(0999DJA111521001) )) T Pattern DISTANCE LEARNING ...

)0999DJA111521001)(0999DJA111521001) Test Pattern

DISTANCE LEARNING PROGRAMME(Academic Session : 2021 - 2022)

JEE(Advanced)TEST # 01

24-10-2021

JEE(Main + Advanced) : LEADER TEST SERIES / JOINT PACKAGE COURSE (PHASE-II)

Test Type : Unit Test # 0112th Undergoing/Pass Students

READ THE INSTRUCTIONS CAREFULLY / Ïi;k bu funsZ'kks a dks /;ku ls i<+ s aGENERAL / lkekU; %1. This sealed booklet is your Question Paper. Do not break the seal till you are told to do so.

;g eksgjcU/k iqfLrdk vkidk iz'ui= gSA bldh eqgj rc rd u rksM+s tc rd bldk funsZ'k u fn;k tk;sA2. Use the Optical Response sheet (ORS) provided separately for answering the questions.

iz'uksa dk mÙkj nsus ds fy, vyx ls nh x;h vkWfIVdy fjLikal 'khV (vks- vkj- ,l-) (ORS) dk mi;ksx djsaA3. Blank spaces are provided within this booklet for rough work.

dPps dk;Z ds fy, bl iqfLrdk esa [kkyh LFkku fn;s x;s gSaA4. Write your name, form number and sign in the space provided on the back cover of this booklet.

bl iqfLrdk ds fiNys i`"B ij fn, x, LFkku esa viuk uke o QkWeZ uEcj fyf[k, ,oa gLrk{kj cukb;sA5. After breaking the seal of the booklet, verify that the booklet contains 44 pages and that all the

20 questions in each subject and along with the options are legible. If not, contact the invigilator forreplacement of the booklet.bl iqfLrdk dh eqgj rksM+us ds ckn Ïi;k tk¡p ysa fd blesa 44 i`"B gSa vkSj izR;sd fo"k; ds lHkh 20 iz'u vkSj muds mÙkj fodYi Bhdls i<+ s tk ldrs gSaA ;fn ugha] rks iz'ui= dks cnyus ds fy, fujh{kd ls lEidZ djsaA

6. You are allowed to take away the Question Paper at the end of the examination.ijh{kkFkhZ iz'ui= dks ijh{kk dh lekIrh ij ys tk ldrs gSaA

OPTICAL RESPONSE SHEET / vkWfIVdy fjLikal 'khV (vks-vkj-,l-) %7. The ORS will be collected by the invigilator at the end of the examination.

vks- vkj- ,l- dks ijh{kk ds lekiu ij fujh{kd ds }kjk ,d= dj fy;k tk,xkA8. Do not tamper with or mutilate the ORS. Do not use the ORS for rough work.

vks- vkj- ,l- esa gsj&Qsj@foÏfr u djsaA vks-vkj-,l- dk dPps dke ds fy, iz;ksx u djsaA9. Write your name, form number and sign with pen in the space provided for this purpose on the ORS.

Do not write any of these details anywhere else on the ORS. Darken the appropriate bubbleunder each digit of your form number.viuk uke vkSj QkWeZ uEcj vks-vkj-,l- esa fn, x, [kkuksa esa dye ls fy[ksa vkSj vius gLrk{kj djsaA buesa ls dksbZ Hkh fooj.kvks-vkj-,l- esa dgha vkSj u fy[ks aA QkWeZ uEcj ds gj vad ds uhps vuq:i cqycqys dks dkyk djsaA

DARKENING THE BUBBLES ON THE ORS / vks-vkj-,l- ij cqycqyks a dks dkyk djus dh fof/k %10. Use a BLACK BALL POINT PEN to darken the bubbles on the ORS.

vks-vkj-,l- ds cqycqyksa dks dkys ckWy ikWbUV dye ls dkyk djsaA

11. Darken the bubble COMPLETELY. / cqycqys dks iw.k ± :i ls dkyk djsaA

12. The correct way of darkening a bubble is as : / cqycqys dks dkyk djus dk mi;qDr rjhdk gS : 13. The ORS is machine-gradable. Ensure that the bubbles are darkened in the correct way.

