p code (1001cja102118038) english classroom …

READ THE INSTRUCTIONS CAREFULLY

GENERAL :

1. This sealed booklet is your Question Paper. Do not break the seal till you are toldto do so.

2. Use the Optical Response sheet (ORS) provided separately for answering the questions.

3. Blank spaces are provided within this booklet for rough work.

4. Write your name, form number and sign in the space provided on the back cover of thisbooklet.

5. After breaking the seal of the booklet, verify that the booklet contains 32 pages andthat all the 19 questions in each subject and along with the options are legible. If not,contact the invigilator for replacement of the booklet.

6. You are allowed to take away the Question Paper at the end of the examination.

OPTICAL RESPONSE SHEET :

7. The ORS will be collected by the invigilator at the end of the examination.

8. Do not tamper with or mutilate the ORS. Do not use the ORS for rough work.

9. Write your name, form number and sign with pen in the space provided for this purposeon the ORS. Do not write any of these details anywhere else on the ORS. Darkenthe appropriate bubble under each digit of your form number.

DARKENING THE BUBBLES ON THE ORS :

10. Use a BLACK BALL POINT PEN to darken the bubbles on the ORS.

11. Darken the bubble COMPLETELY.

12. The correct way of darkening a bubble is as :

13. The ORS is machine-gradable. Ensure that the bubbles are darkened in the correctway.

14. Darken the bubbles ONLY IF you are sure of the answer. There is NO WAY to eraseor "un-darken" a darkened bubble.

15. Take g = 10 m/s2 unless otherwise stated.

PAPER – 1

Please see the last page of this booklet for rest of the instructions

Time : 3 Hours Maximum Marks : 201

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)1001CJA102118038)Paper Code

(1001CJA102118038)E

NG

LIS

H

CLASSROOM CONTACT PROGRAMME(Academic Session : 2018 - 2019)

PHASE : TOAS & TNAS

JEE (Main + Advanced) : ENTHUSIAST COURSE

Test Type : PRE-SCORE Test Pattern : JEE-AdvancedTEST DATE : 15 - 10 - 2018

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Target : JEE (Main + Advanced) 2019/15-10-2018/Paper-1

1001CJA102118038

Space for Rough Work

SOME USEFUL CONSTANTSAtomic No. : H = 1, B = 5, C = 6, N = 7, O = 8, F = 9, Al = 13, P = 15, S = 16,

Cl = 17, Br = 35, Xe = 54, Ce = 58,Atomic masses : H = 1, Li = 7, B = 11, C = 12, N = 14, O = 16, F = 19, Na = 23, Mg = 24,

Al = 27, P = 31, S = 32, Cl = 35.5, Ca=40, Fe = 56, Br = 80, I = 127,Xe = 131, Ba=137, Ce = 140,

· Boltzmann constant k = 1.38 × 10–23 JK–1

· Coulomb's law constant pe9

0

1 = 9×104

· Universal gravitational constant G = 6.67259 × 10–11 N–m2 kg–2

· Speed of light in vacuum c = 3 × 108 ms–1

· Stefan–Boltzmann constant s = 5.67 × 10–8 Wm–2–K–4

· Wien's displacement law constant b = 2.89 × 10–3 m–K· Permeability of vacuum µ0 = 4p × 10–7 NA–2

· Permittivity of vacuum Î0 = 20

1cm

· Planck constant h = 6.63 × 10–34 J–s

Enthusiast Course(TOAS & TNAS)/Pre-Score/15-10-2018/Paper-1

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BEWARE OF NEGATIVE MARKINGHAVE CONTROL ¾® HAVE PATIENCE ¾® HAVE CONFIDENCE Þ 100% SUCCESS

PART-1 : PHYSICSSECTION–I(i) : (Maximum Marks : 15)

