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XII Part Test-8 Page # 1

Q.1 Thecorrect outputfor the given circuit is

B

A

C t2T0T0

A B 2T0

(A) (B) T0

(C) 2T0 (D)

[Semiconductor / Tough]

Q.2 If 10,000 volts are applied across onX ray tubes find the ratio of wavelength ofthe incident electrons

and the shortest wavelength of X ray coming out of the X ray tube, given e / m of electron

= 1.8 1011 C.kg1.(A) 1 : 10 (B) 10 : 1 (C) 5 : 1 (D) 1 : 5

[X-Rasy / Easy]

Q.3 Whena certainmetallicsurfaceisirradiatedwithmonochromaticlightwavelength,thestoppingpotential

for photoelectric current is 3 V0. When the same surface is irradiated with light of wavelength 2 ,the

stopping potential is V0. The threshold wavelengthfor thegiven surface is

(A) 4 (B) 6 (C) 8 (D) 4/ 3

[PEE / Moderate]

Q.4 Statement 1: Nuclear fusion reactions for nucleiofsmall atomic mass (A< 20) can takeplaceonlyat

hightemperatures.

Statement 2: Nuclear fusionreactions for nuclei of small atomic mass (A < 20)are exothermic.

(A) Statement-1 is true, statement-2 is true and statement-2 is correct explanation for statement-1.

(B) Statement-1istrue,statement-2istrue and statement-2isNOTthecorrectexplanationforstatement-1.

(C) Statement-1 is true, statement-2 is false.

(D)Statement-1 is false, statement-2 is true.[Nuclear / Easy]

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Q.5 An LC circuit contains inductance L = 1H and capacitance C = 0.01F. The wavelength of

electromagneticwave generatedis nearly

(A) 0.5 m (B) 5 m (C) 190 m (D) 30 m

[EM Waves / Moderate]

Q.6 A pnjunctiongermanium diode isshown here. Thecurrent inexcessof10mAthrough the diode produces

a large Joule-heating which damages (burns) the diode. Ifwe want touse a 1.5V batteryto forward bias

the diode,whatshouldbethe value ofresistorusedinserieswith the diode,sothatthe maximum current

does not exceed 6mA ?

1.5V

(A) 100 (B) 200 (C) 300 (D) 400

[PN Junction / Moderate]

Q.7 For a p-n-p transistor, the C E input characterstic curves are shown in figure for different voltages of

Vc e

then:

v1 v2v3

Ib

vbe

(A) V1> V

2> V

3 (B) V

3> V

2> V

1 (C) V

1= V

2= V

3 (D)none

[Semiconductor / Easy]

Q.8 The ratio ofmagnetic moment tothe angular momentumis a universal constantfor hydrogenlike atoms

and ions. The value ofthisconstant is

(A)m8

e0

2

(B) m2e (C)

e2m (D)

0

2

e2m

[Bohr / Moderate]

Q.9 A message signalof frequency m

is superposed on a carrierwave of frequency C

to get an amplitude

modulated wave (AM). The frequency of theAM wave will be

(A)m

(B) C

(C)2

mC (D)2

mC

[Communication / Easy]

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Q.10 The refractiveindexfor matterwaves can bedefinedasu

cwherec is some constant. Sorefractive index

formatterwaves.

(A) is inverselyproportional to (B) is independent of

(C) is directlyproportional to (D) is proportional to

[Bhor / Easy]

Q.11 Abeam offastmoving -particleswas directedtowards a thin film ofgold. The partsA', B'and C'of the

transmitted and reflected beams corresponding to the incident partsA, B and C of the beamare shown

in theadjoining diagra. The numberof-particlesin

BA

C

B'

A'

C'

(A) B' will beminimumandin C'maximum (B)A'will bemaximum and inB' minimum

(C)A' willbeminimum and inC'maximum (D) C'willbeminimumandin B' maximum

[Nuclear / Easy]

Q.12 Lightofwavelength fallsonametalhavingworkfunction0

hc

.Photoelectriceffectwilltakeplaceonlyif:

(A) 0 (B) 20 (C) 0 (D)< 20

[PEE / Easy]

Q.13 In an NPN transistor circuit the collector current is 10 mA. If only90% of emitted electron reach the

collector, then

(A)IB = 2mA (B) IC = 1mA (C) IE = 11mA (D) IE =9mA[Semiconductor / Easy]

Q.14 Half lives of two isotopes X and Y of a material are known to be 2 109 years and 4 109 years

respectively. Ifa planet was formed with equal number of theseisotopes, estimate thecurrent age of the

planet, given thatcurrentlythe materialhas 20% of X and 80% of Yby number.

