01_PCM-Special_Test-1(1).pdf

8/10/2019 01_PCM-Special_Test-1(1).pdf

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SPECIAL TEST

JEE MAIN

CODE A

Time:3 Hours. Max. Marks:360

IMPORTANT INS TRUC TION S

1. The question paper consists of '90' objective type questions. There are '30'questions each in

Physics, Chemistry and Mathematics respectively. PleasefilltheOMR answerSheet accordingly

andcarefully.

2. Each question has four choices (1), (2), (3) and (4) out of which ONLY ONE is correct.

3. You will be awarded 4 marks for each question, if you have darkened only the bubble corresponding

to the correct answer and zero mark if no bubble are darkened. In all other cases, minus one (1)

markwill be awarded.

4. There is onlyone 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 3 above.

5. Use Black or Blue Ball Point Pen onlyfor filling particulars.

6. Use ofCalculator, Log Table, Slide Rule and Mobile is not allowed.

7. Rough work is to be done on the space provided at the bottom and in end of the booklet for this purpose

in the Test Booklet only.

8. On completion of the test, the candidate must hand over theAnswer Sheet to the Invigilator. However,

the candidates are allowed to take away this Test Booklet with them.

9. Do not fold or make any stray marks on the Answer Sheet.

USEFUL DATAAtomic weights: Al = 27, Mg= 24, Cu= 63.5, Mn = 55, Cl = 35.5, O = 16, H = 1, P = 31, Ag = 108, N = 14,Li = 7, I = 127, Cr = 52, K=39, S = 32, Na = 23, C = 12, Br = 80, Fe = 56, Ca = 40, Zn = 65.5, Ti = 48,Ba = 137, U = 238, Co= 59, B =11, F = 19, He = 4, Ne = 20, Ar = 40 , Mo = 96

[Take : ln 2 = 0.693, ln 1.1 = 0.095, ln 3 = 1.09, e = 1.6 1019, me= 9.1 1031 kg ]Take

0= 8.85 1012 , g = 10 m/s2 unless otherwise stated


2/12

Page # 2

PHYSI S

Q.1 Figure shows an n-p-n transistor. Choose the

correct statement out of the following :

R1

R2

+10V

(1) Collector-base junctionas well as emitter-

base junction both are forward biased

(2) Collector-base junctionas well as emitter-

base junction both are reverse biased

(3) Collector-base junction is forward biased

and emitter-base junction is reverse biased

(4) Collector-base junction is reverse-biasedand emitter-base junction is forward biased

Q.2 With thehelpof the arrangementshown infigure

which ofthefollowinggates couldbe realised?

+5V

D1

D2

(1) OR (2) NAND

(3) AND (4) NOR

Q.3 A 600 W carrier wave is modulated to a depth

of 75% bya 400Hz sine wave. Find the total

antenna power.

(1) 769 W (2) 796 W

(3) 679 W (4) 637.5 W

Q.4 A moving coil ammeter is to be adapted to

detect small alternating currents. Which of the

diagrams shows how a diode could be

connected in order to make the conversion ?

(1) A

+

(2) A+

(3) A+

(4) A+

Q.5 Four persons A,B, C and D are all moving on

the same circular track with same constant

speed in the anti-clockwise direction.At any

instant they arelocated at thepositions shown

in figure, then the velocity of B, C and D as

observed by A will have the respectively

directions

D B

C

A

(1) a , and

(2) , and

(3) , and

(4) , and


3/12

Page # 3

Q.6 Inthearrangement shown, neglect the mass of

the ropes and pulley. What must be the value

of m to keep the system in equilibrium ? There

is no friction anywhere.

m

30

M

(1) 1 (2) 2M

(3)2

M(4)

4

M

Q.7 Figure shows a disc of mass M and radius R

hinged at the centre. A small ball of mass2

M

is attached to point P with a thread of length

2R and held at rest at position shown. Now,

the ball is released to fall under gravity. With

what angular speed does the disc start turning

when the string becomes taut ?

R P

Ball

(1)R2

g(2)

R

g

(3)g

R(4)

R

g2

Q.8 When force F acts on side of hexagonal body

forwhat rangeofcoefficient offrictionwill body

topple?

Fa

( 1 ) >32

1( 2 ) 23 ( 4 ) K

2

L 2L

T1

T2

(2) K1= K

2

(3) K1< K

2

(4) None of these

Q.14 A proton and a deutron initially at rest are

accelerated with same uniform electricfield for

timet

(1)Both particleswill have same momentum(2) Both particles will have same K.E.