� This section contains FIVE questions.� Each question has FOUR options (A), (B), (C) and (D). ONLY ONE of these four options

is correct.� For each question, darken the bubble corresponding to the correct option in the ORS.� For each question, marks will be awarded in one of the following categories :

Full Marks : +3 If only the bubble corresponding to the correct option is darkened.Zero Marks : 0 If none of the bubbles is darkened.Negative Marks : –1 In all other cases

1. In a continuous printing process, paper is drawn into the press at a constant speed v. Denotingby 'r' the radius of the paper roll at any given time and by 'b' the thickness of the paper, whatis the angular acceleration of the paper roll.

vb

w

a

(A) 2

3bv2 rp (B)

2

32bv

rp (C) 2

3bv4 rp (D)

2

34bv

rp


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2. In the diagram shown below, the rod is uniform having mass M and length L. When it ismaking an angle q = 60°, the rod is released from the state of rest (and spring in its naturallength). The rod comes to state of rest when the angle q reduces to 30°. What should be theinitial compression in the spring (when q = 60°) so that the whole system can remain in thestate of rest? (there is no friction between any surfaces)

\\\ \\\\ \\\\\ \\\\\ \\\\ \\\\\ \\\\\ \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\ q

No FrictionAssume the initial deformation to be zero

(A) ( )3 1

2 3

-l (B) ( )3 3 1

2-

l (C) ( )3 1

4 3

-l (D)

( )2 3 1

3

-l

3. A uniform thin rod AB of mass M and length l attached to a string OA of length 2l

is placed

on a smooth horizontal plane and rotates with angular velocity w around a vertical axis throughO. A peg P is inserted in the plane in order that on striking it the bar will come exactly to rest

lA B

rPeg P

w

O l/2

(A) Location of peg for rod coming to rest is r = 56l

(B) Location of peg for rod coming to rest is r = 34l

(C) Location of peg for rod coming to rest is r = 1312l

(D) Location of peg for rod coming to rest is r = 23l


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4. An almost inertia-less rod of length l = 3.5 m can rotate freely around a horizontal axis passingthrough its top end. At the bottom end of the rod a small ball of mass m and at the mid-pointanother small ball of mass 3m is attached. Find the angular frequency (in SI units) of smalloscillations of the system about the equilibrium position. Gravitational acceleration isg = 9.8 m/s2.

3m

m (A) 2.0 rad/s (B) 2.5 rad/s (C) 3.0 rad/s (D) 3.5 rad/s

5. Particle A and B are moving with constant velocities along positive x and positive y-axisrespectively as shown in figure. The graph of separation between them with time isrepresented by (assume that they will not collide)

A

B

y

x

(A)

s

t

(B)

s

t

(C)

s

t

(D)

s

t


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SECTION-I(ii) : (Maximum Marks: 24)� This section contains SIX questions.� Each question has FOUR options for correct answer(s). ONE OR MORE THAN ONE of

these four option(s) is (are) correct option(s).� For each question, choose the correct option(s) to answer the question.� Answer to each question will be evaluated according to the following marking scheme:

Full Marks : +4 If only (all) the correct option(s) is (are) chosen.Partial Marks : +3 If all the four options are correct but ONLY three options are chosen.Partial Marks : +2 If three or more options are correct but ONLY two options are chosen,

both of which are correct options.Partial Marks : +1 If two or more options are correct but ONLY one option is chosen

and it is a correct option.Zero Marks : 0 If none of the options is chosen (i.e. the question is unanswered).Negative Marks : –2 In all other cases.

� For Example : If first, third and fourth are the ONLY three correct options for a question withsecond option being an incorrect option; selecting only all the three correct options will resultin +4 marks. Selecting only two of the three correct options (e.g. the first and fourth options),without selecting any incorrect option (second option in this case), will result in +2 marks.Selecting only one of the three correct options (either first or third or fourth option), withoutselecting any incorrect option (second option in this case), will result in +1 marks. Selectingany incorrect option(s) (second option in this case), with or without selection of any correctoption(s) will result in –2 marks.

