jee advanced gta-15 total syllabus...sri chaitanya iit academy 2 3 -0 519 _icon all ph iii_jee...

Sri Chaitanya IIT Academy., India A.P, TELANGANA, KARNATAKA, TAMILNADU, MAHARASHTRA, DELHI, RANCHI

A right Choice for the Real Aspirant ICON CENTRAL OFFICE, MADHAPUR - HYD

Sec: Sr. ICON ALL Date: 23-05-19 Time: 09:00 AM to 12:00 Noon Max.Marks:264 Name of the Student: ___________________ I.D. NO:

2015_PAPER-I

Jee Advanced_GTA-15

TOTAL SYLLABUS

Sri Chaitanya IIT Academy 23-05-19_ICON ALL_Ph-III_JEE-Adv_2015-P1_GTA-15_Q'P

Sec: Sr. ICON ALL space for rough work

JEE-ADVANCE-2015-P1-Model Time: 3:00 Hours IMPORTANT INSTRUCTIONS Max Marks: 264 PHYSICS: Section Question Type +Ve

Marks - Ve

Marks No.of

Qs Total marks

Sec – I(Q.N : 1 – 8) Questions with Integer Answer Type 4 0 8 32

Sec – II(Q.N : 9 – 18) Questions with Multiple Correct Choice 4 -2 10 40

Sec – III(Q.N : 19 – 20) Matrix Matching (+2/-1 for every match) 8 -4 2 16

Total 20 88 CHEMISTRY: Section Question Type +Ve

Marks - Ve

Marks No.of

Qs Total marks




Total 20 88 MATHEMATICS: Section Question Type +Ve

Marks - Ve

Marks No.of

Qs Total marks




Total 20 88



PHYSICS Max Marks: 88 SECTION – I

(SINGLE INTEGER ANSWER TYPE) This section contains 8 questions. The answer is a single digit integer ranging from 0 to 9 (both inclusive). Marking scheme +4 for correct answer, 0 if not attempted and 0 in all other cases. 1. Two point sound sources 1S and 2S emitting sound of wavelength λ are kept

separated by a distance 7λ2

as shown. A detector is moved along the line shown. Find

the number of minimas observed by the detector. (Assume λD )

2. Figure shows a ring of radius 2m and a rod of length l . The rod is moving with

velocity 4m/s perpendicular to its length. Find the angular speed (in rad/s) of point of intersection ' ' . . .A w r t O at the instant when 0θ 30 .



3. Consider the arrangement shown in the figure. The mass 2m is 12 kg . Friction coefficient between 2m and ground is 0.25. All other contact surfaces are frictionless. Find the maximum value of 1m in kg for which the system remains in equilibrium.

4. In the arrangement shown the block of mass 8M kg can slide freely on the

horizontal rail. A simple pendulum of length 5L m having a bob of mass

2m kg is suspended from the load. Taking 2π ,g find the time period (in s) of

small oscillations of the pendulum if it is displaced slightly in the plane of paper.



5. A monoatomic gas initially in state 0 0,A P V is taken through a cyclic process ABCA

as shown in the figure. The pressure of point B is twice of that of A. the curve BC is a

rectangular hyperbola. If the net work done by the gas is 0 0xPV , then find the value of

x .

6. A current carrying ring has moment of inertia 2400 10 kg about an axis passing through it centre and perpendicular to its plane. The centre of the ring is at origin. The ring has magnetic moment 2ˆ ˆ3 4M i j A m

. A magnetic field ˆ ˆ3 4B i jT

is

switched on at 0t . The angular velocity of ring (rad/second) is

7. A series L C R circuit with 120R has an angular frequency 5 14 10 rad s . At

resonance, voltages across resistance and inductor are 60 V and 40 V respectively. If

frequency at which the circuit current lags behind the voltage by a phase of 4 radian

is 5 110k rad s , then find the value of k .



8. An 80.0 kg hiker is trapped on a mountain ledge following a storm. A helicopter rescues the hiker by hovering above him and lowering a cable to him. The mass of the cable is 8.00 kg, and its length is 15.0 m. A sling of mass 70.0 kg is attached to the end of the cable. The hiker attaches himself to the sling, and the helicopter then accelerates upward. Terrified by hanging from the cable in midair, the hiker tries to signal the pilot by sending transverse pulses up the cable. A pulse takes 0.250 s to travel the length of the cable. What is the acceleration of the helicopter (in 2m / s )?

