conductivity always increase with decreases in the concentration of Electrolyte The correct option amoung the following 1) S1 is correct and S2 is wrong 2) both S1 and S2 are correct 3) Both S1 and s2 are wrong 4) S1 is wrong S2 is correct Ans. 4

Sol. Conductivity always with in conc. of ionc.

Molar conductivity as dilution 59. Match the refining methods (column I) Watch metals (column-II) Column_I Clumn_II Refinging methods Metals I) Liquation a) Zr II) Zone refinging b) Ni III) Mond procedd c) Sn iV) Van Arkel Method d) Ga 1) I-b II- c III-d IV-a 2) I-c II-d III-b IV-a 3) I-c II-a III-b IV-d 4) I-b II-d III-a IV-c Ans. 2 Sol. Van arkel- Zr Mond’s process – Ni Zone refining- Ga Liquation-Sn

60. The regions of the atmosphere , Where clouds form where we live repectively, are 1) Troposphere and stratosphere 2) Stratosphere and Troposphere 3) Stratosphere and Stratosphere 4) Troposphere and Troposphere Ans. 4 Sol. Troposphere 6-10 km from sea lavel Stratosphere =10-50km.




MATHEMATICS 61. The number of 6 digits numbers that can be formed using the digits 0,1,2,5,7 and 9

which are divisible by 11 and no digit is repeated, is: 1) 36 2) 48 3) 60 4) 72 Ans. 3 Sol. apbqcr is 6 digit number is divisible by 11 If a b c p q r is 0 or multiple of 11 There is only one possible way 9 2 1 7 5 0 0 , , 9,2,1 , , 7,5,0a b c and p q r or , , 7,5,0 , , 9,2,1a b c and p q r Number of 6 digits numbers = 3!.3! 2.2!.3! 36 24 60

62. If 1

sin cos sin 2 cos2sin 1 sin 2 1 , 0;

cos 1 cos2 1

x xx and x x

x x

then for all 0, :2

1) 1 2 cos2 cos4x 2) 31 2 2x

3) 31 2 2 1x x 4) 3

1 2 2x . Ans. 2 Sol.

31 2x

63. If 1 2, ,..... na a a are in A.P. and 1 4 7 10 13 16 114,a a a a a a then

1 6 11 16a a a a is equal to 1) 38 2) 64 3) 76 4) 98 Ans. 3 Sol. Given 6 45 114 2 15 38a d a d We need 4 30 76a d 64. If the coefficients of x2 and x3 are both zero, in the expansion of the expression

1521 1 3 ,ax bx x in powers of x, then the ordered pair (a, b) is equal to

1) (28, 315) 2) (-54, 315) 3) (28, 861) 4) (-21, 714) Ans. 1

Sol. 15 2 32 2 15 15 151 2 31 1 3 1 1 3 3 3 ....ax bx x ax bx C x C x C x

Coefficient of 2x is 15 2 152 13 3 0C a C b 45 945a b

Coefficient of 3x is 15 3 15 2 153 2 13 3 3 0C a C b C 21 273a b

Solving above equations, we get 28, 315a b




65. If 210 ,

ia and z

a i

and 25

z then z is equal to

1) 1 35 5

i 2) 1 3

5 5i

3) 1 35 5

i 4) 3

5 5i

Ans. 3

Sol. 2iz

a i

and

2

2 2 2 3 05 51

z a aa

2 1 33 5 5

iz ii

1 35 5

z i

66. If 4 3 3

2 21

1lim lim ;1x x k

x x kx x k

then k is

1) 38

2) 32

3) 43

4) 83

Ans. 4

Sol. 4

1

1lim 41x

xx

and

3 3

3 3

2 22 2

3lim lim2x k x k

x kx k x k k

x kx kx k

So 3 842 3

k k

67. 1/3 1/3 1/3

4/3

1 2 ........ 2limn

n n nn

is equal to

1) 4

34 23

2) 4

33 324 4

3) 4

33 424 3

4) 3

44 23

Ans. 2

Sol. Given sum= 1 13 41

33

1 0

1 3lim 1 1 2 14

n

n r

r x dxn n

68. If y=y(x) is the solution of the differential equation 2tan sec ,dy x y xdx

,2 2

x

, such that 0 0,y then 4

y

is equal to

1) 12e

2) 2e 3 12

e 4) 1 2e

Ans. 2

Sol. Put tan x tdy t ydt

1d t y t ydt

1d t y

dtt y

ln 1t y t C

So, tan ln tan 1x x y C 0 0 0y C

So the equation will be tan ln tan 1 0x x y Put 24

x y e 2y e




69. If and are roots of the equation 2 sin 2sin 0, 0, ,2

x x

then

12 12

2412 12

is equal to

1)

6

122

8 sin 2)

12

122

8 sin 3)

12

62

8 sin 4)