(A) 2 109 years (B) 4 109 years (C) 6 109 years (D) 8 109 years

[Radio / Tough]

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Q.15 For what value of the quantum numbern will the de broglie wavelength of anelectron in the hydrogen

atombe4a0? {a

0= radius of electron in ground state}

(A) 1 (B) 2 (C) 3 (D) 4

[Bhor / Moderate]

Q.16 A certain radio nuclide starts getting produced at a constant rate = 104 s1by some mechanism at a

certain moment t = 0.At this moment, there are already 105

number of radio-nuclides present in thesample. The mean life of the radionuclide is 20 seconds.At t = 40sec, what will be dN/dt, rounded to

the nearest whole number? [Given that e2 =7.4]

(A) 375 /s (B) +676 /s (C) 676 /s (D) + 762 /s

[Radio / Tough]

Q.17 The K, L and M energy levels of platinum lie roughly at 78, 12, and 3 KeV respectively. The ratio of

wavelength of K linetothatofK line in X-ray spectrum is

(A) 322

(B)223

(C)2522

(D)2225

[X-Rasy / Moderate]

Q.18 A beam of 5 keV -particles and a beam of 5 keV electrons are absorbed bya target. The two beams

deliver equal amounts of energyto the target per second.

Ifelectronofmass

particleofmass = 7.27103, what is the value of

electrontoduetargetonpressure

particle-toduetargetonpressure?

(A) 1.38 104 (B) 1.17 102 (C) 1.45 (D) 85.3

[Bhor / Tough]

Q.19 If the potential difference applied acrossa Coolidgetube is increased :

(A)thewavelengthoftheK line will increase

(B) the wavelengthof the K linewilldecrease

(C)the difference in wavelengthbetween the K andK will decrease

(D) none of these[X-Rasy / Easy]

Q.20 Ina reverse biased p-n junction, almost no current flows because

(A)Electrons and holes recombine beforethey can cross the junction

(B) Onlyminoritycarriers,whose densitiesare verysmall,contribute to thecurrent, when they cross the

junction

(C) The electric field in the neutral regions is verysmall

(D)All theapplied voltage appears across theohmic contacts[Semiconductor / Easy]

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Q.21 AnLEDismadefromsemiconductingmaterialhavinga bandgap of1.1eV. What typeof radiation does

theLED emit?

(A)Ultraviolet (B)Blue light (C)Redlight (D)Infrared

[PEE / Easy]

Q.22 The Davisson-Germer experiment that first demonstrated the wave nature of matter used electrons

acceleratedto 54V. Determine thewavelength of theelectronsin theDavisson-Germer experiment.(A) 1.67 (B) 1.21 (C) 3.45 (D) 5.21

[Bhor / Easy]

Q.23 ThehalflifePo-218is 3 minutes.Whatfractionofa 10gramsampleofPo-218will remainafter 15min?

(A) 1/32 (B) 1/64 (C) 1/25 (D) 1/15

[Radio / Moderate]

Q.24 A 1 KWsignalis transmitted using a communication channel which providesattenuation at the rate of2dB per km. If the communication channel has a total lengthof 5 km, the power of the signalreceived is

(A) 900 W. (B) 100 W. (C) 990 W. (D) 1010 W.

[Communication / Moderate]

Q.25 In Fig. assumingthe diodes to beideal,

(A)D1

is forward biased and D2

is reverse biased and hence current flows fromA to B

(B) D2is forward biased and D

1is reverse biased and hence no current flows from B toA and vice

versa.

(C)D1 andD2 are both forward biased and hence current flows fromA to B.(D)D

1andD

2are both reverse biased and hence no current flows fromA to B and vice versa.

[PN Juncation / Easy]

Q.26 A certain metal has a workfunction. If light of wavelength shines on this metal, thephotoelectrons

havea maximum kinetic energyK. Whatwillbetheir maximum kinetic energyif light ofwavelength2

shinesonthe metal ?

(A) (K +) / 2 (B) (K ) / 2 (C) 2K (D) K / 2

[PEE / Moderate]

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Q.27 Fig.shows Zener diode witha break downvoltageof40V connectedto100 V D.C. source with a series

resistance RS

and a loadresistor (RL). Find the output voltage across R

L.

(A) 40V (B) 20V (C) 50V (D) 60V

[Semiconductor / Easy]

Q.28 The figure shows energy levels of a certain atom. When the ystem moves from level 2E to E, a

photon of wavelength is emitted. The wavelength of photon produced during its transition from

level 4/3E to E level is

(A) 3 (B) 3

4 (C)

4

(D) 2

[Bhor / Moderate]

Q.29 90% ofthe active nucleipresent ina radioactive sample are found to remain undecayedafter 1day. The

percentage of the undecayed nuclei leftafter two days willbe :

(A) 85% (B) 81% (C) 80% (D) 79%

[Radio / Moderate]

Q.30 In a photoelectric effect measurement the stopping potential for a given metal is found to beV0Volts

when radiationof wavelength 0 is used. Ifradiationof wavelength 20 isusedwithsamemetal,thenthe

stopping potential will be observed tobe (Where symbols havetheir usual meaning)

(A) V0 /2 (B) V0+ e2hc

(C) 2V0 (D)V0 e2hc

[PEE / Tough]

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Q.31 The work done in adiabatic compression of 2 moles of ideal monoatomic gas against 2 atm

external pressure if initially temperature and pressure is 300 K and 1 atm.

(A) 360 cal (B) 720 cal (C) 800 cal (D) 1000 cal

[Thermodynamics\Easy]

Q.32 What will be the maximum amount of heat released, when 321gm of a mixture of Fe2O3and

Al is subjected to sparking in absence of air?

