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F II T J E E
PART TEST TEST-I -I (18 Nov Novem embe berr 2012) 2012)
Paper per I Code Time ime Allo Allotte tted: d:
1
11302A
I
Maxi axim mum Marks arks:: 210 210
3 Ho Hour urs s
Please read the instructions speci pecifi fica call lly y for for this this purpo rpose. se. You are not allo llowed to lea leave
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are
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INSTRUCTIONS Check heck all the shee sheets ts of this this questi estion on paper. per. Plea lease ensu ensure re the the sam same SET is mark marke ed on heade ader of all the the she sheets ets insi insid de as ind indica icated ted on the the top top left left corn corner er of this this pag page. In case case SET mark marke ed is not not the the same on all pages, imm immediate iately ly info inforrm the the Inv Invigil igila ator tor and CHAN CH ANGE GE the Ques Questio tion n pape paperr for a corre correct ct one. one. Cautio aution: n: Quest uestio ion n Paper aper CO COD DE as giv given en abov above e MUST be corr correc ectly tly marke arked d in the the answ answer er OMR she sheet befo efore atte attem mptin ting the the pape aper. Wron rong CODE or no CODE will ill give give wrong rong results.
A. Gener eneral al Inst Instru ruct ctio ions ns 1.
Attem Attempt pt ALL ALL the questio questions. ns. Answe Answers rs have have to be marke marked d on the OMR OMR sheets. sheets.
2. This This questio question n pap paper er conta contains ins Three Three Parts. Parts. 3. Part-I Part-I is Physics Physics,, Part-II Part-II is Chem Chemistry istry and Part.1II Part.1II is Mathe Mathema matics. tics. 4. Each Each part part is furthe furtherr divided divided into two two section sections: s: Sectio Section-A n-A
&
Section-C
5. Rough Rough space spaces s are provid provided ed for rough work work inside inside the the questio question n pap paper. er. No a addi ddition tional al sheets sheets will be , provided for rough work. . ~ 6. Blank Blank Papers, Papers, clip boards boards,, log table tables, s, slide slide rule, rule, calcula calculator, tor, cellular cellular phone phones, s, pager pagers s and electro electronic nic device devices, s, in any form, form, are not allowed. allowed.
B. Filling Filling of OMR OMR Sheet Sheet 1. Ensur Ensure e matchi matching ng of OMR OMR sheet sheet with the Questi Question on paper paper before before you start start markin marking g your your answe answers rs on OMR sheet. sheet. 2. On the the OMR OMR shee sheet, t, dark darken en the the appr approp opria riate te bubb bubble le with black black pen pen for for each each chara characte cterr of your your Enrolmen Enrolmentt No. and and write your your Name, Test Test Cen Centre tre and other other details at the designated designated places. places. 3. OMR OMR sheet sheet contains alphabets, alphabets, numerals numerals & special special characters characters for marking marking answers. answers.
C. Markin arking g Sche Schem me For For All Thre Three e Parts Parts.. (i)
Secti Section on-A -A (01 to 10) contains 10 multiple choice questions questions which I:lav.e-onlyone I:lav.e-onlyone correct correct answer. answer. Each Each questio question n carries carries +3 marks marks for correc correctt answe answerr and - 1mark mark for wrong wrong answer. Section-A (11 to 15) contain contains s 5 multiple multiple choice choice question questions s which which have have more more than than one one correc correctt answe answer. r. Each Each question question carrie carries s +4 marks marks for correct correct answer. answer. There There is no negative negative markin marking. g.
(ii)
Secti Section on-C -C (01 to 05) conta contains ins 5 Nume Numerica ricall based based questio questions ns with answe answers rs as numeric numerical al value value and each each question carries +4 marks marks for correct answer. answer. There is no negative marking. marking.