(3) Both particles will have same speed

(4) Both particles will cover same distance

Q.15 A solidspherehaving uniform chargedensityand radius R is shown in figure. A spherical

cavity of radius2

Ris hollowed out. What is

potential ofO ? (Assuming potential at infinity

to be zero)

(1)0

2

24

R11

AO

+++

++

+++

+++ + ++

+

++

+++

++++

+ ++

++++

+

++ ++

+(2)

0

2R

12

5

(3)0

2

12

R7

(4)0

2R

2

3

Q.16 Two concentric spherical shells of radii R and

2R have charges + Q and Q. Which of the

following may represent correct variation of

potential with distance r from origin ?

(1)r2RR

V

(2)r

2RR

V

(3)

r2RR

V

(4)

r2RR

V

Q.17 A capacitor is initially connected to a battery

of EMF 3 V. At t = 0, switch is thrown to Bstate. Now charge on capacitor at any instant

is givenby :

R

R

3V

A

B

C

V

(1) q = C (V + 2V et/RC)

(2) q = C (V 2V et/RC

)(3) q = C (V + 2V et/2RC)

(4) q = C (V + 2V e2t/RC)

Q.18 Current in above question will be given by

equation

(1) RC/teR

V2I (2)

RC/teR

VI

(3) RC2/te

R

VI (4)

RC2/te

R

V3I


5/12

Page # 5

Q.19 In a certain region of space, electric and

magnetic fieldsare crossed :

(1)A charged particle moves undeflected in

theregion onlyifv

is perpendicularto bothE

and B

(2)A charged particle must move undeflected

in the region, ifv

is perpendicular to both E

and B

(3)Ifa positron movesundeflected ifitsvelocity

is v

, an electron will move undeflected its

velocity is v

(4)Achargedparticlemaymoveundeflectedeven

ifitisnot movingwithv

perpendicular toB

Q.20 A conductingloop is being pulledwith speed vfrom region I of magnetic field to region II. If

resistance of the loop is R, current induced in

the loopat the instant shown is :

V

B0 2B0

l

(1)R

vB0, clockwise

(2)R

vB0

, anticlockwise

(3)R

vB3 0, clockwise

(4)R

vB3 0, anticlockwise

Q.21 Whenan a.c. source of e.m.f. E = E0

sin 100t

is connected across a circuit, it is observed that

voltage leads the current by a phase angle

4

.

If the circuit consists possible only R-L, R-C

or L-C in series the two elements could be :

(1) R = 10 , L = 10 mH(2) R = 10, C = 1000 F(3) R = 100, C = 1000 F(4) R = 10 , L = 100 mH

Q.22 The minimum thickness of film which will

strongly reflect the normally incident light of

= 600 nm, the R.I of material of film is 1.25

(1) 120 nm (2) 100 nm(3) 110 nm (4) 90 nm

Q.23 Statement-1 : Low frequency waves are

transmitted viaground waves.

Statement- 2 : When a wave has high

wavelength, it undergoes morediffraction.

(1) Statement-1is true, statement-2is true and

statement-2 is correct explanation for

statement-1.(2) Statement-1is true, statement-2is true and

statement-2 is NOT the correct explanation for

statement-1.

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

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

Q.24 Twoblocks of mass, 1kg and 2 kg are moving

with velocities of i and i4 respectively..

Statement-1 : The kinetic energy of system

appears minimum relative to an observermoving with a velocityof i3 m/s.

Statement- 2: The kinetic energy of any 2

block system is 2rel

2c V

2

1MV

2

1 where

symbols have their usual meanings.



statement-1.



statement-1.



Q.25 Statement-1 : When a block body is thrown

in a furnace, initially it is darkest and finallyit is

brightest.

Statement- 2 : The emissivity as well as

absorptive power of block body is 1.

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

statement-1.



statement-1.