vks-vkj-,l- e'khu tk¡P; gSA lqfuf'pr djsa dh cqycqys lgh fof/k ls dkys fd, x;sa gSaA14. Darken the bubbles ONLY IF you are sure of the answer. There is NO WAY to erase or

"un-darken" a darkened bubble.cqycqys dks rHkh dkyk djsa tc vki mÙkj ds ckjs esa fuf'pr gksA dkys fd, gq, cqycqys dks feVkus vFkok lkQ djus dk dksbZ rjhdk ugha gSA

15. Take g = 10 m/s2 unless otherwise stated. / g = 10 m/s2 iz;qDr djsa] tc rd fd vU; dksbZ eku ugha fn;k x;k gksAQUESTION PAPER FORMAT / iz'ui= dk izk:i %16. The question paper has three parts : Physics, Chemistry and Mathematics.

bl iz'ui= esa rhu Hkkx gSa % HkkSfrd foKku] jlk;u foKku ,oa xf.krA

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THE

SEA

LS W

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UT

BEIN

G IN

STRU

CTED

TO

DO

SO B

Y TH

E IN

VIGI

LATO

R / f

ujh{

kd d

s vuqn

s'kksa d

s fcuk

eqgj

sa u r

ksM+s

Time : 3 Hours Maximum Marks : 240

ALLEN Leader Test Series/Joint Package Course/Phase-II/24-10-2021

PART-1 : PHYSICS

SECTION-I (i) : (Maximum Marks: 12)

Full Marks : +3 If ONLY the correct option is chosen. Zero Marks : 0 If none of the options is chosen (i.e. the question is unanswered) Negative Marks : –1 In all other cases

1. Two particles are held in equilibrium by the gravitational and electrostatic forces between them. Particle-A has mass m and charge q and particle-B has mass m and charge q . The distance between the chargesis d. Which of the following changes may cause the charges to accelerate towards one another?

(A) m is doubled and m is halved. (B) m is double and m is doubled.

(C) q is doubled and q is doubled. (D) d is doubled.

2. Which of the following is dimensionally correct for "pressure" :

(A) Momentum per unit volume

(B) Momentum per unit volume and per unit energy

(C) Energy per unit volume

(D) Force per unit length

3. A body moves with velocity v= lnx where x is its position. The net force on body is zero at

(A) zero (B) x = e (C) x = e (D) x = 1

4. The figure below shows the forces that three charged particles exert on each other. Which of the foursituations shown can be correct.

(I) (II) (III) (IV)

(A) all of the above (B) none of the above

(C) II, III (D) II, III & IV

BEWARE OF NEGATIVE MARKING

This section contains FOUR (04) questions.Each question has FOUR options (A), (B), (C) and (D). ONLY ONE of these four options is thecorrect answer. For each question, choose the option corresponding to the correct answer. Answer to each question will be evaluated according to the following marking scheme :

a a b b

a b a b

a b

2

0999DJA111521001 LTS- 1/20

ALLEN Target : JEE(Main + Advanced) 2022/24-10-2021

SECTION-I (ii) : (Maximum Marks: 16)

Full Marks : +4 If only (all) the correct option(s) is (are) chosen. Zero Marks : 0 In all other cases.

5. Refer the block diagram in which four function machines are shown. Which of the following statementsis/are true?

(A)

(B)

(C)

(D)

6. An electric dipole is fixed along y-axis with its centre at origin. At a given instant a charge particle ismoving along x-axis then

(A) Power of electric force on charge particle is zero.

(B) Acceleration and velocity are perpendicular

(C) Time rate of change in velocity is zero.

(D) If charge is free to move, it always moves along x-axis.

This section contains FOUR (04) questions.Each question has FOUR options for correct answer(s). ONE OR MORE THAN ONE of these fouroption(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:

u = =dzdy

12 2x+ 3− −−−−√

u = =dzdy

14 2x+ 3− −−−−√

v = = ⋅ =dzdx

dzdy

dydx

12x+ 3− −−−−

√

v = = ⋅ =dzdx

dzdy

dydx

12 2x+ 3− −−−−√

LTS- 2/20 0999DJA111521001


7. In a region of space, the electric field . Consider an imaginary cubical volume of edge

‘a’ with its edges parallel to the axes of coordinates. Now,

(A) the total electric flux through the faces 1 and 3 is E a

(B) the charge inside the cubical volume is 2ε E a

(C) the total electric flux through the faces 2 and 4 is 2E a

(D) the charge inside the cubical volume is ε E a

8. Two concentric rings of radii R = m and R = 4m are placed in y-z plane with their centres at origin.

They have uniform charge –q and +Q = 2 q on the inner and outer rings respectively. Consider the

electrostatic potential to be zero at infinity. Then choose the correct option(s) :-

