T : 3 H Mmu M : 252

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 40 pages andthat all the 20 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.

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

Time : 3 Hours Maximum Marks : 252

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*1001CJA102119030*(1001CJA102119030) Test Pattern

CLASSROOM CONTACT PROGRAMME(Academic Session : 2019 - 2020)

JEE(Main+Advanced) : ENTHUSIAST COURSE (SCORE-I)

JEE(Advanced)UNIT TEST14-11-2019

PAPER-1

Eng

lish

E-2/40

Target : JEE (Main + Advanced) 2020/14-11-2019/Paper-1

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 = 58Atomic 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,

1001CJA102119030

· 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

1

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

ALLEN

E-3/40

Enthusiast Course/Score-I/14-11-2019/Paper-1ALLEN

1001CJA102119030


PART-1 : PHYSICSSECTION-I : (Maximum Marks: 40)

� This section contains TEN 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.Zero Marks : 0 If none of the options is chosen (i.e. the question is unanswered).Negative Marks : –2 In all other cases.

1. For a planet moving around the sun in an elliptical orbit, which of the following quantitiesremain constant?(A) The total energy of the sun plus planet system(B) The angular momentum of the planet about the sun(C) The magnitude of force of attraction between the two(D) The magnitude of linear momentum of the planet

2. Two particles, one with constant velocity 50 m/s and the other with zero initial velocity anduniform acceleration 10 m/s2, start moving simultaneously from the same place in the samedirection. They will be at a distance of 125 m from each other after :

(A) 5 sec. (B) ( )5 1 2+ sec. (C) 10 sec. (D) ( )10 2 1+ sec.

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

E-4/40

Target : JEE (Main + Advanced) 2020/14-11-2019/Paper-1ALLEN

1001CJA102119030


3. A dipole of dipole moment p is kept at origin along x direction and fixed. A bead of mass m,charge q can slide on fixed smooth rod kept along line x = c. Bead is given a gentle push sothat it starts moving along +y direction from point P as shown. Whole arrangement is kept ingravity free space. [c is very large in comprision to length of dipole].

y

p P q,mx

(A) Co-ordinate of point where normal between bead and rod is zero is ( )c, 2c

(B) Speed of bead where normal between rod and bead is zero, is é ù-ê úpe ë û2

0

pq 113 32 mc

(C) Acceleration of bead where normal between rod and bead is zero is pe 30

pq12 3 mc

(D) Normal force between bead and rod at point P is pe 30

pq2 c

.

E-5/40


1001CJA102119030


4. Two concentric conducting thin shell of radii a and 2a having charge Q and –Q respectively

kept as shown in figure. Another point charge Q is also kept at a distance a2 from common

center, (initially switch was open) then

Qa

2a

Q–Q

a2

S

(A) Initial energy stored in electric field from r = a to r = 2a is pe2

0

Q4 a , where r is radial

distance from common center.

(B) Electric potential of inner shell is pe0

3Q8 a , (assuming potential at infinity is zero).

(C) If switch S is closed, then charge flow through the switch into the earth is 5Q2 .

(D) Electric field at common center remains unchanged on closing the switch S.

E-6/40


1001CJA102119030

5. The figure shows the variation of electrostatic potential V in volt with the distance of positionof point along x axis from origin due to continuous volume charge distribution in the regionx = –1m to x = +1m, the graph is parabolic (V = 15 – 5x2) and rest portion of graph is straightline. Choose the CORRECT option(s)(e0 ® permittivity of free space = 8.85 × 10–12 N–1 m–2 C2). The direction of

®E along positive

x-axis is considered as positive.

–3 –2 –1 0 +1 +2 +3 x (in meter)

A 10

5

15V=15–5x2

B

V(in volt)

(A) This graph of potential may be due to a thick sheet of infinite dimension(–1m £ x £ 1, –¥ < y £ ¥ and –¥ < z < ¥) with constant volume charge density 1.77 × 10–10 C/m3.

(B) This graph of potential may be due to a thick sheet of infinite dimension(–1m £ x £ 1, –¥ < y < ¥ and –¥ < z < ¥) with constant volume chargedensity 0.885 × 10–10 C/m3.