HfFe2O3= 199kJ/mole HfAl2O3= 399kJ/mole

(A) 200 kJ (B) 300 kJ (C) 400 kJ (D) 100 kJ

[Thermochemistry\Easy]

Q.33 What will be the value of resonance energy of N2O if

HBDE N = N = 400 kJ/mol ; o

fH N2O = 100 kJ mol1

HBDE N N = 950 kJ/mol ; HBD EN = O = 600 kJ mol1

HBDE O = O = 500 kJ/mol

(A) 200 kJ / mol (B) 150 kJ / mol (C) 100 kJ / mol (D) 50 kJ / mol


Q.34 '' for NH3including contribution from vibrational degree's of freedom is

(A)3

4(B)

9

10(C)

6

7(D)

12

13


Q.35 Total work done in given cyclic process is

(A) Greater than zero (B) Less than zero

P

1/V

(C) Equal to zero (D) Can't determine[Thermodynamics\Easy]

Q.36 For the real gas reaction,

2SO2(g) + O2(g) 2SO3(g) H = 440 kJ/mol

If the reaction is carried out in 10 litre rigid vessel the initial pressure is 50 bar which decreases

to 20 bar in the course of reaction. The change in internal energy for the reaction is

(A) 437 kJ (B) 410 kJ (C) 443 kJ (D) 470 kJ


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Q.37 For the reaction,

2NH3 (g) N2(g)+ 3H2(g)Identify the statement which is not correct.

(A) o NHmo

Nmo

Nm 322 S2S3S

(B) Heat absorbed at constant pressure and temperature will be more as compared to heat

absorbed at constant volume.(C) reactantenergyBond > productenergyBond(D) The value ofG is expected to be negative at extremely low temperatures.


Q.38 Which of the following substances will have positive value ofHformation?

(A) Br2(l) (B) O3(g) (C) ZnO(s) (D) H+(aq)


Q.39 Which of the following option(s) will show a increase in Gibbs free energy?

(A) Combustion of propane at 1 bar and 500K.

(B) Vapourisation of any liquid at 1 atm and above its normal boiling point.

(C) Fusion of H2O at 1 atm and 0C if its normal melting point is 0C.

(D) Vapourisation of H2O at 100C and 1 bar if its normal boiling point is 100C.


Q.40 Which of the options contain correct set of parameters which are both amount and path

independent parameters.

(I) Internal energy

(II) Specific enthalpy

(III) Heat exchange at constant pressure condition

(IV) Molar heat exchange at constant volume condition

(V) Temperature

(VI) Work involved

(A) Only II, IV & V (B) All option except VI

(C) All options except III, IV & VI (D) Only II & V


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Q.46 Arrange in order of enolic content :

(a) (b)

(c) (d)

(A) c > d > b > a (B) d > c > a > b (C) a > c> d > b (D) b > c > a > d

[Isomerism/Easy]

Q.47 and are

(A) Chain isomers (B) Metamers (C) Positional isomers (D) Conformers

[Isomerism/Easy]

Q.48 Which of the following can not tautomerize?

(A)

O

O

(B) Ph C C Me

O O

(C)

O

OH

(D)

OO

[Isomerism/Easy]

Q.49 Which of the fiollowing can't show geometrical isomerism?

(A) CH3CH=NOH (B)

(C) C = NOH (D) HO N = N OH

[Isomerism/Easy]

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Q.50 Molecular formula C4H6 can represent different compounds , one of them can not be

...............

(A) Alkyne (B) Diene

(C) Bicyclo compound (D) Spiro compound

[Isomerism/Medium]

Q.51 + HCNA + B

A & B are

(A) Meso compounds (B) diastereoisomers

(C) enantiomers (D) both A & B

[Isomerism/Medium]

Q.52 How many stereoisomer may have this naturaloccuring compound.

(A) 8 (B) 16

(C) 64 (D) 128

[Isomerism/Difficult]

Q.53 Which of the following is not the pair of diastereoisomers.

(A)

HH

HH

ClCl

ClCl

COOHCOOH

COOHCOOH

and

(B)H H

H H

CH3CH3 CH3

CH3

Me Me

Me Me

and

(C) and

(D)H H

H

HOH OH

OH

OH

Me Me

Me

Me

and

[Isomerism/Medium]

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Q.54 Selectincorrectstatement :

(A) Resonance effects bond length

(B) trans-1-bromo-1,2-difluoro ethene and Z-1-bromo-1,2-difluoro ethene are geometrical isomers

(C) In CH2

O

O

COH

COH

most acidic H is connected directly to oxygen not on carbon.

(D) Boiling point ofOH

is less than

OH

OH[Resonance/Difficult]

Q.55 Selectcorrectstatement from the following.

(A)O

O is having very high resonance energy than

O

O

(B) CH3

COOH

is more acidic thanCOOH

(C) CH2

is more stable than OH.

(D) O

is more stable than OCMe||

O

[Resonance/Medium]

Q.56 Which of the following is/are correct.

(A) Order of heat of hydrogenation CC=CCCC=CC < CCC=CC=CCC

(B) Order of heat of combustion

(C) Order of stability of carbocation

N NN

(D) Order of heat of combustion cis-1,4-bis-(t-butyl) cyclohexane < Trans-1,4-bis-(t-butyl)

cyclohexane

[Hyperconjugation/Difficult]

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Q.57 Which of the following reaction will not form aromatic ion.