SECTION – II (ONE OR MORE CORRECT ANSWER TYPE)

This section contains 10 multiple choice questions. Each question has 4 options (A), (B), (C) and (D) for its answer, out of which ONE OR MORE than ONE option can be correct. Marking scheme: +4 for correct answer, 0 if not attempted and -2 in all other cases. 9. Consider the figure shown. A fish is moving up towards the surface of the lake with

speed v . A bird is diving towards the lake surface to catch the upcoming fish with

speed u . Refractive index of water µ . Choose the correct alternatives



A) Speed of the bird as observed by the fish is µ.u v

B) Speed of the fish as observed by the bird is µv u

C) Speed of the bird as observed by the fish may be equal to the actual speed (w.r.t.

ground) of the bird

D) Speed of the fish as observed by the bird may be equal to the actual speed (w.r.t.

ground) of the fish

10. The radius of the orbit of an electron in a Hydrogen – link atom is 04.5a , where 0a is

the Bohr radius. Its orbital angular momentum is 32π

h . It is given that h is Plank

constant and R is Rydberg constant. The possible wavelength(s), when the atom de –

excites, is (are)

A) 932R

B) 916R

C) 95R

D) 43R

11. A thin glass plate of thickness λ ,λ3

t being the wavelength of incident light and

refractive index µ 1.5 is placed in front of lower slit between the lower slit and the



screen in Young’s double slit experiment. If the intensity at a point on the screen

equidistant from the slits is found to be ,I then

A) Intensity at the same point before introduction of glass plate was 32I

B) Intensity at the same point before introduction of glass plate was 43I

C) Central maximum will be in the lower half of screen after introduction of glass

plate

D) Fringe width remains unchanged on introduction of glass plate

12. Equal masses of three different liquids A, B and C are taken at 0 010 , 15C C and 020 C

respectively. The steady state temperature when A and B are mixed, is 013 C and when

B and C are mixed, is 016 C . Which of the following statements is/are correct?

A) Ratio of specific heats of A and B is 23

B) Ratio of specific heats of A and C is 83

C) When A and C are mixed, temperature of mixture is 014011

C

D) When all of three ,A B and C are mixed, temperature of mixture is 015 C



13. A bead is connected with a fixed disc of radius R by an inextensible massless string in

a smooth horizontal plane. If the bead is pushed with a velocity 0V perpendicular to

the string, the bead moves in a curve and consequently collapses on the disc. Then

0V

A) Initial angular acceleration of the particle is 2

02

V

B) Initial angular acceleration of the particle is 2

03

V R

C) Distance travelled by the particle till it collides with the disc is 2

2R

D) Distance travelled by the particle till it collides with the disc is 2

R

14. The given two fixed rings of radius R lie in X Y plane as shown in the figure. Linear

charge density of the rings A and B varies as per the relation 0 sin and

0 cos respectively where is measured from x axis. Distance between the

centre of the two rings is r R .



y

A B

0,0 ,0rx

A) Force of interaction between the two rings is 42

0

0

34

Rr

B) Force of interaction between the two rings is 42

0

0

32

Rr

C) Potential energy of interaction between the two rings is 2 40

304Rr

D) Potential energy of interaction between the two rings is zero

15. An asteroid orbiting around a planet in circular orbit suddenly exploded into two

fragments in mass ratio 1:4. If immediately after the explosion, the smaller fragment

starts orbiting the planet in reverse direction in the same orbit, what will happen to the

heavier fragment?

A) Falls on the planet

B) Starts orbiting the planet in a larger orbit C) Starts orbiting the planet in a small orbit D) It escapes from the gravitational interaction with the planet



16. Consider the circuit shown in figure. The switch S is closed for 0t , and steady –

state conditions are established. The switch is then opened at 0t . Then choose the

correct option(s) for the instant immediately after 0t

5 2R R

2R R1R R

1L

3 2R R

S2L

4 2R RV

A) Current through 4R is 8VR

B) Current through 5R is 8VR

C) Potential difference across 2L is V D) Potential difference across 1L is 32V

17 Consider a planet of mass M and radius R as shown in the figure. A particle is

projected from the surface of the planet at an angle from radial direction and with

velocity equal to the orbital velocity of circular orbit at that point then choose the

correct statements. (Neglect atmosphere)



0V

P

M R

A) Maximum distance of particle from centre of the planet is cosR R

B) Path of the particle is ellipse

C) Time taken by the particle to return to the surface of planet is 3R

GM

D) Time taken by the particle to reach the surface of planet is equal to 3R

GM

18. A semicircular glass tube filled with water containing an air bubble is sealed at its

ends. If the tube is held with its plane vertical and made to move in its plane with a

constant acceleration in horizontal direction, the bubble stays aside of the highest point

as shown in the figure. What can you conclude about acceleration vector of the tube?



