IIT-JEE 2011

r r (

GMm −

(B)

2 1

r r 2

) r r (

GMm −

(C)

1 2

2 1

r r

r GMmr

− (D)

) r r (

r GMmr

1 2

2 1

3. A stick is thrown in the air and lands on the ground at some distance from the thrower. The centre of mass of the stick will move along a parabolic path : (A) in all cases

(B) only if the stick is uniform

(D) only if the stick has a shape such that its centre of mass is located at some point on it and not outside it 4. A simple pendulum of length 1m is attached to the

ceiling of an elevator which is accelerating upward at the rate of 1 m/s². Its frequency is approximately : (A) 2 Hz (B) 1.5 Hz

5. The volume of an air bubble is double as it rises from the bottom of a lake to its surface. If the atmospheric pressure is H m of mercury and the density of mercury is n times that of lake water, the depth of the lake is :

(A) nH (B) 2 n H

6. A bowl made of stainless steel is floating in water, contained in a pan. There is small hole in bottom of the bowl. Water leaks into the bowl through the hole.

Level of free water surface in the pan :

XtraEdge Test Series # 5

Based on New Pattern

Time : 3 Hours

Syllabus : Physics : Laws of motion, Friction, Work Power Energy, Gravitation, S.H.M., Laws of Conservations of Momentum, Rotational Motion (Rigid Body), Elasticity, Fluid Mechanics, Surface Tension, Viscosity.

Chemistry : Gaseous state, Chemical Energetics, Oxidation-Reduction, Equivalent Concept, Volumetric Analysis.

Mathematics : Logarithm & Modulus Function, Quadratic Equation, Progressions, Binomial Theorem, Permutation &

Combination, Complex Number.

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 marking for wrong answer.

• Question 11 to 14 are Reason and Assertion type questions with only one correct answer in each. +3 marks will be awarded for correct answer and -1 mark for wrong answer.

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

(A) always remains constant

(B) remain constant for some times then falls suddenly and then becomes constant

(D) rises gradually for some time and then becomes constant

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.

7. Four identical rods, each of mass m and length l, are joined to form a rigid square frame. The frame lies in the xy plane, with its centre at the origin and the sides parallel to the x and y axes. Its moment of inertia about :

(A) the x-axis is 3 2ml²

(B) the z-axis is 3 4ml²

3 10 ml²

(D) one side is 2 5ml²

8. A U-tube is held in a vertical plane such that its two limbs are vertical with middle portion horizontal as shown in fig. Three liquids A, B and C are poured into it and in steady state their interface are as shown in the figure. Which of the following statements (s) is/are correct ?

Air Air

P Q

Liquid A

Liquid B T

S Liquid C U

(A) Height of column of liquid A is greater than that of C

(B) Density of liquid A is less than that of liquid C (C) Density of liquid B is maximum among these

three liquids

(D) Pressure at R is greater than that of S

9. When a body is weighed in a liquid, the loss in its weight depends upon :

(A) Volume of the body (B) Mass of the body (C) Shape of the body (D) CG of the body

10. A liquid flows through a horizontal tube. The velocities of the liquid in the two section, which have areas of cross-section A1 and A2, are v1 and v2

respectively. The difference in the levels of the liquid in the two vertical tubes is h :

A1 v1

(A) the volume of the liquid flowing through the tube in unit time is A1v1

(B) v2 – v1 = 2gh (C) v22 – v12 = 2gh

(D) the energy per unit mass of the liquid is the same in both sections of the tube

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

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) : Two blocks of masses m1 and m2 are at rest. They are moving towards each other under the mutual internal force. The velocity of centre of mass is zero.

Reason (R) : If no external force act on the system, then velocity of centre of mass unchanged but can never be zero.

12. Assertion (A) : For stable equilibrium force has to be zero and potential energy should be minimum.

Reason (R) : For equilibrium, it is not necessary that the force is not zero.

13. Assertion (A) : As the radius of earth reduces by 50% with out any change in mass, length of a day reduces.

Reason (R) : Angular momentum conservation provides drop in time as I decreases to 25% of the original.

14. Assertion (A) : Cross-sectional area of the water pouring out of a tap decreases as the height from the ground decreases.

Reason (R) : Work done by gravity reduces the cross-sectional area.

