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INSTRUCTIONS A. General:

1. This booklet is your Question paper. Do not open the booklet before being instructed to do so by the invigilators.

2. Blank spaces and blank pages are provided in this booklet for your rough work. No additional sheets will be provided for rough work.

3 Blank papers, clipboards, log tables, slide rules, calculators, cameras, cellular phones, pagers, and electronic gadgets are NOT allowed inside the examination hall.

4. Use a black ball point pen; darken the bubbles on the OMR sheet. B. Question paper format and Marking scheme:

(i) Part–A (01 – 10) contains 10 multiple choice questions which have only one option is correct. Each question carries +3 marks for correct answer and –1 mark for wrong answer.

(ii) Part–A (11 – 16) contains 3 Paragraph. Each Paragraph contains 2 questions which have

one or more than one correct answer. Each question carries +4 marks for all correct answer and 0 mark for all other cases.

(iii) Part–A (17 – 20) contains 4 questions. Each question has matching lists. The codes for the lists have choices (A), (B), (C) and (D) out of which ONLY ONE is correct. +3 marks will be awarded for correct answer and 0 mark for all other cases.

FFIIIITTJJEEEE JJEEEE AADDVVAANNCCEEDD FFUULLLL TTEESSTT

Full Test–1

(Paper–2)

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Please read the instructions carefully. You are allotted 5 minutes specifically for this purpose.

Name of the Candidate ……………………………………………………………………………..

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Enrolment No. ………………………………………………………………………………………

2 JEE Advanced Full Test–1_Paper–2_ 12/04/2018

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PHYSICS

PART–A

SECTION–1

Multiple Choice Questions This Section contains 10 Multiple Choice Questions out of which only one option is correct.

1. Choose the correct ray diagram of an equi convex thin lens which is cut as shown (paraxial condition

satisfied)

(A) (B)

(C) (D)

2. The net electric field E due to the uniformly charged rod at P makes angles 1 and 2 with AP and BP

respectively. Then 1/2.

(A) = 1 (B) > 1 (C) < 1 (D) AP

PB

3. A magnetic field, confined in a cylindrical region of radius R, is changing at the rate of 4 T/s. A

conducting rod PQ of length 3

R2

is placed in the region as shown. The induced emf across the rod

will be :–

(A) 2R

6 Volt24

(B) 2R Volt (C) 2R

Volt6

(D)

2R6 Volt

6

Space for rough work



4. Three immiscible liquids are filled in a container as shown. The base area of the container is A and coefficient of cubical

expansion of the material of the container is 3

2

while the

coefficient of cubical expansion of the liquids are shown in the

figure. The temperature of the system is increased by T. The volume of the liquid flown out of the container is

(A) Al T

3

(B) Al T

(C) 2Al T

3

(D)

Al T

2

5. At t = 0, switch is closed to position 1. Capacitor is initially uncharged. At t2

, switch is shifted to

position 2. Then current as a function of time t is ( is the angular frequency = 1

LC)

(A) CV0cos t (B) CV0(1–cos t) (C) CV0(1–sin t) (D) CV0 sin t 6. The graph shows how the magnitude of magnification produced by a

thin plano–convex lens for a real image varies with image distance v. Which of the following is correct?

(A) focal length of lens is b/c. (B) if the refractive index of the lens material is μ. then the radius of

curved surface will be b

1a

.

(C) if the lens is placed in contact with another thin lens of focal length

2c

b, the focal length of combination will be

2c

3b .

(D) none of these




7. In a screw gauge, there are 100 divisions in circular scale and each main scale division is of 1 mm. When there is no gap between the jaws, 97

th division coincides with the main scale zero and zero of

main scale is not visible. While measuring the diameter of a ball, the circular scale is between 3 mm mark and 4 mm mark such that the 76th division of circular scale coincides with the reference line. Select the correct alternative

(A) the least count of the micrometer is 0.01cm (B) the zero error is –0.04 mm (C) the diameter of the ball is 3.79 mm (D) the main scale reading is 4 mm 8. The current i in an induction coil varies with time according to the graph shown in the figure. Which of

the following graphs shows the induced cmf (E) in the coil with time

(A) (B) (C) (D) 9. An artificial satellite of mass m is moving in a circular orbit at a height equal to the radius R of the earth.

