** PHYSICS **

** SECTION – I **

_____________________________________________________________________________

** PART – A **

** Straight Objective Type **

*This section contains 9 multiple choice questions numbered 1 to 9. Each question has 4 choices (A), (B), (C) and (D) out of which ONLY ONE is correct. *

_____________________________________________________________________________

1. Two blocks of masses 2 kg and 4 kg are connected through a massless inextensible string. The co-efficient of friction between 2 kg block and ground is 0.4 and the coefficient of friction between 4 kg block and ground is 0.6. Two forces F1 = 10 N and F2 = 20 N are applied on the blocks as shown in the figure. Calculate the frictional force between 4 kg block and ground (Assume initially the tension in the string was just zero before forces F1 and F2 were applied)

(A) 24 N (B) 8 N

(C) 18 N (D) 10 N

2. Three large sides blocks are kept stationary over one another as shown in the figure. A horizontal force of 20 N is acting on the middle block as shown in the figure. Choose the incorrect statement.

(A) The acceleration of lowest block will be 4.5 m/s2

(B) The acceleration of uppermost block will be 2 m/s2

(C) The frictional force between middle and lower block will be 12 N.

(D) The frictional force between middle and upper block will be 2N.

3. A particle of mass m kept at the origin is subjected to a force F--> = (pt – qx) i where t is the time elapsed and x is the x co-ordinate of the position of the particle. Particle starts its motion at t = 0 with zero initial velocity. If p and q are positive constants, then:

(A) The acceleration of the particle will continuously keep on increasing with time.

(B) Particle will execute simple harmonic motion

(C) The force on the particle will have no upper limit.

(D) The acceleration of particle will vary sinusoidally with time.

5. Consider the adjacent figure. The cube shaped carriage ABCDEFGH of side l has a mass M and it can slide over two frictionless rails PQ and RS. A shot of mass m is thrown from corner A such that it lands at corner F. The angle of projected as seen from the carriage is 450. While the shot is in the air, the velocity of carriage as seen from the ground is :

6. Two balls of masses 1 kg each are connected by an inextensible massless string. The system is resting on a smooth horizontal surface. An impulse of 10 Ns is applied to one of balls at an angle 300 with the line joining two balls in horizontal direction as shown in the figure. Assuming that the string remains taut after the impulse, the magnitude of impulse of tension is:

(A) 6 Ns (B) 5/2 √3 Ns

(C) 5 Ns (D) 5/√3 Ns

7. A fixed wedge ABC is in the shape of an equilateral triangle of side l. Initially, a chain of length 2l and mass m rests on the wedge as shown. The chain is slowly being pulled down by the application of a force F as shown. Work done by gravity till the time, the chain leaves the wedge will be :

8. In the adjacent figure, all the pulleys are frictionless and massless, all the strings are also massless. The relation between a1, a2 and a3 is (Where a1, a2 and a3 are the accelerations of masses m1, m2 and m3 respectively in the direction as shown in the figure)

STATEMENT-1 : A force F1 is applied on the lower block is case (1) due to which only lowe block moves with constant velocity. A force F2 is applied on the lower block in case (2) due to which both the block moves with constant velocity. F1 and F2 will be equal. (Given that nature of surfaces is same for the cases)

because

STATEMENT-2 : Frictional force between ground and m2 will be same for both the case.

(A) Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1.

(B) Statement-1 is True, Statement-2 is True, Statement-2 is NOT a correct explanation for Statement-1.

(C) Statement-1 is True, Statement-2 is False.

(D) Statement-1 is False, Statement-2 is True.

11. STATEMENT-1 : A sphere rolls down a rough inclined plane without sliding. It gains rotational K.E. due to the work done by friction.

because

STATEMENT-2 : As the force of friction is static, net work done by friction is zero.

(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.

(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for statement-1.

(C) Statement-1 is True, Statement-2 is False.

(D) Statement-1 is False, Statement-2 is True.

12. STATEMENT-1 : When one object collides with another object, the impulse during deformation and restitution will be in same direction.

because

STATEMENT-2 : Due to this impulse the objects first deform and due to the same pulse they again try to regain its original shape.

(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.

(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.

(C) Statement-1 is True, Statement-2 is False.

(D) Statement-1 is False, Statement-2 is True.

13. STATEMENT-1 : When a soda water bottle falls freely from a height h, the gas bubble rises in water from the bottom.

because

STATEMENT-2 : Air is lighter than liquid.

(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.

(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.

