1516-advanced Paper-2 Set-a.pdf

FIITJEE PHYSICS, CHEMISTRY & MATHEMATICS CPT3 - 2

CODE:

Time Allotted: 3 Hours §

BATCHES – 1516

§

PAPER - 2 Maximum Marks: 240

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. 2. 3. 4. 5.

Attempt ALL the questions. Answers have to be marked on the OMR sheets. This question paper contains Three Parts. Part-I is Physics, Part-II is Chemistry and Part-III is Mathematics. Each part is further divided into three sections: Section-A, & B. 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 Blue/Black Ball Point Pen 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 Three Parts. (i)

Section-A (01 – 08) contains 8 multiple choice questions which have one or more than one correct answer. Each question carries +4 marks for correct answer and – 2 mark for wrong answer. Section-A (09 – 12) contains 2 paragraphs. Based upon paragraph, 2 multiple choice questions have to be answered. Each question has only one correct answer and carries +4 marks for correct answer and – 2 mark for wrong answer.

(ii) Section-B (01 – 08) contains 8 Numerical based questions with single digit integer as answer, ranging from 0 to 9 (both inclusive) and each question carries +4 marks for correct answer and No Negative Mark for wrong answer.

Name of the Candidate :__________________________________________ Batch :____________________ Date of Examination :__________________ Enrolment Number :_______________________________________________

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P PA AR RT T –– II :: P PH HY YS SIIC CS S SECTION – A (Multiple Choice Type) This section contains 8 multiple choice questions. Each question has four choices (A), (B), (C) and (D), out of which ONE OR MORE THAN ONE is/are correct. 1.

For a satellite to orbit around the earth, which of the following must be true? (A) It must be above the equator at some time. (B) It cannot pass over the poles at any time. (C) Its height above the surface cannot exceed 36000 km. (D) Its period of rotation must be > 2π R / g where R is radius of earth.

2.

Four rods A, B, C, D of same length and material but of different radii r, r 2 , r 3 and 2r respectively are held in parallel between two rigid walls. The temperature of all rods is increased by same amount. If the rods do not bend, then (A) The stress in the rods are in the ratio 1 : 2 : 3 : 4. (B) The force on the rod exerted by the wall are in the ratio 1 : 2 : 3 : 4. (C) The energy stored in the rods due to elasticity are in the ratio 1 : 2 : 3 : 4. (D) The strains produced in the rods are in the ratio 1 : 2 : 3 : 4.

3.

A body of mass M is attached to the lower end of a metal wire, whose upper end is fixed. The elongation of the wire is l. (A) Loss in gravitational potential energy of M is Mgl. (B) The elastic potential energy stored in the wire is Mgl. (C) The elastic potential energy stored in the wire is 1/2 Mgl. (D) Heat produced is 1/2 Mgl.

4.

When the temperature of a copper coin is raised by 80°C, its diameter increases by 0.2%. (A) Percentage rise in the area of a face is 0.4%. (B) Percentage rise in the thickness is 0.4%. (C) Percentage rise in the volume is 0.6%. (D) Coefficient of linear expansion of copper is 0.25 × 10–4 C°–1. Space for rough work

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5.

During an experiment, an ideal gas is found to obey a condition

P2 = constant. The ρ

gas is initially at temperature T, pressure P and density ρ. The gas expands such that density changes to

ρ then 2

2P

(A) The pressure of the gas changes to

(B) The temperature of the gas changes to 2 T (C) The graph of above process on the P-T diagram is parabola. (D) The graph of the above process on P-T diagram is hyperbola. 6.

Two flat conducting strips of length ‘ l ’ width ‘b’ are separate by a small gap ‘a’ (a << b, l ) perpendicular to the plane of paper. The right end of strips are shorted, and a battery of voltage V0 is connected across the left end. The current is assumed to flow only parallel to the l . Then: (A) The magnetic field between the strips is

i

a

V0

µ 0i . b

i

l

µ ℓa (B) The self inductance of the circuit is 0 . b

(C) The current in the circuit is independent of time. (D) The voltage across the strips as a function of the

⎛ V0 x ⎞ ⎟ ⎝ ℓ ⎠

distance x measured from the shorted end is ⎜ 7.

