Aieee Test Vii

7/25/2019 Aieee Test Vii

http://slidepdf.com/reader/full/aieee-test-vii 1/17Birsa Chowk, Near Bharat Petrol Pump

KAG AITS TESTAIEEE - 2013

Exam Date : 26/01/2014 ES - VII

Time : 180 min. Maximum Marks : 360 Please read the instructions carefully. You are allotted 5minutes specically for this

purpose. You are not allowed to leave the examination hall efore end of the test.

INSTRUCTIONSGeneral

!. "his ooklet is your #uestion Paper. $nswers have to e marked on the provided OMR sheets.%. "his &uestion paper contains 90 &uestions. $ttempt $'' the &uestion(. "he #uestion Paper contains lank spaces for your rou)h work. No additional sheets will e

provided for rou)h work.*. Blank papers, clip oards, lo) tales, slide rule, calculators, cellular phones, pa)ers and electronic

)ad)ets, in any form, are NOT allowed.5. +rite your Name and nrollment No. in the space provided at the ottom of this sheet.-. "his ooklet also contains the answer sheet /0.

Filling in the OMR:1. n the /0, write in ink your Name 2 nrollment No. and put your 3i)nature in theappropriate ox.

4. very &uestion has four choices for its answer (A), (B), (C) 2 (D).. n the /0, for each &uestion numer, darken N'Y one ule correspondin) to what

you consider to e the most appropriate answer, from amon) the four choices.Maring S!he"e:

!6. "he &uestion paper consists of ( section 7#$%SICS, C$EMISTR% & MAT$EMATICS8.!!. 9n each section : #. No. !;(6 carries ' "ar !%. Candidates will e awarded "ar *+r !+rre!t re+ne of each &uestion- ./ (+ne

*+rth) "ar 1ill 2e 3e3!te3 for indicatin) incorrect response of each &uestion. Nodeduction from the total score will e made if no response is indicated for an item in the answersheet.

Ue*l Data:

#h4i!$cceleration due to )ravity ) < !6 m=s% Plank constant h < -.- x !6;(*>;sChar)e of electron e < !.- x !6;! C /ass of electron me <

.! x !6;(! k)

Permittivity of free space ε6 ? 4.45 x !6;!% C%=N;m% @ensity of water ρwater <!6( k)=m(

$tmospheric pressure Pa < !65 A=m% as constant 0 < 4.(!* > ;! mol;!

Che"itr4:/ass of an electron 7m8 < .! x !6;(!) Char)e of an electron 7e8< !.- x !6;! couloms

as Constant 708 < 4.(!* > −! mol−! $vo)adroDs Numer 7Na8 < -.6%( × !6%(

< 6.64%! 'it atm −! mol−! PlanckEs Constant 7h8 < -.-%- × !6?(* >s

< % Cal mol−! ! Faraday < -566 Coulom

! calorie < *.% >oule

$tomic No : A < !, Ae < %, 'i<(, Be < *, B < 5, C<-, N<1, <4, F<, Na<!!, /)<!%, $l<!(, 3i<!*,P<!5, 3<!-, Cl<!1, $r<!4, <!, Ca%6, Cr<%*, /n<%5, Fe<%-, Co<%1, Ni<%4, Cu<%,Gn<(6, $s<((, Br<(5, $)<*1, 3n<56, 9<5(, He<5*, Ba<5-, P<4%, I<%

$tomic /asses: A<%, 'i<1, Be<, B<!!, Na<%(, $l<%1, 3i<%4, 3<(%, <(, Ca<*6, Cr<5%, Co<5,Ni<54.1, Gn<-5.*, $s<15, 9<!%1, He<!(!, Ba<!(1, I<%(4, Ae<*, /)<%*, C<!%,

AIEEE_AITS (Test!II"



<!-, N<!*, P<(!, Br<46, Cu<-(.5, Fe<5-, /n<55, P<%61, $u<!1, $)<!64, F<!,A<%, Cl<(5.5, 3n<!!4.-

Name : ___________________________Roll No :________________________




#$%SI&S

1. One end of a spring of force constant k is fixed to a vertical wall and the other to a block of mass

m resting on a smooth horizontal surface with spin in its natural length. Another wall is at a

distance b from the block. The block is moved to compress the spring by 2b and then released

from rest. The time to strike the wall is nπ ! 12" √m!k"" where =n

A" 2 #" $ %" & '" 1(

2. A string of length (.) m and mass kg1( 2− is tightly clamped at its ends under tension 1.$ *

+dentical wave pulses are produced at one end at intervals of ∆t. The minimum value of ∆t.