Suddenly due to internal explosion the satellite breaks into two parts of equal masses. One part of the satellite stops just after the explosion and then falls to the surface of the earth. The increase in the mechanical energy of the system (satellite + earth) due to explosion will be (Given: acceleration due to gravity on the surface of earth is g)

(A) mgR (B) mgR

2 (C)

mgR

4 (D)

3mgR

4

10. Two soap bubbles of radius 3 cm and 4 cm coalesce to form a single bubble under isothermal

conditions. Then the radius of bigger bubble is (Taking surrounding pressure equal to zero) (A) 7 cm (B) 1 cm (C) 12cm (D) 5 cm




Paragraph Type Question This Section contains 3 paragraph consist of 2 questions each. Out of which only option is correct.

Paragraph for Question 11 and 12

A proton and a deutron are fired with same speed v into a large region having uniform magnetic field at

angle as shown in the figure. The proton and deutron spend time T1 and T2 inside magnetic field before coming out of the field.

11. When proton and deutron comes out of field, they will: (A) move on same line

(B) move on two different lines making angle between them (C) move on two parallel lines (D) come to rest.

12. The ratio 1

2

T

T is equal to :

(A) 2 (B) 4 (C) ½ (D) ¼





A light and thin rod of length l is lying on horizontal table. Two small balls of masses 3m and m are fixed

on two ends of a massless rod. The rod is free to rotate about fixed vertical axel passing through midpoint of rod. A third ball of mass 2m is fastened to ball of mass m through a string of length l as

shown in figure. The ball is projected horizontally with speed V as shown.

13. The angular velocity of rod, just after the string becomes taut is :–

(A) 18v

59 l (B)

9v

59 l (C)

59v

18 l (D)

3v

5 l

14. The impulse imparted by string is :–

(A) mv

10 (B)

5mv

59 (C)

59mv

50 (D)

60mv

59


A capacitor of capacitance 1 F and charge 10 C starts discharging through a resistance of 100 , at that instant a radio–active element has N0 undecayed nuclei. The ratio of number of undecayed nuclei and charge on capacitor remains equal to 100 nuclei per coulomb throughout time.

15. The half life of radio–active element is: (A) 138.6 sec (B) 6.93 sec (C) 1.386 sec (D) 69.3 sec. 16. The initial radioactivity of element is: (A) 100 decays/sec (B) 10 decays/sec (C) 1 decays/sec (D) 5 decays/sec




Matrix Match Type Questions

This Section contains 4 Matrix Match type Questions. Each question has matching lists. The codes for the lists have choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

17. A.C. circuits are shown in list–I and irms vs graph is shown in list–II match the corresponding graph.

List – I List – II

(P)

(1)

(Q)

(2)

(R)

(3)

(S)

(4)

Codes : P Q R S (A) 4 3 1 2 (B) 3 2 1 4 (C) 1 2 3 4 (D) 4 2 3 1




18. Match the acceleration of blocks A and B shown in List–II for the following cases shown in List–I (g = 10 m/s

2)


(P) μ1 = 0 and μ2 = 0.1 (1) aA = aB = 9.5 m/s2

(Q) μ2 = 0 and μ1 = 0.1 (2) aA = 9 m/s2 , aB = 10 m/s

2

(R) μ1 = 0.1 and μ2 = 1.0 (3) aA = aB = g = 10 m/s2

(S) μ1 = 1.0 and μ2 = 0.1 (4) aA = 1 m/s2, aB = 9 m/s

2

Codes : P Q R S (A) 4 1 2 3 (B) 2 3 4 1 (C) 1 2 3 4 (D) 3 2 1 4




19. In Young's double slit experiment set–up with light

of wavelength = 6000 Å, distance between the two slits is 2 mm and distance between the plane of slits and the screen is 2m. y1 = 0.075 mm, y2 = 0.15 mm, y3 = 0.2 mm and y4 = 0.36 mm. I0 is the intensity of light from each slit. Then match the intensity at different points.


(P) b (1) 2 I0

(Q) c (2) 0.38 I0

(R) d (3) 3.414 I0

(S) e (4) I0

Codes : P Q R S (A) 1 2 3 4 (B) 3 1 4 2 (C) 4 3 2 1 (D) 3 1 2 4

20. A particle of mass m is projected with velocity v and at an angle with horizontal then match the following list.


(P) Change in momentum between point of projection and point at

which it strikes on horizontal surface (1) mv cos

(Q) Radius of curvature at highest point (2) 2mv sin

(R) Minimum momentum is (3) mv sin

(S) Magnitude of change in momentum between point of projection

and highest point (4)

