REVIEW TEST-3
Class : XIII (XYZ)
Time : 3 hour Max. Marks : 276
INSTRUCTIONS
1. The question paper contain 28 pages and 3-parts. Part-A contains 9 objective question, Part-B contains
9 questions of "Match the Column" type and Part-C contains 15 subjective type questions.All questions are compulsory.
Please ensure that the Question Paper you have received contains all the QUESTIONS and Pages. If you found some
mistake like missing questions or pages then contact immediately to the Invigilator.
PART-A
(i) Q.1 to Q.9 have More than one are correct alternative and carry 6 marks each.
There is NEGATIVE marking. 1 mark will be deducted for each wronganswer.
PART-B
(iii) Q.1 to Q.9 are "Match the Column" type which mayhave one or more than one matching options and carry8 marks
for each question. 2 marks will be awarded for each correct match within a question.
There is NEGATIVEmarking. 0.5 Markswill be deducted for each wrong match. Marks will be awardedonlyifall the
correct alternatives are selected.
PART-C
(iv) Q.1 to Q.15are "Subjective" questions and carry10 marksfor each. There is NO NEGATIVE marking. Marks will be
awarded only if all the correct bubble are filled in you answer sheet.
2. Indicate the correct answer for each question by filling appropriate bubble in your answer sheet.
3. Use only HB pencil for darkening the bubble.
4. Use of Calculator, Log Table, Slide Rule and Mobile is not allowed.
5. The answer(s) of the questions must be marked by shading the circles against the question by dark HB pencil only.
USEFULDATA
Atomicweights: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 = 65.4,
Radius of nucleus =10–14 m; h = 6.626 ×10–34 Js; me = 9.1 ×10–31 kg, R = 109637 cm–1
PART-B
For example if Correct match
for (A) is P, Q; for (B) is P, R;
for (C) is P and for (D) is S
then the correct method for
filling the bubble is
P Q R S
(A)
(B)
(C)
(D)
PART-C
Ensure that all columns
(3 before decimal and 2 after
decimal) are filled. Answer
having blank column will be
treated as incorrect. Insert
leadingzero(s)ifrequiredafter
rounding the result to 2
decimal places.
e.g. 86 should be filled as
0086.00
.
.
.
.
.
.
.
.
.
.
PART-A
For exampleifonly'B' choice
is correct then, the correct
method for filling the bubble
is
A B C D
For example if only 'B & D'
choices are correct then, the
correct method for filling the
bubble is
A B C D
the wrong method for filling
the bubble are
The answer of the questions
in wrongor anyother manner
will be treated as wrong.

Take g = 10 m/s2 where ever required in this paper.
PART-A
Select the correct alternative. (More than one is/are correct) [9 × 6 = 54]
There is NEGATIVE marking. 1 markwillbe deducted for eachwrong answer.
Q.1 The function f (x) is defined for x  0 and has its inverse g (x) which is differentiable. If f (x) satisfies

)
x
(
g
0
dt
)
t
(
f = x2 and g (0) = 0 then
(A) f (x) isan odd linear polynomial (B) f (x) issome quadratic polynomial
(C) f (2) = 1 (D) g (2) = 4
Q.2 Consider a triangleABC in xyplane with D, E and F as the middle points ofthe sides BC, CAandAB
respectively. Ifthe coordinates ofthe pointsD, E and Fare (3/2, 3/2); (7/2, 0) and (0, –1/2) thenwhich
ofthefollowing are correct?
(A) circumcentre ofthe triangleABC does not lie insidethe triangle.
(B) orthocentre, centroid, circumcentre and incentre oftriangleDEF are collinear but oftriangleABC
are noncollinear.
(C) Equation ofa line passes throughthe orthocentre oftriangleABC and perpendicular to its plane is
k̂
)
j
ˆ
î
(
2
r 




(D) distancebetween centroid and orthocentre ofthe triangleABC is
3
2
5
.
Q.3 Ifa continuous functionf (x)satisfies the relation,  
x
0
dt
)
t
x
(
t f = 
x
0
dt
)
t
(
f +sinx+ cosx– x–1, for
allrealnumbers x, then whichofthe following does not hold good?
(A) f (0) = 1 (B) f ' (0) = 0 (C) f '' (0) = 2 (D) 