(A) + aq. AgNO3 (B) + 2K

(C) + HBr (D) HBF4

[Hyperconjugation/Difficult]

Q.58 Which of the following orders is/areincorrect?

(A) Basic strengthN

>N

N

(B) Acidic strength

Cl|

COOHCHCH3 >Cl|

COOHCHCH 22

(C) Stability of carbocation

CH2

NO2

COOH|

COOH

[GOC/Difficult]

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Q.59 Which of the following is correct order?

(A) Stability of carbocation

C H CH6 5 2 CH = CH CH2 2

(B) Acidic strength

COOH COOH

NO2

NO2

(C) Basic strength

NH2

NH

(D) Bond length (CN)

NH2 NH2

O

[Resonance/Difficult]

Q.60 Select theincorrectoptions.

(A) Stability of free radical

CH2

CH3 CH CH2 2>

(B) Stability of carbanion 232 HCCHHCCHCHC

(C) Stability order of carbocation 0) da

= 4, cb

= 9 then is equal to

(A) 2 (B) 3 (C) 6 (D) 36

[Vector / Easy]

Q.75 A 5 digit number divisible by 3 is to be formed using the numerals 0, 1, 2, 3, 4 & 5 without

repetition. The total number of ways this can be done is :

(A) 3125 (B) 600 (C) 240 (D) 216

[Permutations and Combinations / Difficult]

Q.76 Given a parallelogram ABCD. If |AB|

= a , |AD|

= b & |AC|

= c , then DB AB

. has the

value

(A)3

2

2 2 2a b c (B)

a b c2 2 23

2

(C)

a b c2 2 23

2

(D) none

[Vector / Difficult]

Q.77 If )kji(a

, )kji(b

, and c

are unit vectors perpendicular to the vectora

and

coplanar with a

and b

, then a unit vectord

perpendicular to both a

and c

is

(A) )kji2(6

1 (B) )kj(2

1 (C) )kj2i(6

1 (D) )kj(2

1

[Vector Algebra / Difficult]

Q.78 The number of ways in which 6 men and 6 women can dine at a round table if no two women

are to sit together is given by

(A) 6! 5! (B) 30 (B) 5! 4! (D) 7! 5!

[Permutation and Combination / Easy]

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Q.79 The angle between the planes 3x 4y + 5z = 0 and 2x y 2z = 5 is

(A)3

(B)

2

(C)

6

(D) none of these

[ 3-D/ Easy]

Q.80 The equation of the plane containing the line31x

=

23y =

12z and the point (0, 7, 7)

is

(A) x + y + z = 1 (B) x + y + z = 2 (C) x + y + z = 0 (D) none of these

[ 3-D/ Moderate]

Q.81 Let P(3, 2, 6) be a point in space and Q be a point on the line )k5ji3()k2ji(r

.

Then the value of for which the vectorPQ is parallel to the plane x 4y + 3z = 1 is

(A)4

1(B)

4

1(C)

8

1(D)

8

1

[3-D/ Moderate]

Q.82 Equation of a plane which passes through the point of intersection of lines3

1x =

1

2y =

2

3z and

1

3x =

2

1y =

3

2z and at greatest distance from the origin is

(A) 7x + 2y + 4z = 54 (B) 4x + 3y + 5z = 50

(C) 3x + 4y + 5z = 49 (D) x + y + z = 12.

[ 3-D / Difficult]

Q.83 If the points (2 x, 2, 2), (2, 2 y, 2) (2, 2, 2 z) and (1, 1, 1) are coplanar, then

(A) 1z

1

y

1

x

1 (B) x + y + z = 1

(C) 11z

1

1y

1

1x

1

(D) none of these

[ 3D / Easy]

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Q.84 Statement-1 : If vectors a

and c

are non-collinear then the lines

)ac2(ca6r

and )c3a(car

are coplanar

Statement-2 : There existandsuch that the two values of r

become same.

(A) Statement-1 is true, statement-2 is true and statement-2 is correct explanation for

statement-1.

(B) Statement-1 is true, statement-2 is true and statement-2 is NOT the correct explanation

for statement-1.


(D) Statement-1 is false, statement-2 is true.

[Vector / Easy]

Q.85 If )ba(c)ac(b)cb(ad

, then

(A) d

is a unit vector (B) cbad

(C) 0d

(D) c,b,a

and d

are coplanar..

[Vector Algebra / Easy]

Q. 86 If

a b c = 0 ,

a = 3 ,

b = 5 ,

c = 7 , then the angle between

a b& is :

(A) 6 (B) 32 (C) 35 (D) 3

[Vector / Moderate]

Q.87 The number of ways in which we can get a score of 11 by throwing three dice is

(A) 18 (B) 27 (C) 45 (D) 56

[Permutations and Combinations /Moderate]

Q.88 Vector equation of the line 6x 2 = 3y + 1 = 2z 2 is

(A) r = )ki(kji (B) r =

kj

3

1i

3

1k3j2i

(C) r = k3j2ikj3

1i

3

1 (D) r = k2j3i6k2ji2

whereis a parameter

[3-D / Moderate]

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Q.89 Statement-1 :A student is allowed to select at most n books from a collection of (2n + 1)

books. If the total number of ways in which he can select at least one book is

255, then n = 3.

