IIT-JEE 2012 - XtraEdge Dec 2010

XtraEdge Test Series # 8

Based on New Pattern

Time : 3 Hours

Syllabus :

Physics : Full Syllabus, Chemistry : Full Syllabus, Mathematics : Full syllabus

Instructions : Section - I

• Question 1 to 6 are multiple choice questions with only one correct answer. +3 marks will be awarded for correct answer and -1 mark for wrong answer.

• Question 7 to 10 are multiple choice questions with multiple correct answer. +4 marks and No negative mark for wrong answer.

Section - II

• Question 11 to 14 are Reason and Assertion type question with one is correct answer. +3 marks and –1 mark for wrong answer.

• Question 15 to 23 are passage based single type questions. +4 marks will be awarded for correct answer and -1 mark for wrong answer.

6. Two boys are separated by a distance 50 m and are standing away from a vertical wall. When one of the bopys claps, the other boy hears the echo after 1 s. If velocity of sound in air is 330 ms^–1 then distance of the boy from the wall is –

Q B

(A) 330 m (B) 818 m

Questions 7 to 10 are multiple choice questions. Each question has four choices (A), (B), (C) and (D), out of which MULTIPLE (ONE OR MORE) is correct. Mark your response in OMR sheet against the question number of that question. + 4 marks will be given for each correct answer and NO NEGATIVE marks for wrong answer.

7. A bus is moving with a velocity of 30 m/s towards a huge wall. The driver sounds a horn of frequency 120 Hz. If the speed of sound in air = 330 m/s. Select the correct option -

(A) Frequency received by wall is 120 Hz (B) Frequency received by wall is 132 Hz

(D) Frequency of reflected wave observed by the driver is 144 Hz

8. A cyclist rides along the circumference of a circular horizontal plane of radius R, the friction coefficient being dependent only on distance r from the centre O of the plane as µ = µ₀ 



 



 R – r

1 , where µ₀ is a constant. Which of the following is/are correct ? (A) The radius 'r' of the circle with the centre at the

point along which the cyclist can ride with the maximum velocity, r =

2 R

(B) The radius 'r' of the circle with the centre at the point along which the cyclist can ride with the maximum velocity vmax =

2 1 µgR (C) The maximum velocity vmax= µgR (D) none

9. A bob of mass m is projected with an upward velocity v0 so that it moves in a vertical circle of radius R in a vertical smooth circular tube. The normal reaction on it is zero, the velocity of bob will be –

R v0

(A) 3 v₀

(B) _^









 3 1 v0

(D)

3 v₀

10. A particle of mass 'm' is moving with an acceleration 3

a towards left relative to the trolley car. James bond accelerates towards left with an acceleration of magnitude

a. If the car moves with a rightward acceleration 'a', the magnitude of pseudo-force acting on 'm' viewed by James bond will be –

car a/3 m a/3

James bond

(A) 3

mg (B)

3 ma 2

3 ma 4

This section contains 4 questions numbered 11 to 14, (Reason and Assertion type question). Each question contains Assertion and Reason. Each question has 4 choices (A), (B), (C) and (D) out of which ONLY ONE is correct. Mark your response in OMR sheet against the question number of that question. + 3 marks will be given for each correct answer and – 1 mark for each wrong answer.

The following questions given below consist of an "Assertion" (A) and "Reason" (R) Type questions. Use the following Key to choose the appropriate answer.

(A) If both (A) and (R) are true, and (R) is the correct explanation of (A).

(B) If both (A) and (R) are true but (R) is not the correct explanation of (A).

(C) If (A) is true but (R) is false.

(D) If (A) is false but (R) is true.

11. Assertion (A) : While drawing a line on paper, friction force acts on paper in the same direction along which line is drawn on the paper.

Reason (R) : Friction always opposes motion.

12. Assertion (A) : Work done by a conservative force is always zero in round trip of the point of application of force.

Reason (R) : Sometimes, a conservative force does positive work, negative work and zero work; as a whole, the net work done must be zero for a round trip.

13. Assertion (A) : A particle of mass 'm' is moving with constant speed v along circular path of constant radius.

The net acceleration of the particle is constant in this case.

Reason (R) : The tangential acceleration of the particle moving along circular path is defined as the rate of change of speed of the particle with time.

14. Assertion (A) : The potential energy is only defined for the conservative forces.

Reason (R) : In case of uniform circular motion, the change in kinetic energy of the moving object is zero.

This section contains 3 paragraphs, each has 3 multiple choice questions. (Questions 15 to 23) Each question has 4 choices (A), (B), (C) and (D) out of which ONLY ONE is correct. Mark your response in OMR sheet against the question number of that question. + 4 marks will be given for each correct answer and – 1 mark for each wrong answer.