(C) XO

E (electric field)

(D) XO

E (electric field)


E-7/40


1001CJA102119030

6. A particle is projected from origin with speed u=50 m/s at an angle 30° with X-axis. Due towind particle acquires an extra acceleration a = 6 m/s2 in –ve x-direction. Path of particle isshown in figure.

30°

P

A

Q

Path of particle

N

B

M

X

Y

O

u

x - Coordinates of point A and B are samey- Coordinates of P and Q are same.Point N on the X-axis, point M on the Y-axis.Time taken by particle from O to P, O to Q, O to A and O to B are t1, t2 , t3 and t4 respectively.(Assuming Y along vertical and their is no surface in the space) (g = 10 m/s2 and constant).

(A) The value of t1 + t2 is 5 sec. (B) The value of t3 + t4 is 25 sec.

(C) The length of ON is -125 3 (5 3) m (D) The length of OM is 625 5

13 3æ ö-ç ÷è øm


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1001CJA102119030

7. A man of height h0 = 2m and mass m = 50 kg is bungee jumping from a platform situated at aheight h = 25 m above a lake. One end of an elastic rope is attached to his foot and the otherend is fixed to the platform. He starts falling from rest in vertical position. The length andelastic properties of the rope are chosen so that his speed will have been reduced to zero atinstant when his head reaches the surface of water. Ultimately the jumper is hanging fromthe rope with his head 8m above the water. (take g = 10 m/s2) (air resistance is very-verysmall, center of mass of man at mid-point)

hhhh

(A) The maximum acceleration achieved during the jump is approximately 40 m/s2.(B) Natural length of elastic rope is 13m.(C) When finally man comes to at rest, elongation in the rope is 2m.(D) Total work done by elastic rope is 250 J.

8. A positive charge of q1 is located 3.00 m to the left of a negative charge –q2. Modulus of chargeq1 greater than modulus of negative charge q2. The net electric field intensity is zero at apoint on the line passing through charges at a distance of 1 m from the negative charge. Onthis line there are also points where the potential is zero. Locate these two points relative tothe negative charge(A) at 0.2 m left of negative charge (B) at 0.2 m right of negative charge

(C) at 3

17 m left of negative charge (D) at 3

17 m right of negative charge


E-9/40


1001CJA102119030

9. A particle of mass m is projected up from the bottom of an smooth inclined plane with initialvelocity v0 at angle 45° with an inclined plane of inclination 30° as shown in figure. At thesame time a small block of same mass m is released from rest at a height h, the particle hitsthe block at some point on inclined plane. (take g = 10 m/s2) (size of the block is negligible)

30°45°

m

hv0

(A) The value of height h is 20v3g .

(B) The value of height h is 203v

g .

(C) If the particle stick to the block after collision, the velocity of block parallel to the inclined

plane just after collision will be 0v2

.

(D) If the particle stick to the block after collision, the velocity of block parallel to the inclined

plane just after collision will be 0v 4 12 2 3

æ ö-ç ÷è ø.

10. A cart weighing 20 N can roll without friction along a horizontal path. The cart carries ablock weighing 2 N. The coefficient of friction between the block and the cart is µ = 0.25. Firsta force F1 = 0.2 N is applied to the block and then a force F2 = 2N.

(A) Force of friction between the block and the cart when F1 is applied is 0.18 N.

(B) Acceleration of the block when F1 is applied is 9 cm/s2.

(C) Force of friction between the block and the cart when F2 is applied is 0.50 N.

(D) Acceleration of the block when F2 is applied is 7.5 cm/s2.

SECTION-II : Numerical Value Type (Up to second decimal place)No question will be asked in section II


E-10/40


1001CJA102119030

SECTION–III(i) : (Maximum Marks : 12)� This section contains FOUR questions.� The answer to each question is a SINGLE DIGIT INTEGER ranging from 0 to 9, both

inclusive.� For each question, darken the bubble corresponding to the correct integer 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 answer is darkened.Zero Marks : 0 In all other cases.

1. A point charge q is kept at the center of circular plane surface of cone. A shaded sectionABDCA shown at the slant surface of cone. If electric flux through the shaded section is

0

n qm 80

´ pe where n and m minimum possible integer. Find (n + m). [length AB = h2 ]

37°53°

A B

DC

h

q


E-11/40


1001CJA102119030

2. In a perfectly insulating but viscous medium, a system consists of an insulating charged hollowsphere (having charge Q) and a small dipole as shown. The sphere is fixed and the dipole ismovable, which is released when dipole is at a distance L(>>l) from O (centre of the sphere).The speed of the dipole when the distance reduces to L/2 (assume drag force to be a constant

of magnitude F0 acting on each charge) is 02

F LnKQqmmL

-l , then n is [neglect gravitational

force]

q

O m, –q m, +ql

0

1K4

= pe3. A tractor A is used to hoist the heavy body B with a pulley system as shown in figure. If the

tractor has a velocity 25 km/hr towards right, find velocity (in km/hr) of the body B.

37°vB v = 25km/hrA

AB


E-12/40


1001CJA102119030

4. Figure shows two binary star systems such that the distance of lighter star from the centre of

rotation is same in both cases. If the ratio of time periods of rotation is 1

2

T n 3T 8 2

= , where n is

an integer, find n. [T1 is Time period in first situation, T2 in second]

C12M

MC2

3M

M

Fig.1 Fig.2


E-13/40


1001CJA102119030

SECTION–III(ii) : (Maximum Marks : 16)� This section contains FOUR questions.� The answer to each question is a SINGLE DIGIT INTEGER ranging from 0 to 9, both inclusive.� For each question, darken the bubble corresponding to the correct integer in the ORS.� For each question, marks will be awarded in one of the following categories :


5. A bead can slide on smooth horizontal fixed frame of shape of quater circle ofradius R = 2m with C as center of curvature. A force F K(3 y)= - is applied on the beadalways towards point B, where y (in metre) is separation between position of bead and pointB and K = 1 N/m. Find work done by this force from A to B in J.

C B

F

A


E-14/40


1001CJA102119030

6. Three identical spherical balls kept in equilibrium inside a hemispherical bowl at its bottom.The angle between line of N1 and line of N2, if radius of balls and bowl adjusted such that

normal force between B and C approaching to zero, is 1 xtan

y-æ öç ÷è ø. (x and y are minimum

possible integer;

N1 ® normal between A and B; N2 ® Normal between B and bowl and all surfaces are smooth).

B C

A


E-15/40


1001CJA102119030

7. Two conducting fixed spheres of radii R and 2R are separated by distance r (r >> R) initially,and having equal charges Q each. Now they are connected to each other by conducting wireand then disconnected. If ‘F’ was the magnitude of electrostatic force between them before

connecting and xF9

is the magnitude of electrostatic force between them after disconnectingthen find x.

8. In the given figure, a very small block of mass 1 kg moving with speed 6 m/s on smoothhorizontal surface. The block slides up the curved smooth surface of wedge then slides downand finally returns to horizontal surface. Find total impulse (in N-s) on block in magnitude.

1kg 2kg2m

6 m/s

SmoothSpace for Rough Work

E-16/40


1001CJA102119030

SECTION–IV : (Maximum Marks : 16)� This section contains TWO questions.� Each question contains two columns, Column-I and Column-II.� Column-I has four entries (A), (B), (C) and (D)� Column-II has five entries (P), (Q), (R), (S) and (T)� Match the entries in Column-I with the entries in column-II.� One or more entries in Column-I may match with one or more entries in Column-II.� The ORS contains a 4 × 5 matrix whose layout will be similar to the one shown below :

(A) (P) (Q) (R) (S) (T)(B) (P) (Q) (R) (S) (T)

(C) (P) (Q) (R) (S) (T)(D) (P) (Q) (R) (S) (T)

� For each entry in column-I, darken the bubbles of all the matching entries. For example, ifentry (A) in Column-I matches with entries (Q), (R) and (T), then darken these three bubblesin the ORS. Similarly, for entries (B), (C) and (D).

� For each question, marks will be awarded in one of the following categories :For each entry in Column-IFull Marks : +2 If only the bubble(s) corresponding to all the correct match(es) is (are)

darkenedZero Marks : 0 If none of the bubbles is darkenedNegative Marks : –1 In all other cases


E-17/40


1001CJA102119030

1. Two concentric metal shells of radii rA = 1cm and rB = 2cm are given charges and actionperformed as shown.

A

B

Column-I Column-II

(A) qA = 2mC, qB = 4 mC A grounded (P) Final A

B

q1

q=

(B) qA = 4mC, qB = –4 mC B grounded (Q) Final A

B

q0

q=

(C) qA = –2mC, qB = +4 mC (R) Final A

B

q1

q< , non zero

A and B connected(D) qA = –1 mC, qB = 2 mC (S) qA and qB do not change during the process

A grounded (T) Finally electric field between A and B is zero.Space for Rough Work

E-18/40


1001CJA102119030

2. In the given setup, a block is placed on frictionless horizontal surface, the cords, springs andpulleys are ideal and each spring has spring constant k. Initially all the springs are in naturallength and block is at rest. Now a constant horizontal force F = mg applied on the block inhorizontal direction such that block only translate.

m

P1

P2

Spring 2Spring 1

F = mg

Column-I Column-II

(A) When acceleration of block is zero, (P) Speed of block is g 10m3 k

(B) When acceleration of block is maximum (Q) Ratio of energy stored inin magnitude and towards fixed wall, spring (1) to spring (2) is 1/4.

(C) When magnitude of acceleration of block (R) Displacement of pulley P1 is 2/5 timesis 1/3 times of magnitude of maximum of displacement of block.acceleration,

(D) When displacement of pulley P1 is 4mg9k , (S) Displacement of block is

10mg9k .

(T) Displacement of pulley P2 is 2mg3k .


E-19/40


1001CJA102119030


PART-2 : CHEMISTRYSECTION-I : (Maximum Marks: 40)




1. Which of the following statement(s) is CORRECT?(A) Crystalline solid of Boron is having 12 corners in its each unit.(B) Crystalline solid of Boron is having 20 faces in its each unit.(C) Borax solution is a good buffer.(D) Boric acid consumes one mole of NaOH when it reacts with dil. NaOH.

2. The CORRECT statement(s) is/are :-(A) Xe forms clathrate compound in crystal lattice of ice.(B) Order of Xe-F bond length : XeF2 > XeF4

(C) Order of Xe-F bond length : XeF2 < XeF4

(D) Helium is used as diluent for O2 in modern diving apparatus

3. C —( CH )2 nHO

O– C – OH

O D¾¾® Product(s)

when n = 1, organic product formed is P1when n = 3, organic product formed is P2when n = 4, organic product formed is P3Correct statement(s) is/are is(A) P1 gives Tollen’s test (B) P2 is cyclic anhydride(C) P3 gives 2,4-DNP test (D) P3 gives Tollen’s test

E-20/40


1001CJA102119030


4. 3Na / liquid NH¾¾¾¾¾¾¾® (A) 32

(i ) O(ii)H O¾¾¾¾® (B) D¾¾® (C) 2(i) Red P/ Br

(ii ) KCN¾¾¾¾¾¾® (D) 2H / H O+¾¾¾¾¾® (E)

Find correct statement(s)(A) Both (B) and (C) can show 2,4-DNP test(B) (A) is anti aromatic(C) Both (B) and (C) have carboxylic acid group as functional group(D) (C) to (D) conversion involve nucleophilic substitution

5. Calculate DGreaction (kJ/mol) for the given reaction at 300 K.

2(g) 2(g) (g)A B 2AB+ ��

and at partial pressure of 10–2 bar, 10–1 bar and 10–4 bar respectively for A2, B2 and AB.Given :

ºfHD AB = 180 kJ/mol ; º

fHD A2 = 60 kJ/mol

ºfHD B2 = 29.5 kJ/mol ; º

fSD AB = 210 J/K mol

ºfSD A2 = 190 J/K mol ; º

fSD B2 = 205 J/K mol

Use : 2.303 R × 300 = 5750 J/mole(A) 234.25 kJ/mole (B) 344.5 kJ/mole (C) 270.5 kJ/mole (D) 25 kJ/mole

6. Which of the following is correct when an ideal gas having initial pressure P, volume V andtemperature T is allowed to expand adiabatically until its volume becomes 5.66 V while itstemperature falls to half ? (Given : 100.75 = 5.66, log 2 = 0.30)(A) The gas is diatomic (B) The gas is monoatomic(C) The work done by the gas is 1.25 PV (D) All are correct

E-21/40


1001CJA102119030


7. NaBH4 + I2 ¾® ‘P’ + H2 + NaIWhich of the following statement(s) is/are INCORRECT?(A) ‘P’ is a planar molecule(B) ‘P’ is non polar molecule(C) ‘P’ reacts with MeOH and releases H2 gas.(D) ‘P’ has no electron deficiency at all.

8. 4 2OsO / H O¾¾¾¾¾® (A) 4HIO¾¾¾¾® (B) –dil.OHD

¾¾¾¾® (C) 32

(i )O(ii)Zn / H O¾¾¾¾¾® (D)

Correct statement(s) is/are(A) (A) is vicinol diol (B) (B) is a dicarboxylic acid(C) (B) gives Tollen’s test (D) (D) gives Iodoform test

9. With respect to graphite and diamond, which of the statement(s) given below is (are) correct ?(A) Graphite is denser than diamond.(B) Graphite has higher electrical conductivity than diamond.(C) Graphite has higher thermal conductivity than diamond.(D) Graphite has higher C – C bond order than diamond.

10. Compound (A) D B + NO + O2 2

K CrO2 4 KNO + D3

H S2C

H O2 2 PbSO4

From the above sequence given identify A, B, C and D.

(A) B = PbO (B) A = Pb(NO3)2 (C) C = PbS (D) D = PbCrO4


E-22/40


1001CJA102119030




1. CO

Cl 3 2(CH ) NH¾¾¾¾¾®2

(i)LAH(ii)H O¾¾¾¾® MeI(excess)¾¾¾¾¾¾® 2Ag O

D¾¾¾®

What is the sum of double bond equivalent of final product(s) of above reaction sequence?2. How many of the following compounds will release CO2 gas on strong heating ?

(i)

O

COOHCOOH

(ii) ONH

OH

(iii) H – C – COOHH – C – COOH

(iv) COOH

(v) HOOC – CH2 – COOH (vi) COOHCOOH

(vii)

OCOOH

(viii) OH

OOH


E-23/40


1001CJA102119030

3. In how many reactions products are correctly mentioned.

(i)

NH2

2 2Br / H O¾¾¾¾¾®

NH2

Br

Br Br(ii)

NH2

32 4

HNOH SO¾¾¾¾®

NH2

NO2

47%

(iii)

NO2

4Zn / NH Cl¾¾¾¾¾®

NH—OH

(iv)

NO2

Zn / HCl¾¾¾¾®

NH2

(v)

NH2

32 4

HNOH SO¾¾¾¾®

NH2

NO247%

(vi)

NO2

NO2

4NH HS¾¾¾¾®

NO2

NH2

4.

A B

D C

5 10 20

P(a

tm)

1

½

V(litre)Calculate magnitdue of total work done (in atm. litre) for the above process ABCDinvolving a monoatomic ideal gas.[Given : ln 2 = 0.7]


E-24/40


1001CJA102119030

SECTION–III(ii) : (Maximum Marks : 16)� This section contains FOUR questions.� The answer to each question is a SINGLE DIGIT INTEGER ranging from 0 to 9, both



5. If one mole of a gas initially at 300 K is heated to 500 K. The Gibb’s free energy change, DG forthis gas is given by 3.38 × 10X J. Given : S = 1.5 + 3 × 10–3 T (JK–1mol–1) andCv = 1.5 R. Then the value X is :

6. Give the number of characteristic bond(s) found in the various oxy-acids of phosphorus asgiven below.(P) Number of P–O–P bond(s) in cyclotrimetaphosphoric acid.(Q) Number of P–P bond(s) in hypophosphoric acid.(R) Number of P–H bond(s) in hypophosphrous acid.(S) Number of P–OH bond(s) in pyrophosphoric acid.

P Q R SGive your answer P + Q + R + S (Example if answer is 16 mark it as 1 + 6 = 7 & fill thesingle digit OMR sheet)


E-25/40


1001CJA102119030

7. The total number of reactions in which any of HNO3, H2SO4, NH3 & SO2 are acting as reducingagent.

(i) 3Cu HNO (cold dil.)+ ¾¾® (ii) Sn + HNO3 (conc.) ¾®

(iii) SO2 + NO2 ¾® (iv) 2 4H SO S+ ¾¾®

(v) 2 4H SO 2KI+ ¾¾® (vi) 2 3 2SO KIO H O+ + ¾¾®

(vii) 2 2SO Cl+ ¾¾® (viii) 3 2NH CaOCl+ ¾¾®

8. The number of oxygen atoms bonded to one P-atom in P4O6 is “x” and total number of atomsin ring formation in sodium peroxyborate is “y”. Then (x + y) is.


E-26/40


1001CJA102119030


(A) (P) (Q) (R) (S) (T)(B) (P) (Q) (R) (S) (T)

(C) (P) (Q) (R) (S) (T)(D) (P) (Q) (R) (S) (T)

� For each entry in column-I, darken the bubbles of all the matching entries. For example,if entry (A) in Column-I matches with entries (Q), (R) and (T), then darken these threebubbles in the ORS. Similarly, for entries (B), (C) and (D).



1. Match the Column.Column-I Column-II

(A) 4LiAlH3R CONH CH- - ¾¾¾¾® (P) Schmidt reaction

(B) R – C – NH2

O 2Br / NaOH

D¾¾¾¾¾® (Q) Hoffmon bromamide reaction

(C) R–CH–CH3

COOH

32 4

NaNconc.H SO ,heat¾¾¾¾¾¾¾® (R) R–CH2–NH–CH3

(D) R – NH2 3CHClKOH¾¾¾¾® (S) Foul smelling product

(T) Isocyanate intermediateSpace for Rough Work

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1001CJA102119030

2. Match Column-I with Column-IIColumn-I Column-II

(Characteristics of Products)(A) 3B2H6 + 6NH3

D¾¾® (P) One of the products is a gas

(B) Na2B4O7 + H2SO4 + H2O ¾¾® (Q) One of the product has benzene typestructure

(C) BF3 + NaH 450K¾¾¾® (R) One of the product is a monobasic acid.(D) B2H6

burns in air¾¾¾¾¾® (S) One of the product gives yellow precipitatewith mercuric nitrate

(T) One of the product is an acidic oxideSpace for Rough Work

E-28/40


1001CJA102119030


PART-3 : MATHEMATICSSECTION-I : (Maximum Marks: 40)




1. An unbiased die, with faces numbered 1,2, 3, 4, 5, 6 is thrown 6 times and the list of the 6numbers showing up is noted. If P(Ai) denotes the probability that only i number of numbersappear in the list out of numbers 1, 2, 3, 4, 5, 6 then which of the following is/are correct

(A) >3 4P(A ) P(A ) (B) P(A4) = 623400

6

(C) =

<å6

ii 1

P(A ) 1 (D) max(P(Ai)) = P(A4)

2. Let A, B, C be angles of triangle ABC with vertex º - - = - - =A (4, 1) and x 1 0 and x y 1 0are internal angle bisectors through B and C respectively. Let D, E, F be points of contact ofsides BC, CA and AB with incircle of D ABC. If D¢ , E¢ , F¢ are images of D, E and F throughinternal angle bisector of A. B, C.(A) Equation of incircle of D ABC is - + =2 2(x 1) y 5(B) Circumcircle of D D¢E¢F¢ is - + =2 2(x 1) y 5(C) Area of D ABC is 23 sq.unit(D) Equation of incircle of D ABC is + =2 2x y 25

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3. Which of the following is are true?(A) The value of 404C4 – 4C1

303C4 + 4C2 202C4 – 4C3

101C4 is equal to (404)4

(B) Let + + = + + + +2 25 2 500 1 2 50(1 x x ) a a x a x ...... a x then the value of

- + - + -3 5 7 9 49a a a a ..... a is 24

(C) The value of ´´ ´- + - +

´ ´ ´

11 411 2 11 331 2 C 2C 2 C 21 ...

2 3 3 4 4 5upto 12 terms is

113

(D) The constant term in the expansion of æ ö+ + +ç ÷è ø

152

21 1x xx x

is ( ) ( )+

=

å

515 15

5 r 3rr 0

C C

4. The tangent at any point P on a curve =f (x,y) 0 cuts the y-axis at T. If the distance ofpoint T from P equals the distance of T from the origin then the curve with this propertyrepresents a family of circles. Which of the following are correct?(A) any arbitrary line =y mx cuts every member of this family at the points where the

slopes of these members are equal

(B) =f (x,y) 0 is orthogonal to the family of circles + - = " Î2 2x y ky 0 x R

(C) If =f (x,y) 0 passes through (2, 2) then the intercept made by its director circle on they-axis is equal to 8

(D) If =f (x,y) 0 passes through (–1, 1), then image of its centre in the line =y x is (1, 0)

5. Which of the following statement is/are true.(A) The number of ordered triplets (a, b, c) are there such that LCM (a, b) = 1000,

LCM (b, c) = 2000 and LCM (c, a) = 2000, are 70(B) The number of ways can 11 person sit around a round table so that all shall not have

same neighbors in any two arrangement is 5.9!(C) The number of ways to place 11 identical balls in three distinct boxes so that any two

boxes together will contain more balls than third one is 13C2 – 37C2

(D) The number of ordered triplets (a, b, c) are there such that LCM (a, b) = 1000,LCM (b, c) = 2000 and LCM (c, a) = 2000, are 60

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6. A fair coin is tossed 10 times and the outcomes one listed. Let Hi be the event that the ithoutcome is a head and Am be the event that the list contains exactly m heads, then

(A) H3 and A4 are independent events (B) A1 and A9 are not independent events

(C) H2 and A5 are independent events (D) H4 and H8 are independent events

7. In a D ABC, AB = 9 units, BC = 8 units and AC = 7 units. Let M be the mid-point of BC. IfAM is extended till D such that Ð = °ADB 90 , then

(A) A circle with AB as diameter intersect BC at P, then BP = 6 units(B) A circle with AB as diameter intersect BC at P, then BP : PC = 3 : 1

(C) D =D

(Area of ABD) 57(Area of ACM) 49

(D) None of these

8. Which of the following is/are true

(A) The coefficient of x4 in -- - - - -5 4 3 2 4(1 x )(1 x )(1 x )(1 x )(1 x) is 20

(B) The coefficient of x4 in -- - - - -5 4 3 2 4(1 x )(1 x )(1 x )(1 x )(1 x) is 10

(C) Sum of the co-efficient of terms of degree 13 in the expansion of + + -11 2 10(1 x) (1 y z) is

equal to 104C

(D) The value of = =

é ùæ öê úç ÷è ø æ ö æ ö æ öê ú

ç ÷ ç ÷ ç ÷ê úè ø è ø è øæ öê úç ÷è øë û

å å7 14

nr

k 0 r k

7r 14 nk , where denotes C , is

14 k r rk

76

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9. If pair of tangents are drawn from a variable point P(h,k) to the circle x2 + y2 = 25, suchthat angle between tangents is q and the area covered by the locus of P is A sq. units, thenchoose the correct option/s

(A) if pæ ö

q Î pç ÷è ø

,2 , then A = 25p sq. units

(B) if pæ ö

q Î pç ÷è ø

,2 , then A = 20p sq. units

(C) if p pæ ö

q Î ç ÷è ø

,4 2 , then ( )= p +A 25 2 2 1 sq. units

(D) if p pæ ö

q Î ç ÷è ø

,4 2 , then ( )= p +A 50 2 1 sq. units

10. If = "K(k)! 1.2.3 k, k, being a natural number then which of the following statements about

( )-

+

+

2

n 1

(n 1)! n

(n!) (n 1)! is true (n is a whole number) ?

(A) It is an integer.

(B) It is number of ways of distributing +2(n 1) distinct objects among n people such thatall get equal object except one who gets lesser objects

(C) It is number of ways of dividing +2(n 1) distinct objects among n groups out whichsize of (n – 2) group is n and other (n + 1) and (n – 1)

(D) It is number of ways of distributing (n2 + 1) distinct objects among n groups out of whichsize of (n – 1) group is n objects and one group is (n + 1) objects



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1. ABC be a triangle with vertex A (0, 0), B (3, 1) and C (0, 2). If algebraic sum of perpendiculardistances from A, B, C on a line mx + ny – 1 = 0 is zero and this line passes through point (3,5)then maximum value of k ( ÎNk )such that ( )-m n5 .3 ! is divisible by 10k2 ?

2. The value of - --

=- ×å

10r 10 r 30 30 r

r 10 rr 0

( 1) 4 C C is equal to ×30 kkC 3 and

==å

2030 20 n

r r 20r 0

C C C then the

value of é ù =ê úë ûnk (where [.] represents greatest integer function less than or equal to x)


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3. Three circles 3 2 1C ,C ,C of radius 3, 6, 9 respectively touch as shown in the figure. A chord AB

to circle 1C touch circles 2C and 3C .

BP9

O2O1O3

C3

C2

QA 6

C1

The length of chord AB is a 14 and length of common tangent PQ is b 2 then number ofdivisors of (3b –1 – 2a –1) is

4. An urn contains four balls. Two balls are drawn at random and are found to be white. If

the probability that all the balls are white is mn , where m and n are coprime then the

value of (m + n) =?


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SECTION–III(ii) : (Maximum Marks : 16)� This section contains FOUR questions.� The answer to each question is a SINGLE DIGIT INTEGER ranging from 0 to 9, both



5. The number of ways in which 12 identical balls can be grouped in four marked non emptysets A, B, C, D such that n(A) < n(B) is k then sum of digits of k is

6. On a chess board, the number of ways to place 2 knights of different colours such that theyattack each other, is 48n, then the value of n is

B B

W W


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7. From the point P(h,k) tangents, PA and PB are drawn to the circle + - - + =2 2x y 2x 4y 1 0.Such that slope of chord AB is 2, then the value of h + 2k is :

8. If the probability that a number selected from the set {1, 2, 3, ..., 1000} is divisible by 3 but

neither divisible by 5 nor by 7, ismn , then é ù

ê úë û5m5n

is (where [.] represents greatest integer

function less than or equal to x)?Space for Rough Work

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(A) (P) (Q) (R) (S) (T)(B) (P) (Q) (R) (S) (T)(C) (P) (Q) (R) (S) (T)(D) (P) (Q) (R) (S) (T)

� For each entry in column-I, darken the bubbles of all the matching entries. For example,if entry (A) in Column-I matches with entries (Q), (R) and (T), then darken these threebubbles in the ORS. Similarly, for entries (B), (C) and (D).



1. Match the following Column-I with Column-II Column-I Column-II

(A) Two circles with radii 1r and 2r intersect each other at point A (P) - p10

16and BC be the direct common tangent to circles of length

l

such that Ð BAC = 45° then l

1 22

r r is equal to

(B) The obsulute value of minimum of + - - +2 2(x y 24x 24y 3), (Q) 12

if + - - =2 2x y 6x 8y 0 is


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(C) ABCD and CDEF are two squares of equal area. The ratio (R) 25of the shaded area to the area of rectangle ABFE

B C

A D

O

F

E

(D) In the given figure ABCD and PQRS are two square, (S) 115+10 145

then (Area of square ABCD)(Area of square PQRS) can be

A B

S R

D C

O

P Q

(T) 5


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2. If set A contain 8 distinct elements and set B contains 5 distinct elements then match thecolumn-I with column-II

Column-I (Mapping f : A ® B) Column-II (Number of functions)

(A) Non-decreasing (P) 85

(B) Many-one (Q) 85P

(C) Onto (R) 58 – 5C1 48 + 5C2 × 38 – 5C3 × 28 + 5C4

(D) Strictly increasing (S) 0

(T) 124C


Enthusiast Course/Score-I/14-11-2019/Paper-1

E-39/401001CJA102119030

ALLENSpace for Rough Work

Corporate Office : ALLEN CAREER INSTITUTE, “SANKALP”, CP-6, Indra Vihar, Kota (Rajasthan) INDIA 324005

+91-744-2757575 [email protected] www.allen.ac.in

QUESTION PAPER FORMAT AND MARKING SCHEME :16. The question paper has three parts : Physics, Chemistry and Mathematics.17. Each part has three section 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. .............................................

Target : JEE (Main + Advanced) 2020/14-11-2019/Paper-1

Your Target is to secure Good Rank in JEE 2020 1001CJA102119030E-40/40

ALLEN

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

Que. Marks Marks Marks Marks section+4 0 –2

One or more If only the bubble(s) If none In all I correct 10 corresponding — of the other 40option(s) to all the correct bubbles is cases

option(s) is(are) darkeneddarkened

+3 0Single digit If only the bubble In all

III(i) Integer 4 corresponding — other — 12(0-9) to correct answer cases

is darkened+4 0

Single digit If only the bubble In all III(ii) Integer 4 corresponding — other — 16

(0-9) to correct answer casesis darkened

+8 +2 0 –1 IV Matrix If only the bubble(s) For darkening a bubble If none In all

Match Type 2 corresponding to corresponding to each of the other 16all the correct correct match is bubbles is cases

match(es) is(are) darkened darkeneddarkened

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T : 3 H Mmu M : 252