6/12

Page # 6

Q.26 A voltmeter with resistance 500 is used tomeasure the emf of a cell of internal resistance

4 . The percentage error in the reading of thevoltmeterwillbe

(1) 0.2% (2) 0.8%

(3) 1.4% (4) 2.2%

Q.27 Masses of neutron, proton and electron are

1.0087 U, 1.0073u and 0.0005u respectively.

If a neutron decays into a proton and an

electron, the energyreleased would be about

(1) 0.68 MeV (2) 0.84 MeV

(3) 0.75 MeV (4) 1.22 MeV

Q.28 The figure shown the wavelength spectrum of

X-rays producedwhen 50 keVelectrons strike

amolybdenum target. TheK line onthe figure

is represent by a number(1) 1

(2) 2

(3) 3

(4) none

Q.29 A dentist wants a small mirrorthat whenplaced

2 cm from a tooth, will produce 3 upright

image. What kind of mirror must be used and

what must itsfocal length be?(1) concave mirror, 3.0 cm

(2) concave mirror, 1.5 cm

(3) convex mirror, 3.0 cm

(4) convex mirror, 1.5 cm

Q.30 Copper contains 8.41028 free electrons/m3.

A copper wire of cross-sectional area

7.4107 m2 carries a current of 1 A. The

electron drift speed is approximately:

(1) 10

8

m/s (2) 10

3

m/s(3) 1m/s (4) 104 m/s

HEMISTRY

Q.31 100ml of H2O

2solution havingvolume strength

11.2 Vismixed with50ml of0.5M KIsolution

to liberate I2

gas. All the I2

gas liberated is

trapped to form a 500 ml solution termed as

X. 200 ml of the solution X of I2

required

50 ml hypo solution for conversion to Iand

S4O

62 . Assuming all reactions to undergo

100% completion identify the incorrect

option(s)

(1)Volume strengthofremaining H2O

2solution

will be12

4.78V..

(2) Molarity of I2

in solution X is 0.025 M

(3) Molarity of hypo solution taken is 0.2 M

(4) Moles of tetrathionate ions formedwill be 0.01

Q.32 What will be the correct IUPAC name of the

followingcompound?

Cl OCCH3

O

COOH

(1) 3- Ethanoyl oxy-4-Chloro Cyclopentanoic

acid(2) 3- Chloro-4-Ethanoyloxy Cyclopentanoic

acid

(3) 3- Chloro-4-Ethanoyloxy Cyclopentane

Carboxylic acid

(4) 3- Ethanoyl oxy-4-Chloro Cyclopentane

Carboxylic acid

Q.33 Which of the following option isincorrect

regarding following process :

M + CO(impure)

Product (X)

M + CO(pure)

(1) 'X' is an high spin complex

(2) it is Monds process

(3) 'X' is tetrahedral in shape

(4) 'X' is diamagnetic in nature


7/12

Page # 7

Q.34 For the decomposition of ozone in oxygen

O3(g)O

2(g)

(1)rH = ve

(2)rS = ve

(3) rG = ve at onlylow temperature

(4) rG = ve at onlyhigh temperature

Q.35 22

2

NHCHCNHCHCNHCHHOOC||||||

MeOPhCHO

What will be the correct representationof the

above tripeptide.

(1) Gly-Phe-Ala (2)Ala-Gly-Phe

(3) Gly-Ala-Phe (4)Ala-Phe-Gly

Q.36 Which ofthe following is notplanar?

(1) [Ni(CN)4]2 (2) [PtCl

4]2

(3) [Pd(CN)4]2 (4) [Zn(CN)4]2

Q.37 A closed vessel initially contains a mixture of

two gases A2B and an inert gas. During the

thermaldecomposition of gasA2B asper given

A2B(g)2A(g) + B(g)the pressure changed

from aninitial value of 2 atm to 5.2 atm at the

end of reaction. The rate constant (in min) if

total pressure was measured as 4.8 atm after

10 min is-

(1) 0.3 log 2 (2) 3 ln4.16.1

6.1

(3)200

2ln(4)

10

2ln3

Q.38 4-Pentenoic acid 2SOCl (X)

(Y)

OHdil)iii(

OH)ii(

LAH)i(

3

(Z)

Identify final (major) product:

(1) NCCHCHCHCH||

O

222

(2) CH2=CHCH

2CH

2CH

2N

(3) NCHCHCHCHCH|

HO

2222

(4) CH3CH2CH2CH2CH2 OH

Q.39 Which option isTrue (T)andFalse (F) for

IUPAC name of K3[Fe(CN)

6]?