Passage # 1 (Ques. 15 to 17)

A uniform rod of mass 'm' length 'l' is sliding along its length on a horizontal table whose top is partly smooth and rest rough with friction coefficient µ. If the rod after moving through smooth part, enters the rough with velocity v0.

l v0

Smooth A

B µ (rough)

15. The magnitude of the friction force when its 'x' length (<L) lies in the rough part during sliding will be - (A)

x 2

g ml²

µ (B)

x mgl² µ

µ (D)

l µmgx

16. The minimum velocity v0 with which it must enter so that it lies completely in rough region before coming to rest, is -

(A) lµ g (B) l2µg

2 gl µ

17. If the velocity is double the minimum velocity (v0) as calculated in above question then what distance does its front end A would have travelled in rough region before rod comes to rest ?

(A) 2

3l (B)

2 5l

Passage # 2 (Ques. 18 to 20)

With the help of Archimede's principle, one can understand the floating nature and defects in metal formation. One can easily find out the amount of space left hollow in a sphere. For a body to float, there should be a balance between the weight of the body and the upthrust. The apparent weight felt differs based on the volume immersed in the liquid.

More than one liquid may also balance the mass while floating. In a frame accelerated down with 'a' any mass will experience a normal force of m(g – a).

18. For a cubical block (ρ) to float in a pair of liquids of density ρ₁ and ρ₂ as show, the relation between ρ, ρ₁ and ρ₂ is –

x 2x ρ₁

ρ₂

(A) ρ = 2

2 1+ρ

ρ (B) ρ =

3 2ρ₂+ρ₁

(D) ρ =

2 1+ρ ρ

19. If the container in which a body floats in a liquid falls under gravity, the upthrust felt by the body will be (symbols carry usual meaning) -

(A) zero (B) V_lρ_lg (C) 2

V_l

ρ_l g (D) Vbρb g

20. An ice cube holding a steel ball floats in a cup of water. After all the ice melts, the level in the cup will-

(A) rise

(B) fall

(D) cannot be confirmed without know8ing density of steel ball

Passage # 3 (Ques. 21 to 23)

In espresso coffee machines steam is passed into milk at room temperature for a brief time interval. Some of the steam condenses and the temperature or milk rises. Since the time for which the steam is passed is brief, one can ignore the heat lost to the environment and assume that the usual assumption of calorimetry : Heat lost = Heat gain is valid.

21. Steam at 100ºC is passed into milk to heat it. The amount of heat required to heat 150 g of milk from room temperature (20ºC) to 80ºC is (specific heat of capacity of milk = 4.0 kJ kg^–1K^–1specific latent heat of steam = 2.2 MJ kg^–1, specific heat capacity of water = 4.2 × 10³J kgK^–1)

(A) 3.6 × 10⁴ J (B) 3.6 × 10³J (C) 3.6 × 10² J (D) None of these 22. How many grams of steam condensed into water in

above question -

(A) 1.57 g (B) 15.7 g (C) 157 g (D) None of these 23. If some of heat is allowed to escape to surrounding

(temperature of surrounding is 20ºC) then this amount of steam (mentioned in question 22) is increase the temperature to -

(A) greater than 80ºC (B) less than 80ºC (C) equal to 80ºC (D) can't say anything

CHEMISTRY

Questions 1 to 6 are multiple choice questions. Each question has four choices (A), (B), (C) and (D), out of which ONLY ONE is correct. Mark your response in OMR sheet against the question number of that question. + 3 marks will be given for each correct answer and – 1 mark for each wrong answer.

1. The equivalent weight of MnSO4 is half its molecular weight when it is converted to :

(A) Mn2O3 (B) MnO2

2. The increasing order (lowest first) for the values of e/m (charge/mass) for electron (e), proton (p), neutron (n) and alpha particle (α) is :

(A) e, p, n, α (B) n, p, e, α (C) n, p, α, e (D) n, α, p, e 3. The molecule having one unpaired electron is :

(A) NO (B) CO

4. For the chemical reaction 3X(g) + Y(g) X3 Y(g) the amount of X3 Y at equilibrium is affected by (A) temperature and pressure

(B) temperature only (C) pressure only

(D) temperature, pressure and catalyst

5. The correct order of second ionisation potential of carbon, nitrogen, oxygen and fluorine is

(A) C > N > O > F (B) O > N > F > C (C) O > F > N > C (D) F > O > N > C

6. Which of the following has the maximum number of unpaired electrons?

(A) Mg²⁺ (B) Ti³⁺

7. The statements that are true for the long form of the periodic table are :

(A) it reflects the sequence of filling the electrons in the order of sub-energy level s, p, d and f.

(B) it helps to predict the stable valency states of the elements

(D) it helps to predict the relative ionicity of the bond between any two elements.