A) It points towards the left B) It points towards the right C) Its magnitude is tang D) Its magnitude is cotg

SECTION - III (MATRIX MATCHING ANSWER TYPE)

This section contains 2 questions. Each question has four statements (A, B, C and D) given in Column I and four statements (P, Q, R and S) in Column II. Any given statement in Column I can have correct matching with ONE or MORE statement(s) given in Column II. For example, if for a given question, statement B matches with the statements given in Q and R, then for the particular question darken the bubbles corresponding to Q and R in the OMR sheet. For each correct matching will be awarded +2 marks ONLY and 0 if not attempted and -1 in all other cases.

19. Consider a rectangular slab, whose refractive index varies as 1 ,ya

where 11a m



Match the Colum I with Column II and mark the correct option from the codes given below.

Column-I Column-II A) The equivalent refractive index of slab

for normal incidence P) 95 10

B) The apparent depth point O (in m) in normal view

Q) 0.693

C) The optical path of a ray along OA R) 1.5

D) The time (in second) taken by light ray to go vertically from point O to point A

S) 1.44

20. Apply Kirchhoff’s laws to the given below:

Given, 2 2

1 210 , 4 , 3t tCi e A i A V e V (Potential drop across capacitor)

1 22 , 4 , 2 , 3C F L H R R

Now, match the following columns and select the correct option from the codes given below:



Column-I Column-II A) Current through inductor p)

B) Potential drop across inductor q)

C) Potential difference between points a

and c a cV V

r)

D) Potential difference between point a and

b s)

t)



CHEMISTRY Max Marks: 88 SECTION – I

(SINGLE INTEGER ANSWER TYPE) This section contains 8 questions. The answer is a single digit integer ranging from 0 to 9 (both inclusive). Marking scheme +4 for correct answer, 0 if not attempted and 0 in all other cases. 21. How many stereoisomers are possible for the following molecule?

H

3H C

CHCH CHCOOH

22. How many resonance structures can be drawn for the following molecule (including

the given)?

2H N

23. No. of electrons involved in reduction of one nitric acid molecule during reduction of

very dilute nitric acid to ammonium nitrate with zinc is……..

24. How many of the following species are paramagnetic

3 322

3 4 3 346 4 6, , , , , ,NO Cr NH Ni CO CuCl Cu NH Co NH

2ClO 4

2 26 5, , , ,Fe CN Fe CO KO NO

25. Total number of covalent bonds in 3 2C O is…….



26. The de Broglie wave length of an electron in a certain orbit of hydrogen atom is 013.3A . So the number of waves present in an orbit is_______

27. The combustion of 10 g coke raised the temperature of 1.0 kg water from 010 C to 050 C . Calculate the calorific value of coke. (Specific Heat of 2 1 /H O cal g ).

28. What weight of glucose . . 180mol wt would have to be added to 1700 g of water at

020 C to lower its vapour pressure 0.001 mm? The vapour pressure of pure water is

17 mm Hg at 020 C .


This section contains 10 multiple choice questions. Each question has 4 options (A), (B), (C) and (D) for its answer, out of which ONE OR MORE than ONE option can be correct. Marking scheme: +4 for correct answer, 0 if not attempted and -2 in all other cases. 29. Which of the following is/are optically active?

A)

HOOC

H

COOH

H B) HOOC

H

COOH

H



C)

HOOC

H

COOH

H D) HOOC

H

COOH

H

30. Identify the principal product of the following reaction?

2CH CH O

2CH CH O

2, , ?NaOHethanol water heat H O

A) CH O

CH O

B)

CH O

C)

OH

OH D) O

O



31. Which reaction will occur at the fastest rate?

A)

HBr

Br

B)

HBr

Br

C)

HBr

Br

D)

HBr Br

32. Which of the following exhibit mutarotation? A) Glucose B) Maltose C) Fructose D) Galactose 33. Which of the following reagents are correct for the given reaction?