(C) Statement-1 is True, Statement-2 is False.

(D) Statement-1 is False, Statement-2 is True.

LINKED COMPREHENSION TYPE

This section contains 2 paragraphs P14-16 and P17-19. Based upon each paragraphs, 3 multiple choice questions have to be answered. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct.

______________________________________________________________________

P14-16 : Paragraph for Question Nos.14 to 16

Two blocks of masses 25 kg and 5 kg are placed on a horizontal table as shown in the figure. A massless string passes over a frictionless and massless pulley whose one end is connected to 25 kg block and other end is connected to block M. The coefficient of friction between two blocks is m = 0.3 and between the 5 kg block and ground is zero. The system is released from rest. (Take g = 10 m/s2)

** PART – B**

** Matrix-Match Type**

This section contains 3 questions. Each question contains statements given in two columns which have to be matched. Statements (A, B, C, D) in column I have to be matched with statements (p, q, r, s) in column II. The answers to these questions have to be appropriately bubbled as illustrated in the following example.

If the correct match are A-p, A-s, B-q, B-r, C-p, C-q and D-s, then the correctly bubbled 4 × 4 matrix should be as follows :

** CHEMISTRY**

** SECTION – II **

_____________________________________________________________________________

** PART – A**

Straight Objective Type

This section contains 9 multiple choice questions numbered 1 to 9. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct.

1. At what molar concentration of HCI will its aqueous solution have an [H+] to which equal contribution come from HCI and H2O at 900C.

[Kw of H2O = 10–12M2 at 900C]

(A) √50 × 10–8 (B) √40 × 10–7 M

(C) √50 × 10–7 (D) √30 × 10–7

2. 100 ml of 0.5 M hydrazoic acid (N3H Ka = 3.6 × 10–4 ) and 400 ml of 0.1 M cyanic acid (HOCN1 Ka = 8 × 10–4) are mixed. Which of the following is true for final solution?

(A) [H+ ] = 2 × 10–2 M (B) [N3– ] 3.6 × 10–2 M

(C) [OCN– ] = 4.571 × 10–3 M (D) [OCN– ] = 6.4 × 10–3 M

3. Adding a few drops of hydrochloric acid to a beaker containing water results in the formation of hydrated species. Identify which hydrated species can exist in solution

(1) H3O+ (2) H3O2+

(3) H5O2+ (4) H2CIO–

(A) 1 only (B) 1 and 2

(3) 1, 2 and 3 (4) 1, 2, 3 and 4

4. Identify the incorrect statement regarding inter-halogen compounds CIF3 and FCI3.

(A) FCI3 is not possible as F does not have vacant d-orbitals to allow octet-expansion.

(B) All bond lengths in CIF3 are not identical.

(C) CIF3 has umbrella shaped geometry.

(D) F – CI – F bond angle is 900.

Aspirin is a pain reliever with pKa = 2. Two tablets each containing 0.09 gm of aspirin are dissolved in 100 ml solution. The restaurant pH is

(A) 0.5 (B) 1.1

(C) 2.2 (D) 3.5

6. The vapour density of completely dissociated NH4CI would be

(A) half that of NH4CI(g)

(B) less than half that of NH4CI

(C) more than half that of NH4CI

(D) depends on amount of NH4CI taken at start

7. In the unbalanced reaction :

AI + KMnO4 + H2SO4 ® KHSO4 + AI2 (SO4)3 + MnSO4 + H2O

If the stoichiometric coefficients of AI, H2SO4, MnSO4 and H2O are w, x, y and z respectively, the numerical value of (x/y-z/w) will be

(A) 2.0 (B) 2.1

(C) 1.2 (D) 2.4

8. Which of the features of an tom is not a direct result of Rutherford’s experiment?

(A) extra ordinary hollow nature of atom

(B) existence of circular electronic orbits

(C) small size of the nucleus

(D) exceptionally high density of nuclear material

9. If electrons were to fill up progressively with orbit saturation (neglecting Auf Bau rule) and each orbital were to accommodate three electrons, instead of two; which of the following would NOT hold correct for the new electronic arrangement in Zirconium atom (Z = 40)?

(A) the number of p-electrons would be double the number of s-electrons

(B) spin quantum number would become super flows

(C) Zirconium would continue to belong to the 4th period (in new periodic table)

(D) Zirconium would show retention of block

**ASSERTION - REASON TYPE **

This contains 4 questions numbered 10 to 13. Each question contains STATEMENT-1 (Assertion) and STATEMENT-2 (Reason). Each question has 4 choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

10. STATEMENT-1 : Le Chatliers principle is not applicable to Fe(s) + S(s) ? FeS(s)

STATEMTN-2 : Le Chatliers principle aims to push the reaction into stress – free environment.