6. A bead is connected with a fixed disc of radius R by an inextensible massless string in asmooth horizontal plane. If the bead is pushed with a velocity v0 perpendicular to the string,the bead moves in a curve and consequently collapses on the disc. Then :

V0

l

(A)Initial angular acceleration of the particle is l

202

v.

(B)Initial angular acceleration of the particle is l

203

v R

(C)Distance travelled by the particle till it collides with the disc is l2

2R

(D)Distance travelled by the particle till it collides with the disc is l2

RSpace for Rough Work


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7. A dumbbell constructed by affixing small identical balls each of mass m at the ends of a lightrod of length l stands vertically on a frictionless floor touching a frictionless wall as shown inthe figure. If the lower ball is gently pushed away from the wall, the dumbbell begins to slide.Denoting acceleration due to gravity by g. Mark the CORRECT statements

g

(A) The maximum speed of the lower ball is attained when upper ball looses contact.(B) The maximum speed of the lower ball is attained when tension in the light rod is zero.

(C) The maximum speed of the lower ball is 8g27l

.

(D) The speed of the upper ball when lower ball acquires maximum speed is 10g27l

.


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8. A small bob can slide downwards from point A to B along either of the two different curvedsurfaces shown in cross-section in the diagram. These possible trajectories are circular arcsin vertical plane, and they lie symmetrically about straight line AB. During the motion, bobdoes not leave contact with surface.

A

B

I

II g

(A) If friction is neglected every where bob will take a smaller time through path I as comparedto time through path II.

(B) If friction is neglected every where bob will take a smaller time through path II as comparedto time through path I.

(C) If friction is neglected every where bob will reach point B with same speed through boththe paths.

(D) If friction is significant along both paths then bob will reach B with a smaller speed, if itfollows path II, as compared to if it follows path I.

9. A man can swim with a velocity v relative to water. He has to cross a river of width d flowingwith a velocity u (u > v). The distance through which he is carried down the stream by theriver is x. Which of the following statements are correct ?

(A) If he crosses the river in minimum time, duxv

=

(B) x can not be less then duv

(C) For x to be minimum, he has to swim in a direction making an angle of 1 vsin2 u

-p æ ö+ ç ÷è ø

with

the direction of flow of river.(D) x can not be equal to zero.



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10. A cart moving with horizontal velocity 1vr ejects a ball with a velocity 2vr in the verticaldirection relative to the moving cart. The ball must pass horizontally through a smallstationary hoop appropriately oriented and located at a height ‘h’ above the launch point.Later the ball passes through a second hoop that is fixed horizontally on the cart and centeredat the launch point. You may ignore air resistance.

v2

v1 v1

h

dWhich of the following statement(s) is/are CORRECT ?

(A) The height h is 22v

2gæ öç ÷è ø

(B) The cart has traveled a distance 2v1v2/g

(C) The cart has travelled a distance v1v2/g (D) The height h is 2v22/g

11. The point particle of mass m interacts with the stationary Center. The potential energy isaU brr

= + . At the initial moment the point was at a distance 0ar 2b

= , from the center and

Had zero speed.

(A) The minimum distance rmin that the mass can approach the center is a

4b .

(B) A stable equilibrium position of the material point is arb

= .

(C) The magnitude of the force acting on the material point at the point r0 is 3 b4

(D) The particle executes SHM about the stable equilibrium position.Space for Rough Work

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SECTION–I(iii) : (Maximum Marks : 12)� This section contains TWO paragraphs.� Based on each paragraph, there are TWO questions.� Each question has FOUR options (A), (B), (C) and (D) ONLY ONE of these four options


Full Marks : +3 If only the bubble corresponding to the correct answer is darkened.Zero Marks : 0 If none of the bubbles is darkened.Negative Marks : –1 In all other cases

Paragraph for Questions 12 and 13A small particle of mass m is fixed to the perimeter of a ring of same mass and radius r. Thesystem comprising of particle and ring is placed on a horizontal plane. Friction is negligibleon horizontal plane. Initially particle is at top most point, then the system is released fromrest. Answer next two questions when the particle is at the same height as the centre of ringafter being released from topmost point. Assume that the ring stays in vertical plane duringits motion under consideration.