(A) Potential at origin is zero

(B) Field at origin is zero

(C) Field at x = 2 is zero

(D) From origin to x = 2, field is towards origin

= x + yE E 0 i E 0 j

03

0 03

03

0 03

1 6–√ 2

2–√

0999DJA111521001 LTS- 3/20


SECTION-I (iii) : (Maximum Marks: 12)

Full Marks : +3 If ONLY the correct option is chosen. Zero Marks : 0 If none of the options is chosen (i.e. the question is unanswered). Negative Marks : –1 In all other cases.

Paragraph for Questions 9 and 10

A physical quantity which is completely specified by a number (magnitude) in terms of an appropriateunit is known as a scalar quantity. Certain physical quantities can only be completely specified by anumber (magnitude) alongwith a proper unit, as well as direction such quantities are known as vectors. The dot product of two vectors is defined as the product of the magnitude of two vectors multiplied bythe cosine of the angle between the two. Dot product between two vectors can be positive, zero ornegative according as the angle between them is acute, 90° or obtuse. For two vectors

and the dot product .

The dot product of two vectors is the product of two quantities one of which is the modulus of the firstvector (or second) and the other is the projection of second vector along the first (or the first vector alongthe second).

9. If the vectors and are perpendicular to each other, then the value of m is

(A) (B) (C) (D) 12

10. Work done by a constant force for displacement is given by . What is the work done by a

force when its point of application gets displaced by ?

(A) 18J (B) 20J (C) 30J (D) 24J

This section contains FOUR (04) questions.This section contains TWO paragraphs.Based on each paragraph, there are TWO questionsEach question has FOUR options (A), (B), (C) and (D). ONLY ONE of these four options is correctFor each question, choose the option corresponding to the correct answer.Answer to each question will be evaluated according to the following marking scheme:

= + +A Ax i Ay j Az k = + +B B x i B y j B z k ⋅ = + +A B AxB x AyB y AzB z

4 + − 3i j k 2m + 6m +i j k

314

−18 −

23

F s W = ⋅F s

= (4 + 2 − 6 )NF i j k ( − − 3 )mi j k

LTS- 4/20 0999DJA111521001



Electric field in a region is given by following equation where and

and an imaginary cube is made as shown in the diagram.

11. Find total flux through this cube due to the given electric field.

(A) 4πK (B) 6πK (C) 16K (D) 8K

12. Find total charge encloses in this imaginary shown cube.

(A) 4Kπε (B) 8Kπε (C) 6Kπε (D) 2Kπε

=E K ( − )r r 0

| − |r r 02 = x + yr i j

= +r 0 i j

0 0 0 0

0999DJA111521001 LTS- 5/20


SECTION-III : (Maximum Marks: 24)

Full Marks : +4 If only the correct answer is given. Zero Marks : 0 In all other cases

1. In a new system of units mass, acceleration and frequency are taken as fundamental units. If unit of massis 100g, unit of acceleration is 2 m/s and unit of frequency is 4 sec in the new system of units then findthe value of 0.1 J in this system.

2. A free water molecule of dipole moment p = π × 10 C lies in xy-plane in gravity free space. Themoment of inertia of the molecule about its centroidal axis perpendicular to the plane containing themolecules, that is, z-axis is 2 × 10 kgm . If the molecule is kept in a uniform electric field parallel to x-y plane having field intensity E = 2 × 10 N/C, the dipole oscillates about z-axis. The frequency of smalloscillations is n × 10 Hz. Write the value of n.

3. An electric field given by pierces Gaussian’s cube of side 1m placed at origin such

that its three sides represents x, y and z axes. The net charge enclosed within the cube is given by –nε .Find the value of n.

4. A neutral spherical conductor having cavity A and B of radius ‘1cm’ and ‘2cm’ respectively. Radius ofspherical conductor is 10 cm. If cavity ‘A’ contains charge 2µC and ‘B’ contains charge of –1µC. Electricpotential at the centre of conductor is k × 10 volt. Then what is the value of k.