2NO 2NO

2NH

Reagents

A) 0

2 3 2. ,0 5 .i NaNO HCl C ii H PO

B) 02 2 4 2. ,0 5 . ,i NaNO H SO C ii NaNO Cu

C) 2 2 5. .i HNO ii C H OH and heat

D) 2 2. .i KNO HCl ii H O (steam)



34. Which of the following mixture/solution will show pH approximately equal to 9?

A) 100 mL of 3 33 10 100 4.24 10M HCl mL of M NaCN

B) 34100 0.01 100 2 10mL of M NH OH mL of M NaOH

C) 0.2 M sodium butyrate; aK for butyric acid is 52.0 10

D) 625 10 M Ca OH solution

35. If radius of anion is 0.20 nm, the maximum radius of cations which can be filled in respective voids are correctly matched in:

A) 0.045r nm triangular void

B) 0.0828r nm for tetrahedral void

C) 0.1464r nm for octahedral voids

D) 0.1444r nm for tetrahedral void 36. Find out the false statements among the given below

A) 3

4Cu CN

has tetrahedral geometry and 2dsp hybridization

B) 4

6Ni CN

is octahedral and Ni has 2 3d sp hybridization

C) 24ZnBr is tetrahedral and diamagnetic

D) 3

3 6Cr NH

has octahedral geometry and 3 2sp d hybridization



37. Which of the following ores can be concentrated by froth floatation process? A) Zinc blend B) Copper pyrites C) Argentite D) Horn silver 38. Which of the following statement(s) is/are correct? A) 2 2Be C H O Marsh gas

B) 4 3 2Al C H O gas is a content of CNG

C) 2 2CaC H O gas used for welding purpose with 2O gas

D) 3 2 2Ca P H O gas used in Holme’s signals with 2CaC SECTION - III

(MATRIX MATCHING ANSWER TYPE) This section contains 2 questions. Each question has four statements (A, B, C and D) given in Column I and four statements (P, Q, R and S) in Column II. Any given statement in Column I can have correct matching with ONE or MORE statement(s) given in Column II. For example, if for a given question, statement B matches with the statements given in Q and R, then for the particular question darken the bubbles corresponding to Q and R in the OMR sheet. For each correct matching will be awarded +2 marks ONLY and 0 if not attempted and -1 in all other cases.

39. Match the following Column – I with Column – II

Column-I (Metal)

Column-II (process involved in commercial extraction from their ore)

A) Pb P) Bessemerization

B) Cu Q) Roasting

C) Zn R) Pyrometallurgy

D) Fe (steel from pig iron) S) Self – reduction method



40. Match the following (Symbols have their usual notation) Column-I Column-II

A) ΔG P) Δ ΔU PV

B) ΔH Q) nFE

C) ΔS for isothermal expansion of n moles of ideal gas R) lnRT K

D) 0ΔG S) 2 1ln /nR V V



MATHS Max Marks: 88 SECTION – I

(SINGLE INTEGER ANSWER TYPE) This section contains 8 questions. The answer is a single digit integer ranging from 0 to 9 (both inclusive). Marking scheme +4 for correct answer, 0 if not attempted and 0 in all other cases. 41. Let 1 2 3 4, , ,n n n n

be the vectors whose magnitudes are respectively equal to areas of faces

1F , 2F , 3F , 4F of a tetrahedron and whose directions are perpendicular to these faces in

outward direction then 1 2 3 4n n n n

=

42. If 6 5 3 2P x x x x x x and , , , are the roots the equation

4 3 2 1 0Q x x x x , then P P P P

43. If :f R R be a differentiable function, such that

2 2 4 , ,f x y f x f y xy x y R then ' 1 ' 0f f

44. Let sin sin sin sin f x x x x x x x x x x , (where [.] denotes largest

integer function). Then the number of points of discontinuity in 0,

45. The sum of 25 terms of an A.P., whose all the terms are natural numbers, lies between

1900 and 2000 and its 9th term is 55. Then the first term of the A.P is



46. There are 6 red balls and 6 green balls in a bag. Five balls are drawn out at random

and placed in a red box. The remaining seven balls are put in a green box. If the

probability that the number of red balls in the green box plus the number of green balls

in the red box is not a prime number, is pq

where p and q are relatively prime, then

find the value of 13

p q

where . represents greatest integer function.

47. A cricket team consists of 10 pairs of twin brothers. On the first day of training, all 20

players stand in a circle in such a way that all pairs of twin brothers are neighbours.