0
dx
)
x
(
f = e
ROUGHWORK

Q.4 Stepwise hydrolysis ofP4O10 takes place via formation of
(A) Tetrametaphosphoric acid
(B) Tetrapolyphosphoric acid
(C) Pyrophosphoric acid
(D) Orthophosphoric acid
Q.5 Monochlorinationof(S)-2-chlorobutane cangive
(A) (S)-1,2-dichlorobutane (B) (R)-1,2- dichlorobutane
(C) (2R, 3S)-2,3-dichlorobutane (D) (2R,3R)-2,3-dichlorobutane
Q.6 Select the correct statement about the compound NO[BF4]
(A) It has 5  and 2  bond
(B) Nitrogen-oxygenbondlength is higher thannitric oxide (NO)
(C) It is a diamagnetic specie
(D) B–Fbond length in this compound is lower thanin BF3.
ROUGHWORK

ROUGHWORK
Q.7 A blast breaks a bodyinitiallyat rest ofmass 0.5 kg into three pieces, two smaller pieces ofequalmass
andthethird double the massofeither ofsmallpiece.After the blast the two smaller massesmoveat right
anglesto oneanother with equal speed. Find thestatementsthat is/aretruefor this case assumingthat the
energyofblast is totallytransferred to masses.
(A)Allthe three pieces share the energyofblast equally
(B) The speed ofbigger mass is 2 times the speed ofeither ofthe smaller mass
(C) The directionofmotionofbigger mass makes an angle of135°with the directionofsmaller pieces
(D) The bigger piece carries double the energyofeither piece.
Q.8 You wish to lift a heavy block through a height h by attaching a string of negligible mass to it and
pulling so that it moves at a constant velocity. You have the choice of lifting it either by pulling the
string (i) vertically upward or (ii) along a frictionless inclined plane (see diagram).Which one of the
following statements is true?
(A) The magnitude of the tension force in the string is smaller in case (i) than in case (ii).
(B) The work done on the block by the tension force is the same in both cases.
(C) The work done on the block by the tension force is smaller in case (ii) than in case (i).
(D) The work done on the block by the gravitational force is smaller in case (ii) than in case (i).
Q.9 The wiresAand B shown in the figure are made of the same materialand have radii
rA and rB respectively. The block between them has a mass m. When the force F is
mg/3, one of the wires breaks.
(A) A breaks if rA = rB
(B) A breaks if rA < 2rB
(C) Either A or B may break if rA
= 2rB
(D) The lengths ofAand B must be known to predict which wire will break

PART-B
MATCH THE COLUMN [9 × 8 = 72]
There is NEGATIVE marking. 0.5 markwillbe deducted for each wrong matchwithin a question.
INSTRUCTIONS:
Column-Iand column-IIcontains fourentrieseach. Entries ofcolumn-Iare to be matchedwith some
entriesofcolumn-II.Oneormorethanoneentriesofcolumn-Imayhavethematchingwiththesameentries
ofcolumn-IIandoneentryofcolumn-Imayhaveoneormorethanonematchingwithentriesofcolumn-II.
Q.1 ColumnI ColumnII
(A) 


x
e
x 3 t
n
dt
x
x
n
Lim
l
l
is (P) 0
(B) 





 



1
x
1
x
x
2
4
e
e
Lim is (Q)
2
1
(C)
n
4
)
1
n
(
sin
1
n
5
.
0
n
sin
)
1
(
Lim 2
n
n







 





is where n  N (R) 1
(D) The value ofthe integral 







 










1
0
2
1
1
dx
2
x
2
x
2
1
tan
1
x
x
tan
is (S) nonexistent

Q.2 Consider thematricesA= 







1
1
4
3
andB = 





1
0
b
a
andlet Pbe anyorthogonalmatrix and Q = PAP
APT
and R = PTQKP also S = PBPT and T = PTSKP
ColumnI ColumnII
(A) Ifwe varyK from 1 to n then the first row (P) G.P. withcommonratio a
first columnelementsat Rwillform
(B) Ifwe vary K from1 to n then the 2nd row 2nd (Q) A.P. with common difference 2
columnelementsat R willform
(C) Ifwe varyK from1 to n then the first row first (R) G.P. with common ratio b
columnelementsofT willform
(D) Ifwe varyK from3 to n thenthe first row 2nd column (S) A.P. with common difference – 2.
elements ofT willrepresent the sumof