Because

Statement-2 :

01n2

+

11n2

+ +

n1n2

= 4n

(A) Statement-1 is true, statement-2 is true and statement-2 is correct explanation for statement-1.

(B) Statement-1 is true, statement-2 is true and statement-2 is NOT the correct explanation for

statement-1.



[Permutations and Combinations / Difficult]

Q.90 Consider the planesP

1: x y + z = 1

P2: x + y z = 1

P3: x 3y + 3z = 2

Let L1, L

2, L

3be the lines of intersection of the planes P

2and P

3, P

3and P

1, and P

1and P

2

respectively.

Statement-1 : At least two of the lines L1, L2and L3are non-parallel.

Statement-2 : The three planes do not have a common point.

(A) Statement-1 is true, statement-2 is true and statement-2 is correct explanation forstatement-1.

(B) Statement-1 is true, statement-2 is true and statement-2 is NOT the correct explanation

for statement-1.



[3-D / Moderate]

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ANSWERKEY

PHYSICS

Q.1 D

Q.2 A

Q.3 A

Q.4 BQ.5 C

Q.6 B

Q.7 A

Q.8 B

Q.9 B

Q.10 A

Q.11 B

Q.12 CQ.13 C

Q.14 D

Q.15 B

Q.16 B

Q.17 D

Q.18 D

Q.19 D

Q.20 BQ.21 D

Q.22 A

Q.23 A

Q.24 B

Q.25 B

Q.26 B

Q.27 A

Q.28 AQ.29 B

Q.30 D

MATHEMATICS

Q.61 B

Q.62 D

Q.63 C

Q.64 AQ.65 A

Q.66 D

Q.67 C

Q.68 B

Q. 69 D

Q. 70 C

Q.71 C

Q.72 CQ.73 C

Q.74 C

Q.75 D

Q.76 A

Q.77 B

Q.78 A

Q.79 B

Q.80 CQ.81 A

Q.82 B

Q.83 A

Q.84 A

Q.85 C

Q.86 D

Q.87 B

Q.88 CQ. 89 D

Q.90 D

CHEMISTRY

Q.31 B

Q.32 B

Q.33 C

Q.34 BQ.35 B

Q.36 B

Q.37 D

Q.38 B

Q.39 C

Q.40 A

Q.41 B

Q.42 BQ.43 C

Q.44 D

Q.45 A

Q.46 A

Q.47 B

Q.48 A

Q.49 C

Q.50 DQ.51 B

Q.52 C

Q.53 B

Q.54 B

Q.55 B

Q.56 B

Q.57 C

Q.58 DQ.59 A

Q.60 C

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SOLUTION

SOLUTION

Q.1 BA BA

B

CBBA

0 T0 C = )1.11( = 0

T0 2T

0 C = )1.11( = 0

2T0 C = )0.01( = 0

Q.2meV2

hc

photon

hceV

Q.3hc

= + c . (3v0) in case I

2hc

=+ c. v0 in case II

where0

hc

= (0 threshold wavelength)

Q.4 To overcome coulomb repulsion .

Q.5 =LC

1=

266 101010

1

= 107

f =2

107

= 7

8

10

103 2= 60

Q.6 The basic equationofdiode-circuit isRI + V

0= V

B

R =I

VV 0B

V =B 1.5V

V =RIR V0

R

Here VB= 1.5V, V

0= 0.3V, I = 5mA = 6 103A

R =6

102.1

106

3.05.1 3

3

= 0.2 103= 200

Q.7 InformationBased.

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Q.8 Current I =

v

r2

e

magnetic moment= Ir2

angularmomentum=mvr

ratio =m2

e

Q.9 InformationBased.

Q.10 =u

c cv

c

Q.11 Numberof nucleus decreases as deviation angle increases.

Q.12hc

0

hc

0

Q.13 10% of IE= I

B

IB

=1mA I

E= I

C+ I

B= 10 + 1 = 11 mA

Q.14 Let total sum of number of isotopes at the formation of the planet was No and currently is N

Nx=

2

N0 t1e = 0.2 N ....(i)

Ny =

2N0 t2e

= 0.1 N ....(ii)

Dividingequation(ii)by(i)

t)( 21e

= 4

(12) t = ln 4

t4

1

2

1

10

2ln9

=2ln2

t = 8 109 years

Q.15 2R = n2n2 a

0= n n = 2

Q.16 Nrdt

dN

t

0

N

N

dtNr

dN

0

ln0Nr

Nr

= t

(r N) = (r N0)et

dt

dN= r N = (r N0) e

t = 20/t

54 e

20

1010

= 5000e2 = 5000/7.4 = + 676 per second Ans.

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Q.171

hc

= 78 12 378

hc

2

= 2

1

=22

25

Q.18 If n particles each with mass m and speed v collide inelastically with the target per sec.

then rate of energy transfer = n .)E.K(nmv2

1 2

andRateofmomentumtransfer=nmv=n )KE(m2Since both beam transfer equal energy, n1 (KE)1 = n2 (KE)2 ,butKE1 = KE2 n1= n2

ratio of momentum transferred =222

111

)KE(m2n

)KE(m2n=

2

1

m

m= 7270

Q.19 K or K characteristics

Q.20 InformationBased

Q.21 =Ehc =

1.11240 nm ~ 1100 nm infra red.