[State (T) for True and (F) for False]

(i) potasium hexacyanido ferate(III)

(ii)tripotasium hexacyanidoferate

(iii) potasium haxacyanidoferate(3)

(iv) tripotasium hexacyanido ferate (III)(1) TTTF (2) TTFF

(3) TFFF (4) TFTF

Q.40 1.7 gm ofanammonium saltwere treated with

100 ml of normal NaOH solution and boiled

till nomoreofammonia gas was given off.The

excess ofNaOH solution left over required 60

mlofnormal sulphuricacid.The% ofammonia

in salt is-

(1) 20% (2) 30%

(3) 40% (4) 50%

Q.41 X. X will be

(1) (2)

(3) (4) None

Q.42 Unknown salt 'A' + K2Cr

2O

7+ conc.

H2SO

4 Reddish brown fumes.

Which is thecorrect statement regarding the

above observation

(1) It confirms the presence of Clion

(2) It confirms the presence of Brion

(3) It confirms the presence of both

(4) It neither confirms Clnor Brunless it is

passed through NaOH solution

Q.43 1 mol Fe reacts completelywith0.7mol ofO2

to give a mixture of only FeO & Fe2O

3. The

mol ratio of Fe+3 to Fe+2 in product mixture is:

(1) 1 : 2 (2) 2 : 1

(3) 2 : 3 (4) 4 : 1

Q.44 Suitable reagent(s) to convert acetyl chloride

into acetaldehyde is / are :

(a) NaC2H

5OH (b) NaBH

4

(c) H2/PdBaSO

4 (d) LiAlH (CMe

3)

3

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


8/12

Page # 8

Q.45 If the number of Silicon atoms is restricted to

23 only, what would be the number of oxygen

atoms and magnitude of negative charges

respectively in the structure of Pyroxene

(single chainSilicate)?

(1) 70,48 (2) 70, 46

(3) 23, 48 (4) 23, 46

Q.46 At 27C if temperature of 1 mol of gas is

increased by 50C the % change in kinetic

energy of systemis-

(1) 16.67 (2) 18.57

(3) 85.18 (4) 7.66

Q.47HOCPh

||O

+ HO

18

HCl (X)

Major product (X) is.

(1)

O

PhCO18

(2)

O

PhCO

18

(3)

O

PhCO (4) PhO

Q.48 Identify the correct sequence of increasing

number of-bonds in the structure of thefollowingmolecules.

I H2S

2O

6 IIH

2S

2O

3III H

2S

2O

5

(1) I, II and III (2) II, I and III

(3) II, III and I (4) I, III and II

Q.49 The progress of reaction

A(g)xB(g) + yC(g) with time is presented

in figure.What is the value of KC

at300K.

0.5

1.0

1.5

2.0

2.5

3.0

[B]

[A]

t (in sec)

conc. (M)

(1) 1 (2) 2

(3) 3 (4) 4

Q.50

EtOA

OH3

B

HCl

)Hg(Zn C

Cis:

(1) (2)

(3) (4)

Q.51

List - I (ppt.) List - II (colour)

(P) Ag2CrO

4 (1) Yellow

(Q) Cu2[Fe(CN)

6] (2) White

(R) BaSO4

(3) Chocolate brown

(S) PbI2

(4) Scarlet Red

Codes:

P Q R S

(1) 4 2 1 3

(2) 2 3 4 1

(3) 4 3 2 1

(4) 3 4 1 2

Q.52 An aqueous solution contain .

5M Ca(OH)2

& .1M NH4OH K

b(105).

Then (NH4

+) will be equal to-

(1) 104 M (2) 106 M

(3) 2 106 M (4) 2 105 M

Q.53

Above compound is hydrated maximum at

which position?

(1) 1 (2) 2

(3) 3 (4) equal


9/12

Page # 9

Q.54 Why is the E value of Mn+3 / Mn+2 couple

much more positive than Cr+3/Cr+2 .

(1)Due tolarger thirdionisationenthalpyofMn

(2) Due larger third ionisation enthalpy of Cr

(3) Due tosmallerthirdionisation enthalpyofMn

(4) Due to lesser hydration enthalpy of Cr

Q.55 2 Litre 2 M aqueous CuSO4

is electrolysed

using platinum electrodes and 2 96500 C

charge is passed through it then what would

be new conc. of (Cu2+) in solution.

