FIITJEE Phase Test (JEE-Advanced) - fiitjeeranchi.com JEE... · PHYSICS, CHEMISTRY & MATHEMATICS Time Allotted: 3 Hours Maximum Marks: 183 Please read the instructions carefully

PHYSICS, CHEMISTRY & MATHEMATICS

Time Allotted: 3 Hours

Maximum Marks: 183

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

▪ You are not allowed to leave the Examination Hall before the end of the test.

INSTRUCTIONS

Caution: Question Paper CODE as given above MUST be correctly marked in the answer OMR sheet before attempting the paper. Wrong CODE or no CODE will give wrong results.

A. General Instructions

1. Attempt ALL the questions. Answers have to be marked on the OMR sheets.

2. This question paper contains Three Sections.

3. Section-I is Physics, Section-II is Chemistry and Section-III is Mathematics.

4. Each Section is further divided into Two Parts: Part-A & C in the OMR. Part-B of OMR to be left unused.

5. Rough spaces are provided for rough work inside the question paper. No additional sheets will be provided for rough work.

6. Blank Papers, clip boards, log tables, slide rule, calculator, cellular phones, pagers and electronic devices, in any form, are not allowed.

B. Filling of OMR Sheet

1. Ensure matching of OMR sheet with the Question paper before you start marking your answers on OMR sheet.

2. On the OMR sheet, darken the appropriate bubble with HB pencil for each character of your Enrolment No. and write in ink your Name, Test Centre and other details at the designated places.

3. OMR sheet contains alphabets, numerals & special characters for marking answers.

C. Marking Scheme For All Two Parts.

(i) Part-A (01-07) – Contains seven (07) multiple choice questions which have One or More correct answer. Full Marks: +4 If only the bubble(s) corresponding to all the correct options(s) is (are) darkened. Partial Marks: +1 For darkening a bubble corresponding to each correct option, provided NO incorrect option is darkened.

Zero Marks: 0 If none of the bubbles is darkened. Negative Marks: −2 In all other cases. For example, if (A), (C) and (D) are all the correct options for a question, darkening all these three will

result in +4 marks; darkening only (A) and (D) will result in +2 marks; and darkening (A) and (B) will result

in −1 marks, as a wrong option is also darkened

(i) Part-A (08-13) – Contains six (06) multiple choice questions which have ONLY ONE CORRECT answer Each question carries +3 marks for correct answer and -1 marks for wrong answer.

(ii) Part-C (01-05) contains five (05) Numerical based questions with single digit integer as answer, ranging

from 0 to 9 (both inclusive) and each question carries +3 marks for correct answer. There is no negative marking.

Name of the Candidate :____________________________________________

Batch :____________________ Date of Examination :___________________

Enrolment Number :_______________________________________________

BA

TC

HE

S –

CP

A1

92

0

FIITJEE – Phase Test (JEE-Advanced)

CPT - 1

CODE: 820304.0

PAPER - 1

IT−2020−One Year CRP (1920) (PAPER-1) (CPT-1)-(PCM) JEE ADV-

2

Ranchi (Lalpur) :7th Floor, Hari Om Towers, (Opp. Women’s College, Arts Block), Circular Road, Ranchi, Ph : 0651- 2563187/88/89/90. Ranchi (SOP, Doranda): Samriddhi Complex, Ground Floor, Near St. Xavier’s School, South Office Para Doranda, Ranchi.

Corp. off. : FIITJEE House 29-A, Kalu Sarai, Sarvapriya Vihar, New Delhi – 16. Ph : 46106000/10/13/15, Toll Free No. 1800114242. Fax : 011-26513942, Web:www.fiitjee.com

Useful Data PHYSICS

Acceleration due to gravity g = 10 2m / s

Planck constant h = 6.6 × 10–34 J-s Charge of electron e = 1.6 × 10–19C Mass of electron me = 9.1 × 10–31 kg

Permittivity of free space 0 = 8.85 × 10–12 C2/N-m2

Density of water water = 103 kg/m3 Atmospheric pressure Pa = 105 N/m2 Gas constant R = 8.314 J K–1 mol–1

CHEMISTRY

Gas Constant R = 8.314 J K−1 mol−1

= 0.0821 Lit atm K−1 mol−1

= 1.987 2 Cal K−1 mol−1

Avogadro's Number Na = 6.023 1023

Planck’s Constant h = 6.626 10–34 Js = 6.25 x 10-27 erg.s 1 Faraday = 96500 Coulomb 1 calorie = 4.2 Joule 1 amu = 1.66 x 10-27 kg 1 eV = 1.6 x 10-19 J