This section contains SIX (06) questions.The answer to each question is a SINGLE DIGIT INTEGER ranging from 0 to 9, both inclusive.For each question, enter the correct integer value of the answer in the place designated to enter theanswer.For each question, marks will be awarded in one of the following categories :

2 –1

2 –30

–48 2

6

11

= 4 − 3( + 2)E i y2 j

0

4

LTS- 6/20 0999DJA111521001


5. A solid conducting sphere of radius 'a' having charge q is surrounded by a concentric conducting sphericalshell of inner radius 2a and outer radius 3a as shown in figure. If the amount of heat produced when

switch is closed is . Fill the value of α.

6. Referring to the spherical equipotential lines, Express electric field as function of r. If your answer is

then give the value of a. (Here r & a in SI unit)

α( )Kq2

24a

ar 2

0999DJA111521001 LTS- 7/20


SECTION-IV : (Maximum Marks: 16)

For each entry in Column-I Full Marks : +2 If only the option(s) corresponding to all the correct match(es) is (are) chosen Zero Marks : 0 In all other cases

1. In a new system (say TK system) of measurement, the fundamental quantities length, mass and time aremeasured in Akshay, Shahrukh and Aamir respectively. 1 Akshay = 1 km 1 Shahrukh = 1 Quintal (100 kg) 1 Aamir = 1 minute

Column-I Column-II

(A) One unit of acceleration in TK system. (P) SI unit

(B) One unit of kinetic energy in TK system (Q) MKS unit

(C) One unit of pressure in TK system (R) MKS unit

(D) One unit of work in TK system (S) MKS unit

(T) SI unit

This section contains TWO (02) 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. For each entry in Column-I, darken the options of all the matching entries. For example, if entry (A) inColumn-I matches with entries (Q), (R) and (T), then chosen these three options. Similarly, for entries(B), (C) and (D).For each question, marks will be awarded in one of the following categories :

×518 10−4

×518 10−3

×518 100

×518 104

×518 105

LTS- 8/20 0999DJA111521001


2. In each figure of column-I, a spherical uniform charge distribution is given in column-II, direction ofelectric field is represented by arrows. Match the direction of electric field due to charge distribution atgiven point in figures of column-I.

Column-I Column-II

(A)

A solid hemisphere, uniformly positive charged directionof resultant electric field at point P must be (point P lieson diameter AB as shown) (P)

(B)

A solid uniformly positive charged hemisphere witha hemispherical cavity and C and C are the centresof hemispheres, direction of resultant electric field at pointC can be (Q)

(C)

A solid uniformly positive charged hemisphere witha hemispherical cavity and C and C are the centres

of hemispheres, where R is radius

of hemisphere and radius of cavity is . Direction

of resultant electric field at point P must be

(R)

(D)

A solid hemisphere, uniformly charged, direction ofresultant electric field at centre C can be

(S)

(T)

1 2

2

1 2

P = P =C1 C2R4

R2

0999DJA111521001 LTS- 9/20


PART-2 : CHEMISTRY



1. Ratio of number of protons to neutrons present in 27.83 × 10 molecules of (where D is H ).

(A) (B) 1 (C) 27.83 (D) 27.83 × 10

2. A 5000 W gas discharge lamp emits 5.0 W of UV radiation in narrow range centered around 198 nmwavelength. Then number of photons of this wavelength emitted in one minute : (Given : h = 6.6 × 10 J-S, C = 3 × 10 m/s)

(A) 2 × 10 (B) 3 × 10 (C) 5 × 10 (D) 8.3 × 10

3.

Correct IUPAC name of is :

(A) 3-carboxy cyclohex-4-en-1-ol (B) 5-carboxy cyclohex-3-en-1-ol

(C) 5-hydroxy cyclohex-2-ene-carboxylic acid (D) 3-hydroxy cyclohex-5-ene-carboxylic acid

4. Alcohol and phenol can be differentiated by :

(A) NaOH (B) NaHCO (C) Na (D) NaNH

This section contains FOUR (04) questions.Each question has FOUR options (A), (B), (C) and (D). ONLY ONE of these four options is the correctanswer. For each question, choose the option corresponding to the correct answer. Answer to each question will be evaluated according to the following marking scheme :