Choose the INCORRECT statement(s): (A) The flux of electric field is equal to number of field lines crossing the surface. (B) The flux of electric field over a closed surface is always non-zero. (C) The flux of gravitational field over any closed surface can never be positive.

r r

r

r

(D) The flux is equal to φ = E ⋅ S where E is electric field and S is the Area Vector. 8.

A gas took part in three thermal processes in which it is heated from the same initial state to the same final P temperature. The process are shown on the P-V diagram by straight lines 1-2, 1-3 and 1-4. Q1, Q2 and Q3 are amount of heat supplied to the gas in the process 1 → 2, 1 → 3, 1 → 4 respectively. (A) Q3 > Q2 (B) Q1 < Q2 (C) Q3 > Q1 (D) Q3 < Q2 O

Isotherm

2 3

4

1 V

Space for rough work

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Comprehension Type This section contains 2 paragraphs. Based upon each paragraph, 2 multiple choice questions have to be answered. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct. Paragraph for Questions 9 and 10 Read the paragraph carefully and answer the questions. A particle of mass m and charge q is accelerated by a potential difference V volt and made to enter a magnetic field region at an angle θ with the field. At the same moment another particle of same mass and charge is projected in the direction of the field from the same point. Magnetic field induction is B. 9.

What should be the speed of second particle so that the particles meet again and again after regular interval of time? (A) (C)

10.

2qV m qV 2m

(B)

qV m

(D) none of these

Find the time interval after which they meet

2π qB 2πm (C) cos θ qB (A)

2πm qB 2πm (D) sin θ qB (B)

Space for rough work

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Paragraph for Questions 11 and 12 Read the paragraph carefully and answer the questions. The volume of n moles of an ideal gas with degree of freedom f is varied according to the law a V = where ‘a’ is a constant. T 11.

The amount of heat received by the gas in this process if the gas temperature is increased by ΔT is ⎡f ⎤ ⎡f ⎤ (A) n ⎢ − 1⎥ RΔT (B) n ⎢ + 1⎥ RΔT ⎣2 ⎦ ⎣2 ⎦ ⎡f ⎤ (C) n[f + 2]RΔT (D) n ⎢ + 2⎥ RΔT ⎣2 ⎦

12.

The molar specific heat of the gas at constant pressure is ⎛f ⎞ ⎛f ⎞ (A) ⎜ + 1⎟ R (B) ⎜ + 2 ⎟ R ⎝2 ⎠ ⎝2 ⎠ 5 ⎛f ⎞ (C) R (D) ⎜ − 2 ⎟ R 2 ⎝2 ⎠ Space for rough work

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Integer Answer Type This section contains 8 questions. The answer to each question is a single digit integer, ranging from 0 to 9 (both inclusive). 1.

A certain amount of a monoatomic ideal gas undergoes a process ρun = c where ρ is the density and u is the internal energy of the gas. It was found that the ratio of

ΔW 2 = , ΔQ 3

what is the value of n? 2.

Switch K is closed for long time in the figure as shown. Find the current i as soon as the switch is opened.

K

2Ω

1Ω

1.5H

1Ω

15 V

i

3.

In a room where the temperature is 30°C a body cools from 61°C to 59°C in 4 minutes. What will be the time (in min) taken by the body to cool from 51°C to 49°C?

4.

A spherical ball of density ρ and radius 0.003 m is dropped into a tube containing a viscous fluid up to the 0 cm mark as shown in the figure. Viscosity of the fluid = 1.260 N.m–2 and its density ρL = ρ/2 = 1260 kg.m–3. Assume the ball reaches a terminal speed at the 10 cm mark. Find the time taken (in sec) by the ball to traverse the distance between the 10 cm and 20 cm mark. (g = 10 m/s²) Space for rough work

5.