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Useful Data
PHYSICS Acceleration due to gravity
g
=
2
10 m/s
34
h = 6.6 x10-
Planck constant
J-s
Charge of electron me =9.1
Mass of electron
x 10-31kg
Permittivity of free space 3
Density of water
Pwater = 10 kg/m
3
Atmospheric pressure R = 8.314 J K-1 mor l
Gas constant
CHEMISTRY Gas Constant
R
Avogadro's Number Na Planck's constant h 1 Faraday 1 calorie 1 amu 1 eV
= = = = = = = = = =
8.314 J K,-l mor 1 0.0821 Lit atm K-1 mor 1 1.987", 2 Cal K-1 mol-1 6.023 x 1023 6.625 x 10-34 J.s 6.625 x 10-27 erg.s 96500 coulomb 4.2 joule 1.66 x 10-27 kg 1.6 x 10-19 J
Atomic No:
H=1, He = 2, Li=3, Be=4, B=5, C=6, N=7, 0=8, N=9, Na=11, Mg=12, 8i=14, AI=13, P=15, 8=16, G1=17, Ar=18, K =19, Ca=20, Cr=24, Mn=25, Fe=26, Co=27, Ni=28, Cu = 29, Zn=30, As=33, Br=35, Ag=47, 8n=50, 1=53, Xe=54, Ba=56, Pb=82, U=92. Atomic masses- H=1 He=4 U=7 Be=9 B=11 C=12 N=14 0=16 - F:!::19,Na=23, Mg=24, A I = 27, 8i=28, P=31',8=32', CI=35.5, K=39, Ca=40, Cr=52, Mn=55, Fe=56, Co=59, Ni=58.7, Cu=63.5, Zn=65.4, As=75, Br=80, Ag=108, 8n=118.7, 1=127,Xe=131, Ba=137, Pb=207, U=238.
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PART -I
SECTION -A Straight Objective Type This section contains 10 multiple choice questions numbered 1 to 10. Each question has 4 choices (A), (B), (C) and (0), out of which ONLY ONE is correct. 1.
A toy car is moving on a closed track whose curved portions are semicircles of radius 1m. The adjacent graph describes the variation of speed of the car with distance moved by it (starting from point P). The time t required for the car to complete one lap is equal to 6k second. Find k. (take nln2 "'"2)
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(0) 16
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2.
Y A particle Pisto be projected from a fixed point A on the ground with a fixed speed u. Another particle Q is also to be projected from B :::; a point B which is directly above the point A. The trajectory of the particle Q touches all possible trajectories (for different angle of projection) of the particle P in the vertical x-y plane. The equation of trajectory of the particle Q is, (Take the point A as origin, horizontal axis x-axis and vertical axis y-axis. Consider the figure.) u: P
x
A
Rough work
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A small coin is placed on a stationary horizontal disc at a distance r from its centre. The disc starts rotating about a fixed vertical axis through its centre with a constant angular acceleration u. Determine the number of revolutions N, accomplished by the disc before the coin starts slipping on the disc. The coefficient of static friction between the coin and the disc is Ils.
{ ( ~ g ) ' + a ,r
{(";g)' ( 8)
(A)
5.
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(C)
4.
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A wedge of mass M resting oil a horizontal frictionless surface is acted upon by a force F in the horizontal direction as shown in figure. The net horizontal force acting on the shaded portion of the wedge is (8) F/3 (A) F (0) zero (C) F/6 A person rolls a small ball with speed u along the floor from point A. If x = 3R, determine the required speed u so that the ball returns to A after rolling on the circular surface in the vertical plane from 8 to C and becoming a projectile at C. (Neglect friction and radius of ball)
(A)
~J9R
A
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F
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2
Rough work
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In the figure shown when the massless spring isin relaxed state its free end is at point B. A very small block 'is pressed against the spring by a distanceS and then released from rest. Except the portion Be where coefficient of kinetic friction is J.1K, track is smooth everywhere. Determine the spring compression S so that the block 'enters a small hole at :E. Consieer aU vall:les shown in the figure.
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7.
The wheel of radius R rolls without slipping on horizontal rough surface, and its centre 0 has an horizontal 3cceleration aDin forward direction. A point P on the wheel is a d istance r f rom 0 and angular position 8 from horizontal. For a given values of aD,Rand r, determine the angle 8 for which point P has no acceleration in this position. (A) cos
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~
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-1
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Rough work
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The two identical rectangular steel frames with the dimensions shown are fabricated from a bar of the same material and are hinged. Rectangular at the midpoints A and 8 of their sides(3m x 1m). If the frame is resting in the position shown on a horizontal surface with negligible friction, determine the velocity v with which each of the upper ends of the frame hits the horizontal surface if the cord 0 is cut. (Take the value of dimensions shown in figure c = 1 m, b = 3/2 m and e = 74° . e e 3 d 4 I.e., 510"2=5 an cos"2=5&g= .