(A) Statement-1 is True, statement-2 is True; Statement-2 is a correct explanation for Statement-1.

(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.

(C) Statement-1 is True, Statement-2 is False.

(D) Statement-1 is False, statement-2 is True.

11. STATEMENT-1 : Passing H2 gas through a muddy solution of ferric chloride result in colour change.

because

STATEMENT-2 : H2 is a reducing agent.

(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.

(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.

(C) Statement-1 is True, Statement-2 is False.

(D) Statement- is False, Statement-2 is True.

12. STATEMENT-1 : A bowler bowling the last crucial over in an India – Pakistan 20-20 match breathes heavily due to excitement and tension, leading to significant change in the pH of blood.

because

STATEMENT-2 : pH of blood = pKa + log [HCO3- ]/[H2 CO3 ]

(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.

(B) Statement-1 is True, Statement-2 is True; statement-2 is NOT a correct explanation for Statement-1.

(C) Statement-1 is True, Statement-2 is False.

(D) Statement-1 is False, Statement-2 is True.

13. STATEMENT-1 : Agl is yellow and more soluble than Ag2S in water.

because

STATEMENT-2 : Agl shows colour due to d – d transition and is more soluble as it is more covalent.

(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.

(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.

(C) Statement-1 is True, Statement-2 is False.

(D) Statement-1 is False, Statement-2 is True.

**LINKED COMPREHENSION TYPE **

This section contains 2 paragraphs C14-16 and C17-19. Based upon each paragraph, 3 multiple choice questions have to be answered. Each question has 4 choices (A0, (B), (C) and (D), out of which ONLY ONE is correct.

C14-16 : Paragraph for Question Nos. 14 to 16

The molecular orbital description of borazine takes into consideration the formation of s and pbonds in the ring. Because of the difference in electronegativity between boron and nitrogen, the pcloud in borazine is lumpy with more electron density localized on nitrogen, rather than boron. This partial localization weakens the p - bonding in the ring. In addition nitrogen retains some of its basicity and boron retains some of its acidity. Polar species such as HCI can therefore attack the double bond between N and B centres leading to addition reactions.

15. Identify the species not isoelectronic to borazine

(A) H3BO3 (B) H3B3O3

(C) ZnC3 (D) benzene

16. Identify which does not have sp3 hybridization

(A) AI centre in AI2CI6

(B) B centre in B2H6

(C) C centre in Zwitter – ion of alanine, smallest a - amino acid

(D) carbanionic carbon in allyl

C17-19 : Paragraph for Question Nos. 17 to 19

The pH value for pure water is 7.0 at 270C, where natural rain water is slightly acidic. This is mainly due to presence of CO2 in atmosphere. In many cases, however rain water is more acidic due to presence of SO3 and NO2 gas obtained by oxidation of SO2 & NO gas. In some cases acid rain due to SO3 and NO2 consist of pH of 4.5 to a value as low as 1.7 at 270C the acidity constants are

17. The pH of 0.01 M aqueous solution of Na2SO3 will be

(A) 8.5 (B) 9

(C) 9.25 (D) 9.5

18. If rain water consists of 2.463 litre SO3 gas dissolved in 1 litre water at partial pressure of 2 atm, then pH of solution is

(R = 0.0821 litre atm/K mole) (log2 = 0.3)

(A) 0.7 (B) 1.4

(C) 0.6 (D) 0.4

19. If acid rain in Assam it was found that 1 litre rain water consist of 2.463 litre equimolar mixture of SO3 and NO2 gas dissolved at a partial pressure of 0.1 atm. Find out the pH of the solution if HNO2produced is 60% dissociated under given condition at 270C. (R = 0.0821 litre atm/mole K) (log 1.8 = 0.25)

(A) 2 (B) 2.75

(C) 2.25 (D) 1.75

** PART – B**

** Matrix-Match Type **

This contains 3 questions. Each question contains statements given in two columns which have to be matched. Statements (A, B, C, D) in column I have to be matched with statements (p, q, r, s) in column II. The answers to these questions have to appropriately bubbled as illustrated in the following example. If the correct match are A-p, A-s, B-r, C-p, C-q and D-s, then the correctly bubbled 4 × 4 matrix should be as follows:

** MATHEMATICS **

** SECTION – III **

** PART – A **

**Straight Objective Type **

This section contains 9 multiple choice questions numbered 1 to 9. Each question has 4 choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

1. The order and degree of the differential equations of the family of hyperbolas centred at origin; principal axis along co-ordinate axis and of length √(a2+λ) and √(b2+λ) where a, b are fixed real numbers and λ is a real parameter is

(A) 1, 1 (B) 2, 1

(C) 1, 2 (D) 3, 2

8. Let f: [k, k + 1, …, 2007] ® [1, 2, 3, …, n] be defined by f(x) = [ 2007 / x ] (where [.] denotes the greatest integer function). The maximum value of k such that it is not possible to make f an onto function for any vale of n is

(A) 50 (B) 40

(C) 51 (D) none of these

9. Let f and g be continuous and differentiable functions. If f(0) = f(2) = f(4); f(1) + f(3) = 0; g(0) = g(2) = g(4) = 0 and if f(x) = 0 and g’(x) = 0 do not have a common root, then the minimum number of zeros of f’(x)g’(x) + f(x) g”(x) in [0, 4] is

(A) 3 (B) 4

(C) 5 (D) 2

**ASSERTION – REASON TYPE **

This contains 4 questions numbered 10 to 13. Each question contains STATEMENT-1 (Assertion) STATEMENT-2 (Reason). Each question has 4 choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

__________________________________________________________________________

10. Statement-1 : if f(x) = [x] (sinx + cosx – 1), (where [.] denotes the greatest integer function) then f’(x) = [x](cosx – sinx) for any x Î non-integer.

because

Statement-2 : f’(x) does not exist for any x Î integer.

(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.

(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.

(C) Statement-1 is True, Statement-2 is False

(D) Statement-2 is False, Statement-2 is True

11. Statement-1 : The function f(x) = (x2 + x – 2) (x2 + 2x – 3) has local extremum at x = 1.

because

Statement-2 : f(x) is continuous and differentiable and f’(1) = 0

(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.

(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.

(C) Statement-1 is True, Statement-2 is False.

(D) Statement-1 is False, Statement-2 is True.

12. f(x) is a polynomial of degree 3 passing through origin having local extrema at x = + 2.

because

Statement-2 : Both y = f(x) and the circle are symmetric about origin.

(A) Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1.

(B) Statement-1 is True, Statement-2 is True, Statement-2 is NOT a correct explanation for Statement-1.

(C) Statement-1 is True, statement-2 is False.

(D) Statement-1 is False, Statement-2 is True.

13. Statement-1 : The function f(x) = a1e|x|+ a2|x|5 where a1, a2 are constant is differentiable at x = 0 if a1 = 0.

because

Statement-2 : e|x| is a many one function.

(A) Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1.

(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.

(C) Statement-1 is True, Statement-2 is False.

(D) Statement-1 is False, Statement-2 is True.

**LINKED COMPREHENSION TYPE **

This section contains 2 paragraphs C14–16 and C17–19. Based upon each paragraph, 3 multiple choice questions have to be answered. Each question has 4 choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

C14-16 : Paragraph for Question Nos. 14 to 16

f(x) is continuous and differentiable function. Given f(x) takes values of the form + √I where I denotes set of whole numbers whenever x = a or b; otherwise f(x) takes real values. Also f(c) = -3/2 and |f(a)|<|f(b)|.

14. The number of rational values that f(a) + f(b) + f(c) can take is / are

(A) 4 (B) 2

(C) 3 (D) 5

15. The number of values that (f(a))2 + (f(b))2 + (f(c))2 can take is

(A) 4 (B) 2

(C) 7 (D) 7

16. The possible number of triplets (f(a), (f(b), (f(c)) is / are

(A) 4 (B) 5

(C) 7 (D) 6

18. In the above question the value of n is

(A) 3 (B) 4

(C) 5 (D) 6

19. If the area bounded by y = u(x) and y = | v(x) | consists of p different parts then p equals

(A) 6 (B) 4

(C) 8 (D) 7

** PART – B**

** Matrix-Match Type **

This section contains 3 questions. Each question contains statements given in two columns which have to be matched. Statements (A, B, C, D) in Column I have to matched with statements (p, q, r, s) in Column II. The answers to these questions have to be appropriately bubbled as illustrated in the following example.