Q.22 l =mv

h=

km2

h= 3119

34

101.9106.1542

1063.6

2

1mv2 = k

Q.23 15 min is 5 times of 3 min 5 half lite 1 fraction left=

32

L

2

1 5

Q.24 gain in dB = 10 log

t

0

P

P

Q.26hc

, K' = 2

hc=

2

K=

2

K

Q.28 2E E =

hc

3

E4 E =

hc

' = 3

Q.29 Decay in 1 day is 10% 1 decay in second day = 990100

10 1 nuclei left = 100 10 9 = 81.

Q.30 eV0= 0

hc

02

hc

'eV 00 2

hc

'VVe V' = V0= e2hc

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SOLUTION

Q.31 For adiabatic irreversibleprocessnCv,m(T2 T1) = Pext(V2 V1)

= Pext

1

1

2

2

P

nRT

P

nRT

2 2

3R (T2 300) = 2

1

300R2

2

RT2 2

T2= 420KW =U = nCv,m(T2 T1)

= 2 2

3R (420 300)

= 720 cal

Q.32 Fe2O3+ 2Al Al2O3+ 2Fe (s)H = 399 + 199 = 200 kJH = 200 1.5 = 300 kJ

Q.33 N (g) + O (g)2 2 N O(g)22

1

2

1

H (N O,g)f 2

atoms

BDEN N BDEO=O+

(RE + BE + BE )N=N N=ON O2

Hf(N2O,g) = BDENN+ 21

BDEO=O [ ON2RE + BEN=N+ BEN=O]

100 kJ = 950 +2

1500 [ ON2RE + 400 + 600]

100 kJ = 1200 kJ ON2RE 1000

ON2RE = 100 kJ / mole

Q.34 Cv= RnR2

nR

2

nvib

rottr = R9R6R2

3R

2

3

Cp= 9R + R = 10R

= 910

C

C

V

P

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Q.35 TCyclic process will be clockwise whenP plotted against V.Hence work done is negative.

P

VQ.36 For constant volume process

H =U + VP

U =H VP= 440 kJ 10 103 (20 50) 105 103 kJ= 410 kJ

Q.37 2NH3 (g)N2(g)+ 3H2(g)(1)Srxn> 0

Srxn= 0]S2[]3SS[ 3NH2H2N MMM

3NH2H2N MMM S22SS

(2)Process is endothermicH = +veng= 2H =U +ngRT

(3)Hrxn> 0

H = productofEBttanacReofEB > 0= productofEBttanacReofEB

(4) G =H TS

H,S = +veG < 0 at high temperature.

Q.38 Hformation of element in nature state is zero.Hfof O3 is endothermicHfof ZnO is exothermic & HfofH

+(aq) is zero.

Q.39 G =H TS(i) Combustion is spontaneous reaction so Hisveas H > TS(ii) G is ve for vaporisation above boiling point as TS > H

(iii) Gis+ve forfusionat0Cas H=+veand S=ve(iv)G is ve asS = +ve &H = +ve but TS >H

Q.40 II, IV& V are intensive and path independent properties. Internal energy, H depends on amount andw depends on amount as well as path dependent.

Q.41 (B) is incorrect

0Tqrev forall cyclic process.

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Q.42 dS =T

PdVdTnC m,v

P

nR

T

P

V

S

T

Q.43 q = CT = 10 20 = 2000 J

U = q + wU = 2000 5 3 100 = 500 JH =U +(PV)= 500 + 10 100 = 1500 J

Q.44 = 80% =

2

12

T

TT

in[D] =85%whichismorethanreversible process it is not possible.

Q.45 (1) H =U +ngRTve ve + 0.5 RT

(2) H U +ngRT+ve = +1 +1 RT

(3) N2+ 3H2 2NH3x =U +ngRT

ve = ve ve(4) C2H4+ 3O22CO2+ 2H2O(l)

x =U +ngRTve = ve ) (3)

Q.46 With increase in acidity ofH and stabilityof enol formed its% contentincreases.

Q.47 Structures of given compound are MeOCH2Et and EtOCH2Me so metamers.

Q.49 Not required

Q.50 Molecular formula C4H6D. B. E. 2

Possibility 2bondor 1bond & 1 ringor 2 ring

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Q.51 HCN +

ThusA& B are diastereoisomers.Ans:B

Q.52

Q.53 (A)

H

H

H

H

Cl

Cl

Cl

Cl

COOH

COOH

COOH

COOH

Cl

Cl

Cl

Cl

H

H

H

H

COOH

COOH

COOH

COOH

Diastereoisomers

(B) Chiral carbonis not present

(C) and Geometrical isomers are diastereoisomers.

(D)H

H

H

H

H

H

H

HO

HOH

OH

OH

OH

OH

OHOH

Me

Me

Me

Me

Me

Me

MeMe

H

HH

HHOOH

OHOH

Me

Me

Me

Me

Diastereoisomers]

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Q.54 (A) Resonance effectbondlength

(B)C = C

F

Br

H

F

cis-1-bromo-1,2difluoro ethene

C = CF

BrF

H

Z-1-bromo-1, 2difluoro ethene

Identical

(C) CH2

COOH

COOH

most acidic (eq. R.S.)

(D)OH

B.P.