12

122

4 sin

Ans. 2 Sol. 2 2sin , 2sin sin 8sin

1212 12 12

24 24 1212 12

2sin 8

70. If the length of perpendicular from point ,0, , (where 0 ) to the line 1 1

1 0 1x y z

is 3 ,

2 then value of is

1) -1 2) -2 3) 1 4) 2. Ans. 1

Sol. Let ,1, 1P t t be the foot of perpendicular from ,0,A on 1 11 0 1x y z

AP having d.r.s ,1, 1t t should be perpendicular to line with d.r.s 1,0, 1

1 0t t 12

t Perpendicular distance = 2 22 31 12

t t

21 32 12 2

1 1 0, 12 2

Since 0, we have 1

71. The line x =y touches a circle at the point P (1, 1). If the circle also passes through the point (1,-3), then its radius :

1) 2 2) 2 2 3) 3 4) 3 2 Ans. 2

Sol. The required circle will be 2 21 1 0x y x y

It passes through 2 21, 3 1 1 3 1 1 3 0 4

So equation of circle will be 2 2 6 2 2 0x y x y having radius as 2 2

72. If the circles 2 2 5 2 0x y kx y k and 2 2 3 1 0,2 2yx y kx k R

Intersect at the points P and Q, then the line 4 5 0x y k passés through P and Q, for:

1) no value of k 2) exactly 2 values of k 3) infinitely many values of k 4) exactly one value of k Ans. 2




Sol. Chord PQ is radical axis which is nothing but ' 0S S 1 14 02 2

kx y k

Comparing it with 4 5 0x y k , we get 1 14 2 2

4 5

kkk

On solving we get 2 different values of k

73. The region represented by 2 2x y and x y is bounded by a :

1) rhombus of side length 2 units 2) Square of area is 16 sq. units

3) rhombus of area 8 2 sq. units 4) Square of side length 2 2 un

Ans. 4

Sol. When we plot the graph, we get the region bounded by 2x y , which is a square

of side 2 2

74. If

2

3/2

sin 1 sin, 0

, 0

, 0

p x xx

xf x q x

x x x xx

is continuous at x = 0, then the ordered pair (p, q) is

equal to:

1) 1 3,2 2

2) 3 1,2 2

3) 5 1,2 2

4) 3 1,2 2

Ans. 4 Sol. f x is continuous at 0x 0 0 0f f f

2

30 0 2

sin 1 sinlim limx x

p x x x x xqx x

0 0

1 11 1 21 1 lim 2 limx x

xxp q p q

x x

12

2p q 3 1, ,

2 2p q

75. Assume that each born child is equally likely to be a boy or a girl. If two families

have two children each, then the conditional probability that all children are girls

given that at least two are girls is :

1) 117

2) 110

3) 111

4) 112




Ans. 3 Sol. At least 2 girls is mentioned in question

Family1 Family2 2 BOYS AND 2 GIRLS BB GG

BG BG BG GB GB GB GB BG GG BB

1 BOY AND 3 GIRLS BG GG GB GG GG BG GG GB

4 GIRLS GG GG P( getting 4 girls) =1/11

76. ABC is a triangular park with AB = AC = 100 m. A vertical tower is situated at the midpoint of BC. If the angles of elevation of the top of the tower at A and B are

1cot 3 2 and 1cos 2 2ec respectively, then the height of the tower (in metres) is:

1) 25 2) 10 5 3) 1003 3

4) 20

Ans. 4

Sol. Given 13 2

ODAB

and 2 2OBOD

2 2 2OB OD BD and 2 22100 AD BD OD=20

77. If

12 22

1tan3 2 102 10

f xdx xA Cx xx x

where C is a constant of

integration, then

1) 1 , 3 154

A f x x 2) 21 , 9 154

A f x x

3) 1 , 9 127

A f x x 4) 1 , 3 181

A f x x

Ans. 1

Sol. Put

2

22 22

1

1 819 18

dt tx t I dtt t

t

2 2

2 2

9 91 11 118 189 936

t tdt dtt t

t t




1

2

1 1tan54 3 18 9

t tI Ct

78. If the line 2 12x y is tangent to ellipse 2 2

2 2 1x ya b

at 93, ,2

then the length of

latus rectum of ellipse is 1) 9 2) 12 2 3) 8 3 4) 5 Ans. 1

Sol. 93,2

lie on 2 2

2 2 1x ya b

2 2

9 81 14a b

1 62

y x is tangent 2

2 64a b

On solving we get length of latus rectum as 22 9b

a

79. If for some ,x R the frequency distribution of the marks obtained by 20 students in a test is:

Marks 2 3 5 7 No. of students 21x 2 5x 2 3x x x

Then the mean of the marks is: 1) 2.5 2) 3.0 3) 2.8 4) 3.2 Ans. 3 Sol. 2 21 2 5 3 20x x x x x 2 12 0x x 3x