8. Benzyl chloride (C6H5CH2Cl) can be prepared from toluene by chlorination with?

(A) SO2Cl2 (B) SOCl2

9. Which of the following are examples of aldol condensation?

(A) 2CH3CHO ^dil^.^NaOH→ CH3CHOHCH2CHO (B) 2CH3COCH3 ^dil^.^NaOH→

CH3COH(CH3)CH2COCH3

(A) have 4n π electrons (B) have (4n + 2) π electrons (C) be planar

(D) be cyclic

The following questions given below consist of an "Assertion" (A) and "Reason" (R) Type questions. Use the following Key to choose the appropriate answer.

(A) If both (A) and (R) are true, and (R) is the correct explanation of (A).

(B) If both (A) and (R) are true but (R) is not the correct explanation of (A).

(C) If (A) is true but (R) is false.

(D) If (A) is false but (R) is true.

11. Assertion (A) : Addition of bromine to trans-2-butene yields meso-2,3-dibromobutane.

Reason (R) : Bromine addition to an alkene is an electrophilic addition.

12. Assertion (A) : In water, orthoboric acid behaves as a weak monobasic acid.

Reason (R) : In water, orthoboric acid acts as a proton donor

13. Assertion (A) : Nuclide ₁₃³⁰ Al is less stable than ⁴⁰₂₀ Ca

Reason (R) : Nuclides having odd number of protons and neutrons are generally unstable.

14. Assertion (A) : The electronic structure of O3 is ^O

O • •

• •

••

O • •

• • • • Θ

⊕

Reason (R) : ^O O • •

• •

••

O • •

• • structure is not allowed because octet around O cannot be expanded.

Passage # 1 (Ques. 15 to 17)

The noble gases have closed-shell electronic configuration and are monoatomic gases under normal conditions. The low boiling points of the lighter noble gases are due to weak dispersion forces between the atoms and the absence of other interatomic interactions.

The direct reaction of xenon with fluorine leads to a series of compounds with oxidation numbers +2, +4 and +6. XeF4 reacts violently with water to given XeO3. The compounds of xenon exhibit rich stereochemistry and their geometries can be deduced considering the total number of electron pairs in the valence shell.

15. Argon is used in arc welding because of its - (A) low reactivity with metal

(B) ability to lower the melting point of metal (C) flammability

(D) high calorific value

16. The structure of XeO3 is

(A) linear (B) planar (C) pyramidal (D) T-shaped 17. XeF4 and XeF6 are expected to be

(A) oxidizing (B) reducing (C) unreactive (D) strongly basic Passage # 2 (Ques. 18 to 20)

Riemer-Tiemann reaction introduces an aldehyde group, on to the aromatic ring of phenol, ortho to the hydroxyl group. This reaction involves electrophilic aromatic substitution. This is a general method for the synthesis of substituted salicylaldehyde as depicted below.

CH3

[I]

O Na

CH3

Θ ⊕

CHO aq.HCl

CH3

CHO

(I) (II) (III)

18. Which one of the following reagents is used in the above reaction?

(A) aq.NaOH + CH3Cl (B) aq.NaOH + CH2Cl2

(A) :CHCl (B) ⁺CHCl2

(A) O Na

CH₃ Θ ⊕

CH₂Cl

(B) O Na

CH₃ Θ ⊕

CHCl₂

(C)

O Na

CH₃ Θ ⊕

CCl₃

(D) O Na

CH₃ Θ ⊕

CH₂OH

Passage # 3 (Ques. 21 to 23)

Several short-lived radioactive species have been used to determine the age of wood or animal fossils.

One of the most interesting substances is 6C¹⁴ (half-life 5760 years) which is used in determining the age of carbon-bearing materials (e.g. wood, animal fossils, etc.). Carbon-14 is produced by the bombardment of nitrogen atoms present in the upper atmosphere with neutrons (from cosmic rays).

7N¹⁴ + 0n¹ → ₆C¹⁴ + 1H¹

Thus carbon-14 is oxidised to CO2 and eventually ingested by plants and animals. The death of plants or animals put an end to the intake of C¹⁴from the atmosphere. After this the amount of C¹⁴in the dead tissues starts decreasing due to its disintegration as per the following reaction :

6C¹⁴ → ₇N¹⁴ + –1β⁰

The C¹⁴ isotope enters the biosphere when carbon dioxide is taken up in plant photosynthesis. Plants are eaten by animals, which exhale C¹⁴ as CO2. Eventually, C¹⁴participates in many aspects of the carbon cycle. The C¹⁴lost by radioactive decay is constantly replenished by the production of new isotopes in the atmosphere. In this decay-replenishment process, a dynamic equilibrium is established whereby the ratio of C¹⁴to C¹² remains constant in living matter. But when an individual plant or an animal dies, the C¹⁴ isotope in it is no longer replenished, so the ratio decreases as C¹⁴ decays. So, the number of C¹⁴ nuclei after time t (after the death of living matter) would be less than in a living matter. The decay constant can be calculated using the following formula,

t1/2 = λ 693 . 0

The intensity of the consmic rays have remain the same for 30,000 years. But since some years the changes in this are observed due to excessive burning of fossil fuel and nuclear tests.