If energy of interaction between the particle placed at the vertices of a regular tetrahedron of side R is −K find the value of K.

m

2

Gm , then R

R

R R

m R

R

m

R

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6.

An inductance ‘L’ and a resistance ‘R’ are connected in series with a battery of emf ε. If maximum rate of energy stored in the field is

7.

Side of the regular hexagon is 2 meter magnetic field at point O due to the network shown in the figure is 3B0 ×10−7 tesla. Then value of B0 is

8.

Kε 2 , then find ‘K’. 4R

i = 6A

A pump draws water from the surface of a reservoir and pumps it with a velocity v through its outlet, which is at the same level as the water level in the reservoir. In this process the pump draws an electric power P. If the pump has to deliver the water with a velocity 2v through its outlet, the power required is k*P. What is the value of k assuming that the efficiency of the pump is 100% irrespective of the discharge velocity? Space for rough work

P PA AR RT T –– IIII :: C CH HE EM MIIS ST TR RY Y SECTION – A (Multiple Choice Type) This section contains 8 multiple choice questions. Each question has four choices (A), (B), (C) and (D), out of which ONE OR MORE THAN ONE is/are correct. Faridabad (Delhi-NCR) FIITJEE Ltd., Sec-15A Market, Near Vidya Mandir Public School, Ajrounda Chowk, Faridabad, Haryana-121007: Ph-0129-4174571 Website: www.fiitjee.com

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1.

The appropriate reagent for the following transformation O

CH3

is: (A) (C)

CH 2CH 3

Zn ( Hg ) , HCl

(B)

NH 2 .NH 2 , OH −

CH 2 SH

(D)

Red P + HI

CH2SH,H,+ heat H NH 3 Br2 + H 2O NaOH ⎯⎯⎯⎯ → ⎯⎯⎯ → ⎯⎯⎯ → Product or ( HOBr )

2.

The product is:

H3C

(A)

Optically active

(B)

A compound in which both the chiral centres have the same absolute configurations

(D)

Having plane of symmetry

H2N

(C)

H H3C HO

Space for rough work

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O

3. CH 3

C

18

O

CH 2

H O |H⊕

2 →P + Q Ph ⎯⎯⎯⎯

Where P is an acid and Q is an alcohol. Hence P and Q are, respectively. O

18

O

(A) CH 3

C

OH

and PhCH 2

(B)

OH

O

(C) CH3

C

18

CH3

18

CH2

OH

OH and PhCH2

OH

O

(D) OH and Ph

C

CH3

C

OH and Ph

CH2

OH

4.

A solution contains Na2CO3 and NaHCO3. 10 ml of this solution required 2.5 ml of 0.1 M H2SO4 for neutralization using phenolphthalein as indicator. Methyl orange is then added when a further 2.5 ml of 0.2 M H2SO4 was required. Choose the correct statement(s) (A) The amount of Na2CO3 per litre solution is 5.3 g (B) The amount of NaHCO3 per litre solution is 6.2 g (C) The N- factor of Na2CO3 in this titration using methyl orange as indicator would have been 2 (D) Phenolphthalein changes its colour as soon as Na2CO3 is completely converted into NaHCO3 as pH of solution falls slightly below 8.

5.

Choose the correct statement(s) (A) For the reaction: H3PO3 + NaOH → NaH2PO3 + H2O, the normality of H3PO3 solution is equal to its molarity (B) The maximum normality of a solution of H3PO3 for its reaction with excess NaOH solution will be double its molarity (C) With excess NaOH, H3 PO3 may convert in to Na3PO3 (D) In the half reaction: H3PO3 ⎯⎯ → PH3. The equivalent weight of H3PO3 will be M/6 where M = MW of H3 PO3 Space for rough work

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6.

O ⊕

H3 O NaOH HCN ⎯⎯⎯ → P ⎯⎯⎯ → Q ⎯⎯⎯ → R where R is? Δ

(A)

(B)

COOH

COOH

OH

(C)

OH

(D)

COOH

O

COOH

O

7.

25 ml of 0.50 M H2O2 solution is added to 50 ml of 0.20 M KMnO4 in acidic solution. Which of the following statement(s) is/are true? (A) 0.10 mole of oxygen is liberated (B) 0.005 mole of KMnO4 does not react with H2O2 (C) 0.0125 gmole of oxygen gas is evolved (D) 0.0025 mole of H2O2 does not react with KMnO4

8.

White phosphorus has (A) six P-P single bonds (B) four P-P single bonds (C) total four lone pair of electrons (D) polymeric structure (P)n where n is very high Space for rough work

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Comprehension Type This section contains 2 paragraphs. Based upon each paragraph, 2 multiple choice questions have to be answered. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct. Paragraph for Questions 9 and 10 Read the paragraph carefully and answer the questions. A compound ‘A’ with molecular formula C8H8O2 when heated with AlCl3, forms ‘B’ which when treated with KMnO4, H+ and on heating forms another compound (C). When (C) is treated with bromine water it gives a ppt. When ‘A’ is hydrolysed, we get two products (D) and (E). The compound ‘A’ does not give any colouration with neutral FeCl3 solution but the compound ‘D’ does give a violet colouration with FeCl3 solution. Calcium salt of ‘E’ when heated forms a compound that gives a positive iodoform test. On the basis of the above passage, answer the following questions: 9.

Which of the following represents the correct structure of the compound (A)? O

(A)

C

O

(B) O

CH3

O

C

OH

(C) CH3

(D) C

None of these

CH3

O

10.

The ppt. obtained when (C) is treated with Br2 water is due to which of the following? OH

(A) Br

OH

(B) Br

Br

OH

(C) C

OH

Br

Br

O

O

C

OH

Br

OH

(D) Br

Br

COOH Br

Br

Space for rough work

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Paragraph for Questions 11 and 12 Read the paragraph carefully and answer the questions. In a given sample of gas all molecules do not possess same speed. Due to inter molecular collisions taking place frequently, the velocities of the molecules are continuously changing though the number of molecules in a given velocity range remains always constant at constant temperature called steady state of the gas. The average velocity fails to give correctly the fail K.E of gas. It is the R.M.S velocity that is used for this purpose for correctness. 11.

Oxygen has a density of 1.429 g| Li at STP. The RMS velocity of O2 molecules in mS-1 is equal to (A) 461 (B) 416 (C) 496 (D) 580

12.

By how many folds the temperature of the gas would increase when the RMS velocity of gas molecules in a container of fixed volume is increased from 500 ms–1 to 1000 ms–1? (A) 2 (B) 6 (C) 8 (D) 4 Space for rough work

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SECTION−B Integer Answer Type This section contains 8 questions. The answer to each question is a single digit integer, ranging from 0 to 9 (both inclusive). 1.

The ratio between the root mean square velocity of H2 at 50K and that of O2 at 800K is

2.

Pentaerythritol, used in making explosives, is obtained from the reaction of acetaldehyde and excess of formaldehyde in the presence of Ca(OH)2. Find the total number of OH groups present in pentaerythritol

3.

When OHC – (CHOH)4 – CH2OH is subjected to periodic acid oxidation, how many moles of formic acid are obtained from one mole of given compound?

4.

Count the number of oxygen’s linked to only one Nitrogen atom in the following compounds and reports their total number. N 2O 3, N 2O 5.

5.

Let the interhalogen compounds be represented by general formula AXn. Find the sum of sum the various possible values of ‘n’ and report the value of . 2

6.

The compressibility factor of 1 mole of a Vander Waals’ gas is 1.5 at 0°C and 100 atm, what is the nearest integral value of 9b where b (Lmol–1 is the Vander Waals’ constant assuming ”a” to be negligible”.

7.

How many of the following nitrates or nitrites upon heating strongly will give NO2 and O2 gases both? NH4NO3 , NH4NO2, AgNO3, NaNO3, KNO3, N2H5NO2, Pb(NO3)2, Cu(NO3)2,

8.

The number of tripeptides formed by three different amino acids are? Space for rough work

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P PA AR RT T –– IIIIII :: M MA AT TH HE EM MA AT TIIC CS S SECTION – A (Multiple Choice Type) This section contains 8 multiple choice questions. Each question has four choices (A), (B), (C) and (D), out of which ONE OR MORE THAN ONE is/are correct. 1.

6k

∞

If S = ∑

k =1

(

)(

3k − 2k 3k +1 − 2k +1

)

, then S is greater than or equal to

(A) 1 (C) 3 2.

(B) 2 (D) 5

Let f(x) = ax2 + bx + c, where a, b, c ϵ I and (b2 – 4ac) is not perfect square, then

⎛ ⎛ ⎛ p ⎞ ⎞⎞ ⎜ min ⎜⎜ f ⎜ ⎟ ⎟⎟ ⎟ ⎜ ⎟ ⎝ ⎝ q ⎠ ⎠⎠ ⎝ (A) 49 (C) 225

−1

(where p, q ϵ I) may be (If

p 3 = ) q 7 (B) 196 (D) 361

3.

If f(x) = x4 + 4x + a = 0, a ϵ R, then which of these is not true (A) no real roots for a > 4 (B) two real and equal roots for a = –1 (C) no real roots for all a < 3 (D) two real and distinct roots for all a > 3

4.

If z is a complex number which satisfies the equations 3|z – 12| = 5|z – 8i| and |z – 4| = |z – 8|, then Im(z) can be (A) 8 (B) 15 (C) 16 (D) 17 Space for rough work

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5.

If |z – 1 – 2i| ≤ 1, then ⎛4⎞ (A) min.(arg(z)) = tan−1 ⎜ ⎟ ⎝3⎠ (C) min.(| z |) = 5 − 2

(B) max.(arg(z)) < (D) max.(| z |) =

3π 4

(6 + 2 5 )

6.

In a 17-sided regular polygon, then number of acute angle triangles by joining the three vertices of given polygon (Equilateral triangles are being excluded) is equal to ‘m’ and number of right angled triangles are n, then m + 3n is divisible by (A) 8 (B) 12 (C) 24 (D) 17

7.

79 + 97 is divisible by (A) 16 (C) 64

8.

(B) 24 (D) 72

Two cards are drawn from a pack of 52 cards one by one without replacement. Let p1 be the probability of getting both aces and p2 be the probability of the second card an ace,

⎛1 1⎞ 2 + ⎟ is a 3-digit number abc, then (a + b + c) is divisible by p p 2⎠ ⎝ 1 (B) 3 (D) 5

then given m = ⎜ (A) 2 (C) 4

Space for rough work

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CPA B-LOT (CPT3-2) PT-3 PAPER-2 (PCM) SET-A

Comprehension Type This section contains 2 paragraphs. Based upon each paragraph, 2 multiple choice questions have to be answered. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct. Paragraph for Questions 9 and 10 Read the paragraph carefully and answer the questions. z is a complex number, C1 ≡ z −

9 1 3π and C3 ≡ z − 1 − i = 2 . + z − = 2 , C2 ≡ arg(z − 3i) = 5 5 4

9.

The number of intersecting points of curve C1 and C3 is/are (A) 0 (B) 1 (C) 2 (D) 4

10.