If the correct matches are A-p, A-s, B-q, B-r, C-p, C-q and D-s, then the correctly bubbled 4 × 4 matrix should be as follows:

Joined:31 Mar 2012Posts:81PHYSICSSECTION – I_____________________________________________________________________________

PART – A

Straight Objective TypeThis section contains 9 multiple choice questions numbered 1 to 9. Each question has 4 choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

_____________________________________________________________________________1. Two blocks of masses 2 kg and 4 kg are connected through a massless inextensible string. The co-efficient of friction between 2 kg block and ground is 0.4 and the coefficient of friction between 4 kg block and ground is 0.6. Two forces F1 = 10 N and F2 = 20 N are applied on the blocks as shown in the figure. Calculate the frictional force between 4 kg block and ground (Assume initially the tension in the string was just zero before forces F1 and F2 were applied)

(A) 24 N (B) 8 N

(C) 18 N (D) 10 N

2. Three large sides blocks are kept stationary over one another as shown in the figure. A horizontal force of 20 N is acting on the middle block as shown in the figure. Choose the incorrect statement.

(A) The acceleration of lowest block will be 4.5 m/s2

(B) The acceleration of uppermost block will be 2 m/s2

(C) The frictional force between middle and lower block will be 12 N.

(D) The frictional force between middle and upper block will be 2N.

3. A particle of mass m kept at the origin is subjected to a force F--> = (pt – qx) i where t is the time elapsed and x is the x co-ordinate of the position of the particle. Particle starts its motion at t = 0 with zero initial velocity. If p and q are positive constants, then:

(A) The acceleration of the particle will continuously keep on increasing with time.

(B) Particle will execute simple harmonic motion

(C) The force on the particle will have no upper limit.

(D) The acceleration of particle will vary sinusoidally with time.

5. Consider the adjacent figure. The cube shaped carriage ABCDEFGH of side l has a mass M and it can slide over two frictionless rails PQ and RS. A shot of mass m is thrown from corner A such that it lands at corner F. The angle of projected as seen from the carriage is 450. While the shot is in the air, the velocity of carriage as seen from the ground is :

6. Two balls of masses 1 kg each are connected by an inextensible massless string. The system is resting on a smooth horizontal surface. An impulse of 10 Ns is applied to one of balls at an angle 300 with the line joining two balls in horizontal direction as shown in the figure. Assuming that the string remains taut after the impulse, the magnitude of impulse of tension is:

(A) 6 Ns (B) 5/2 √3 Ns

(C) 5 Ns (D) 5/√3 Ns

7. A fixed wedge ABC is in the shape of an equilateral triangle of side l. Initially, a chain of length 2l and mass m rests on the wedge as shown. The chain is slowly being pulled down by the application of a force F as shown. Work done by gravity till the time, the chain leaves the wedge will be :

8. In the adjacent figure, all the pulleys are frictionless and massless, all the strings are also massless. The relation between a1, a2 and a3 is (Where a1, a2 and a3 are the accelerations of masses m1, m2 and m3 respectively in the direction as shown in the figure)

STATEMENT-1 : A force F1 is applied on the lower block is case (1) due to which only lowe block moves with constant velocity. A force F2 is applied on the lower block in case (2) due to which both the block moves with constant velocity. F1 and F2 will be equal. (Given that nature of surfaces is same for the cases)

because

STATEMENT-2 : Frictional force between ground and m2 will be same for both the case.

(A) Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1.

(B) Statement-1 is True, Statement-2 is True, Statement-2 is NOT a correct explanation for Statement-1.

(C) Statement-1 is True, Statement-2 is False.

(D) Statement-1 is False, Statement-2 is True.

11. STATEMENT-1 : A sphere rolls down a rough inclined plane without sliding. It gains rotational K.E. due to the work done by friction.

because

STATEMENT-2 : As the force of friction is static, net work done by friction is zero.

(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.

(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for statement-1.

(C) Statement-1 is True, Statement-2 is False.

(D) Statement-1 is False, Statement-2 is True.

12. STATEMENT-1 : When one object collides with another object, the impulse during deformation and restitution will be in same direction.

because

STATEMENT-2 : Due to this impulse the objects first deform and due to the same pulse they again try to regain its original shape.

(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.

(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.

(C) Statement-1 is True, Statement-2 is False.

(D) Statement-1 is False, Statement-2 is True.

13. STATEMENT-1 : When a soda water bottle falls freely from a height h, the gas bubble rises in water from the bottom.

because

STATEMENT-2 : Air is lighter than liquid.

(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.