Number of ways this can be done is 1! 2kk , then k equals =

48. If 0 0

2 2 4 4 3 31 3 4 1 0 1

1 2 3 4 4 3A and B

, n N and I is an identity matrix of

order 3, then 2 2 3 4 40 0 0 0 0 0det 10A A B A A B terms is equal to




This section contains 10 multiple choice questions. Each question has 4 options (A), (B), (C) and (D) for its answer, out of which ONE OR MORE than ONE option can be correct. Marking scheme: +4 for correct answer, 0 if not attempted and -2 in all other cases.

49. If 222 2 2

x y z zy x z zy y z x y z

then which of the following is/are correct?

A) x y is a factor of B) 2x y is a factor of

C) 3x y is a factor of D) is independent of z

50. There are n seats round a table marked 1, 2, 3,………n. The number of ways in which

m n persons can take seats is

A) mpn B) 1 !mcn m C) !mcn m D)

11 mpn

51. The equation sin 1 sin 1 cosx x x has (where [x] is the greatest integer x)

A) no solution in ,2 2

B) no solution in ,2

C) no solution in 3,2

D) no solution for x R



52. If f(m) =0

30 2030

m

i i m i

where pq

=qCp , then which of the following is/are

correct? 0,ifp p qq

A) Maximum value of f m 2550C

B) 500 1 ... 50 2f f f

C) f m is always divisible by 50 1 49m

D) The value of 50

50 2

0100C

mf m

53. The curve 3 2y ax bx cx is inclined at 045 to x-axis at (0,0)but it touches x-axis at (1,0) then which of the following is/are correct?

A) ' 1 0f B) '' 1 2f C) ''' 2 12f D) 2 2f

54. If 2

, 01 , 0 1

, 1

x

x

x

e k xf x e x

e x

is one-one and monotonically increasing x R ,

then A) Maximum value of k is 1 B) maximum value of k is 3

C) Minimum value of is 0 D) minimum value of is 1



55. If a circle passes through the point 73,2

and touches 1x y and 1x y , then the

centre of the Circle is at :

A) (4, 0) B) (4, 2) C) (6, 0) D) (7, 0)

56. The values of ‘x’ satisfying the equation 1 1sin sin sin sinx x is/are given by

(n is any integer).

A) 1n B) n C) 1n D) 2 1n

57. For a R (the set of all real numbers), a 1,

a a a

a 1n

1 2 n 1l t60n 1 na 1 na 2 na 3 ....... na n

then a =

A) 5 B) 7 C) 152

D) 172

58. If 2

0

,2

xe dx then

A) 22

0 2xe dx

B) 2

0

12

xxe dx

C) 22

0 4xx e dx

D) 22

0 4xx e dx



SECTION - III (MATRIX MATCHING ANSWER TYPE)

This section contains 2 questions. Each question has four statements (A, B, C and D) given in Column I and four statements (P, Q, R and S) in Column II. Any given statement in Column I can have correct matching with ONE or MORE statement(s) given in Column II. For example, if for a given question, statement B matches with the statements given in Q and R, then for the particular question darken the bubbles corresponding to Q and R in the OMR sheet. For each correct matching will be awarded +2 marks ONLY and 0 if not attempted and -1 in all other cases. 59. Match column I with column II:

Column-I Column-II

A) If the binomial coefficients of the thr , 1 thr and

2 thr terms in the expansion of 141 x are in A.P., then r can be equal to

P) 5

B)

The sum of the coefficients in the polynomial expansion of

12 3 41 ... 1 , ,

mnx x x x x x n m N

is

Q) 4

C)

Sum of the series

12

11 . 1 ....

nr n rn r r

rr

C i i i

where

4 ,n k k I is equal to (where 1i )

R) 0

D) If 373 80 ,k N ,then k is S) 3



60. Match the following

Column-I Column-II A) Locus of point of intersection of

perpendicular tangents one each to 2 24 , 8 2y a x a y a x a is

P) x a

B) If the chord of contact of P w.r.t. 2 4 0y ax subtends a right angle at its

vertex, then P lies on

Q) 4x a

C) Common normal to 2 4y ax and 2 4x ay is

R) 3 0x a

D) If tangents from P to the parabola 2 4y ax intersect coordinate axes in

concyclic points, then P lies on

S) 3x y a

jee advanced gta-15 total syllabus...sri chaitanya iit academy 2 3 -0 519 _icon all ph iii_jee...

Documents