2 2v cos

g

Codes : P Q R S (A) 3 1 4 2 (B) 2 4 3 1 (C) 2 4 1 3 (D) 4 2 1 3




CHEMISTRY

PART–A

SECTION–1


1. Which of the following is INCORRECT for first order reaction ? (A) On introducing catalyst both rate constant and rate of reaction increases. (B) On increasing temperature both rate constant & rate of reaction increases. (C) On decreasing volume both rate constant & rate of gaseous reaction increases. (D) On increasing concentration of gaseous reactant at constant volume & constant temperature both

total pressure and rate of the reaction increases. 2. Electromagnetic radiation of 50Å when passed through Be

3+. de–broglie wavelength (in Å) of ejected

electron is (Take : hc = 1240 nm–eV) (A) 50 (B) 2.22 (C) 2.46 (D) 0.77 3. At 25ºC for cell : A(s) |A

2+(aq.) || B

3+(aq.) |B(s), Following observation is made :

Standard emf ( In volt) of the cell for discharging is–

(A) 0.4 volt (B) 1.6 volt (C) 2.4 0.059

6

volt (D) 2.4 volt

4. Na

+ ion can form complex with which of the following ligand.

(A) Cryptands (B) Crown ether (C) Both (A) and (B) (D) None 5. Which of the following reaction does not form nitrogen molecule. (A) Heating of ammonium dichromate (B) Ammonia reacts with bleaching powder (C) Ammonia reacts with excess of chlorine (D) Nitrogen monooxide reacts with red hot copper




6. Chromate changes its yellow colour into orange by the addition of (A) H2O (B) acid (C) alkali (D) All are correct 7. If nitrite ion is present in mixture then which of the following colour is observed by the sulphanilic acid–

1–naphthylamine reagent test. (A) Red (B) Black (C) Blue (D) Green 8. Which compound is suitable for 'P' in following reaction :

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

9. Which of the following will react fastest with Br2 water :

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

10. Product is :

(A) (B) CH3 – CH2 – COOH

(C) (D)




Paragraph Type Question This Section contains 3 paragraph consist of 2 questions each. Out of which only option is correct.


The concept of unit cell is extremely important in understanding the structure of crystalline solids. The unit cell is the smallest unit having all the characteristic properties of the entire crystal. The crystal can be built by the repeated translation of its unit cell in three dimension. In fcc unit cell in addition to 8 lattice point at the eight corners, there are six lattice point at the centres of the six–faces. In fcc there are two distinct type of holes.

11. Packing fraction in fcc arrangement is –

(A) /8 (B) /4 (C) 3

8

(D)

3 2

12. Number of next nearest neighbours of atom in the fcc is (A) 6 (B) 8 (C) 12 (D) 24

Paragraph for Question 13 and 14 Isomerism is commonly considered, to be the characteristic of only organic compounds, but it is also

found although less frequently among inorganic substances (coordination compound). 13. The type of isomerism shown by [Fe(H2O)3Cl3] (A) Geometrical (B) Optical (C) Linkage (D) Hydrate 14. The number of stereoisomer form by [Co(en)2Cl2]

+.

(A) 2 (B) 3 (C) 4 (D) None of these





The reagent composed of HCl and ZnCl2 is called the Lucas reagent. Secondary and tertiary alcohols react with the Lucas reagent by the SN1 mechanism :

When a primary alcohol reacts with the Lucas reagent, ionization is not possible–the primary

carbocation is too unstable. Primary substrates react by an SN2 mechanism, which is slower than the SN1 reaction of secondary and tertiary substrates. For example, when 1–butanol reacts with the Lucas reagent, the chloride ion attacks the complex from the back, displacing the leaving group.

15. Which of the following alcohol react with ZnCl2 / HCl immediately :

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

16. Among the following compound which cannot react with ZnCl2 / HCl is :

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




Matrix Match Type Questions This Section contains 4 Matrix Match type Questions. Each question has matching lists. The codes for

the lists have choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

17.


(P) H2(g) 2H(g) (1) Hºatomisation

(Q) Br2(l) 2Br(g) (2) o

fH

(R) 2

1I (s) I(g)

2 (3) Bond dissociation enthalpy

(S) 2 2

1CO(g) O (g) CO (g)

2 (4)

o

combustionH

Codes : P Q R S (A) 3 1 2 4 (B) 2 3 1 4 (C) 1 2 3 4 (D) 4 3 2 1 18. Which of the following is correctly.