This section contains 3 paragraphs, each has 3 multiple choice questions. (Question 15 to 23) Each questions has 4 choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

Passage : I (No. 15 to 17)

The energy of a body is defined as the capacity of doing work. The energy possessed by a body by virtue of its motion is called as kinetic energy and the energy possessed by a body by virtue of its position or configuration in some field is defined as potential energy. When work is done on a body, its kinetic or potential energy increases. On the other hand, when the work is done by the body, its potential or kinetic energy decreases. According to work energy theorem, the workdone is equal to change in energy, i.e., W = ∆E.

15. Choose the correct statement related to validity of work-energy theorem

(A) it is valid in all inertial frames only (B) it is valid in non-inertial frames only (C) it is valid in both frames

(D) None of these

16. Consider the following two statements

(i) Linear momentum of a system of particles is zero (ii) Kinetic energy of a system of particles is zero.

Then

(A) (i) implies (ii) and (ii) implies (i)

(B) (i) does not imply (ii) and (ii) does not imply (i) (C) (i) implies (ii) but (ii) does not imply (i) (D) (i) does not imply (ii) but (ii) implies (i)

17. Two protons are brought towards each other. The potential energy of the system will

(A) increase (B) decrease (C) remains same (D) None of these Passage : II (No. 18 to 20)

Three blocks (A, B and C) are each pushed by equal forces F, frictionlessly across a horizontal surface for a distance of 2 m as shown in fig. Here the masses are such that MA > MB > MC.

2m F A

2m F B

2m F C

18. Which of the block will be travelling faster after two metre push ?

(A) block A (B) block B (C) block C

(D) all moving with same speed

19. Which of the blocks will have received the greatest impulse during 2 m push

(A) block A (B) block B (C) block C

(D) all will have the same impulse

20. Which of the blocks would have greatest kinetic energy at the end of 2 m push

(A) block A (B) block B (C) block C

(D) all will have the same kinetic energy Passage : III (No. 21 to 23)

A tube of very small bore is called capillary. If a glass capillary tube is dipped into a liquid such as water, which wets the glass, the liquid rises in the tube. However, if the glass capillary tube is dipped in a liquid such as mercury which does not wet the glass, the liquid falls in the tube. This phenomenon is known as capillarity.

21. A liquid rises in the capillary tube more than water does. Which one of the following in the cause of it (A) temperature of liquid is higher than water (B) surface tension of water is less than the liquid

22. Water rises to a height of 1.25 cm in a capillary tube.

If the hight of the tube is 1 cm, then water will (A) stay at the top of the tube

(B) continuously flow out of the tube

(D) no rise in the tube

23. In gravity free space, the liquid in a capillary tube will rise to

(A) same height as on earth (B) less height as on earth

C ^HEMISTRY

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.

1. Helium atom is two times heavier than a hydrogen molecule. At 298 K, the average kinetic energy of a helium atom is

(A) two times that of a hydrogen molecule (B) same as that of a hydrogen molecule (C) four times that of a hydrogen molecule (D) half that of hydrogen molecule

2. In van der Waals equation of state for a nonideal gas the term that accounts for intermolecular forces is

(A) (V – b) (B) 



 

 + ₂ V p a

3. White phosphorus reacts with caustic soda. The products are PH3 and NaH2PO2. This reaction is an example of

(A) oxidation (B) reduction

4. Which of the following reactions is a redox reaction?

(A) Cr2O3 + 6HCl → 2CrCl3 + 3H2O (B) CrO3 + 2NaOH → Na2CrO4 + H2O (C) 2CrO42–

+ H⁺ Cr2O72–

+ OH^–

(D) Cr2O72– + 6I^–+ 14H⁺ 2Cr³⁺ + 3I2 + 7H2O 5. The reaction of cyanamide, NH2CN(s), with oxygen

was run in a bomb calorimeter and ∆U at 300 K was found to be –743 kJ mol^–1. The value of ∆H at 300K for the combustion reaction

NH2CN(s) + (3/2) O2(g) → N2(g) + CO2(g) + H2O (1) would be

(A) – 741.75 kJ mol^–1 (B) –743 kJ mol^–1 (C) – 744.25 kJ mol^–1 (D) – 740.5 kJ mol^–1

6. The combustion reaction occurring in an automobile is 2C8H18(s) + 5O2(g) → 16CO2(g) + 18H2O(1). This reaction is accompanied with

(A) ∆H = –ve, ∆S = + ve, ∆G = + ve (B) ∆H = + ve, ∆S = –ve, ∆G = + ve (C) ∆H = – ve, ∆S = +ve, ∆G = – ve (D) ∆Η = +ve, ∆S = +ve, ∆G = – ve

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.