If curve C4, C5 and C6 are the reflections of the curve C1, C2 and C3 respectively in the real axis, then 9 1 π (A) C4 ≡ z − + z − = 2 (B) C5 ≡ arg(z − 3) = 5 5 4 (C) C6 ≡ z + 1 + i = 2

(D) None of these Space for rough work

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Paragraph for Questions 11 and 12 Read the paragraph carefully and answer the questions. In an examination, in an objective test there are two sections containing 10 questions each. In section-I, each objective question have 5 choices and only one choice is correct. Section-II has 4 choices for each question and one or more than one choice may be correct. Marks for sectionII is awarded only if a student gives all correct choices. There is no negative marking for any section. For each question in section-I and section-II, 1 and 3 marks will be awarded respectively. 11.

The probability of getting marks less than 40 for a student is 10

⎛ 1 ⎞ ⎟ ⎝ 75 ⎠

10

(A) ⎜

10

⎛ 74 ⎞ ⎟ ⎝ 75 ⎠

(C) 1 − ⎜ 12.

⎛ 74 ⎞ ⎟ ⎝ 75 ⎠

(B) ⎜

10

⎛ 1 ⎞ ⎟ ⎝ 75 ⎠

(D) 1 − ⎜

If a student attempts four questions, 2 from section-I and 2 from section-II, then the probability that he gets 4 marks is 64 56 (A) (B) 5625 5625 224 326 (C) (D) 5625 5625 Space for rough work

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SECTION−B Integer Answer Type This section contains 8 questions. The answer to each question is a single digit integer, ranging from 0 to 9 (both inclusive). 1.

If

1,

α 1,

α 2,

α 3,

α4 be

the

roots

(ω − α1) (ω − α 2 ) (ω − α3 ) (ω − α 4 ) 2

2

2

2

(ω − α1) (ω − α2 ) (ω − α3 ) (ω − α 4 )

of

x5

–

1=

0,

then

the

value

of

+ ω2 is....................

2.

For all complex numbers z1, z2 satisfying |z| = 12 and |z –3–4i| = 5 respectively, then 2max.|z1 – z2| –19min.|z1 – z2| is equal to

3.

A dictionary is printed consisting of 7 lettered words only that can be made with the letters of the word CRICKET. If the words are printed in the alphabetical order, (i.e. rank of the word). Then the difference between 2 positions of C in the word of rank 531 is .................. (As in the word INDIA, two ‘I’s are numbered 1 and 4 with difference 3)

4.

If the probability that 4th power of a positive integer ends in the digit 6 is p, then the value of |30p – 5| is................

5.

A letter is known to have come either from "KRISHNAGIRI" or "DHARMAPURI". On the post mark only the two consecutive letters "RI" are visible. Let E be the event that it came from Krishnagiri, then the odds against that of the event E are m : n, then |2m – 3n| is........................... (m, n are co-prime)

6.

If (1 + x)10 = a0 + a1x + a2x2 +......+ a10x10, then (a0 – a2 + a4 + a6 + a8 – a10)2 + (a1 – a3 + a5 – a7 + a9)2 is equal to pq, then q – 3p is ....................... (p, q ϵ N).

7.

If the entire graph of the expression y = x2 + kx – x + 9 is strictly above the x-axis, then the number of integral values of k is a two-digit number, the sum of these two-digits is ......................

8.

A bug crawls along the edges of a regular tetrahedron ABCD with edges of length l. It starts at A and at each vertex chooses it’s next stage at random. The probability that 1⎛ 1 ⎞ after n steps it is again at A is ⎜ ⎟ , (p, q, r ϵ N, and none of them is a perfect 1 + 2 p2 ⎜⎝ qr ⎟⎠ square), so p + q + r is Space for rough work

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CPA B-LOT (CPT3-2) PT-3 PAPER-2 (PCM) SET-A

Paper Code

FIITJEE COMMON TEST BATCHES: ONE YEAR CPA (1516)-Advance-(B LOT)

PHASE TEST-III (PAPER-2) ANSWER KEY SET-A PART – I (PHYSICS) 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.

SECTION-A A, D B, C A, C, D A, C, D B, D A, B, D A, B, D A, B, C D B A A

1. 2. 3. 4. 5. 6. 7. 8.