10
1 2)
ms
c
(8) 8 m /s (D) 4 m /s
(A) 5 m /s (C) 3 m /s 9.
A car C of mass m is initially at rest on the boat A of mass M tied to the identical boat 8 of same, mass M through a massless inextensible string as shown in the figure. The car accelerates from rest to velocity Vowith respect to boat A in time to sec. At time t = tothe car applies brake and comes to rest relative to boat in negligible time. Neglect friction between boat and water find the velocity of boat A just after applying brake. (A)
Mmvo (2M + m)(M + m)
(8)
Mmvo (M + 2m)(M + m)
(C)
2Mmvo (M+2m)(M+m)
(D) zero
Rough work
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In the figure shown a river of width 4 km is flowing with the speed of 5 km/h. A swimmer whose swimming speed relative to the water is 4 km/h, starts swimming from a point A on a bank. On the other bank B is a point which is directly opposite to A. What minimum distance (in km) the swimmer will have to walk on the other bank to reach the point B.
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Multiple Correct Choice Type This section contains 5 multiple choice questions. Each question has 4 choices (A), (8), (C) and (0) for its answer, out which ONE OR MORE is/are correct. 11.
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Under the action of force P, the constant acceleration of block 8 is 6 m/sec2 up the incline. For the instant when the velocity of 8 is 3 m/sec up the incline. Choose the correct option(s) (A) Velocity of 8 relative to A is 1m/s (B) Acceleration of 8 relative to A is 2 m/s2 (C) The velocity of point C of thecable(in
ground frame) is 4 m/s
(0) Velocity of 8 relative to A is 2m/s
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Two identical particles A and B of mass m each are connected inextensible string of length separation Va
e . Both
e . The
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together by a light and
particle are held at rest in air in same horizontal level at a
particles are released simultaneously and one of them (say A) is given speed
vertically upward. Choose the correct options(s). Ignore air resistance. 2
(A) The maximum height attained by the centre of mass of the system of A and B is
V
o
8g
(B) The kinetic energy of the system of A and B when the centre of mass is at its highest point, is
mv02
__
2 2
(C) The maximum height attained by the centre of mass of the system of A and B is
o
V
4g
(D) The kinetic energy of the system of A and B when the centre of mass is at its highest point, is
mv20
__
4 In the adjacent figure a uniform rod of length
14.
e and
mass m is kept
l '(
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at rest in horizontal position on an elevated edge. The value of x (consider the figure) is such that the rod will have maximum angular acceleration e x . , as soon as it is set free.
(A) x is equal to (C)
e x . is
er;;
(B)
e x . is
equal to g13 2e
2,,3
g,13
equal to --
(D) x is equal to ~
e
Rough work
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A Block 'A' is placed on a smooth horizontal surface and a particle C is suspended with the help of light fad ffOm point B of the block as shown. Now both the -block A and the partiole C are given velocity Votowards left. The block A strikes a fixed wall and suddenly stops. Then, (The rod BCis free to rotate about 8)
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(A) the smallest velocity Vofor which the particle C will swing in a full circle about the point 8 is
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(C) velocity of point C at the highest .point of the circle {for the smallest value of vo)is zero. (0) velocity of point C at the hi@hestpoint of the circle (for the smallest value of vo) is
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SECTION-C
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I Integer Answer Type x
This section contains 5 questions. The answer to each of the questions is a single-digit integer, ranging from 0 to 9. The appropriate bubbles below the respective question numbers in the ORShave to be-darkened. For example, if the correct answers to question numbers X, Y, Z and W (say) are 6, 0, 9 and 2, respectively, then the correct darkening of bubbles will look like the as shown;
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A disc 'A' of mass M is placed at'rest on the smooth incline surface of inclination e . A batl B of mass m is suspended vertically from the centre of the disc A by a light inextensible string of length figure.