Q.3 ColumnI ColumnII
(A) Given two vectors b
and
a


such that |
b
|
|
a
|


 = |
b
a
|


 = 1 (P) 30°
The angle between the vectors b
a
2


 and a

is
(B) In a scalene triangleABC, if a cosA= b cos B (Q) 45°
then  C equals
(C) In a triangleABC, BC = 1 andAC = 2. The maximumpossible (R) 60°
value which the Acanhave is
(D) In a  ABC  B = 75° and BC = 2AD whereAD is the (S) 90°
altitude fromA, then  C equals

Q.4 Matchthe column:
ColumnI ColumnII
(A) (P) Conformationofmaximumtorsionalstrain
(B) (Q) Conformationwithstrongintramolecular hydrogenbond
(C) (R) Highest boilingpoint
(D) (S) ConformationofminimumVanderWaalstrain

Q.5 ColumnI ColumnII
(Co-ordinationcompound) (Type ofisomerism shown)
(A) Na2[Pt(SCN)2(Ox)2] (P) Ionizationisomerism
(B) [CrCl2(NH3)4]NO3 (Q) Linkageisomerism
(C) [Pt(NO2)(Gly)(NH3)] (R) Geometricalisomerism
(D) K3[Fe(OH)2(C2O4)2] (S) Opticalisomerism
Q.6 Match the names ofcarboxylic acids incolumnI withpka valueincolumnII.
ColumnI ColumnII
(A) Benzoic acid (P) 4.17
(B) Ethanoicacid (Q) 4.14
(C) o-methylbenzoic acid (R) 4.74
(D) p-flourobenzoic acid (S) 3.91

Q.7 Aglass diskwhose plane surfaces areparallelis cut asshowninfigure thenthe lenses so
obtained are moved apart. What willhappen to a beamofparallelrays falling on to the
system. ( f is the focallengthofconverging lens).
EFFECT
(A) (P) Emergingraysareconverging&imagedistancefromL2<f
(B) (Q) Emerging rays are diverging &imagedistancefromL2 < f
(C) (R) Emerging rays are converging &imagedistancefromL2 > f
(D) (S) Emerging rays are diverging &imagedistancefromL2 > f

Q.8 Abodyinitiallymovingtowards right explodesinto two pieces1 and2. Directionofmotionofthe pieces
is shown incolumn I and possible mass ratio are shownin column II
ColumnI ColumnII
(A) (P) m1 > m2
(B) (Q) m1 = m2
(C) , v1 > v2 (R) m1 < m2
(D) (S) Impossible for anymasses

Q.9 A projectile islaunched at angle  to horizontalfromL and it hits thetarget T on levelground.
ColumnI Column II
(A) Magnitude ofradialacceleration (P) Increases
(B) Magnitude oftangentialacceleration (Q) Decreases
(C) Power deliveredbygravity (R) First increases, then decreases
(D) Torque ofgravityabout T (S) First decreases, then increases

PART-C
SUBJECTIVE: [15 × 10 =150]
Q.1 Suppose V = 


2
0
2
dx
2
1
x
sin
x , find the value of

V
96
.

Q.2 One of the roots of the equation 2000x6 + 100x5 + 10x3 + x– 2 = 0 is ofthe form
r
n
m 
, where m
is non zero integer and n and r are relativelyprime naturalnumbers. Find the value of m + n + r.

Q.3 Acircle C is tangent to the x and yaxis in the first quadrant at the points Pand Q respectively. BC and
AD are paralleltangents to the circle with slope – 1. Ifthe pointsAand B are on the y-axis whileC and
D are on thex-axis and the area ofthefigureABCD is 900 2 sq. units thenfindthe radius ofthe circle.

Q.4 Let f (x) = ax2 – 4ax+ b(a> 0) be definedin1  x  5. Suppose the average ofthe maximumvalue and
the minimumvalue ofthe functionis 14, and the difference betweenthe maximumvalue and minimum
value is 18. Find the value of a2 + b2.

Q.5 If the 









 bx
1
ax
1
x
1
1
x
1
Lim 3
0
x
existsand has the valueequalto l, thenfind the valueof
b
3
2
a
1


l
.