List – I (Metals) List – II (Biological components)

(P) Magnesium (1) Chlorophyll

(Q) Iron (2) Haemoglobin

(R) Cobalt (3) Vitamine B12

(S) Calcium (4) Bones

Codes : P Q R S (A) 1 2 3 4 (B) 1 2 4 3 (C) 2 1 4 3 (D) 2 4 3 1




19.

List – I (Reaction) List – II (Reagents)

(P)

(1) Br2 / CCl4

(Q)

(2) HBr / HOOH

(R)

(3) Br2 /

(S)

(4) H+ / KBr

Codes : P Q R S (A) 3 1 4 2 (B) 3 4 2 1 (C) 3 1 2 4 (D) 1 3 4 2 20.

List – I (Compound) List – II (Reagent for (+) ve test)

(P)

(1) NaOH / I2

(Q)

(2) Br2 / H2O

(R)

(3) Alc. AgNO3

(S)

(4) NaOH / CHCl3

Codes : P Q R S (A) 2 1 3 4 (B) 4 1 2 3 (C) 2 4 3 1 (D) 2 3 4 1




MATHEMATICS

PART-A

SECTION–1


1. An urn contain x red balls & y ( 4) black balls. If probability of getting two red balls in first two draws

(without replacement) is 1

2, then value of x will be equal to -

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

2. Choose correct option for function ƒ : R R, ƒ(x) = sec(tan-1

x) – sin(cot-1

x)

(A) function is neither even nor odd (B) range of function is [0, ) (C) function is many one onto (D) function is periodic 3. The diameter of smallest circle which touches the parabola y

2 = 4x & the circle x

2 + y

2 – 12x + 31 = 0

both is

(A) 1

52

(B) 1

53

(C) 5 (D) 2 5

4. Let A = 2 2

3 5

& B = 1 0

0 2

. If X be a matrix such that A = BX, then value of det(adj X) is equal to

(Here adj X and det X denotes adjoint of matrix X and determinant of matrix X respectively) (A) 16 (B) 8 (C) 4 (D) 2

5. Let ƒ(x) =

xsin , 0 x 2

4

3 x, 2 x 4

x 4 , 4 x 5

, where {.} denotes fractional part of x in the interval (0, 5). Choose the

correct option - (A) global maxima does not exist (B) global minima does not exist (C) global minimum value of function = –1 (D) jump of discontinuity at x = 4 is 2 6. In how many ways six '+' signs can be arranged in the 6 × 6 square matrix, if any row or columns does

not remains empty is - (A) 4(6!) (B) 5! (C) 6! (D) 5(5!)




7. If roots of the equation x3 + ax2 + bx – 1 = 0 form an increasing G.P., then choose the incorrect option

- (A) a + b = 0

(B) b can take any value from the set [3, ) (C) one root is smaller than one & other root is greater than one

(D) a (–, –3) 8. A dice is thrown six times, it is known that each time a different digit is shown. The probability that sum

of 11 will be obtained in the first three throws is -

(A) 5

24 (B)

1

36 (C)

3

20 (D)

1

12

9. If Tn is the numerically greatest term in the expansion of (2 – 3x)

11 for x = 1, then value of ƒ(n) = tan

-1

(cotn) will be equal to -

(A) 5

82

(B)

58

2

(C)

38

2

(D) 7 – 2

10. Let an invertible function ƒ(x) = 21 x , 0 x 1

x, 1 x 0

& g(x) is its inverse, then jump of discontinuity of g(x)

at x = 1 is -

(A) 3

2 (B) 2 (C) 1 (D) does not exist

Paragraph Type Question

This Section contains 3 paragraph consist of 2 questions each. Out of which only option is correct.


Let z1 & z2 are two complex numbers which lies on a conic 2|z – 1 – i| = |z + 1 + i|, (where i = 1 ) &

whose amplitudes are minimum & maximum respectively. On the basis of above information, answer the following questions: 11. The largest distance of conic from origin is -

(A) 2

3 (B) 3 2 (C)

42

3 (D) 2 2

12. The radius of circle which passes through origin, z1 & z2 is -

(A) 1

2 (B) 2 (C)

5

3 2 (D)

52

3





Let a circle S whose centre is (h, k), k > 0 touches pair of lines 4xy – 3y

2 + 12 – h = 0 at point A & B.

On the basis of above information, answer the following questions : 13. The centre of a circle which intersects the circle 'S' at point A & B orthogonally, is - (A) (2, 1) (B) (–2, –1) (C) (–4, –3) (D) (0, 0) 14. Area (in square unit) of triangle OAB is equal to -

(A) 288

5 (B)

48

5 (C)

864

25 (D)

144

5


Given two orthogonal unit vectors a &b . Let vector r satisfy the equation r b r a .