12. Mark the INCORRECT option :

(A) Speed of centre of mass of system is gr4

(B) Angular velocity of system is w = gr

(C) Contact point of ring with ground is instantaneously at rest.(D) Centre of ring is instantaneously at rest.

13. Mark the CORRECT option :-

(A) Instantaneous acceleration of the centre of ring is g2

(B) Acceleration of centre of ring initially points towards left and then towards right.(C) The force exerted by the ring on the ground at the instant given is 3mg(D) The force exerted by the ring on the ground at the instant given is 2mg



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Paragraph for Questions 14 and 15When an object is seen from rotating frame of referance, coriollis force acts on the objectwhich is equal to 2m(v )´w

rr where vr is velocity of object with respect to rotating frame and wis angular velocity of rotating frame.

14. A stone is dropped from ‘h’ height at a place at 60° Latitude on northern hemisphere. Wherewill it land on ground (Ignore centrifugal force and consider height ‘h’ to be small in comparisonto radius of earth = R)(A) To north of place (B) to south of place(C) To east of place (D) to west of place

15. By what displacement stone is pushed due to coriolis force when it hits ground in previousproblem.

(A) 3 /2g 2h

12 gw æ ö

ç ÷è ø

(B) 3/2g 2h

6 gw æ ö

ç ÷è ø

(C) 3 /23 g 2h

4 gw æ ö

ç ÷è ø

(D) 3 /2g 2h

g2 3w æ ö

ç ÷è ø

SECTION –II : Matrix-Match TypeNo question will be asked in section II


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SECTION–III : (Maximum Marks : 16)� This section contains FOUR questions.� The answer to each question is a THREE DIGIT INTEGER ranging from 111 to 333, both

inclusive.� For each question, darken the bubble(s) corresponding to the correct integer in the ORS.� For each question, marks will be awarded in one of the following categories :

Full Marks : +4 If only the bubble(s) corresponding to the correct answer is darkened.Zero Marks : 0 In all other cases.

1. A particle is moving with displacement varying as x = (2t3–15t2+36t) where x is in meters andt is in seconds. Particle starts its motion at t = 0.

List–I List–II(P) Magnitude of displacement at time t = 2 sec (in m) (1) 36

(Q) Distance travelled in time t = 0 to t = 2 sec (in m) (2) 28

(R) Speed of the particle at t = 5 sec (in m/s) (3) 30



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2. Given structures are lying in vertical plane and are hinged at x. Every structure is made upof 2 identical rods with mass M & length L each. Initially all are at rest and released. Initially,in every case, one of the rods of the structure is vertical and the other horizontal.

List- I List- II

(P) Initial angular acceleration about x is 3g4L

æ öç ÷è ø

(1)

x

(Q) Maximum kinetic energy acquired by the (2)

xstructure is 3 102Mg L4

é ù+ê úê úë û

(R) Angle turned by the structure till it acquires (3)

xmaximum kinetic energy is 1 1tan2 3

-pæ ö+ç ÷è ø


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3. A block of mass m lies on wedge of mass m. The wedge in turn lies on smooth horizontalsurface. Friction is absent every where. The wedge block system is released from rest. Allsituation given in list-I are to be estimated in duration the block undergoes on verticaldisplacement ‘h’ starting from rest. Match the statement in list-I with the results in list-II.(g is acceleration due to gravity).