Q.6 Calculate the Hvaporization [CH3COOH( l )] in kJ/mol
Given data
Hsolution [KF. CH3COOH(s)] in glacial acetic acid = –3 kJ/mole
Hsolution [KF(s)] inglacialacetic acid = +35 kJ/mole
The strength ofH-bond between F–(g) and CH3COOH (g) = +46 kJ/mole
Lattice enthalpyof KF.CH3COOH(s) = +734 kJ/mole
Lattice EnthalpyofKF(s) = +797 kJ/mole

Q.7 The gaseousdecomposition reaction
A(g)  2B(g) + C(g)
is observedto first order over the excess ofliquidwater at 25°C, it is found that at the end of10min, the
totalpressure ofsystemis 188 torr and after verylong time it is 388 torr.
Calculate rate constant ofthe reaction(inhr–1)
Given : vapour pressure of H2O at 25° is 28 torr (ln2 = 0.7, ln3 = 1.1, ln10 = 2.3)

Q.8 When1 moleofA(g) is introducedina closed rigid 1 litre vesselmaintained at constant temperature the
following equilibriaare established.
A(g) l B(g) + C(g) :
1
C
K
C (g) l D(g) + B(g) :
2
C
K
The pressure at equilibriumis twice the initialpressure. Calculatethe value of
1
2
C
C
K
K
if
eq
eq
]
B
[
]
C
[
=
5
1

Q.9 Totalentropychange (system+ surrounding) for the process H2O (l,–8°C) H2O (s, –8°C) at 1 atm
and – 8°C is 1 J/K mol.
Find Cp,m (H2O, l) in J/K mol.
Given : Hmelting(at –8°C) = + 5784.95 J/mol, Hmelting(at 0°C) =6006 J/mol
Cp,m(H2O, s) = 36 J/K mol ln 





265
273
= 0.03

Q.10 The equilibriumconstant Kp for the reaction
N2O4 (g) l 2NO2(g) is 4.5 at temperature T.
What would be the average molar mass (in gm/mol) ofanequilibriummixture ofN2O4 & NO2 formed
bythe dissociationofpure N2O4 at a total pressure of2 atmat temperature T.

Q.11 Arocket isprojected straight up andexplodes into three equallymassive fragments just asit reaches the
top ofitsflight (refer figure). Oneofthe fragmentsisobserved to come straight downin 2sec,while the
other two take4secto cometo ground, aftertheburst. Find theheighth(inm)atwhichthefragmentation
occurred.

Q.12 BoardAis placed on board Bas shown. Bothboards slide, without moving withrespect to eachother,
along africtionlesshorizontalsurface at aspeed 6 m/s. Board Bhits aresulting boardC "head-on".After
the collision, boards B and C stick together and boardAslides on top ofboard C and stops its motion
relative to C in the positionshown on the diagram. What is the length (in m) of eachboard?All three
boards have the same mass, size and shape. The coefficient ofkinetic friction between boardsAand C
and between boardsA& B is .

Q.13 Asideview ofasimplifiedformofverticallatchB is asshown. Thelower
memberAcan be pushed forward in its horizontalchannel. The sides of
the channels are smooth, but at the interfaces ofAand B, which are at
45°withthehorizontal, there exists a static coefficient offriction=0.4.
What is theminimumforce F(inN) that must be appliedhorizontallytoA
to start motionof the latch B if it has a mass m= 0.6 kg ?

Q.14 The essentialelements ofone formofsimple speed governorare asshown:
to a vertical shaft a horizontalrod is mounted symmetricallyand on the
horizontal rod are freely sliding brake shoes. When the shaft turns at a
frequency of rotation f = 10 Hz, the brake shoes press against the inner
surface ofa stationarycylindricalbrake drum. Ifthe brake shoes are each
ofmassm= 1kg, and their thickness dimension is negligible compared to
the inner radius ofthe brake drumr =0.1 m, and the coefficient ofsliding
friction between the shoes and the drumis = 0.5, find the power
required inwatt to turnthegovernor shaft.
[Take: 2 = 10]

Q.15 Aring ofmass m= 1kg canslide over asmoothverticalrod.Alight string attached
to the ring passing over a smooth fixed pulleyat a distance ofL = 0.7 mfromthe
rod asshownin the figure.At the other endofthe string massM = 5 kgis attached,
lying overa smooth fixed inclined plane ofinclinationangle37°. The ring isheld in
levelwith thepulleyand released. Determine the velocityofring (inm/s) when the
string makes an angle (  37°) withthe horizontal. [sin37°=0.6]