21. Why do we use the carbon dating to calculate the age of the fossil?

(A) Rate of exchange of carbon between atmosphere and living is slower than decay of C¹⁴

(B) It is not appropriate to use C¹⁴ dating to determine age

(C) Rate of exchange of C¹⁴dating to determine age organism is so fast that an equilibrium is set up between the intake of C¹⁴ by organism and its exponential decay

(D) none of the above

22. What should be the age of the fossil for meaningful determination of its age?

(A) 6 years (B) 6000 years

(D) can be used to calculate any age

23. A nuclear explosion has taken place leading to increase in concentration of C¹⁴ in nearby areas. C¹⁴ concentration is C1 in nearby areas and C2 in areas far away. If the age of the fossil is determined to be T1 and T2 at the respective places then

(A) The age of the fossil will increase at the place where explosion has taken place and T1 – T2 =

(B) The age of the fossil will decrease at the place where explosion has taken place and T1 – T2 =

(D)

1. z is a complex number satisfying |z – 3| ≤ 4 and the possible positions of P are

(A) 72 (B) 36

7. Tangents are drawn from the point (α, 3) to the circle

(B) exists and the coefficient is divisible by 29 (C) exists and the coefficient is divisible by 63 (D) exists and the coefficient is divisible by 65 9. Suppose a1, a2, ... real numbers, with a1 ≠ 0. If a₁, a2, infinite number of solutions

10. An equation of a circle through the origin, making an intercept of 10 on the line y = 2x + 5/ 2 , which

The following questions given below consist of an "Assertion" (A) and "Reason" (R) Type questions. Use the following Key to choose the appropriate answer.

(A) If both (A) and (R) are true, and (R) is the correct explanation of (A).

(B) If both (A) and (R) are true but (R) is not the correct explanation of (A).

(C) If (A) is true but (R) is false. Reason (R) : In any triangle bisector of an angle of divides the triangle into two similar triangles.

12. Assertion (A) : Let p < 0 and α1, α2, ... α9 be the

Reason (R) : If two rows of a determinant are identical then determinant equals zero.

13. Assertion (A) : If Assertion (A) : The parametric equations of the line of intersection of the given planes are x = 3 + 14t, y = 1 + 2t, z = 15t.

Reason (R) : The vector 14 + ^{^}i 2 + 15 ^{^}j ^{^}k is parallel to the line of intersection of the given planes.

Passage # 1 (Ques. 15 to 17)

A and B are two points on the boundary of a circular field of radius R and centre O. ∠AOB = θ. A circle with centre A and radius AB meets the circular field again at C and the line AO produced at E. L, M are points on the boundary of the field lying between C and A, A and B, respectively.

15. AB is equal to

(A) R sin θ (B) 2R sin (θ/2) (C) R cos θ (D) 2R cos (θ/2)

16. Area of the segment AMB is equal to (A) (1/2) R² θ (B) (1/2) R²sin θ (C) (1/2) R² (θ – sin θ) (D) none of these

17. If the area AMBECL is 1/n^th of the field, then sin θ + (π – θ) cos θ is equal to

(A) nπ (B)

n 1 – n π (C) (n – 1)π (D) (n + 1)π Passage # 2 (Ques. 18 to 20)

Let ABCD be a square with each side of length 2 units. C₂is thecircle through vertices A, B, C, D and C1 is the circle touching all sides of the square ABCD. L is a line through A.

18. If P is a point on C1 and Q is a point on C2, then

2 2 2 2

QD QC QB QA

PD PC PB PA

+ + +

+ +

+ is equal to

(A) 0.75 (B) 1.25

19 A circle touches the line L and the circle C1

externally such that both the circles are on the same side of the line, then the locus of the centre of the circle is-

(A) ellipse (B) hyperbola

moves such that its distances from the line BD and the vertex A are equal. If locus of S cuts M at T2 and T3 and AC at T1, then area of ∆T₁T2T3 is

(A) 1/2 sq. units (B) 2/3 sq. units (C) 1 sq. unit (D) 2 sq. units

Passage # 3 (Ques. 21 to 23)

The sum of three terms of a strictly increasing G.P. is αS and sum of the squares of these terms is S². 21. α² lies

(A) (1/3, 2) (B) (1, 2)

term is

(A) 10/3 (B) 7/3

23. If we drop the condition that the G.P. is strictly increasing and take α² = 3, then common ratio is given by

(A) ± 2 (B) ± 1

At a Glance

In document XtraEdge Dec 2010 (Page 71-78)