60°

mh

m

List–I List–II(P) Work done by normal reaction acting on the block is (1) Positive

(Q) Work done by normal reaction (exerted by block acting on wedge) is (2) Negative

(R) Net work done by gravity on the wedge (3) Zero

4. A block of mass m is attached to a fixed position 'O' on a smooth inclined wedge of mass M.The block oscillates along the incline with amplitude A and angular frequency w. The wedgeis located on a rough horizontal surface. The normal reaction by ground on the wedge is N. Ifthe wedge always remains at rest then match the List-I with List-II :-

60°

M

Smooth

m

O

Rough

List-I List-II

(P) Force of friction on the wedge (1)m

6 kp

(Q) Time taken by the block to move from mean position to A/2. (2)12 mw2 A sin(wt +f)

(R) Time taken by the block to move from A/2 to A. (3)m

3 kp



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PART-2 : CHEMISTRYSECTION–I(i) : (Maximum Marks : 15)




1. pH of a 0.1M solution HCl is changed by 0.3 unit due to dilution, calculate change in osmoticpressure if temperature of solution is 300K. (R = 1/12 litre atm/K/mole)(A) 2.5 atm (B) 5 atm (C) 7.5 atm (D) 1.25 atm

2. A white crystalline solid (A) on boiling with caustic soda solution gave a gas (B) which whenpassed through an alkaline solution of K2[HgI4] gave a brown precipitate. The substance(A) on heating gave a gas (X) which rekindled a glowing splinter but does not give brown

fumes with nitric oxide. The gas (X) is:(A) NH3 (B) O2 (C) O3 (D) N2O

3. A reagent is added to a solution of manganous salt in cold dil. HNO3. A purple

colour appeared due to the formation of permanganic acid. The reagent is :(A) NaBiO3 (B) (NH4)2 C2O4 (C) H2O2 (D) KNO3


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4. The final product / product mixture in the reaction sequence :

SO H3

1. Fused NaOH2. CH COCl3

3. AlCl /3

(A) Mixture of o-hydroxy acetophenone & p-hydroxy acetophenone

(B)

OHCO H2

+

OH

CO H2

(C)

OH

(D)

OHCHO

+

OH

CH=O

5. Which of the following statements is correct ?

(A) Lysine is example of basic & nonessential amino acid

(B) The IUPAC name of isoprene is 2-chloro-1,3-butadiene

(C) Lactose is example of disacchride which is formed by combination of C1 of b-D-galactose

& C4 of b-D-glucose followed by elimination of H2O

(D) Glucose gives +ve test with Tollen's ; Fehling ; schiff reagent & NaHSO3 solution


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6. Which statement(s) is/are correct -

(A) When FeCl3 is added to excess of hot water, a positively charged colloidal solution form.(B) Amount of electrolyte required to cause coagulation is higher for lyophobic than lyophillic

colloids

(C) High pressure is favaourable for physical as well as chemical adsorption(D) Physical and chemical adsorption both decreases entropy of universe.

7. Incorrect statement(s) is/are from the following -

(A) Adsorption is always exothermic in nature(B) CaCl2 cause more coagulation of gold sol than AlCl3

(C) Surface tension of associated colloids increase with increase in concentration

(D) With increase in concentration, molar conductance of strong electrolyte decreases rapidlythan associated colloids.

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8. Which of the following aqueous metal ions is/are correctly represented with proper

Observation on addition of NaOH?

(A) Cu2+ ® Blue precipitate is formed which is soluble in excess NaOH to gives dark blue

solution.

(B) Zn2+ ® At first white precipitate is formed which is dissolved in excess NaOH to give

colourless solution

(C) Cd2+ ® At first white precipitate is formed which is not dissolved in excess NaOH

(D) Ag+ ® At first brown precipitate is formed which is not dissolved in excess NaOH.9. Which of the following is/are giving precipitate with Na2S solution.