7. 10 volume H2O2 solution is present, then it means (A) 10 ml of H2O2 solution liberates 1 ml of oxygen

at STP

(B) 1 ml of H2O2 solution liberates 10 ml of oxygen at STP

(D) 0.0303 g of H2O2 in 1 ml of the solution liberates 10 ml O2 at STP

8. Silver metal in ore is dissolved by potassium cyanide solution in the presence of air by the reaction

4Ag + 8KCN + O2 + 2H2O → 4KAg (CN)2 + 4KOH (A) The amount of KCN required to dissolve 100 g

of pure Ag is 120 g.

(B) The amount of oxygen used in this process is 0.742 g

(D) The volume of oxygen used at STP is 5.20 litres.

9. Identify the intensive properties among the following:

(A) Enthalpy (B) Temperature (C) Volume (D) Refractive index 10. During the Joule Thomson effect

(A) A gas is allowed to expand adiabatically from a high pressure region to a low pressure region (B) A gas is allowed to expand adiabatically at

constant pressure (C) ∆Η = 0 for ideal gas (D) ∆U = 0 for ideal gas

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) : At zero degree Kelvin the volume occupied by a gas is negligible.

Reason (R) : All molecular motion ceases at 0 K.

12. Assertion (A) : Compressibility factor for hydrogen varies with pressure with positive slope at all pressures.

Reason (R) : Even at low pressures, repulsive forces dominate hydrogen gas.

13. Assertion (A) : Enthalpy of graphite is lower than that of diamond.

Reason (R) : Entropy of graphite is greater than that of diamond.

14. Assertion (A) : The temperature of a gas change when it undergoes an adiabatic expansion.

Reason (R) : During an adiabatic expansion of a real gas, the internal energy of the gas remains constant.

This section contains 3 paragraphs, each has 3 multiple choice questions. (Question 15 to 23) Each questions has 4 choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

Passage : I (No. 15 to 17)

Redox reactions are those in which oxidation and reduction take place simultaneously. Oxidising agent can gain electron whereas reducing agent can lose electron easily. The oxidation state of any element can never be in fraction. If oxidation number of any element comes out be in fraction, it is average oxidation number of that element which is present in different oxidation states.

15. N N N–H

3 In this compound HN3 (hydrazoic acid),

oxidation state of N¹ N² and N³ are (A) 0, 0, 3 (B) 0, 0, –1 (C) 1, 1, –3 (D) –3, –3, –3

16. Equivalant weight of chlorine molecule in the equation

3Cl2 + 6NaOH → 5NaCl + NaClO3 + 3H2O (A) 42.6 (B) 35.5

17. The oxidation number of sulphur in K2S2O8 is

(A) + 2 (B) + 4

Passage : II (No. 18 to 20)

Real gases show deviations from ideal behaviour.

Consequently, the observed molar volume of a gas is found to be different from theoretically calculated volume from ideal gas equation. The extent of deviations is measured in terms of compressibility factor, Z. It is found that gases which can be liquefied

easily show larger deviation. Further, it is found that higher the speed of the gas molecules, less are the deviations. However, for every gas, there is a particular temperature above which they show ideal behavior over an appreciable range of pressure. This temperature is called Boyle temperature. The plots of compressibility factor versus pressure for a few gases and for the same gas at different temperatures are given below in figs (a) and (b) respectively. The ideal gas equation has, therefore, been modified and for real gases, we apply van der Wasl's equation,



 

 + ₂ V

P a (V – b) = RT for 1 mole of the gas.