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

15. Value of r.b is equal to -

(A) a (B) 0 (C) b (D) r

16. r b b is equal to -

(A) a b a

2

(B)

a b a

2

(C) b a a (D)

b a a

2




Matrix Match Type Questions

This Section contains 4 Matrix Match type Questions. Each question has matching lists. The codes for the lists have choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

17. Match List-I with List-II and select the correct answer using the code given below the list.

List-I List-II

(P) The equation ||x – 2| – a| = 3 have exactly three distinct real solutions for x, then value of 'a' is equal to

(1) 1

(Q) The number of ordered pair(s) (k, x) satisfying the

equation cosec2((k + 3)x) + k

2 – 1 = 0 in the interval x

(0, ) is equal to (where k R)

(2) 2

(R)

The value of

r

nk 1

rn 3r 1

k 1

k

lim

k

is equal to

(3) 3

(S)

The value of 4

3

2 2 2 ....log

3 3 3.....

is equal to

(4) 4

Codes: P Q R S (A) 4 1 3 2 (B) 1 4 2 3 (C) 3 3 2 1 (D) 3 4 1 2 18. Match List-I with List-II and select the correct answer using the code given below the list.

List-I List-II

(P) Let ƒ(x) = |x + 1| + |1 – x| + |x – 4|. If maximum &

minimum value of ƒ(x) is M & m respectively for x [–1, 4], then value of (M – m) is equal to

(1) 7

(Q) If 1 1sin x sin y

2

, then value of

4 4

2 2 2 2

x y 1

x x y y

equal

to

(2) 3

(R) In a triangle ABC, if A-B = 120º & R = 8r, where R &

r have their usual meanings, then value of 8cosC is equal to

(3) 2

(S) Let ƒ : R [4, ) be onto function such that ƒ'(x) + ƒ'(2 – x) = 0 and ƒ(2) = 5. If ƒ(x) is a quadratic polynomial,

then value of

3

1

dx

f x

(4) 8

Codes: P Q R S (A) 3 2 4 1 (B) 2 3 1 4 (C) 2 3 3 1 (D) 3 1 2 4




19. An altitude BD & internal angle bisector BE are drawn in triangle ABC through vertex B. Angles BEC,

ABD, ABE & BAC are in A.P. (in decreasing order of magnitude). Match List-I with List-II and select the correct answer using the code given below the list.

List-I List-II

(P) BAC (1)

2

(Q) ABC (2)

3

(R) BCA (3)

12

(S) EBD (4)

6

Codes: P Q R S (A) 1 2 4 3 (B) 4 1 2 3 (C) 2 3 1 4 (D) 3 4 3 2 20. Match List-I with List-II and select the correct answer using the code given below the list.

List-I List-II

(P) If equation of plane containing lines

x 2 y 3 z 5

3 5 7

&

x 2 y 4 z 6

1 4 7

is x – ay +

bz + c = 0,

(1) 2

(Q) The sum of order & degree of the differential equation representing all parabolas whose axis is x-axis, is

(2) 3

(R) The area bounded by the curve [x] + [y] = 1, where x, y

0 & [.] denotes greatest integer function, is

(3) 6

(S) If value of expression

m

i 0

9 7

i m i

is maximum where

n

r

nC

r

then value of m is equal to

(4) 8

Codes: P Q R S (A) 3 4 2 1 (B) 4 2 3 1 (C) 1 3 4 2 (D) 3 2 1 4




FFIIIITTJJEEEE JJEEEE AADDVVAANNCCEEDD FFUULLLL TTEESSTT ANSWER KEY

Full Test–1

(Paper–2)

PHYSICS CHEMISTRY MATHEMATICS

PART–A PART–A PART–A

1. B 1. C 1. B

2. A 2. B 2. B

3. D 3. D 3. C

4. D 4. C 4. B

5. A 5. C 5. B

6. C 6. B 6. C

7. C 7. A 7. B

8. C 8. D 8. C

9. C 9. B 9. A

10. D 10. B 10. C

11. C 11. D 11. B

12. C 12. A 12. C

13. A 13. A 13. D

14. D 14. B 14. A

15. D 15. D 15. B

16. B 16. C 16. B

17. A 17. A 17. C

18. D 18. A 18. B

19. B 19. A 19. B

20. C 20. D 20. D



HINTS AND SOLUTION PHYSICS



CHEMISTRY



MATHEMATICS PART–A

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