Atomic No.: H=1, He=2, Li=3, Be=4, B=5, C=6, N=7, O=8, F=9, Na=11, Mg=12, Al = 13, Si = 14, P = 15, S = 16, Cl = 17, Ar =18, K=19, Ca=20,Cr=24, Mn=25, Fe=26, Co=27, Ni=28, Cu=29, Zn=30, As=33, Br = 35, Ag = 47, Si = 21, Sn = 50, Ti = 22,I = 53, Xe = 54, Ba = 56, Pb = 82, U = 92, V = 50. Atomic masses: H =1, He=4, Li=7, Be=9, B=11, C=12, N=14, O=16, F=19, Na=23, Mg=24, Al=27, Si=28, P=31, S=32, Cl=35.5, K=39, Ca=40, Cr=52, Mn=55, Fe=56, Co=59, Ni=58.7, Cu=63.5, Zn = 65.4, As = 75, Br = 80, Ag = 108, Sn = 118.7, I = 127, Xe = 131, Ba = 137, Pb = 207, U = 238.


3



SSEECCTTIIOONN –– II :: PPHHYYSSIICCSS

PART – A

(Multi Correct Choice Type) This section contains 7 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE OR MORE may be correct.

1. For a curved track of radius R, banked at angle

(A) A vehicle moving with a speed 0 Rgtan = is able to negotiate the curve without calling

friction into play at all

(B) A vehicle moving with a speed 0 is able to negotiate the curve with calling friction into

play

(C) A vehicle is moving with a speed 0 must also have the force of friction into play

(D) The maximum value of the angle of banking for a vehicle parked on the banked road can stay

there without slipping, is given by 1

stan− = (s = coefficient of static friction)

2. Two balls of equal masses are thrown simultaneously in vertical upward direction with same speeds

10 m/s and 20 m/s. Which of the following is true about maximum height reached by centre of

mass?

(A) it is equal to mean of the maximum height reached by the balls

(B) it is less than the mean of maximum height reached by the balls

(C) it is more than the mean of maximum height reached by the balls

(D) acceleration of centre of mass of balls is g till first ball strikes the ground

3. A particle is projected from origin with velocity

( )ˆ ˆu j 2k= + m/s. Horizontal surface lies in X – Y plane,

then (take g = 10 m/sec2)

(A) Time of flight = 2

5sec

(B) horizontal range = 2

5m

(C) Maximum height 1

10m

(D) Maximum height = 1

5m

0 ( )ˆX i

( )ˆZ k

( )ˆY j

Space For Rough Work


4



4. A book leans against a crate on a table. Neither is moving. Which of the following statements connecting this situation is/are CORRECT? (A) The force of the book on the crate is less than that of crate on the book (B) there must be friction acting on the book or else it will fall (C) The net force acting on the book is zero (D) The direction of the frictional force acting on the book is in the same direction as the fractional force acting on the crate

5. A block A (5kg) rests over another block B (3kg) placed over a smooth horizontal surface. There is

friction between A and B. A horizontal force F1 gradually increasing from zero to a maximum is applied to A so that the blocks move together without having motion relative to each other. Instead of this, another horizontal force F2 gradually increasing from zero to a maximum is applied to B so that the blocks move together without relative motion. The magnitudes of friction between the blocks in the two cases are f1 and f2 respectively during the variation of F1 and F2 respectively. Then

(A) f1max > f2max (B) F1max : F2max = 3 : 5 (C) F1max : F2max = 5 : 3 (D) f1 < F1

6 A train carriage moves along the X-axis with a uniform acceleration a . An observer A in the train sets

a ball in motion on frictionless floor of the carriage with a velocity U relative to the carriage. The

direction of U makes an angle θ with the X-axis. Let B be an observer standing on the ground outside the train. The subsequent path of the ball will be

(A) a straight line W.r.t. observer A (B) a straight line w.r.t. observer B (C) parabolic w.r.t. observer A (D) parabolic w.r.t. observer B 7 A block of weight 9.8 N is placed on a table. The table surface exerts an upward force of 10 N on the block. Assume g = 9.8 m/s2. (A) The block exerts a force of 10 N on the table (B) The block exerts a force of 19.8 N on the table (C) The block exerts a force of 9.8 N on the table (D) The block has upward acceleration.



5



PART – A (Single Correct Choice Type)

This section contains 6 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

8 Two particles are projected simultaneously from two

points, O and O’ such that d is the horizontal distance and h is the vertical distance between them. They are projected at the same inclination α to the horizontal with the same speed v. The time after which their separation becomes minimum is (A) d/(v cos α) (B) 2d/(v cos α) (C) d/(2v cos α) (D) d/v

9 The pull P is just sufficient to keep the block of weight 14N in

equilibrium as shown. Pulleys are ideal. The tension T in the upper cable is (A) 8N (B) 16N (C) 14N (D) 2N

10 Two blocks of masses m1 = 1kg and m2 = 2kg are

connected by a non-deformed light spring. They are lying on a rough horizontal surface. The coefficient of friction between the blocks and the surface is 0.4. What minimum constant force F has to be applied in horizontal direction to the block of mass m1 order to move the other block? (g = 10 m/s2) (A) 8N (B) 15N (C) 10N (D) 25N

11 If wedge is moving with acceleration a as shown in the figure

then value of net force on m is

(A) ma (B) 2 ma

(C) mg (D) zero

m MM

aM


h

d O’

O

α

α


6



12. System shown in figure is released from rest pulley and spring is massless and

friction is absent everywhere and spring is relaxed. The speed of 5kg block when 2kg block leaves the contact with ground is (K = 40 N/m & g = 10 m/s2) (Initially spring is in natural length)

(A) 2 m / s (B) 2 2 m / s

(C) 2 m/s (D) 4 2 m / s

2kg 5kg

13. An external agent moves the block m slowly from A to B, along a rough hill with coeficient of friction µ. Find the work done by agent in this interval.

(A) µmgL (B) mg(H + µL) (C) mg(H+L) (D) mgH

Rough hill H

B

A

L

PART – C

(Integer Type) This section contains 5 questions. The answer to each question is a single-digit integer, ranging from 0 to 9. The correct digit below the question number in the ORS is to be bubbled.

1. A ball is thrown horizontally from the top of a

tower of unknown height. Ball strikes a vertical wall whom plane is normal to the plane of motion of ball. Collision is elastic and ball falls on ground at mid-point between tower and wall. Ball strikes the ground at angle of 30% with horizontal. The height of tower is.

2. Four blocks are arranged on a smooth horizontal

surface as shown. The masses of the blocks are given (see the diagram). The coefficient of static friction between the top and the bottom blocks is µs. What is the maximum value of the horizontal force F, applied to one of the bottom blocks as shown, that makes all four blocks move with the same acceleration? µs = 0.25, m = 1kg, M = 3 kg

3 A force ( )ˆ ˆF yi xj N= − + acts on a particle as it undergoes counterclockwise circular motion in x-y

plane in a circle of radius 4 m and with the centre at origin. The work done by the force when the

particle undergoes one complete revolution is (assume x, y are in m) p 4 Joule, then p is


H

30

8 3


7



4. Two trolley A and B are moving with accelerations a and 2a

respectively in the same direction (where a = 2 m/sec2). To an observer in trolley A, the magnitude of pseudo force acting a block of mass 2kg on the trolley B is x. Find the value of x

5. All surfaces are frictionless ratio of acceleration

of block B and acceleration of block A. Masses of blocks A, B, C are respectively 1kg, 2kg, 1kg.

B

A

a

a = y. Find the value of y.


m

2m

m

B

C

A


8



SSEECCTTIIOONN –– IIII :: CCHHEEMMIISSTTRRYY

PART – A

(Multi Correct Choice Type) This section contains 7 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE OR MORE may be correct.

1. Which of the following statement (s) is/are true for the given species. N2, CO, CN– and NO+ (A) All species have linear shapes

(B) All species have same dipole moments (C) All species are isoelectronic (D) All species have identical bond order and are paramagnetic in nature

2. For the reaction;

PCl5(g) PCl3(g) + Cl2(g)

The forward reaction at constant temperature is favoured by (A) Introducing Cl2 gas at constant volume

(B) Increasing the volume of the container (C) Introducing PCl5 at constant volume (D) Introducing an inert gas at constant volume

3. Which of the following statement(s) is/are true regarding the log10K vs 1/T plot shown in the figure:

(A) Plot P shows that the Ea is independent of temperature (B) Plot Q describes the behaviour of temperature dependence of Ea. (C) Arrhenius behaviour is described by P (D) The slope of curve P gives the value of –Ea/2.303R 4. Which of the following is/are the best representation(s) of the curves by plotting pH vs log C for the

salt hydrolysis

(A)

(B)

(C)

(D)


pH

logC →

9 8 7 6 5 4

0.1 0.2 0.3 0.4 0.5 0.1 0.2

For NH4Cl salt

pH

logC →

9 8 7 6 5 4

0.1 0.2 0.3 0.4 0.5 0.1 0.2

=tan–1(–1/2)

For HCOONa salt

pH

logC →

9 8 7 6 5 4

0.1 0.2 0.3 0.4 0.5 0.1 0.2

For NaCl salt

pH

logC →

9 8 7 6 5 4

0.1 0.2 0.3 0.4 0.5 0.1 0.2

For HCOONH4 salt

log10K

1/T →

P

Q

Ea = activation energy


9



5. Select wrong statement(s) about alkali metals (A) All form amide of the type MNH2

(B) All form superoxides of the type MO2 (C) All form ionic hydrides of the type MH (D) All forms nitrides of the type M3N 6. Which of the following statement(s) is/are correct for an electron of quantum numbers n=4 and m=2 (A) the value of l may be 2 (B) the value of l may be 3 (C) the value of s may be +1/2 (D) the value of l may be 0, 1 2, 3 7. Which of the following statement(s) is/are correct (A) hybridisation of C in C3O2 is sp2 (B) in Cr2O7

2–,six Cr–O bonds are identical (C) Three centre two electron bonds exists in B2H6 (D) In KMnO4, the colour is attributed to charge transfer spectrum

PART – A

(Single Correct Choice Type)


8. Consider the following nuclear reactions involving X and Y

X → Y + 4

2He

Y → 18 1

8 1O H+

If both neutrons as well as protons in both the sides are conserved in nuclear reaction, then identify period number and moles of neutrons in 4.6 gm of X respectively

(A) 3, 2.4 NA (B) 3, 2.4 (C) 2, 4.6 (D) 3, 0.2 NA

9. In dry ice, there are (A) Ionic bond (B) Covalent bond (C) Hydrogen bond (D) None of these

10. The melting point of AlF3 is 104°C and that of SiF4 is –77°C (it sublimes) because (A) There is a very large difference in the ionic character of Al–F and Si–F bonds

(B) In AlF3, Al3+ interacts very strongly with the neighbouring F– ion to give a three dimensional structure but in SiF4 no intraction is possible

(C) the silicone ion in the tetrahedral SiF4 is not shielded effectively from the fluoride ions wheras in AlF3, the Al3+ ion is shielded on all sides.

(D) The attractive forces between the SiF4 molecules are strong whereas those between the AlF3 molecules are weak.

11. SO3 decomposes at a temperature of 900 K and at a total pressure of 1.5 atm. At equilibrium, the

density of mixture is found to be 1.1 g/L in a vessel of 90 litres. The degree of dissociation of SO3 is (A) 100% (B) 90% (C) 95% (D) 33%

12. For the reaction Ag(CN)2

-Ag

+ + 2CN

-

, the equilibrium constant at 25°C is 4 × 10–19. What will be the Ag+ ion concentration in the solution, which was originally 0.1 M KCN and 0.03 M AgNO3

(A) 7.5 × 10–18 M (B) 1.33 × 10–19 M (C) 2.5 × 10–20 M (D) None of these

13. In an ore containing uranium the ratio of U238 and Pb206 nuclei is 3. What will be the age of the ore,

assuming that all the lead present in the ore is the final stable product of U238. The half life of U238 is 4.5 × 109 years

(A) 1.5 ×109 years (B) 13.5 ×109 years (C) 3 ×109 years (D) 1.85 ×109 years



10



PART – C

(Integer Type) This section contains 5 questions. The answer to each question is a single-digit integer, ranging from 0 to 9. The correct digit below the question number in the ORS is to be bubbled.

1. If the concentration of H+ ion of 1 N solution of HCN is yx 10− and have Ka = 4 × 10–10 then the

total value of x and y is 2. At a certain temperature, the half life periods for the catalytic decomposition of ammonia were found

to be as below: Pressure (mmHg) 50 100 200 t1/2 3.52 1.92 1.0 What is the order of reaction? 3. Find out the number of waves made by a Bohr electron in one complete revolution in its third orbit of

H-atom. 4. At what minimum atomic number, a transition from n = 2 to n = 1 energy level would result in the

emission of x-rays with = 3 ×10–8 m. (R = 1.0967 × 107) 5. A diatomic molecule has a dipole moment 1.2 D. If the bond length is 1.0 Å, the 1/x fraction of

charge exists on each atom. Find the value of x.

space for rough work


11



SSEECCTTIIOONN –– IIIIII :: MMAATTHHEEMMAATTIICCSS

PART – A (Multi Correct Choice Type)

This section contains 7 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE OR MORE may be correct.

1. Let [x] denote the GIF, if f(x) = [x sinx], then f(x) is

(A) continuous at x = 0 (B) continuous in (−1, 0)

(C) differentiable at x = 1 (D) differentiable in (−1, 1) 2. Let f(x) be a non constant twice differentiable function defined on (– ∞, ∞) such that

f(x) = f(1 –x) and 1

f ' 04

=

. Then

(A) f’(x) vanishes at least twice on [0, 1] (B) 1

f ' 02

=

(C)

1/2

1/2

1f x sinxdx 0

2−

+ =

(D)

1/2 1

sin t sin t

0 1/2

f(t)e dt f(1 t)e dt = −

3. If

nnr

rnr 0

CA lim

n .(r 3)→=

= +

, then which of these are correct?

(A) A is an irrational number (B) loge(A – 2) is a rational number (C) A is a rational number (D) log2(A + 2) is a rational number 4. Let g(x) be a function defined on [–1, 1]. If the area of the equilateral triangle with two of its vertices

at (0, 0) and (x, g(x)) is 3 / 4 then the function g(x) is

(A) 2g(x) 1 x= − (B)

2g(x) 1 x= −

(C) 2g(x) 1 x= − − (D)

2g(x) 1 x= +

5. If

1

n 1 k

n,k

0

I x (logx) dx−= , then its value may be

(A) k 1

k!

n +(k is an even natural number) (B)

k 1

k!

n +

−(k is an odd natural number)

(C) k

k 1

k!( 1)

n +− (D)

k 1

k!

n +(k is an odd natural number)

6. Let [x] denote the GIF, if f(x) = [x sinx], then f(x) is

(A) continuous at x = 0 (B) continuous in (−1, 0)

(C) differentiable at x = 1 (D) differentiable in (−1, 1)



12



7. Let f(x) be a non constant twice differentiable function defined on (– ∞, ∞) such that

f(x) = f(1 –x) and 1

f ' 04

=

. Then

(A) f’(x) vanishes at least twice on [0, 1]

(B) 1

f ' 02

=

(C)

1/2

1/2

1f x sinxdx 0

2−

+ =

(D)

1/2 1

sin t sin t

0 1/2

f(t)e dt f(1 t)e dt = −

PART – A

(Single Correct Choice Type)


8. The set of values of so that f(x) = 2

x 1

x 1

−

− + does not take any value in the interval

11,

3

− −

is

(A) 1

,4

− −

(B) [2, )

(C) 1

, 24

−

(D) 1

,4

− −

[2, )

9. Let f : R → 0,2

defined by f(x) = tan–1 (x2 + x +), then the set of values of for which f is onto,

is

(A) [0, ) (B) [-2, 1]

(C) 1

,4

(D) none of these

10. The value of x 0lim→

2x

sinx.tanx

, where [] denotes greatest integer function, is

(A) 0 (B) 1 (C) limit does not exist (D) 2

11. If a1 = 1 and an = n(1 + an–1) n 2, then the limit nlim→

1 2

1 11 1

a a

+ +

…..

n

11

a

+

=

(A) e (B) loge2 (C) e1/2 (D) log2e 12. For some g, let f(x) = x(x+3) eg(x) be a continuous function. If there exists only one point x = d such

that f(d) = 0, then (A) d < -3 (B) d > 0

(C) -3 d 0 (D) -3 <d < 0



13



13. Let f(x) = 2

1 sinx, x 0.Then

x x 1, x 0

+

− +

(A) f has a local maximum at x = 0 (B) f has a local minimum at x = 0 (C) f is increasing everywhere (D) f is decreasing everywhere

PART – C (Integer Type)

This section contains 5 questions. The answer to each question is a single-digit integer, ranging from 0 to 9. The correct digit below the question number in the ORS is to be bubbled.

1. If f(x) is a continuous function x R and the range of f(x) = (2, 26 ) and g(x) =( )f x

a

is

continuous x R ([.] denotes the greatest integer function), then the least positive integral value of a is

2. If

3(x 2)f(x) .sin(x 2) acos(x 2)

a

−= − + −

. Then minimum value of a

16

is, ([.] = G.I.F).

3. The number of values of y in [−2, 2] satisfying the equation |sin2x| + |cos2x| = |siny| is

4. If

1

2 2

0

f(x) x xy x y f(y)dy = + + , then 6

f7

is equal to

5. The area of the largest rectangle with lower base on the x-axis & upper vertices on the curve y = 12 – x2 is A, then the largest prime factor of the value of (A + 3) is ………..



14



FIITJEE COMMON TEST BBAATTCCHHEESS:: CCPPAA 11992200

PPHHAASSEE TTEESSTT –– 11 ((PPAAPPEERR -- 11))

PPAAPPEERR CCOODDEE :: 882200330044..00 ANSWER KEY

Q. No. PHYSICS CHEMISTRY MATHEMATICS

1 (ABCD) (AC) (ABD)

2 (BD) (BC) (ABCD)

3 (AC) (ABCD) (A)

4 (BC) (ABC) (BC)

5 (CD) (BD) (ABC)

6 (BC) (ABC) (CD)

7 (AD) (BCD) (ABC)

8 (C) (B) (A)

9 (A) (B) (C)

10 (A) (B) (A)

11 (B) (C) (A)

12 (B) (A) (D)

13 (B) (D) (A)

1 (6) (7) (6)

2 (4) (2) (4)

3 (8) (3) (4)

4 (4) (2) (7)

5 (2) (4) (7)


15



HINTS & SOLUTIONS PHYSICS

PART-A 1. A, B, C, D FBD of block

N cos θ = mg Horizontal N sin θ = mg tan θ

If 2V

mgtanR

=

2. B, D

2

1 22

cmmax

u u

u 2H

2g 2g

+

= =

3. A, C

Hu 1=

Vu 2=

v2uT

g=

2

vuH

2g=

HR T.u=

4. B, C FBD of block

5. C, D

1max 2maxf f= = Lumster starts from between 5kg , 3kg (LSF)

1max

5 3f (LSF)

3

+ =

2max

5 3f (LSF)

5

+ =

6. B, C

In carriage frame acceleration is constant while in ground frame velocity is constant. 7 A, D

2N

W

2N

+

W

1N

3W

f

N

mg


16



FBD of block

N – mg = ma 8 C As vertical component is same. Vertical gap is constant. Separation is minimum when horizontal separation is zero. 9 A 10. A When m2 moves kx = µm2g and

Fx - µm1gx - 21kx 0

2=

11. B

Fnet = manet = m( 2a)

12. B At that instant Fs = kx = weight of 2kg block loss in (spring + gravitational) potential energy of 5kg block = its kinetic energy 13. B Work done against friction W = µmg (Horizontal distance)

Integer Type 1. 6 Sol:

AP is the motion of projectile in absence of Cv all, which is half of a normal projectile with range R = 2

OP and angle of projection = 30° and height H

H = 2 2u sin

2g

R = 2u sin2

g

H = 21 sin

62 sin2

=

2. 4 For maximum F, friction on m in forward direction is limiting. 3. 8

The force acts along the tangential direction 4. B Pseudo force = mass of observed body × (Acceleration of frame of observation)

3030

A

P

H

O BP'

mg

N


17



5. D

For A, mg sin - T = ma1 ……….(1)

For C, T = ma1 ……….(2)

For B, Tension at all points ultimately

2mg sin = 2ma2 ……………(3)

a2 = g sin

Solving (1) and (2),

CHEMISTRY 1. A,C 2. B,C 3. A,B,C,D 4. A,B,C 5. B,D 6. A,B,C 7. B,C,D 8. B 9. B 10. B 11. C

3 2 2

1SO (g) SO (g) O (g)

2+

Initial 1 0 0 Final 1 - x x x/2 Total moles = 1 – x + x + x/2 = 1 + x / 2

m

0 3

d (mixture)Initial moles

Final moles d (SO initially)= ….(i)

PM = d0RT

So d0 = RM 1.5 80

1.624g / LRT 0.0821 900

= =

According to equation (i)

1 1.1

1 x / 2 1.624=

+

x = 0.95 or 95% dissociation 12. A 0.1 M KCN and 0.03 M AgNO3 are mixed

19

2

1Ag 2CN Ag(CN) K 10

4

+ − −+ =

K is extremely high, assume that whole Ag+ is converted into Ag(CN)2–.

2Ag 2CN Ag(CN)+ − −+

Initial 0.03 0.1 0 Final 0 0.1–2×0.03 0.03 Now 0.03 M Ag(CN)2

– dissociates (K = 4 × 10–19)

2Ag(CN) Ag 2CN− + −+

0.03 – x x 0.04 + 2x

2

2

[Ag ][CN ]K

[Ag(CN) ]

+ −

−=

m

2m

m

a2

a1

A

g

a1

TTT

T

T

T

TT

TT


18



19

23

2

K[Ag(CN) ] 4 10 (0.03 x)[Ag ]

0.04 2x[CN ]

−+

−

−= =

+

Suppose x to be very much small

Then 19

184 10 0.03[Ag ] 7.5 10 M

0.04

−+ − = =

13. D

0

t

N2.303log

t N =

238 206U Pb→

N0 x 0 Nt x – y y

So 0

t

N x

N x y=

− Given

x y3

y

−=

So x 4

x y 3=

−

92.303 4

t 4.5 10 log0.693 3

=

t = 1.85 × 109 years PART C 1. 7

2 2

aK(1 )V V

= =

− v = 1 lit

So 10 24 10− =

52 10 [H ]− + = = because c = 1

2. 2

n 1 n 1

1 2 2

2 1 1

t a p

t a p

− −

= =

(t1 and t2 are two half lives)

3. 3 rn for H = r1 × n2 r3 for H = 0.529 × 10–8 × 9 cm ( r1 = 0.529 Å)

But 1n

vv

n=

v3 = 82.19 10

3

cm/sec ( v1 = 2.19 × 108 cm/sec)

No. of waves in one complete round = 3 3 3 3

3

2 r 2 r 2 r v m

h / mv h

= =

( = h/mv)

= 8 8 28

27

2 22 0.529 9 10 2.19 10 9.108 103

7 3 6.62 10

− −

−

=

4. 2

2

2 2

1 2

1 1 1Rz

n n

= −

5. 4

Electronic charge = 18

8

1.2 10 esucm

d 1 10 cm

−

−

=

Actual value of charge = 4.8 × 10–10 esu


19



Fraction of charge = 10

10

1.2 10 1

44.8 10

−

−

=

MATHEMATICS PART – A 1. A, B, D Define f(x) from [–2, 2]. 2. A, B, C, D

1 1

f ' f '2 2

= −

,

and

1 3

f ' f ' 04 4

= − =

.

3. A

( )nn 1

r 2r

r 0nr 0

CA lim x dx e 2

n

+

→=

= = = −

.

4. B, C 5. A, B, C Do it by parts

6. C, D ( )f x 0=

7. A, B, C Interior of a circle and a parabola.

8. A 9. C

2

2 1 1x x x

4 2

+ + = +

(for

1

4 = )

So, f is onto for 1

,4

10. A Let f(x) = x2 = sinx.tanx, f(0) = 0 and f’(x) < 0, for x → 0.

2x

0sinx.tanx

.

11. A

n 1

n

1 a 1

a n−

+= ,

n 1

n

a1 1 1lim 1 ....... e

1.2.3.......n n 1 11 21+

→

= + + + =

+


20



12. D f’(x) = eg(x) ((2x + 3) +(x2 + 3x)g’(x)). Clearly, f’(d) = 0 – 3 < d < 0.

13. A

x 0 x 0lim f(x) f(0) lim f(x)

− +→ → .

PART – C 1. 6

For a = 6, 7, ……., f(x)

0 1 g(x) 0a

= .

2. 4 a [64, ) .

3. 4 On squaring we will get 2 positive values of (x, y), and so number of y’s will be 4. 4. 7

1 1

2 2

0 0f(x) x y f(y)dy x f(y)dy= + ………………. (I)

2f(x) Ax Bx = + , replace f(x) and f(y) in (I) and comparing.

5. 7 ABCD is a rectangle with A, B on x-axis and C, D on parabola.

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