OH

OH

Q.55 (A) Ester group resonance wi th itself in a better way not to other so both have same resonanceenergy.

(B) Due to Ortho effect.(C) Negative onmore electronegative element ismorestable.(D) Equivalent R.S.are more stable thanunequivalent R.S.

Q.56 is less stable than so havinghigherheat of hydrogenation

Hence 'A' is incorrect. Heat of combustion of cyclo alkanes increases from cyclohexane (Higher No. of Catom) to cyclo

propane hence B is correct. Stabilityof Carbocation.

N N N

ResonanceStabilise

LessI effect

HigherI effect

> >+

++

Hence C is incorrect. Stabilityorderof disubstituted cyclohexane areis given as

H

H

H H

tBu

>

tBu

tBu tBu

So D is incorrect.

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Q.57 (A) + aq. AgNO3 Ph

Ph

Ph

Ph

Aromatic

(B) + 2K

Aromatic

(C) + HBr

OH

Antiaromatic

(D) HBF4OH

OH

Aromatic

Q.58 (A)N

+ I,N

N

I of N

(B)

Cl|

COOHCHCH3 more (I),

Cl|

COOHCHCH 22 Less (I)

(C)

CH2

NO2

more (I),

CH2

CH3

more (+I),

(D)

COOH|

)CH(|

COOH

32 COOH|

COOHmore I.

Q.59 Stability ofcarbocation: C H CH6 5 2 CH = CH CH2 2

DancingResonance

Moredelocalisation

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Basic strength :

NH2

NH

5 RS 6 RSLess availablefor donation

Q.60 (A) Stability offreeradical :

CH2

CH3 CH CH2 2>

More delocalisation

(B)Stabilityof carbanion: 232 HCCHHCCHCHC

ve on more EN

More stable

(D)Stability of resonantingstructures :

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SOLUTION

Q.61 The number of ways can be deduce as follows :

1 women and 4 men = 4C1 6C4= 60


3 women and 2 men = 4C3 6C

2= 60


Required number of ways = 60 + 120 + 60 + 6 = 246 Ans.

Q.62 Let, the required vector be= kdjdid 321 , where

51ddd 2322

21 , (given) .........(i)

Now, each of the given vectors c,b,a

is a unit vector

cos =|a||d|

ad

=|b||d|

bd

=|c||d|

cd

or ad

= bd

= cd

|d|

= 51 cancels out and |c||b||a|

= 1

Hence, 3

1

(d1 2d 2+ 2d3) = 4

1

( 4d1+ od2 3d 3) = d

d1 5d

2+ 2d

3= 0

and 4d1+ 5d

2+ 3d

3= 0

On solving,5

d

1

d

5

d 321

=(say)

Putting d1, d

2and d

3in (i), we get= 1

Hence, the required vectors are k5ji5 . Ans.

Q.63

432 3

100

3

100

3

100

3

100= 33 + 11 + 3 + 1 = 48. Ans.

Q.64 (Volume)2 = cba

cba

=

cccbca

bcbbba

ccabaa

=

12/12/1

2/112/12/12/11

=

2

1. Ans.Ans.

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Q.65 Denoting a

, b

, c

by the given vectors respectively. These vectors will be collinear if there

is some constant K such that c

a

= K(b

a

)

a 60 = 20K and 55 = 11 K

a = 100 + 60 = 40

Q.66 5 + 8.9.5 = 365; 1st place is five + where 1st place is not five 75 |5

+5|

9|

8|

Q.67 ( a

+b

) (b

+ c

) = 3j (2i +4j ) = 6 k

Hence the required unit vector is k .

Q.68 Here, b)3y3x6(a)y12x3(p3

b)2y6x4(a)4x4y2(q2

On comparing, we get

3x + 12y = 2y 4x + 4 & 6x + 3y + 3 = 4x 6y 2

7x + 10y = 4 .........(i)

and 2x + 9y = 5 .........(ii)

On solving equations, we get x = 2, 1. Ans.

Q.69 cba

= 0

1434111

= 0 or 1 = 0 =1

Also |c|

= 3 1 +2 + 2 = 3 Ans.

Q.70 Since a

is perpendicular to d

, so x y + 2z = 0 (i)

Moreover , |b

| = | c

| so a

b

= a

c

as a

makes equal angles with b

and c

.

Thus xy 2yz + 3xz = 2xz + 3xy yz

xz 2xy yz = 0 (ii)

Also x2 + y2 + z2 = 12 (iii)

and y < 0, Substituting the value of y from (i) in (ii) we get x2 + 2xz + z2 = 0 so x = z

and y = z. Again substituting these value (iii) we get z2 = 4 i.e. z = 2 but y < 0 and y

= iz.

So z = 2 = y and x = 2

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Q.71 Subtracting the first two equations we get y z = 4. From the third we get x + z = 3 which

are satisfied by (2, 5, 1).

Q.72 The total number of possible outcomes is 64.

The number of possible outcomes in which 2 does not appear on any die is 54.

Therefore, the number of possible outcomes in which atleast one die shows a 2 is

64

54

= 1296 625 = 671.