£
M
as shown in the
If the acceleration of the 'disc B immediately after the system is
released from rest
. (M+km)gsin2e
IS '
2'
M+msin
.
Fmdk.
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A uniform rod AB of mass M and length "1/2R is moving in a vertical plane inside a hollow sphere of radius R. The sphere is rolling on a fixed horizontal surface without slipping with velocity of its centre of mass 2v. When the end B is at the lowest position, its speed is found to be v as shown in the figure. If the kinetic energy of the rod at this instant is
Mv i
2
.
Hollow sphere
Find K.
K
3.
4.
A small particle is given an initial velocity va = 1a m/s along the tangent to the brim of a fixed smooth hemisphere bowl of radius ra = 15"1/2m as shown in the figure. The particle slides on the inner surface and reaches point B, a vertical distance h =15 m below A and a distance r from the vertical centerline, where its velocity v makes an angle e with the horizontal tangent to the bowl through B. If e = 15 K O . Find the value of K . (take g = 1a m/s2)
A smooth disc of mass M and radius
; vertical centre line
1
is placed at rest horizontally
on a smooth horizontal surface. A massless pin is fixed at point P at a distance U2 from centre 0 of the disc as shown in the figure. Now a thin uniform rod of mass M and length L is placed horizontally on the surface of the disc parallel to the line OP such that its mid point and centre 0 of the disc just coincide as shown in figure. Now rod has given angular velocity (u o = 24 rad/sec in counter clockwise direction as shown. As a result, the end of the rod strikes the pin P and sticks to it rigidly. Calculate the angular velocity of disc just after collision. 5.
One end of the pile of chain falls vertically through a hole in its support and pull the remaining links steadily. The links which are at rest acquire the velocity of the hanging position suddenly and without having interaction with the remaining stationary links and with the support. If the acceleration a of the falling chain is g/k. Find k. Ignore any friction.
x
Rough work
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PART -
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II
SECTION-A Straight Objective
Type
This section "Contains 10 mulliplechoice questions numbered 1 to (B), (C) and (0), out 'of which ONLY ONE is correct.
lO. Each
question .has 4 choices (A),
1.
In a small sample of H atoms 'inexcited state n 5, transition to ground state releases aU possible lines except the ones in Paschen series. How many spectral .Iines are released in the emission spectra: (A) 6 (B) 7 (C) 8 (0) 9
2.
The following equilibria is maintained in a closed vessel:
=
N (g ) + 3H (g)~2NH3{g) 2
Moles@equilibrium
2
1
3
2
.Equilibrium is now disturbed by removing x moles of H2 and simultaneously doubling the volume Ofvessel. At new equilibrium, 17 gms of NH3 is obtained. Find x. (A) 1 (B) 1.3 (C) 1.9 (0) 2.5 3.
Asolid particle having spherical shape is assumed to react only on its surface. However the amount of reactant contained in it is detennined 'by its volume. Consider the following rate ~aw for a solid particle shrinking due to reaction: --
dV dt
= k S(S = surface
area)
The order of the above reaction will be: (A) 0 (C) 2/3
(B) 1 (0) 3/2.
:",
j
4.
Pure S03(g) is heated in a solid vessel to create the following equilibrium: ~
2S03 (g)~2S02
(g)+02(g)
The vapour density of the equilibrium mixture is: (A) 16 (B) 26 .•.•.•...•.......•....
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6
1.0- at room temperature. The .density of fonnic acid is 1.15 g/cm3. What percentage of fonnic acid molecules convert to formate anion: (A) .0..0.01% (C).o ..o.o3%
(S) .0..0.02%
(0) .0.'.0.04%
6.
Reactions at the very first instant of their life, Le. shortly after start, follow: (A) Pseudo zero order kinetics (S) Pseudo first order kinetics (C) Pseudo second order kinetics (0) Pseudo third order kinetics
7.
If Aufbau rule is not obeyed and instead electronic filling occurs orbit by orbit till saturation is reached, calculate the percentage change in total of (n + £ ) values for unpaired electrons in an atom of manganese. (A) 2.0
(S) 4.0
(C) 6.0
(0) 8.0 3
8.