(1) 2M (2) 1.5 M

(3) 1 M (4) 0.5 M

Q.56 MeCHO ,NaOH

AAA ,KOH

B B i s :

(1) Me(CH=CH)3CHO

(2) MeCH=CHCHO

(3) Me(CH=CH)2CHO

(4) CHO)CHCH(Me 4

Q.57 Thepointofdissimilarity between lanthanides

and actinides is-

(1) Three outermost shells are partially filled

(2) Theyshowoxidation state of +3 (common)

(3) They arecalled inner-transition elements

(4) They are radioactivity in nature

Q.58 An orbital having one radial nodes and two

angular nodes maybe-

(1)xyd3 (2) yzd4

(3) 22 yxd5 (4) 4pz

Q.59 Statement-1 : NH2 NH

2gives Prussian

blue colour during Lassaigne test (element

detection test).

Statement-2 : NaCN gives Prussian blue

colour of Fe4[Fe(CN

6)]

3with FeSO

4, FeCl

3.

(1) Statement-1is true, statement-2 is true and


statement-1.

(2) Statement-1 is true, statement-2 is true and


statement-1.

(3) Statement-1 is true, statement-2 is false.(4) Statement-1 is false, statement-2 is true.

Q.60 In the Castner process for the extraction of

sodium, theanodeis made of ................ metal.

(1) Copper (2) Carbon

(3) Sodium (4) Nickel

M THEM TI S

Q.61 A tangent toellipse 116

y

25

x 22 at any point

P meets the line x = 0 at point Q. Let R be

the image of Q in the line y = x, then circle

whose extrimities of diameter are Q and R,

passes through a fixed point, whosecoordinate

is

(1) (3, 0) (2) (5, 0)

(3) (0, 0) (4) (4, 0)

Q.62 Any ordinateMPof ellipse 116

y

25

x 22 meets

the auxiliarycircle at Q, then locus of point of

intersection of normals at P and Q to curves is

(1) x2 + y2 = 8 (2) x2 + y2 = 34

(3) x2 + y2 = 64 (4) x2 + y2 = 81

Q.63 A variable line having intercepts e and e' on

co-o rd inate ax es, wh ere2

'e,

2

eare

eccentricities of a hyperbola and its conjugate

hyperbola , then the line touches the circle

x2 + y2 = r2 whose radius is

(1) 1 (2) 2

(3) 3 (4) cannot be found

Q.64 The s et of va lue s of 'x ' f or wh ich

n21x x2tan4

1

1Lim

(where n N) is a

non-zerofinite quantity, is

(1)

2

1,

2

1(2)

2

1,0

(3) ( 1, 1) (4)

0,

2

1


10/12

Page # 10

Q.65 The coordinate of one of the points on the

curve f (x) = 2x1

x

for which normal is

parallel to bisector of IInd and IVth quadrant,

is

(1) 32,2 (2) 8

3,3

(3)

3

2,2 (4)

2

3,3

Q.66 The set of values of 'x' for which function

f(x )=x lnx x + 1 takes positive value only,

is

(1) (1, ) (2) ,e

1

(3) [e, ) (4) (0, 1)(1,)

Q.67 The number of points where the function

f(x) = max{| tan x |, cos | x |} is non-differen-

tiable in the interval (, ) are(1) 4 (2) 6

(3) 3 (4) 2

Q.68 A function 'g' is defined for x > 0 such thatg(1) = 1 and g'(x2) = x3 x > 0, then thevalue of g(4) equals

(1)3

13(2) 3

(3)5

67(4) None of these

Q.69 Let f(x) =

1x;3xx

1x;

1x;1x

2

be a strictly

increasing function at x = 1, then the set of

values of ''are(1) (2, 3) (2) [2, 3)

(3) [2, 3] (4)

Q.60 Let f(x) = 2x3 3(a + 1) x2 + 6ax 12 has

maxima and minimaat x1

and x2respectively

and if 2x1

= x2

then the value of 'a' is

(1) 1 (2)3

1

(3) 1 (4) 2

Q.71

6

xcos4 cos 2x cos

x6

5dx is

(1) C2

x2sin

4

x4sinx

(2) C2

x2sin

4

x4sinx

(3) C2

x2sin4

x4sinx

(4) C2

x2sin

4

x4sinx

[Note: Where 'C' is constant of integration.]