Q.73 Let A be the origin of reference and the position vector of B, C, D be d,c,b

, w.r.t. A. So

AB = b

, CD= cd

, AD = d

, BC= bc

, cAC

and bdBD

. The L.H.S. is equal

to )cd(b

. The R.H.S. is

222 |bd||c||bc||d|K

= bd2bbddccbc2bbccddK

= 2K )cd(b

.

Hence K =2

1

Q.74 We know that

)ba(

)dc(

= dbcbdaca

= 9

4 = 2 36.

since ba

and dc

are perpendicular so= 6. Ans.

Q.75 Reject 0 + reject 3 5! + 4 4! = 120 + 96 = 216

Q.76 To find

a b a . i.e.

a2

a b. (1)

now

a b c

a b2 2

+ 2

a b. =

c2 (2)

substitute the value of

a b. from (2) in (1) ]

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Q.77 Let kzjyixc

. Since c,b,a

are coplanar,,

so

111

111

zyx

= 0 0 x 2y 2z = 0

Also c

is perpendicular to a

, so x + y z = 0.

Therefore1

z

1

y

2

x

and x2 + y2 + z2 = 1

( c

being a unit vector). We have x = 6

2, y =

6

1, z =

6

1.

Thus )kji2(6

1c

and

112111

kji

|ca|6

1ca

ca

1d

= )k

j

(2

1

)k

3j

3i

0(|ca|6

1

Q.78 No. of ways in which 6 men can be arranged at a round table = (6 1)! = 5! ways

Now women can be arranged in 6! ways

Total number of ways = 6! 5! Ans.

Q.79 = cos1

950

1046= cos1 (0) =

2

. Ans.

Q.80 The equation of plane containing the line

3

1x

=2

3y =

1

2z

is a(x + 1) + b(y 3) + c(z + 2) = 0 ... .. .. ..(1)

where 3a + 2b + c = 0 ..........(2)

This passes through (0, 7, 7)

a + 4b 5c = 0 ........(3)

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From equation (2) and (3),

14

a

=

14

b

=

14

c

or1

c

1

b

1

a

Thus, the required plane isx + y + z = 0. Ans.

Q.81 Let O be the origin, as Q l ies on the given l ine, OQ = )k5ji3(k2ji .

Also OP = k6j2i3 . As PQ is parallel to the plane x 4y + 3z = 1.

PQ )k3j4i( = 0

OPOQ )k3j4i( = 0 (1 + 4 + 6) + ( 3 4 + 15) (3 8 + 18) = 0

11 + 8 13 = 0 =4

1. Ans.

Q.82 Any point on the first l ine is P(3 + 1, + 2 , 2 + 3) and on the second line is

Q( + 3, 2 + 1, 3 + 2) P and Q represent the same point if = = 1 and the point of

intesection of the given lines is P(4, 3, 5) . The planes given is (a), (b), (c) and (d) all pass

through P. The plane at greatest distance is one which is at a distance equal to OP from the

origin. So the distance of the plane from the origin is 222 534 = 50 which is satisfied

by the plane in(b). Ans.

Q.83 Given points are coplanar,

1z222

12y22122x2

1111

= 0

(Volume of the tetrahedron with given vertices is zero)

0z11101y11

011x1

1111

= 0

z111

1y11

11x1

= 0

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z0x

0yx

11x1

= 0

133

122

RRRRRR

x(0 + y) z (y + xy x) = 0

xy + yz + zx = xyz

1z

1

y

1

x

1

Q.84 If the lines have a common point then there existsand such that

6 = 1 + and 1 + 2 = 1 + 3

= 3, = 2

Q.85 )cb(a

=

c)ba(b)ca(

)ac(b

= a)bc(c)ab(

)ba(c

= b)ac(a)bc(

Since the dot product is commutative, we have

0)ba(c)ac(b)cb(a

Q.86

a b c Square

a b a b2 2 2 . =

c 2

cos=

c a b

a b

2 2 2

2

Q.87 Coefficient of x11 in (x + x2 + ... + x6)3

= coefficient of x8 in (1 x6)3 (1 x)3

= coefficient of x8 in (1 3x6) (1 + 3C1

x + 4C2

x2 + ...)

= 10C8 3(4C2) = 27

Q.88 The line can be written as1

3/1x =

2

3/1y =

3

1z which passes through the point whose

position vector is kj3

1i

3

1

and is parallel to the vector k3j2i and hence its

equation is r = kj3

1i

3

1 + k3j2i .

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Q.89 Let

S =

01n2

+

11n2

+ +

n1n2

(i)

Using

rn

=

rnn

, we can write (i) as

S =

1n1n2

n21n2

1n21n2

(ii)

Adding (i) and (ii), we get

2S =

1n21n2

01n2

= 22n+1

S = 22n = 4n

The number of ways of choosing r books out of 2n + 1 is

r1n2

. We are given

255n1n2

21n2

11n2

4n 1 = 255 4n = 256 = 44 n = 4 .

Q.90 If l, m, n denote the direction ratios of L1 then l + m n = 0 and l 3m + 3n = 0l= 0, m = n direction ratios of L

1are 0, 1, 1 similarly for L

2and L

3, we find that the

direction ratios of both are 0, 1, 1 showing that L1, L

2, L

3are parallel, thus statement-1 is

false.

Statement-2 is true, because solving the given equations we get x = 0, y z = 1 and

y z = 2/3 which is not possible.

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