29 ND+4 1

2

27.83× 1019

NA

19

–34 8

16 20 18 16

3 2

LTS- 10/20 0999DJA111521001




5. In photoelectric effect work function of any metal is 2.5 eV. The most energetic emitted electron arestopped by potential of 1.5 Volt, then -

(A) Energy of incident photons is 4eV

(B) Energy of incident photons is 1eV

(C) Wavelength of emitted electron is 1nm

(D) Photocurrent increases with the application of photons of high frequency

6. Find the number of moles in 600 amu of C H O :

(A) (B)

(C) (D)

7. Which of the following is not correct about member of any homologous series :

(A) They can not be represent by same general formula

(B) They have similar physical properties

(C) They have similar chemical properties

(D) They differ by a –C H or its multiple

8. Select correct statement(s) :

(A) C H – has four alkyl groups (B) C H – has eight alkyl groups

(C) CH – has one alkyl groups (D) C H – has two alkyl groups


2 n m

600(24+ n+ 16m)

×600

(24+ n+ 16m)

1NA

× 1.67×600

(24+ n+ 16m)10−24 600×NA

(24+ n+ 16m)

2 5

4 9 5 11

3 3 7

0999DJA111521001 LTS- 11/20





In a H-like species there are two energy levels A and B above the ground state having principal quantumnumbers of n and n respectively. A sample of this H-like species has all atoms/ions in excited levels Aor B only and none in any other energy level. Energy of level B is greater than that of level A and a totalof 15 different lines are emitted from this sample on returning to ground state out of which 6 lines areemitted due to electronic transitions between the levels n and n only. Also energy difference betweenlevels n and n , En – En = 4.53 eV.

9. The correct option is -

(A) n = 2, n = 5 (B) n = 6, n = 3 (C) n = 5, n = 2 (D) n = 3, n = 6

10. Calculate minimum wavelength in the above transition -

(A) (B) (C) (D)


11. Heterocyclic compound is –

(A) I & II (B) II & III (C) III & IV (D) I, II, III & IV

12. Compound which is not amine –

(A) I (B) II (C) III (D) IV


1 2

1 2

2 1 2 1

2 1 2 1 2 1 2 1

43RH

98RH

90011RH

3635RH

LTS- 12/20 0999DJA111521001




1. 90 g of a silver coin was dissolved in strong nitric acid, and excess of sodium chloride solution wasadded. The silver chloride precipitate was dried and weighed 71.75 g. Calculate the percentage of silver inthe coin (Atomic mass of Ag = 108) Ag + 2HNO → AgNO + NO + H O AgNO + NaCl → AgCl + NaNO Fill your answer as sum of digits (excluding decimal places) till you get the single digit answer.

2. In collection of H-atoms, all electron jump from 5 excited state to ground level finally, without emittingany line in infrared region. Total number of possible different radiations are -

3. An unknown trivalent metal reacts with oxygen to form its oxide. If mass of the oxide formed is 25%more than the mass of metal taken then calculate atomic wt. of the metal. (Multiply your answer by 1000 then sum digits of your multiplied answer till you get single digit answer)

4. Out of the following compounds how many can react with NaHCO :

5. Number of compounds having no any carboxyl (COOH) group. (i) Citric acid (ii) Salicylic acid (iii) Barbituric acid (iv) Carbolic acid (v) Ascorbic acid (vi) Nitrolic acid (vii) Picric acid (viii) Cinnamic acid (ix) Aspirin (x) Benzene sulphonic acid

6. Degree of unsaturation of following compound is :


3 3 2 2

3 3

th

3

0999DJA111521001 LTS- 13/20




1. Match the column :

Column-I Column-II

(A) N (P) 40% carbon by mass

(B) CO (Q) Empirical formula CH O

(C) C H O (R) Vapour density = 14

(D) CH COOH (S)14N electrons in a mole (N =Avogadro no.)