which allows constructive interference between successive pulses is,

A" (.(- s #" (.1( s %" (.2( s '" (.)( s

. The xz/plane separates two media A and # of refractive indices .2and-.1 21 =µ=µ A ray of

light travels from A to #. +ts direction in the two media are given by unit vectors 'iu ba1

+= and

.dc2 'iu += then 0 ) A" c 0 a #" a 0 c %" d 0 b '" b 0 d

). $ charges of eual magnitude, positive and negative, are at the corners of a regular hexagon

345678, such that the field at the centre O is twice that created by a single positive charge

placed at 5. +t is possible tat the positive charges are placed at

A" 3, 4, 5 #" 4, 5, 6 %" 4, 5, 7 '" 3, 5, 7

-. 9or the resistance values shown in Ω, the current through ( Ω resistor from left to right is

A" (.)A #" −(.)A %" (.& A '" −(.&A

$. A block is gently dropped on a conveyor belt moving at .ms 1− +f ,-.(=µ the displacement

of the block relative to conveyor belt before slipping between the two stops is

A" 2.: m #" 1.& m %" (.; m '" 1.2 m

(Space for Rough Work)


(

)(

)( &(v44

)(4



:. A 3/tube, with separation between two limbs as d, contains the same liuid in the two limbs.

5hen moved horizontally with acceleration a in the plane of the limbs, the level difference is

A" ad ! 2g #" ad ! g %" 2ad ! g '" gd ! a

&. <adioactive materials 21 6=6 have mean lives T = 1(T respectively. The ratio of nuclei is 1 at

time (t = and e01 at time =t

A" T #" 1(T!11 %" 11T '" 1(T!;

;. A light rigid rod has identical point masses of > at the two ends. +f an impulse >v? = is given

to one point mass perpendicular to the rod, the angular velocity of the rod is

A" v!@ #" 2v!@ %" v!@ '" v!)@

1(. A ball of density ρ is immersed in a liuid of density ρ to a depth h and released. The height it

umps above the surface of the liuid is

A" h #" h!2 %" 2 h '" h

11. +n a 7oungBs double slit experiment, λ= -(d and .d1((' = +f the intensity at the screen

centre bright fringe" is ,lo the intensity on the screen directly in front of one of the slit is

A" ol-(.( #" ol:-.( %" ol '" ol2-.(

12. 4essel A has water at %1(( o while vessel # has ice at .%(

o Two identical conducting rods

are first connected in parallel between the vessels and then connected in series between the

vessels. The rate of melting of ice in the two cases is in the ratio

A" 1 0 2 #" 2 0 1 %" ) 0 1 '" 1 0 )

1. A closed pipe has a gas of density 1ρ

and an open pipe has a gas of density.2

ρ Thecompressibility of b other gases is eual. The first overtones of both resonate of length ratio is

A" √ 1ρ 0 ) √ 2ρ #" √ 2ρ 0 ) √ 1

ρ %" √ 2ρ 0 √ 1ρ '" √ 1

ρ 0 ) √ 2ρ

1). +f 7oungBs double slit experiment is performed in water,

A" the fringe width will decrease #" the fringe width will increase

%" the fringe width will be unchanged '" there will be no fringe pattern





1-. The resistance between terminals A and # of the infinite circuit with each resistance < is

A" √ C 1" < #" 2 − √" < %" 1 D √" < '" 2 D √" <

1$. Each segment of the wire frame shown has length 1 m and carries current 2 A in direction shown.

+f a uniform magnetic field of ) T acts normal to the plane of the frame, the magnitude of the

magnetic force acting on the frame is

A" 2) * #" ( %" 1$ * '" & *

1:. 2 identical glass "-.1 g =µ euiconvex lenses of focal length f are kept in contact. The space

between the lenses is filled with water ".!) w =µ The focal length of the combination is

A" f #" f!2 %" )f! '" f!)