(A) Na2[Fe(CN)5NO] (B) Ni+2

(C) Co+2 (D) Ba+2

10. Which of the following statements are incorrect ?

(A) Benzyl amine and aniline can be distinguished using CHCl3 & alcoholic KOH

(B) 1-butyne & 2-butyne can be distinguished using Tollen's reagent

(C) Peptide linkage is non planer

(D) Almost all amino acids in protein are in L-configurationSpace for Rough Work


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11. MixedAcid P

(Monosubsitituedbenzene)

Na(Hg)+ conc. H SO2 4

Q NaNO2

+ HCl , 0º-5ºC R KCNCuCN S SnCl2

HCl T

Correct statement are :

(A) Q is NH2

(B) S is CN

(C) T is CH –NH2 2

(D) P is treated with Zn + NH4Cl , NHOH

is formed


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Paragraph for Questions 12 and 13

Two volatile liquids A and B are mixed in mole ratio 1 : 3, to form an ideal liquid solution.

Vapour pressure of pure A and B are 600 torr and 200 torr, respectively, at 300K. Volume of

container for vapour is 76 litre. (R = 1/12 litre atm/K/mole)

12. Calculate the mole of A in vapour phase at 300 K, assuming negligible amount of vapour is

present compared to liquid in container.

(A) 2 mole (B) 0.3 mole (C) 1.2 mole (D) 0.6 mole

13. The minimum number of distillation steps required, so that mole fraction of A become 0.9 in

distillate.

(A) 1 (B) 2 (C) 3 (D) 4Space for Rough Work


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Paragraph for Questions 14 and 15The most important copper oxide containing minerals are azurite {Cu3(OH)2(CO3)2}, malachite

{Cu2(OH)2(CO3)}, cuprite (Cu2O), tenorite (CuO). Extraction of copper from these low grade

ores involves leaching followed by reduction.

14. Some Cu is obtained just on leaching by dil.H2SO4 in :

(A) Malachite (B) Tenorite (C) Cuprite (D) Azurite

15. Malachite leached

with bacteria (solution)

Cu metal can be extracted from solution on treatment with :

(A) Ag (B) FeO (C) H2 (D) H2SO4



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1. Component A and B are mixed to form a solution. Match correct nature of solution withcomponents mixed -List-I (Components) List-II (Nature)(P) Ethanol + cyclohexane (1) Negative deviation

(Q) Water + HNO3 (2) Ideal solution

(R) Ethyl bromide + ethyl iodide (3) Positive deviation

2.

Zn , Mn+2 +2

Cd , Hg+2 +2

Zn , Cu+2 +2

(NH ) S4 2

(NH ) S4 2

(NH ) S4 2

Reagent...?

Reagent...?

Reagent...?

ppt of both ions

ppt of both ions

ppt of both ions

volume of ppt decrease



(P)

(Q)

(R)

(I) Reaction Sequence in which final product have ppt. of one metal ion

(II) Missing Reagent

(1) dil HCl

(2) CH COOH solution3

(3) Conc. HNO3

D



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3. List-I List-II

(P) Nylon-6 (1) Computer disc

(Q) Bakelite (2) Tyre cords , Ropes

(R) HDPE (3) Buckets , Dustbins & Bottles, Pipes

4. List-I List-II

(Lassign test / Element) (Reagent / Observartion)

(P) S & N both (1) FeCl3 , blood red colouration

(Q) S only (2) Sodium nitropruside / Purple colour

(R) Cl only (3) AgNO3 / White curdy precipitate


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PART-3 : MATHEMATICSSECTION–I(i) : (Maximum Marks : 15)




1. If ( ) ( ) ( ) dxxfxxFdxxf 23then, òò = is equal to

(A) ( ) ( )( )ò- 2222

21 dxxFxFx (B) ( ) ( )( )ò- dxxFxFx 222

21

(C) ( ) ( ) ÷øö

çèæ - ò dxxFxFx 22

21

21

(D) None of these

2. A number is chosen at random from the numbers 10 to 99. By seeing the number a man willlaugh if product of the digits is 12. If he choose three numbers with replacement then theprobability that he will laugh at least once is