The pH elt which a .0..01 M AI+ solution is 99.99% precipitated is : (Ksp AI(OHh (A) 6.67 (S) 7.67 (C) 8.67 (0) 1. 0
9.
The styx number for S2H6 is: (A) 2.012 (C) 2.0.02
10.
1 x 10-18 at 25°C)
(S) 2222 (0) 21.02
.H
F
8]~'c=o
82~C=O .
CI
83 ~C=O
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=
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=
83 .. . • . • . • . • . • . . . . . .
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Multiple Correct Choice Type This section contains 5 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for its answer. out which ONE OR MORE is/are correct. . ; ,
11.
Identify the correct statements w.r.t. the titration curves shown below:
14
:
Strong Base
pH
Weak Base
7
'." ;
o (A)
Volume of strong acid added ~ equivalence point with strong base is at pH = 7
(B) equivalence point with weak base is at pH 7 (C) phenolphthalein (8 - 9.8) can be used as indicator in both titrations =
(D) chlorophenol red (4.8 - 6.4) can be used as indicator in both titrations. 12.
For solution of alkali metal (M) in liquid NH3• identify which of the following equilibria would simultaneously exist: (A) M+(x+y)NH3~M(NH3): - ~ (C) 2eam ~e2(am)-2
+e-(NH3)y
(B) 2M(am)+2e-~M2(am) (D) M(+am) +e-22~M(-am) ,
Rough Work
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Which of the following would be observed in the Lewis dot structure of N40:
14.
(A) positive charge on N
(8) negative charge on N
(C) oxygen atom at1he tenninus
(0) electronic delocalization
Which of these statements correctly compare between SF4 and SF6: (A) both molecules have same hybridization for Satom (8) both molecules have at (east one linear F - S - Flink (C) SF6 has higher boiling point lhan SF4 (0) SF4 reacts vigorously with water whereas SF6 is inert towards water
15.
Inorganic benzene surpasses organic benzene in which property: (A) melting point
n»x»> ••.m
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,(C) molar mass ....,
(8) edge length of its hexagon »»»
-(0) total number of electrons in the molecule >:')"H »»;»_ » Y '
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\'
Z
\V
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1.
Ammonium carbamate is heated at 227°C in a closed vessel of volume 8210 ml containing 0.2 mole of Argon gas. The manometer attached to the vessel shows a pressure of 1 atm. Find K p for the decomposition of ammonium carbamate. NH2COONH4 (s)~2NH3
2.
(g)+C02
(g)
Silver (I) ferrocyanide and Bismuth(III) sulphide are sparingly soluble salts with identical water
( ~ J.
solubility. The ratio of their Ksp is
Find (a + b).
3.
On the Moh's hardness scale, what value is assigned to Gypsum mineral (CaS 04.2H2 0)
4.
How many gases/va pours are involved either as reactants or products in Serpeck's process used for concentration of bauxite.
5.
The magnitude of potential energy of electron in nth excited of He + ion is ~ times the kinetic 81
2
energy of electron in the first excited state of U+ ion. Find 'n'. .
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SECTION -A Straight Objective Type This section contains 10 multiple choice questions numbered 1 to 10. Each question has 4 choices (A), (8), (C) and (D), out of which ONLY ONE is correct. 1.
Let f(x) = {(0.1 )3 !X 1 }. (where 1 .] denotes greatest integer function and {.} denotes fractional part) If f(x + T) f(x) V x ~ 0, where T is a fixed positive number then the least value of T, is =
W2
~4
(C) 6(D) 2.
none of these
The minimum value of the function f(x) = _1_ - {x} occurs at x equals to . 2{-x} (where {.} represents fractional part function) 1 (A) n + J 2' n EI (C) n+
3.
1
1 (8) n - J2 ' n E I
1 (D) n + -, n E I
~' n EI
2",2
2
Consider the function f defined by
f(x)
o
,
{ -1
,
when x ='0 or x is irrational
. m m . . non-zero rational number -, n > 0 and - IS In lowest term n n n which of the following statement(s) is(are) true? (A) x 0 is a point of discontinuity of f (8) any non-zero rational number is a point of continuity of f (C) any irrational number is a point of continuity of f . (D) any irrational number is a point of discontinuity of f =
when x
.