Mean= 4

2 214

1

2 1 3 2 5 5 3 72.8

20

i ii

ii

n x x x x x x

n

80. Let 2 , .xf x e x and g x x x x R Then the set of all ,x R where the function h(x)=(fog)(x) is increasing, is:

1) 1 ,0 1,2

2)

1 11, ,2 2

3) 0, 4) 10, 1,

2

Ans. 4 Sol. ' 0 ' ' 0h x f g x g x 2

1 2 1 0x xe x 2 2 1 0x x x

81. If a directrix of a hyperbola centred at origin and passing through 4, 2 3 is

5 4 5x and its eccentricity of hyperbola (e) satisfy the equation 1) 4 24 24 27 0e e 2) 4 24 8 35 0e e 3) 4 24 24 35 0e e 4) 4 24 12 35 0e e . Ans. 3

Sol.

2 2

2 2

41,5

x y axa b e

2 2 24 , 15ea b a e 4, 2 3 lie on

2 2

2 2 1x ya b




2 2

16 12 1a b

2 2 2

16 12 11a a e

2 22

16 12 14 4 1

5 5e e e

4 24 24 35 0e e

82. Let 3 3 3 3 33

2 2 2 2 2 2

5 1 2 7 1 2 33 1 ........1 1 2 1 2 3

S

then upto 10th terms is

1) 620 2) 600 3) 680 4) 660 Ans. 4

Sol.

2210 10

1 1

6 1 3 12 1

4 1 2 1 2n n

n n n nS n

n n n

=660

83. Let 2 , .f x x x R For any ,A R define : .g A x R f x A

If [0,4],S then which one of the following statements is not true?

1) f g S f S 2) f g S S

3) g f S g S 4) g f S S .

Ans. 3

Sol. 0,16f S and 2,2g S and 4,4g f S and 0,4f g S

84. Which one of the following Boolean expressions is a tautology?

1) p q p q 2) p q p q

(iii) p q p q (iv) ~ ~p q p q

Ans. 1 Sol. Take &p F q T , we get ~p q p q and ~p q p q as F Take &p F q F , we get ~ ~p q p q as F

85. The value of 2

0

sin 2 1 cos3 ,x x dx

(where [t] denotes Greatest Integer Function)

1) 2 2) 3) 2 4) Ans. 4

Sol.

2

0

sin 2 1 cos3I x x dx

using f(a + b - x) property

2

0

sin 2 1 cos3I x x dx

2

2

00

1I I dx x I




86. If the system of linear equations 5, 2 2 6, 3 ,x y z x y z x y z

, R has infinitely many solutions, then the value of is

1) 7 2) 10 3) 12 4) 9

Ans. 2

Sol.

2 1 3 1

1 1 1 5 1 1 1 51 2 2 6 0 1 1 1

,1 3 0 2 1 5

AD R R R R

3 2

1 1 1 50 1 1 1

20 0 3 7

R R

many solutions if 3 =0, 7 =0 10

87. Let 3,0, 1 , 2,10,6 1,2,1A B and C be the vertices of a triangle and M is the

midpoint of AC. If G divides BM in the ratio, 2 :1, then cos GOA (O being

origin) is equal to :

1) 12 15

2) 115

3) 16 10

4) 130

Ans. 2

Sol. BM is median and G is centroid of the triangle G(2, 4, 2) and A(3, 0, -1)

dr’s of OG = 1,2,1 and dr’s of OA = 3, 0, -1

3 0 1 1cos1 4 1 9 0 1 15

GOA

88. If 0, 1, 3Q is the image of P in the plane 3 4 2 0x y z and R is the point

3, 1, 2 . then the area (in sq.units) of PQR is :

1) 914

2) 912

3) 2 13 4) 652

.

Ans. 2

Sol. 1 1 10 1 3 2(1 12 23 1 4 9 1 16

x y z

1 1 1( , , ) 3, 2,1P x y z 0, 1,3 3, 1, 2Q and R




Area of 1 1 912 2

PQR PQ PR sq.units

89. All the pairs (x,y) that satisfy the inequality 2

2

sin 2sin 5

sin

2 14

x x

y

also satisfy the

equation:

1) 2sin sinx y 2) sin 2sinx y 3) sin sinx y 4) 2 sin 3sinx y

Ans. 3

Sol. 22 2 2sin 1 4sin 2sin 5 sin sin2 4 2 4xx x y y

LHS min value is 4 and RHS max value is 4

LHS=RHS=4 sin x = 1 and sin2 y = 1 sin x =|sin y| = 1

90. Let :f R R be differentiable at c R and 0.f c If ,g x f x then at

,x c g is

1) not differentiable 2) differentiable if ' 0f c

3) not differentiable if ' 0f c 4) differentiable if ' 0f c

Ans. 2

Sol.

' '( )( ) ( )

( )f x

g x f xf x

If '( )f c =0 then ' '( ) ( ) 0g c g c g is differentiable if '( )f c =0

... Prepared by Sri Chaitanya Faculty

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