IVIII II I

P(a)

T3T2

P (b) 1.4

1.2 1.0 1.5 1.6

Z Z

1.0

18. If Vo is the observed volume of a gas and Vi is the ideal gas volume, then the compressibility factor (Z) for the gas is

(A)

i o

V (B)

o i

V V

19. In fig (b), the correct order of temperatures is (A) T1 > T2 > T3 (B) T3 > T2 > T1

20. The gas which can be liquefied most easily is

(A) I (B) II

Passage : III (No. 21 to 23)

A student wanted to apply his knowledge of thermodynamics to obtain practical applications. He performed a number of experiments. In one experiment, he took a closed vessel in which he dissolved 28 g of iron in hydrochloric acid at 27ºC.

In another experiment, he dissolved the same amount of iron but in an open vessel. However, he compressed the gas to 10 atm pressure at 27ºC and then again allowed to expand it isothermally and reversibly until the pressure fell down to 1 atm. In one case, he used the work obtained to lift a heavy body of mass 20 kg till the pressure fell down to atmospheric pressure and in another case, he used the work obtained to heat up 1 litre of water (Assume that hydrogen behaves like an ideal gas).

21. In the second experiment, the work done by the system, if the gas were not condensed, would have been nearly

(A) 1246 J (B) zero (C) 2492 J (D) 1145 J

22. The work done by the compressed gas would be nearly

(A) 1247 J (B) 2500 J (C) 4000 J (D) 5000 J

23. The rise in temperature of the water would be (A) 1.25º (B) 2.50º

MATHEMATICS

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.

1. The equation 1 x 4 3

x+ − − + x+8−6 x−1 = 1 has (A) no solution (B) only one solution (C) only two solution (D) more than two solutions 2. The positive integer n for which

2 × 2² + 3 × 2³ + 4 × 2⁴ + .... + n × 2ⁿ = 2^{n + 10} is

(A) 510 (B) 511

3. If log30 3 = c, log305 = d then the value of log308 (A) 2(1 – c – d) (B) 3(1 + c + d)

log3(x + 2) (x + 4) + log1/3(x + 2) < log 7 2 1

3 is (A) (–2, –1) (B) (–2, 3)

5. If an =

∑

= n

0 r nCr

1 , then

∑

= n

0 r nCr

r equals

(A) 2

nan (B)

4 nan

6. The coefficient of x^k in the expansion of E = 1 + (1 + x) + (1 + x)² + ... + (1 + x)ⁿ is (A) ⁿCk (B) ⁿ⁺¹Ck

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.

7. If z1, z2, z3, z4 are the vertices of a square in that order, then

(A) z1 + z3 = z2 + z4

(B) |z1 – z2| = |z2 – z3| = |z3 – z4| = |z4 – z1| (C) |z1 – z3| = |z2 – z4|

(D) (z1 – z3)/(z2 – z4) is purely imaginary

8. Let a and k be two natural numbers greater than 1. If a^k – 1 is prime then

(A) a = 2 (B) k is prime

9. If x satisfies log3(2x + 1) < log35 then x contains the interval.

(A) 



 

 − 0, 2

1 (B) [0, 2)

10. Let an =

n 1 1



 

 + . Then for each n ∈ N (A) an ≥ 2 (B) an < 3 (C) an < 4 (D) an < 2

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) : If a, b, c ∈ R and 2a + 3b + 6c = 0, then the equation ax² + bx + c = 0 has at least one root in [0, 1].

Reason (R) : If a continuous function f defined on R assumes both positive and negative values, then it vanishes at least once.

12. Assertion (A) : There exists no A.P. whose three terms are 3 , 5 and 7 .

Reason (R) : If tp, tq and tr are three distinct terms of 14. Assertion (A) : The set of all x satisfying the equation

This section contains 3 paragraphs, each has 3 multiple choice questions. (Question 15 to 23) Each questions has 4 choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

Passage : I (No. 15 to 17) then p(x) equals

(A) x (B) x –

If n is a natural number define polynomial Pn(x) of degree n as follows :

22. The number of solutions of the system of congruences x ≡ –3 (mod 49)

• Behavior is a mirror in which everyone displays his image.

• Behavior is what a man does, not what he thinks, feels, or believes.

• Behave the way you'd like to be and soon you'll be the way you behave.

XtraEdge Test Series

In document XtraEdge_2009_09 (Page 64-71)

IIT-JEE 2011

IIT-JEE 2011

XtraEdge Test Series # 5

C HEMISTRY

MATHEMATICS

∑

∑

XtraEdge Test Series

C ^HEMISTRY