IS
=
4.
If co-domain is R, then which of the following functions is not a surjective (onto) function? (A) f(x) = Inlln(x-[x))1. (where [.] denotes the G.I.F) (8) f(x) x + cos (n[x)), (where [.] denotes the G.I.F) =
(C) f(x)
= tan-1 x - ~
(D) f(x) =
,, 1 + x 2
x
2 x
-1 ......................
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(B) cos e - sin 1 (D) cos e + sin 1
(A) sin e - cos 1 (C) sin e + cos 1 6.
The differential equation of a family of cUlves whose angle of intersection with the family of parabolas
l= kx, (k = parameter), is ~, 4
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=
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(B)dy= 2y-x dx 2y + x
(C) dy dx
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=
7.
The value of x for which the function f(x) sin-1 sin Ixl is increasing can be given by (A) x sin x < 0 (B) x sin x > 0 (C) x cos x < 0 (D) x cos x > 0
8.
If Ibl > la +cl then atleast one root of the equation ax + bx + (A)(-2,0) (B)(-1, 1) (C) (0, 2). (D) (1, 3)
4
J
3
C =
0 lies in the interval
x
9.
Let f(x)
:=
IOQ1I2(1-
T')dt
then the value of f(2) + f(2 -log23), is
1
(B) 1 (D) 3 - 210g23
(A) 0 (C) 2
10.
1 (1
5
x ) +3 (B) -In -+c 5 1+x
5
1 (1+ (D) -In -- X ) +c 5 1+x ......................
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Let f : R -7 R,f{x) = x + In(1 + x2)then (A) lis injective (8) limf(x) = too X---..-co
(C) there is a point on the graph of y (D) f is bijective '
=
f(x) where tangent is not parallel to any of the chords
If .Iim (log3 (ax2 + 3x +1)Y09(X-')3 = e , where e is a finite real number then
12.
X- 42
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13.
(8) 'a' can have more than one values (D) e = e-1I3
Let a function f(x), x ~ 0 be such thatf(x) + f(!
.
(A) 1-
(C)
14.
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1 = f(x).
x)
(8)
, n 1 2tan- !xl
(D)
f(!)',
x
then f(x) can be
M + 1 2 1+klnlxl
Let 9 be the inverse of the continuous function f. Let there be a point (a, /3 ), where a ~ /3 , is such that it satisfies each of y f(x) and y g(x) then (A) the equation f(x) g{x) has infinitely many solutions (B) the equation f(x) g{x) has atleast 3 solutions (C) f must be a decreasing Junction of x (D) 9 can be an increasing function of x =
=
= =
15.
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Let f(x)
ax: + bx +c . If f(x) is not a constant function and both minimum and maximum values dx + ex +f of f(x) exist then (A) f(x) must be a continuous function (8) 4ac must be more then b 2 2 (0) ae must not be equal to bd (C) 4fd must be more then e » y.»» ••.•.•...•••..
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SECTION-C
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1.
The number of integers belonging to the interval [-3, 30] but not belonging to the range of the function f(x) x{x} - x [-x], X E R, is (where [.] and {.} denote the greatest integer function and fractional part respectively) =
,where 0 < a < ~ < 1~ - a 1 tan- ~ - tan- a
2.
Find the maximum possible integral value of
3.
Let I(e) = cos' x cos~c x sin (e') dx. If the value 01 2~
f
f -(
13 , is
~l-r ( ~l
is 'k' then the value of
64 k2, is 4.
Consider a rectangle with vertices A '" (0, 0), B", (4, 0), C '" (4, 6), D", (0, 6). Let S be the region consisting of all points Pinside the rectangle such that d(P, DC) < d(P, AB) < max.{d(P, BC); d(P, AD)}, where d(P, MN) denotes distance of the point P from the line joining points M and N. The area of the region S in square units, is
5.
If Rolle's theorem is applicable to the function, f(x)
=
Inx over the interval [a, b], where a, b X
then the value of a + b, is ...•.•....... .,
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Rough Work
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