3 3 6 5 6 1 2 8

PART – II (CHEMISTRY)

PART – III (MATHS)

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.

SECTION-A A, B, C, D A, B A A, C, D A, B, D C B, C A, C B D A D

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.

SECTION-A A, B A, B B, C, D A, D B, D B, D A, C B, D C A D C SECTION-B

1. 2. 3. 4. 5. 6. 7. 8.

SECTION-B 1 4 5 7 8 1 3 6

1. 2. 3. 4. 5. 6. 7. 8.

1 6 3 7 3 4 2 8

SECTION-B

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CPA B-LOT (CPT3-2) PT-3 PAPER-2 (PCM) SET-A

HINTS & SOLUTIONS PHYSICS 1.

A, D Since centripetal force is towards centre of earth, the centre of orbit is at the centre of earth. This means that orbit must be above equator at atleast two points. R is the period of a surface satellite, obviously the satellite be some distance above 2π g the surface.

2.

B, C The strain and stress in the rods is same and force is σ × A.

3.

A, C, D At equilibrium position, Mg is balanced by elastic forces. Heat will be produced as the oscillations fade out. (Air friction)

4.

A, C, D Thermal expansion is like photographic enlargement.

5.

B, D The process is P2V = C or PV−1/2 = C i.e., polytropic coefficient x = –1/2. 1−x x

This can also be written as P

T = C or

x 1 − PT x

= C.

6.

A, B, D Use Ampere’s law (Like an infinite sheet of current).

7.

A, B, D

r r Flux = ∫ E.dS . This is proportional to the number of field lines. For gravitation, the field is

always attractive thus flux over a closed surface is always negative. 8.

A, B, C ΔU = 0, since temperature change is same for all the three processes. Now work done is area under the PV graph.

9.

D The horizontal components of speeds should be same for repeated meeting. Therefore the speed must depend on θ.

10.

B The meeting can happen only at integral multiples of pitch i.e., integral multiples of time period of complete resolution of the helix.

For 11 & 12 11.

A

12.

A The process is polytropic, i.e., TV = C Compare with TV x−1 = C ⇒ x – 1 = 1 or x = 2 R ⎞ nf ⎛ Now, Δu = RΔT , Δθ = n ⎜ Cv + ΔT , 1 − v ⎟⎠ 2 ⎝

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CPA B-LOT (CPT3-2) PT-3 PAPER-2 (PCM) SET-A

1.

⎛f ⎞ CP = ⎜ + 1⎟ R . ⎝2 ⎠ 3 The process is polytropic or TV

−

1 n

= C ⇒ x −1=

or x = 1 −

Tn =C V

−1 n

1 n

R ΔT 1− n R ⎞ ⎛f Δθ = n ⎜ R + ΔT . 1 − n ⎟⎠ ⎝2

Now, Δw = n

2.

3 Current through the inductor will not change all of a sudden. (Otherwise there will be infinite EMF in the induction).

3.

6 Use Newton’s law of cooling. (Average from)

4.

5 Use FV = −6πηRv . At terminal velocity, viscous force, buoyant force and gravitational force balance out.

5.

6

u=− 6.

Gm1m2 . R

1

u=

1 2 Li 2

t ⎛ − ⎞ du di τ ⎜ = Li , i = i∞ 1 − e ⎟ dt dt ⎜ ⎟ ⎝ ⎠ t

di i∞ − τ = e . dt τ t ⎡ t − ⎞⎤ L E du Li2∞ ⎢ − τ ⎛⎜ τ ⇒ = e 1 − e ⎟ ⎥ , i∞ = , τ = R R ⎜ ⎟⎥ dt τ ⎢ ⎝ ⎠⎦ ⎣ E2 Maximum value is . ⇒ k = 1. 4R

7.

2 Use B =

8.

µ 0i [sin α + sin β] 4π

8 Use work-energy theorem.

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