(A) 1 – æ öç ÷è ø

335

(B) + - ´2 2

32(45 43 45 43)

45

(C) 98

125 (D) 1 – æ öç ÷è ø

34345

3. Number of complex numbers satisfying equation 3z z= & arg (z + 1) = 4p

simultaneously is-

(A) 1 (B) 2 (C) 3 (D) 44. Area bounded by 2 28z 8z 20zz 144- - + = is (where z is a complex number)-

(A) p (B) 6p (C) 12p (D) 4p5. Let A, B, C are 3 points on the complex plane represented by complex numbers a, b, c respectively

such that |a| = |b| = |c| = 1, a + b + c = 1 and abc = 1, then(A) area of triangle ABC is 2 (square unit).(B) triangle ABC is an equilateral triangle.(C) triangle ABC is right isosceles triangle(D) orthocentre of triangle ABC lies outside the triangle.



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6. Consider a cube of side length 9 units. Let (x, y, z) be coordinates of points on or inside thecube such that x, y, z Î I and 0 £ x, y, z £ 9. If total number of ways of selecting two distinctpoints among these such that their mid-point is also having integral coordinates is N, then(A) N is divisible by 30 (B) N is divisible by 31(C) N is divisible by 32 (D) Number of factors of N is 40

7. ‘n’ similar balls each of weight w, are weighted in pairs. The sum of the weight of all thepossible pairs is 120. When weighted in triplets the sum of the weights is 480. Then n divides:(A) 25 (B) 30 (C) 60 (D) 75

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8. Let z = a + ib (where a, b Î R and i 1= - such that |2z + 3i| = |z2|.Identify the correct statement(s) ?(A) |z|maximum is equal to 3.(B) |z|minimum is equal to 1.

(C) If |z|maximum when z = a + ib (a, b Î R and i 1= - ) then (a3 + b3) is equal to 27.

(D) If |z|minimum when z = x + iy (x, y Î R and i 1= - ) then (x2 + 2y2) is equal to 2.9. Consider two complex number z and w satisfying |z| = 1 and |w – 2| + |w – 4| = 2. Then which

of the following statement(s) is(are) correct ?(A) Re(zw) can never exceed 4.(B) If argz = argw, then |z + 2| is equal to 3.(C) The minimum value of |z – w| is equal to 2.(D) The maximum value of |z – w| is equal to 6.

10. Let S be the set of 2 × 2 matrices given by a bS A , where a,b,c,d Ic d

ì üé ùï ï= = Îí ýê úï ïë ûî þ

, such that

AT = A–1. Then -(A) number of matrices in set S is equal to 6.(B) number of matrices in set S such that |A – I2| ¹ 0 is equal to 3.(C) symmetric matrices are more than skew-symmetric matrices in set S.(D) all matrices in set S are singular.

11. If M and N are orthogonal matrices of order 3, then which of the following is (are) orthogonalmatrix ?(A) M2017 (B) MTN (C) M2N2 (D) MN


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Paragraph for Questions 12 and 13

Let z1 and z2 are two moving points such that 1iz 3 4i 5- + = and 2

2

z 3iargz 2 3i 2

æ ö+ p=ç ÷- +è ø

12. Number of complex numbers which satisfy z1 = z2 is/are(A) 0 (B) 1 (C) 2 (D) 4

13. If z = z1 = z2 then 2 2z 1 3i z 9 3i- + + + + is

(A) 25 (B) 50 (C) 100 (D) 225


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1001CJA102118038

Paragraph for Questions 14 and 15N is a square matrix of order ‘n’ such that;l = maximum number of distinct elements if N is triangular.m = maximum number of distinct elements if N is diagonal.p = minimum number of zeroes if N is triangular.and l + 5 = p + 2m.

14. ‘m’ players of equal strength play one game each with each other. P(A) = probability thatat least one player wins all matches he(they) play. P(B) = probability that at least one playerlosses all his (their) matches. Which of the following is not correct

(A) P(A) = 5

16 (B) P(B) = 7

16 (C) ( ) 532

P A BÇ = (D) ( ) 1532

P A BÈ =

15. A man is known to speak the truth ‘p’ out of ‘l’ times. When a die is thrown he either says3 has turned up or says 3 has not turned up. Now if a die is thrown & man says that theoutcome is '3'. If P(A) is the probability that outcome is actually 3, then

(A) P(A) = 631 (B) P(A) =

611 (C) p + l = 18 (D) p + l = 37




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1. Let M is a 2 × 2 matrix such that 1 1M1 2

-é ù é ù=ê ú ê ú-ë û ë û

and 2 1 1M

1 0é ù é ù

=ê ú ê ú-ë û ë û. If æ ö

= ç ÷è ø

a bMc d

, a,b,c,d Î I

then match the entries of List-I to corresponding entries of List-IIList-I List-II

(P) a + d (1) 0(Q) b (2) 1(R) c (3) 4

2. Let (x,y) be a pair of real number satisfying 2 2

y56x 33yx y

+ = -+

and 2 2

x33x 56yx y

- =+

.

List-I List-II(P) 65|x| (1) 4

(Q) 65|y| (2)165

(R) x2 + y2 (3) 7


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1001CJA102118038

3. Let a, b & c are unequal natural numbers and + + ++ + + = D+ + +

2 2

2 2

2 2

a b ab bc ac baba cb b c bc caca ab cb ac c a

List-I contains values of a,b,c and List-II contains corresponding values of D. Now match entriesof List-I with corresponding entries of List-II

List-I List-II(P) a = 1, b = 2, c = 4 (1) 1

(Q) a = 1, b = 3, c = 5 (2) 2(R) a = 1, b = 1, c = 2 (3) 0

4. If A and B are non-singular matrices of order three such that ( )1 1 1

adj AB 1 p 11 1 p

é ùê ú= ê úê úë û

and

|B2 adj(A)| = p2 – 3, then p is

List-I List-II

(P) Values of |adj A B| (1) 2(Q) Values of P (2) 0

(R) Sum of all possible values of ( )adj AB

AB is (3) 1

Note : |x| represents determinant value of matrix X.


Enthusiast Course (TOAS & TNAS)/Pre-Score/15-10-2018/Paper-1

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QUESTION PAPER FORMAT AND MARKING SCHEME :16. The question paper has three parts : Physics, Chemistry and Mathematics.17. Each part has two sections as detailed in the following table.

I have read all the instructionsand shall abide by them.

____________________________Signature of the Candidate

I have verified the identity, name and Formnumber of the candidate, and that questionpaper and ORS codes are the same.

____________________________Signature of the Invigilator

NAME OF THE CANDIDATE ................................................................................................

FORM NO. .............................................

Que. No. Category-wise Marks for Each Question MaximumSection Type of Full Partial Zero Negative Marks of the

Que. Marks Marks Marks Marks section+3 0 –1

I(i) Single If only the bubble If none In allcorrect option 5 corresponding to — of the other 15

the correct option bubbles is casesis darkened darkened

+4 +1 0 –2One or more If only the bubble(s) For darkening a bubble If none In all

I(ii) correct 6 corresponding corresponding to each of the other 24option(s) to all the correct correct option, provided bubbles is casesoption(s) is(are) NO incorrect option darkened

darkened darkenedParagraph +3 0 –1

Based If only the bubble If none In all I(iii) (Single 4 corresponding to — of the other 12

correct the correct option bubbles is casesoption) is darkened darkened

+4 0Three digit If only the bubble(s) In all

III Integer 4 corresponding — other — 16(111-333) to correct answer cases

is darkened

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