(T) 25 % carbon by mole

2. Column-I Column-II

(A) Isobutane (P) Contains 1º carbon atoms

(B) Neohexane (Q) Contains 2º carbon atoms

(C) Isooctane (R) Contains 3º carbon atoms

(D) Isodecane (S) Contains 4º carbon atoms

(T)Parent carbon chain contains odd number ofcarbon atoms in IUPAC


2

2

6 12 6

3A A

LTS- 14/20 0999DJA111521001


PART-3 : MATHEMATICS



1. Number of values of satisfying the matrix equation

is -

(A) 2 (B) 3 (C) 4 (D) 6

2. If a = b, b = c, c = d, d = e then pqrs is equal to (a, b, c, d, e > 0 and a, b, c, d, e ≠ 1) -

(A) (log a) (B) (log e) (C) log a (D) log e

3. If &

, then value of P + Q is -

(A) 0 (B) 1 (C) 2 (D) 3

4. Let A be a 3 × 3 matrix such that a = a = 2 & all the other a = 1. Let A = xA + yA + zI, then thevalue of (x + y + z) where I is a unit matrix of order 3, is-

(A) 0 (B) 1 (C) 2 (D) 3

This section contains FOUR (04) questions.Each question has FOUR options (A), (B), (C) and (D). ONLY ONE of these four options is the correctanswer. For each question, choose the option corresponding to the correct answer. Answer to each question will be evaluated according to the following marking scheme :

θ ∈ [0, 2π]

[ ] [ ] =cos θ

sin θ

sin θ

− cos θ

cos 2θ

− sin 2θ

0

1

⎡

⎣⎢⎢

12

−3√2

sin θ

− cos θ

⎤

⎦⎥⎥

p q r s

e2

a2

e a

P = cosec + cosec + cosec + cosec + cosec + cosecπ8

2π8

3π

8

13π

8

14π

8

15π

8

Q = 8 sin sin sinπ18

5π18

7π18

11 33 ij–1 2

0999DJA111521001 LTS- 15/20




5. Which of the following determinant(s) reduces to zero-

(A) (B)

(C) (D)

6. If matrix A = , then choose correct option(s), (here det(X) denotes determinant of matrix X)

(A) A is a triangular matrix (B) det(A – I) = 0

(C) (D)

7. Let and , , and

, then which is/are always true-

(A) I > I (B) I > I (C) I > I (D) I > I

8. If tan12° tan24° tan48° = ktanx°, where k ∈ I and x ∈ (0, 180), then which of the following can be true -

(A) k = 1, x = 6 (B) k = 1, x = 174

(C) k = –1, x = 6 (D) k = –1, x = 174


∣

∣

∣∣∣∣

1

1

1

a

b

c

− bca2

− cab2

− abc2

∣

∣

∣∣∣∣

∣

∣

∣∣∣∣

1

51

201

2

52

202

3

53

203

∣

∣

∣∣∣∣

∣

∣

∣∣∣∣

0

b− a

c− b

a− b

0

a− c

b− c

c− a

0

∣

∣

∣∣∣∣

∣

∣

∣∣∣∣

a

p

u

λa+ μb

λp+ μq

λu+ μω

b

q

ω

∣

∣

∣∣∣∣

⎡

⎣

⎢⎢⎢⎢

1

1

0

0

0

1

0

1

0

⎤

⎦

⎥⎥⎥⎥

2 10

=A20

⎡

⎣

⎢⎢⎢⎢

1

10

10

0

1

0

0

0

1

⎤

⎦

⎥⎥⎥⎥=A8

⎡

⎣

⎢⎢⎢⎢

1

8

8

0

1

0

0

0

1

⎤

⎦

⎥⎥⎥⎥

θ ∈ (0, )π6 = sin( )I 1 (tan θ) cotθ = sin( )I 2 (sin θ) cotθ = tan( )I 3 (tan θ) cotθ

= tan( )I 4 (sin θ) cotθ

1 2 4 3 3 1 3 2

LTS- 16/20 0999DJA111521001





A Pythagorean triple is a triplet of positive integers (a,b,c) such that a + b = c . Define the matrices A,B

and C by & .

On the basis of above information, answer the following questions :

9. T (A + B + 3C) equals - (where T (A) denotes trace of matrix A)

(A) 17 (B) 18 (C) 20 (D) 21

10. If Pythagorean triple (a,b,c) is written as row matrix [a b c] then which of the following matrix a productis not a Pythagorean triplet ?

(A) [3 4 5]A (B) [3 4 5]B (C) [3 4 5]C (D) None of these


Given p,q ∈ {0,1,2,3,......19,20}. Consider the system of equation x + y + z = 4 2x + y + 3z = 6 x + 2y + pz = q

11. Number of ordered pairs (p,q) so that the system of equation has unique solution-

(A) 20 (B) 21 (C) 420 (D) 1

12. Number of ordered pairs (p,q) so that the system has either no solution or an infinite number of solutions-

(A) 21 (B) 1 (C) 20 (D) 420


2 2 2

A =

⎡

⎣

⎢⎢⎢⎢

1

2

2

2

1

2

3

2

3

⎤

⎦

⎥⎥⎥⎥B =

⎡

⎣

⎢⎢⎢⎢

1

−2

2

2

−1

2

2

−2

3

⎤

⎦

⎥⎥⎥⎥C =

⎡

⎣

⎢⎢⎢⎢

−1

2

2

−2

1

2

−2

2

3

⎤

⎦

⎥⎥⎥⎥

rT

r

0999DJA111521001 LTS- 17/20




1. If sin θ + sin α = 2sinθ + 2sinα where θ, α ∈ [0, π], then number of possible values of θ + α is equal to

2. If x, y & z are different even integers and minimum value of

is N, then is

3. If , then absolute value of sum of elements of adj A is

(where adj(X) denotes adjoint of matrix X)

4. If and

, then is

5. The complete set of values of 'x' satisfying the inequality is (0, a) ∪ (a, b), then the

value of (a + b) is

6. Let and Z = Y X Y. If where M = [m ] is a 2 ×

2 matrix, then sum of digits of λ where , is


2 2

∣

∣

∣∣∣∣

1+ +x2 x4

1+ xy + x2y2

1+ xz+ x2z2

1+ xy + x2y2

1+ +y2 y4

1+ yz+ y2z2

1+ xz+ x2z2

1+ yz+ y2z2

1+ +z2 z4

∣

∣

∣∣∣∣

N32

A. adj ( ) =A2

⎡

⎣

⎢⎢⎢⎢

1

2

1

0

1

0

2

0

1

⎤

⎦

⎥⎥⎥⎥

A =21. 52. 51. 18log18 log23 log21 log52

51. 11log11 log23

B = ( ) + ( ) + ( ) + ( ) + ( )log9 tan 226∘ log9 tan 228∘ log9 tan 260∘ log9 tan 262∘ log9 tan 264∘ AB

|3x− 2| > −1log1/2

X = [ ] ,Y =3

3

0

3

⎡

⎣

⎢⎢⎢

78

−−√

−12 2√

12 2√

78

−−√

⎤

⎦

⎥⎥⎥T M = Y Z 2015 Y T

ij

λ =− −m21 m11 m22

32015

LTS- 18/20 0999DJA111521001




1. Column-I Column-II

(A) Value of (cos24°cos36°cos84°) is (a & b are

coprime numbers), then the value of (a + b) is(P) 12

(B)Value of is , (a & b

are coprime numbers), then the value of (a + b) is(Q) 13

(C)

Let , if then the maximum value

of sinα + sinβ is , (a & b are coprime numbers), then

the value of (2a + b) is

(R) 17

(D)Value of is (a & b are

coprime numbers), then the value of (2a + 3b) is (S) 18

(T) 21


− 1a−−√

b

cos cos cos cos∣∣∣

2π17

4π17

8π17

16π17

∣∣∣

ab

α+ β = , α, β ∈ (0, )π5

π2

− 1a−−√

b

(cot + cot − tan )π12

π8

π8 (a+ )b√

0999DJA111521001 LTS- 19/20


2. Consider a system of linear equations a x + b y + c z = d (where a ,b ,c ≠ 0 and i = 1,2,3 ) & (α,β,γ) is itsunique solution, then match the following conditions.

Column-I Column-II

(A) If a = k, d = k , (k ≠ 0) and α + β + γ = 2, then k is (P) 1

(B) If a = d = k ≠ 0, then α + β + γ is (Q) 2

(C) If a = k > 0, d = k + 1, then α + β + γ can be (R) 0

(D) If a = k < 0, d = k + 1, then α + β + γ can be (S) 3

(T) –1

i i i i i i i

i i2

i i

i i

i i

LTS- 20/20 0999DJA111521001


Space for Rough Work

0999DJA111521001 LTS- 21/20

(0999DJA111521001) )) T Pattern DISTANCE LEARNING ...

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