Q.72 If P =3

n/1n

1r

33

n n

)rn(

Lim

and = 1

0

3x1

dxthen ln P is equal to

(1)ln 2 1 + (2)ln 2 3 + 3(3) 2ln 2 (4)ln 4 3 + 3

Q.73 If b,a

and c

are non-coplanar vectors such

that

(x + y 3) a + (2x y + 2)b

+ (2x + y + ) c = 0

holds true for some x and y then is

(1)3

7(2) 2

(3)3

10(4)

3

5


11/12

Page # 11

Q.74 If cba and acb

then

(1) 0ca

(2) cbca

(3) |c||a| (4) None

Q.75 If z1and z2 are roots of quadratic equationaz2 + bz + c = 0 such that Im(z

1z

2) 0 then

(1) a, b, c are all real

(2) atleast one of a, b, c is real

(3) atleast one of a, b, c is imaginary

(4) a, b, c are all imaginary.

Q.76 Let A =

2

2

2

z54

9y3

86x

,

B =

3z2416y2253x2

be two matrices

and if Tr. (A) = Tr. (B), then the value of

(x + y + z) is equal to

(1) 0 (2) 1

(3) 2 (4) 3

[Note : Tr.(P) denotes trace of matrix P.]

Q.77 A fair dice is rolled three times, then the

probability of getting a number larger than the

previous number is

(1)216

5(2)

54

5

(3)61 (4)

365

Q.78 Three numbers are chosen at randomfrom the

set of first 20 natural numbers, then the

probability that their product is a multiple of 3

is

(1)285

194(2)

57

1

(3) 19

13(4) 4

3

Q.79 Consider line L2

1x =

3

1y

=8

10z .

Point P(1, 0, 0) and Q are such that PQ is

perpendicular to line L and the mid-point of

PQ lies on the line L then Q is

(1) (3, 4, 2) (2) (5, 8, 4)

(3) (1, 1, 10) (4) (2, 3, 8)

Q.70 Let A(1, 1, 1), B(2, 3, 5) and C(1, 0, 2)

be three points then equation of plane parallel

to planeABCand atdistance 2 unit fromorigin

is

(1) 2x 3y + z + 2 14= 0

(2) 2x 3y + z 14= 0

(3) 2x 3y + z + 2 =0

(4) 2x 3y + z 2 = 0

Q.81 The area of figure bounded by the curve

y = 2 x x2 and the straight liney = x is

(1)2

9(2) 9

(3)2

7(4) 7

Q.82 The orderofdifferentialequation corresponding

to y = c1

co s2 x +c2

cos2 x + c3

sin2 x + c4

is

(1) 2 (2) 4

(3) 3 (4) None of these

Q.83 Consider I1=

1

0

2x dxxcose ,

I2=

1

0

2x dxxcose2

, I3=

1

0

2 dxxcose 22x

,

I4

= 1

0

dxe 22

x

then correct sequence is

(1) I2

> I4

> I1

> I3

(2) I2

< I4

< I1

< I3

(3) I1

< I2

< I3

< I4

(4) I1

> I2

> I3

> I4


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Page # 12

Q.84 The area encl osed by y = x 3, its normal at

(1, 1) and x-axis is equal to

(1)4

7(2)

4

9

(3)

4

5(4) 2

Q.85 T he common tangent between

9x2 16y 2 = 144 and x2 + y2 = 9 cuts the

coordinate axes at A and B, then the product

OA OB equals

(1)7

75(2)

7

150

(3)

14

75(4) None of these

Q.86 Let

f (x)=4

1x +

12

)1x( 3+

20

)1x( 5+

28

)1x( 7......

for x (0, 2), then

2

3'f is equal to

(1)

2

1(2)

4

1

(3)5

1(4)

3

1

Q.87 If curves x2 = 9a (9 y) and x2 = a (y + 1)

intersect orthogonally then value of 'a' is

(1) 1 (2) 2

(3) 3 (4) 4

Q.88 If dx)x(f = g (x), then dx)x(f 1 is

(1) x f1 (x) + C

(2) C)x(gf 1

(3) C)x(fg)x(fx 11

(4) C)x(g 1

[Note: Where 'C' is constant of integration.]

Q.89 Forces of magnitude 3 and 4 units act along

k3j2i6 and k6j2i3 respectively

on a particle and displaces it from (2, 2, 1)

to (4, 3, 1), then the work done is

(1)

7

124(2)

7

120

(3)7

115(D) None

Q.90 For any two statements p and q,

~ (p q) (~ p q) is logicallyequivalentto(1) p (2) ~ p

(3) q (4) ~ q

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