(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.

(C) Statement-1 is True, Statement-2 is False.

(D) Statement-1 is False, Statement-2 is True.

LINKED COMPREHENSION TYPE

This section contains 2 paragraphs P14-16 and P17-19. Based upon each paragraphs, 3 multiple choice questions have to be answered. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct.

______________________________________________________________________

P14-16 : Paragraph for Question Nos.14 to 16

Two blocks of masses 25 kg and 5 kg are placed on a horizontal table as shown in the figure. A massless string passes over a frictionless and massless pulley whose one end is connected to 25 kg block and other end is connected to block M. The coefficient of friction between two blocks is m = 0.3 and between the 5 kg block and ground is zero. The system is released from rest. (Take g = 10 m/s2)

PART – BMatrix-Match TypeThis section contains 3 questions. Each question contains statements given in two columns which have to be matched. Statements (A, B, C, D) in column I have to be matched with statements (p, q, r, s) in column II. The answers to these questions have to be appropriately bubbled as illustrated in the following example.

If the correct match are A-p, A-s, B-q, B-r, C-p, C-q and D-s, then the correctly bubbled 4 × 4 matrix should be as follows :

CHEMISTRYSECTION – II_____________________________________________________________________________

PART – AStraight Objective Type

This section contains 9 multiple choice questions numbered 1 to 9. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct.

1. At what molar concentration of HCI will its aqueous solution have an [H+] to which equal contribution come from HCI and H2O at 900C.

[Kw of H2O = 10–12M2 at 900C]

(A) √50 × 10–8 (B) √40 × 10–7 M

(C) √50 × 10–7 (D) √30 × 10–7

2. 100 ml of 0.5 M hydrazoic acid (N3H Ka = 3.6 × 10–4 ) and 400 ml of 0.1 M cyanic acid (HOCN1 Ka = 8 × 10–4) are mixed. Which of the following is true for final solution?

(A) [H+ ] = 2 × 10–2 M (B) [N3– ] 3.6 × 10–2 M

(C) [OCN– ] = 4.571 × 10–3 M (D) [OCN– ] = 6.4 × 10–3 M

3. Adding a few drops of hydrochloric acid to a beaker containing water results in the formation of hydrated species. Identify which hydrated species can exist in solution

(1) H3O+ (2) H3O2+

(3) H5O2+ (4) H2CIO–

(A) 1 only (B) 1 and 2

(3) 1, 2 and 3 (4) 1, 2, 3 and 4

4. Identify the incorrect statement regarding inter-halogen compounds CIF3 and FCI3.

(A) FCI3 is not possible as F does not have vacant d-orbitals to allow octet-expansion.

(B) All bond lengths in CIF3 are not identical.

(C) CIF3 has umbrella shaped geometry.

(D) F – CI – F bond angle is 900.

Aspirin is a pain reliever with pKa = 2. Two tablets each containing 0.09 gm of aspirin are dissolved in 100 ml solution. The restaurant pH is

(A) 0.5 (B) 1.1

(C) 2.2 (D) 3.5

6. The vapour density of completely dissociated NH4CI would be

(A) half that of NH4CI(g)

(B) less than half that of NH4CI

(C) more than half that of NH4CI

(D) depends on amount of NH4CI taken at start

7. In the unbalanced reaction :

AI + KMnO4 + H2SO4 ® KHSO4 + AI2 (SO4)3 + MnSO4 + H2O

If the stoichiometric coefficients of AI, H2SO4, MnSO4 and H2O are w, x, y and z respectively, the numerical value of (x/y-z/w) will be

(A) 2.0 (B) 2.1

(C) 1.2 (D) 2.4

8. Which of the features of an tom is not a direct result of Rutherford’s experiment?

(A) extra ordinary hollow nature of atom

(B) existence of circular electronic orbits

(C) small size of the nucleus

(D) exceptionally high density of nuclear material

9. If electrons were to fill up progressively with orbit saturation (neglecting Auf Bau rule) and each orbital were to accommodate three electrons, instead of two; which of the following would NOT hold correct for the new electronic arrangement in Zirconium atom (Z = 40)?

(A) the number of p-electrons would be double the number of s-electrons

(B) spin quantum number would become super flows

(C) Zirconium would continue to belong to the 4th period (in new periodic table)

(D) Zirconium would show retention of block

ASSERTION - REASON TYPE

This contains 4 questions numbered 10 to 13. Each question contains STATEMENT-1 (Assertion) and STATEMENT-2 (Reason). Each question has 4 choices (A), (B), (C) and (D) out of which ONLY ONE is correct.10. STATEMENT-1 : Le Chatliers principle is not applicable to Fe(s) + S(s) ? FeS(s)

STATEMTN-2 : Le Chatliers principle aims to push the reaction into stress – free environment.