1&. >agnetic moment of an electron mass m" in the nth orbit of hydrogen atom is

A" neh ! πm #" neh ! )πm %" meh ! 2πn '" meh ! )πn

1;. F is closed at .(t = The ratio of the currents through % and 2%

A" is constant #" increases with time

%" decreases with time '" first increases and then decreases



A

#

2%

%

4

<

<



2(. @et 21 G =G be the maximum kinetic energies of photoelectrons emitted by light of

wavelengths .= 21 λλ +f ,2 21 λ=λ then

A" 21 G G 2 = #" 21 G 2G = %" 21 G G 2 < '"

21 G 2G >

21. +n a meter bridge setup, let < @ and αα e the temperature coefficients of resistivity for the

resistances in the left gap and right gap. The balance point is at the 1( cm mark. +f the

temperature increases by T due to heating, then the shift in cm" in the balance point is

A" T"; < @ α−α #" ;!T"; < @ α+α %" T";< @ α+α '" ;!T" < @ α−α

22. 9or tubes of same length shown, the ratio of freuencies =sr p n0n0n0n

A" 12 0 $ 0 0 ) #" 1 0 2 0 ) 0 %" ) 0 2 0 0 1 '" $ 0 2 0 0 )

2. 5hile drawing cooling curve between the temperature of hot water and time we should stir the

water uniformly. This needs to be done to ensure that

A" temperature of water in the calorimeter is same at all places

#" cooling will occur fast to save the time of experiments

%" steam should not form in the water

'" none of these

2). A solid of mass (.2 kg is supplied heat at the constant

rate of 2-( 5. The plot of its temperature in G"against time in hours" is shown. +ts latent heat of

vapourization is

A" 1$ kg?1(-.) −× #"1$ gcal1(-.) −×

%" 1) kg?1(-.) −× '"1) gcal1(-.) −×


1 2 )

&((

((


H I r F



2-. The least count of a screw gauge is (.(1 mm. +t measures a diameter to be )(.(( mm. Then the

maximum percentage error in the measurement of diameter is

A" 1.2-J #" (.2-J %" (.((2-J '" none of these

)r *. 26 t) 30 : T+) statements (A" an, (-" are ien. ie ans+er as

A" +f A" is true, <" is true and <" is the correct explanation for A"K

#" +f A" is true, <" is true and <" is not the correct explanation for A"K

%" +f A" is true, <" is true '" if A" is false.

2$. A" A proton and an electron experience same magnitude force in the same electric field.

<" Electric force on a test charge is independent of its mass.

2:. A" Efficiency of any heat engine is "T!T1L@

− where L@ T=T are the

lowest and highest temperatures attained in the heat cycle.

<" Efficiency of any engine is ratio of the work done to the energy supplied.

2&. A" +n the experiment to find the specific heat of a liuid using a calorimeter,

the current is kept constant by adusting the rheostat.

<" A variable current will damage the heating coil in the heater.

2;. A" +n OhmBs law experiment, the potential drop and the current for a resistance wire was

measured as -.( 4 and 2.(( A. The error in resistance computed is J.-.2±

<" The ammeter was connected in series and the voltmeter in parallel with resistance.

(. On rear view mirror used in automobiles generally it is printed Mobects in mirror are closer than

they appearN.

A" This is not actually true. +t is to alert drivers to get sufficient time to apply breakes.<" The rear view mirror forms a virtual image.





&$EMIST-%

1. The synthesis of /octyne is achieved by adding a bromoalkane into a mixture of sodium amide

and an alkyne. The bromoalkane and alkyne respectively are

A" %L%%L%Land%L%L%L%L#r%L 22222 ≡

#" %L%%L%L%Land%L%L#r%L 2222 ≡ %" %L%%Land%L%L%L%L#r%L 2222 ≡

'" 222 %L%L%L#r%L and %L%%L%L2 ≡

2. The correct statement about the following disaccharide is

A" <ing a" is pyranonse with α/gycosidic link

#" <ing a" is furanonse with α/gycosidic link%" <ing b" is furanonse with α/gycosidic link

'" <ing b" is pyranonse with β/gycosidic link

OCH3

HBr In the reaction the products are

(A) (B)

(C) (D)

OCH3 and H2Br Br and CH3Br

Br and CH3OBr OHand CH3Br



O

LOL2

%

O%L2%L

2O

O L

%L2OL

L

L

OL

OL

L

L

OLL

OL

L

OL

L

%L2OL



). Hlots showing the variation of the rate constant k" with temperature T" are given below. The

plot that follows Arrhenius euation is

A" #"

%" '"

-. The ionization isomer of %l" *O!%l"OL%r P 2)2

A" 22)2 %l" *O"OL%r P #" " *O%l"OL%r P 22)2

%" %l"O*O%l"OL%r P )2 '" OL" *O%l"OL%r P 222)2

$. +f α is the degree of dissociation of ,FO *a )2 the vant LoffBs factor i" used for calculating the

molecular mass is

A" α+1 #" α−1 %" α+ 21 '" α− 21

:. An ionic compound has a unit cell consisting of A ions at the corners of a cube and # ions on the

centres of the faces of the cube. The empirical formula for this compound would be

A" A# #" #A2 %" A# '" #A

&. 5hich of the following is a polyamide Q

A" Teflon #" *ylon/$$ %" Terylene '" #akelite



k

T

k

T

k

T

k

T



;. Aluminium oxide may be electrolysed at %1(((o to furnish aluminium metal Atomic mass

2:= amu K 1 9araday = ;$,-(( %oulombs". The cathode reactions iso.

Ale.Al → + −+

To prepare -.12 kg of a aluminium metal by this method would reuire

A" %1();.-

:

× of electricity #" %1(&.1

:

× of electricity%" %1();.- )× of electricity '" %1();.- 1× of electricity

)(. %onsider the reaction 0 .22 *L2L. * → + carried out at constant temperature and pressure. +f ∆L

and ∆3 are the enthalpy and internal energy changes for the reaction, which of the following

expressions is true Q

A" (L =∆ #" 3L ∆=∆ %" 3L ∆<∆ '" 3L ∆>∆

)1. 5hich one of the following statements is *OT true about the effect of an increase in temperature

on the distribution of molecular speeds in a gas Q

A" The most probable speed increases

#" The fraction of the molecules with the most probable speed increases%" The distribution becomes broader

'" The area under the distribution curve remains the same as under the lower temperature

)2. +n a multi C electron atom, which of the following orbitals described by the three uantum

numbers will have the same energy in the absence of magnetic and electric field Q

a" (m,(l,1n === b" (m,(l,2n ===

c" 1m,1l,2n === d" 1m,2l,n ===

e" (m,2l,n ===

A" a" and b" #" b" and c" %" c" and d" '" d" and e"

). #ased on lattice energy and other considerations which of the following alkali metal chlorides is

expected to have the highest melting point Q

A" @i%l #" *a%l %" G%l '" <b%l

)). The molecular shapes of ))) 6e9and%9,F9 are

A" The same with 2, ( and 1 lone pairs of electrons on the central atom, respectively

#" The same with 1, 1 and 1 lone pair of electrons on the central atoms, respectively

%" 'ifferent with (, 1 and 2 lone pair of electrons on the central atoms, respectively

'" 'ifferent with 1, ( and 2 lone pairs of electron on the central atoms respectively





)-. The pink colour of permanganate ion is due to

A" *o unpaired electron

#" Hresence of unpaired electron

%" %harge transfer from metal to ligand orbital

'" %harge transfer from ligand to metal orbital.

)$. The oxidation state of chromium in the final product formed by the reaction between Gl and

acidified potassium dichromate solution is

A" )+ #" $+ %" 2+ '" +

):. The number of hydrogen atom s" attached to phosphorus atom in hypophosphorous acid is

A" 8ero #" Two %" One '" Three

)&. 5hat is the conugate base of −OL Q

A" 2O #" OL2 %" −O '" 2O

−

);. +n silicon dioxide

A" Each silicon atom is surrounded by our oxgen atoms and each oxygen atom is bonded to two

silicon atoms

#" Each silicon atoms is surrounded by two oxygen atoms and each oxygen atom is bonded to

two silicon atoms

%" Filicon atom is bonded to two oxygen atoms

'" Three are double bonds between silicon and oxygen atoms

-(. 5hich of the following compound shows optical isomerism Q

A"2

) " *L%uP +

#" 2

) 8n%lP − %"

)2 "O%%r P −

'"

$ "%*%oP −

-1. Tertiary alkyl halides are paractically inert to substitution by2

*F mechanism because o(f

A" +nsolubility #" +nstability %" +nductivity effect '" Fteric hindrance

-2. +n both '*A and <*A, heterocyclic base and phosphate ester linkages are at

A" 2R

-R

%and% respectively of the sugar molecule

#" -R

1R %and% respectively of the sugar molecule

%" -R

1R %and% respectively of the sugar molecule

'" 1R

-R %and% respectively of the sugar molecule





-. The decreasing order of uncleophilicity among the nucleophiles(i) (ii)

(iii) (iv)

CH3 C O

O

CH3O

CN CH3 S

O

O

O

A" i", ii", iii", iv" #" iv", iii", ii", i"

%" ii", iii", i", iv" '" iii", ii", i", iv"

-). Of the five isometic hexanes, the isomer which can give two monochlorinated compound is

A" n/hexane #" 2, /dimethylbutane

%" 2, 2/dimethylbutane '" 2/methylpentane

--. Amongst the following the most basic compound isA" #enzylamine #" Aniline %" Acetanilide '" p/nitroaniline

-$. 5hich types of isomerism is shown by 2, /dichlorobutane Q

A" 'iastereo isomers #" Optical %" Seometrical '" Ftructural

-:. The reaction

R C

X

O

+ Nu R C

Nu

O

+ X

is fastest when 6 is

A" %l #" 2 *L %" -2LO% '" O%O<





-&. P /cresol racts with chloroform in alkaline medium to give the compound A which adds hydrogen

cyanide to form, the compound #. Te latter on acidic hydrolysis gives chiral carboxylic acid. The

structure of the carboxylic acid is

(A) (B)

(C) (D)

CH3

OH

CH(OH)COOH

CH3

OH

CH(OH)COOH

CH3

OH

CH2COOH

CH3

OH

CH2

COOH

-;. )!1t can be taken as the time taken for the concentration of a reactant to drop to !) of its initial

value. +f the rate constant for a order reaction is G, the )!1t can be written as

A" (.1( ! G #" (.2; ! G %" (.$(; ! G '" (.:- ! G

$(. An amount of solid LF *L) is placed in a flask already containing gas at a certain temperature

at (.-( atm. pressure. Ammonium hydrogen sulphide decomposes to yield *L and FL2

gases and pressure in the falsk rises to (.&) atm. The euilibrium constant for LF *L)

decomposition at this temperature isA" (.( #" (.1& %" (.1: '" (.11





MAT$EMATI&S

$1. +f "1 b, b 2 + is a point in the angle between the lines (-y2x,(1yx =−+=+− containing

the origin, then the number of integral values that b can take is

A" - #" %" 2 '" (

$2. +f the area of the triangle formed by 22xy",1xmy =+= is ), then 2

m can be

A" )! #" !) %" ;!- '" -!;

$. Three distinct numbers are randomly chosen from the first ten natural numbers. The reciprocal of

the probability that the smallest and largest are and : is

A" ) #" 12 %" ( '" )(

$). The are bounded by parabola x12y2 = and its latus rectum is

A" ; #" 1$ %" 2) '" $

$-. The locus of the centres of circles, for which one end of a diameter is 1, 1" while the other end ison the line ,yx =+ is

A" 1yx =+ #" -"yx2 =− %" -y2x2 =+ '" -yx =+

$$. +f A, ", #), ", %, )" be the vertices of a triangle, then the distance between its orthocentre

and circumcentre is

A" √2 #" 2√2 %" 1!√2 '" 1

$:. 3sing some or all of U(, 1, 2, , ), -V without repetition, the number of natural numbers that can

be formed is

A" 1$(( #" 1$2( %" 1$( '" 1:2(

$&. *umber of distinct normal lines to ellipse 222 $-"y1"x- =+ from the point (, ;" is

A" 1 #" 2 %" '" )

$;. +f H and I are the ends of a pair of conugate diameters and % is the centre of ,$y;x) 22 =+

then the area of triangle %HI is suare units is

A" 2 #" %" $ '" 12





:(. @ength of the focal chord or the parabola ax)y2 = at distance p from the vertex is

A" p!a) 2 #" 2 a! p) %" 2 p!a) '" a! p) 2

:1. +f the portion of the line 1kxy =+ intercepted between the lines kxy=(kx)y ==+ subtends

a right angle at the origin, then k can be

A" 2− #" 1− %" 2!1− '" (

:2. The locus of the point of intersection of the tangents at the extremities of a chord of the circle222 byx =+ which touches the circle ( by2yx 22 =−+ is

A" "y2 b bx 2 −= #" "y b b2x 2 −= %" "y2 b bx2 += '" "y b b2x

2 +=

:. #oxes A, #, % each has four balls numbered 1, 2, , ) A child chooses one ball from each of the

boxes. +f a, b, c are the numbers on the balls chosen from A, #, %K then the child wins a toy if .c ba += The odds in favour of the child to win a toy is

A" 0 2 #" 0 2; %" 1 0 1- '" - 0 -;

:). 9our unit vectors u and , if ,1RR <− /u then the angle between u and lies in the interval

A" P(, π!$" #" P(, π!)" %" P(, π!" '" Pπ!$, π!

:-. A plane passes through 1, −2, " = −1, 2, −1" and is parallel to the line .)

z

1y

2

2x=

+=

− The

direction ratios of the normal to the plane can be

A" 2, , ) #" ), (, : %" −2, (, −1 '" 2, (, −1

:$. The line of the family ("2yx b"$yxa =+++++ farther from the point 2, " is

A"()yx =−−

#"(yx) =+−

%"(2y)x =−+

'"(&yx) =++

::. +f (c, b,a > with abc2 = and ,

x b b

ax b

aax

"xf = then

A" fx" is increasing in −c, c" #" fx" is decreasing in "c,c< −−

%" fx" has a local maximum at cx = '" fx" has a local minimum at cx =





:&. @et a relation < in the set of real numbers be a<b iff .(ab1 >+ The relation < is

A" <eflexive and symmetric #" Fymmetric and transitive

%" Transitive '" An euivalence relation

:;. The ratio of the radii of the inscribed and circumscribed circle for an isosceles triangle with base

angle 2x is

A" sin )x tan x #" sin 2x tan x

%" sin )x tan 2x '" sin 2x tan 2x

&(. The are of the region V1yxRyRRxR0"y,xU< 22 ≤+∩≤= is

A" π!& #" -π!& %" π!2 '" π!&

&1. +f dxx1

x1+

1

(

)

&

1 ∫ ++

= and ∫ ++

=1

(

;

2 ,dxx1

x1+ then

A"12

++1 << #" 1++21

<< %"21

++1 << '" 1++12

<<

&2. @et ek" be the eccentricity of the conic .k xy = Then =− R"$e")eR

A" 2W #" 1 %" 2!12− '" (

&. @et 1% and 2% be two fixed non/concentric circles with 2% inside .%1 A circle % inside 1%

touches 1% internally and 2% externally. Then the locus of the centre % is

A" a circle #" a parabola %" a hyperbola '" an ellipse

&). 9or the standard ellipse of eccentricity e, the angle between the normals at points with eccentric

angle θ and θ+π "2! is α. Then k 0eR2sin0cot2R 2=θα where =2k

A" 2e1− #" 2e1+ %" 22 "e1 − '"22 "e1 +

&-. @et x(", b blnxx)"xf 2 <≤+−+−= and .x,1&x"xf ≥−= +f fx" has a local

minima at ,x = the complete set of values of b is

A" P−1, 2 #" < C 1, 2" %" P1, 2" '" < C −1, 2"




http://slidepdf.com/reader/full/aieee-test-vii 17/17

)r *. 86 t) 0 : T+) statements (A" an, (-" are ien. ie ans+er as

A" +f A" is true, <" is true and <" is the correct explanation for A"K

#" +f A" is true, <" is true and <" is not the correct explanation for A"K

%" +f A" is true, <" is true '" if A" is false.

&$. @et 6 be a family of sets and < be a relation defined on 6 by MA is disoint from #N.

A" The relation < is reflexive.

#" The relation < is not transitive.

&:. A" , ba

"xg"xf "xh+f = then ∫ ∫ ∫ = .

ba

dx"xgdx"xf dx"xh

<" ∫ ∫ = .dx"xf k dx"xf k

&&. A" +f 'ia += and ,k '2 −= then proection of " 2a + on .(" =−2a

<" +f 'ia += and ,k '2 −= then " 2a + is perpendicular to ". 2a −

&;. A" +n a cycle uadrilateral A#%', .('sin%sin#sinAsin =+++

<" +n a cycle uadrilateral A#%', .('cos%cos#cosAcos =+++

;(. A" A#% is a horizontal triangular field with bA% = and .cA# = A vertical pole standing

at a point ' on #% subtends angle x at # = y at %. +f ,'A%#A' ∠=∠ then

.ycotcxcot b =

<" The bisector of an angle of a triangle divides the opposite side in the ratio of the sides

containing the angle.



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Aieee Test Vii