(A) Statement-1 is True, statement-2 is True; Statement-2 is a correct explanation for Statement-1.

(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.

(C) Statement-1 is True, Statement-2 is False.

(D) Statement-1 is False, statement-2 is True.

11. STATEMENT-1 : Passing H2 gas through a muddy solution of ferric chloride result in colour change.

because

STATEMENT-2 : H2 is a reducing agent.

(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.

(C) Statement-1 is True, Statement-2 is False.

(D) Statement- is False, Statement-2 is True.

12. STATEMENT-1 : A bowler bowling the last crucial over in an India – Pakistan 20-20 match breathes heavily due to excitement and tension, leading to significant change in the pH of blood.

because

STATEMENT-2 : pH of blood = pKa + log [HCO3- ]/[H2 CO3 ]

(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.

(B) Statement-1 is True, Statement-2 is True; statement-2 is NOT a correct explanation for Statement-1.

(C) Statement-1 is True, Statement-2 is False.

(D) Statement-1 is False, Statement-2 is True.

13. STATEMENT-1 : Agl is yellow and more soluble than Ag2S in water.

because

STATEMENT-2 : Agl shows colour due to d – d transition and is more soluble as it is more covalent.

(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.

(C) Statement-1 is True, Statement-2 is False.

(D) Statement-1 is False, Statement-2 is True.

LINKED COMPREHENSION TYPE

This section contains 2 paragraphs C14-16 and C17-19. Based upon each paragraph, 3 multiple choice questions have to be answered. Each question has 4 choices (A0, (B), (C) and (D), out of which ONLY ONE is correct.

C14-16 : Paragraph for Question Nos. 14 to 16

The molecular orbital description of borazine takes into consideration the formation of s and pbonds in the ring. Because of the difference in electronegativity between boron and nitrogen, the pcloud in borazine is lumpy with more electron density localized on nitrogen, rather than boron. This partial localization weakens the p - bonding in the ring. In addition nitrogen retains some of its basicity and boron retains some of its acidity. Polar species such as HCI can therefore attack the double bond between N and B centres leading to addition reactions.

15. Identify the species not isoelectronic to borazine

(A) H3BO3 (B) H3B3O3

(C) ZnC3 (D) benzene

16. Identify which does not have sp3 hybridization

(A) AI centre in AI2CI6

(B) B centre in B2H6

(C) C centre in Zwitter – ion of alanine, smallest a - amino acid

(D) carbanionic carbon in allyl

C17-19 : Paragraph for Question Nos. 17 to 19

The pH value for pure water is 7.0 at 270C, where natural rain water is slightly acidic. This is mainly due to presence of CO2 in atmosphere. In many cases, however rain water is more acidic due to presence of SO3 and NO2 gas obtained by oxidation of SO2 & NO gas. In some cases acid rain due to SO3 and NO2 consist of pH of 4.5 to a value as low as 1.7 at 270C the acidity constants are

17. The pH of 0.01 M aqueous solution of Na2SO3 will be

(A) 8.5 (B) 9

(C) 9.25 (D) 9.5

18. If rain water consists of 2.463 litre SO3 gas dissolved in 1 litre water at partial pressure of 2 atm, then pH of solution is

(R = 0.0821 litre atm/K mole) (log2 = 0.3)

(A) 0.7 (B) 1.4

(C) 0.6 (D) 0.4

19. If acid rain in Assam it was found that 1 litre rain water consist of 2.463 litre equimolar mixture of SO3 and NO2 gas dissolved at a partial pressure of 0.1 atm. Find out the pH of the solution if HNO2produced is 60% dissociated under given condition at 270C. (R = 0.0821 litre atm/mole K) (log 1.8 = 0.25)

(A) 2 (B) 2.75

(C) 2.25 (D) 1.75

PART – BMatrix-Match Type

This contains 3 questions. Each question contains statements given in two columns which have to be matched. Statements (A, B, C, D) in column I have to be matched with statements (p, q, r, s) in column II. The answers to these questions have to appropriately bubbled as illustrated in the following example. If the correct match are A-p, A-s, B-r, C-p, C-q and D-s, then the correctly bubbled 4 × 4 matrix should be as follows:

MATHEMATICSSECTION – III

PART – A

Straight Objective Type

This section contains 9 multiple choice questions numbered 1 to 9. Each question has 4 choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

1. The order and degree of the differential equations of the family of hyperbolas centred at origin; principal axis along co-ordinate axis and of length √(a2+λ) and √(b2+λ) where a, b are fixed real numbers and λ is a real parameter is

(A) 1, 1 (B) 2, 1

(C) 1, 2 (D) 3, 2

8. Let f: [k, k + 1, …, 2007] ® [1, 2, 3, …, n] be defined by f(x) = [ 2007 / x ] (where [.] denotes the greatest integer function). The maximum value of k such that it is not possible to make f an onto function for any vale of n is

(A) 50 (B) 40

(C) 51 (D) none of these

9. Let f and g be continuous and differentiable functions. If f(0) = f(2) = f(4); f(1) + f(3) = 0; g(0) = g(2) = g(4) = 0 and if f(x) = 0 and g’(x) = 0 do not have a common root, then the minimum number of zeros of f’(x)g’(x) + f(x) g”(x) in [0, 4] is

(A) 3 (B) 4

(C) 5 (D) 2

ASSERTION – REASON TYPE

This contains 4 questions numbered 10 to 13. Each question contains STATEMENT-1 (Assertion) STATEMENT-2 (Reason). Each question has 4 choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

__________________________________________________________________________

10. Statement-1 : if f(x) = [x] (sinx + cosx – 1), (where [.] denotes the greatest integer function) then f’(x) = [x](cosx – sinx) for any x Î non-integer.

because

Statement-2 : f’(x) does not exist for any x Î integer.

(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.

(C) Statement-1 is True, Statement-2 is False

(D) Statement-2 is False, Statement-2 is True

11. Statement-1 : The function f(x) = (x2 + x – 2) (x2 + 2x – 3) has local extremum at x = 1.

because

Statement-2 : f(x) is continuous and differentiable and f’(1) = 0

(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.

(C) Statement-1 is True, Statement-2 is False.

(D) Statement-1 is False, Statement-2 is True.

12. f(x) is a polynomial of degree 3 passing through origin having local extrema at x = + 2.

because

Statement-2 : Both y = f(x) and the circle are symmetric about origin.

(A) Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1.

(B) Statement-1 is True, Statement-2 is True, Statement-2 is NOT a correct explanation for Statement-1.

(C) Statement-1 is True, statement-2 is False.

(D) Statement-1 is False, Statement-2 is True.

13. Statement-1 : The function f(x) = a1e|x|+ a2|x|5 where a1, a2 are constant is differentiable at x = 0 if a1 = 0.

because

Statement-2 : e|x| is a many one function.

(A) Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1.

(C) Statement-1 is True, Statement-2 is False.

(D) Statement-1 is False, Statement-2 is True.

LINKED COMPREHENSION TYPE

This section contains 2 paragraphs C14–16 and C17–19. Based upon each paragraph, 3 multiple choice questions have to be answered. Each question has 4 choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

C14-16 : Paragraph for Question Nos. 14 to 16

f(x) is continuous and differentiable function. Given f(x) takes values of the form + √I where I denotes set of whole numbers whenever x = a or b; otherwise f(x) takes real values. Also f(c) = -3/2 and |f(a)|<|f(b)|.

14. The number of rational values that f(a) + f(b) + f(c) can take is / are

(A) 4 (B) 2

(C) 3 (D) 5

15. The number of values that (f(a))2 + (f(b))2 + (f(c))2 can take is

(A) 4 (B) 2

(C) 7 (D) 7

16. The possible number of triplets (f(a), (f(b), (f(c)) is / are

(A) 4 (B) 5

(C) 7 (D) 6

18. In the above question the value of n is

(A) 3 (B) 4

(C) 5 (D) 6

19. If the area bounded by y = u(x) and y = | v(x) | consists of p different parts then p equals

(A) 6 (B) 4

(C) 8 (D) 7

PART – BMatrix-Match Type

This section contains 3 questions. Each question contains statements given in two columns which have to be matched. Statements (A, B, C, D) in Column I have to matched with statements (p, q, r, s) in Column II. The answers to these questions have to be appropriately bubbled as illustrated in the following example.

If the correct matches are A-p, A-s, B-q, B-r, C-p, C-q and D-s, then the correctly bubbled 4 × 4 matrix should be as follows: