IIT-JEE 2012

PHYSICS

Questions 1 to 4 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. A container has a liquid filled upto the height H.

There is a hole at height H/4. The area of hole is 'a'.

Density of liquid is ρ. Torque due to the efflux coming out about an axis passing through 'A' and perpendicular to the plane of figure is –

H/4 H

–→–→

–→

A (A) 4

agH²

ρ (B)

4 agH 3ρ ²

3_ρ (D) ρagH²

2. A container has a hole at a height of 2m. If the time taken by the efflux to strike the inclined plane perpendicularly is 1 sec. Then the height of liquid level initially is (Take g = 10 m/s²) –

45º 2m.

(A) 2 m (B) 5 m

3. A block of mass 2 kg is kept at origin at t = 0 and is having velocity 4 5m/s in positive x direction. Its potential energy is defined as U = –x³ + 6x² + 15 (SI units). Its velocity when the applied force is minimum (after the time t = 0) is –

(A) 8 m/s (B) 4 m/s

4. A particle of mass m is released from point A on smooth fixed circular track as shown. If the particle is released from rest at t = 0, then variation of normal reaction N with (θ) angular displacement from initial position is –

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 Energetic, 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 4 are multiple choice questions with only one correct answer. +3 marks will be awarded for correct answer and -1 mark for wrong answer.

Section - II

• Question 5 to 9 are multiple choice question with multiple correct answer. +4 marks will be awarded for correct answer and -1 mark for wrong answer.

Section - III

• Question 10 to 11 are Column Matching type questions. +8 marks will be awarded for the complete correctly matched answer (i.e. +2 marks for each correct row) and No Negative marks for wrong answer..

Section - IV

• Question 12 to 19 are Numerical type question. +4 marks will be awarded for correct answer and –1 mark for wrong answer.

m A

R O

(A)

3mg

θ (B)

3mg

(C)

3mg

θ (D)

3mg

Questions 5 to 9 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 –1 mark for each wrong answer.

5. A vessel filled with liquid is resting on the rough horizontal surface. A hole is made in the vessel as shown. Then –

•

(A) The torque due to friction about the centre of gravity is of into the plane of the paper

(B) The torque due to normal reaction force between container and ground about center of gravity is out of the plane of paper

(D) Torque due to normal reaction force between container and ground about center of gravity is zero

6. A trolley of mass m1 is to be moved such as to keep block A of mass m2 at rest with respect to it. A bucket of mass m3 (with water) in it is placed on trolley. Coefficient of friction between the block A and trolley is µ. The trolley is moved with acceleration so that block does not slip –

(A) The minimum coefficient of friction between bucket and trolley is µ/2

(B) The acceleration of trolley is g/µ

1 1/µ

(D) Force on trolley is (m1 + m2 + m3) g/µ

7. As shown is figure the string BC is 10 cm long and has a linear mass density of 10 kg/m while the string ED is massless. If both strings are inextensible and pulley is ideal then when the system is released from rest the ratio of tension in the string.

D B

2kg 4kg

E C

(A) at points E and C is 4 5

(B) at points E and C is 5 4 (C) at points D and E is 1 (D) at points D and E is

2 1

8. A wedge of mass m1 and a block of mass m2 is in equilibrium as shown. Inclined surface of the wedge has an inclination α with the horizontal and all contacts are smooth. The normal reaction on the wedge may be –

(A) m2g cos α (B) m2g sin α cos α (C) m1g + m2g cos² α (D) m1g+m2gsinα cosα 9. A rough L-shaped rod is located in a horizontal plane

and a sleeve of mass m is inserted in the rod. The rod is rotated with a constant angular velocity ω in the horizontal plane. The lengths l1 and l2 are shown in figure. The normal reaction and frictional force acting on the sleeve when it just starts slipping are (µ = coefficient of friction between rod and sleeve) –

L-shaped rod l1

sleeve

(A) N = mω²l¹ (B) f = mω²l² (C) N = m g²+ω⁴_l²₁ (D) f = µN

This section contains 2 questions (Questions 10, 11).

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, T) 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, A-T; B-Q, B-R; C-P, C-Q and D-S, D-T then the correctly bubbled 4 × 5 matrix should be as follows :

A B C D

Q R S T

S T P

P P Q R

R R Q Q

S S T

T P Q R S T

Mark your response in OMR sheet against the question number of that question in section-II. + 8 marks will be given for complete correct answer (i.e. +2 marks for each correct row) and NO NEGATIVE MARKING for wrong answer.

10. As shown block C of mass 5 kg is pulled by a force F and its acceleration is found to be 3 m/s². The masses of blocks A and B are 10 kg and 5 kg respectively while the string passing over ideal pullies is ideal and is under tension T. If acceleration of blocks A and B are a1 and a2 respectively then if all surfaces are smooth and g = 10 m/s² –

B aC=3 m/s²

T A

Column-I Column-II

(A) F (P) 2

(B) T (Q) 1

(D) 2 a2 (S) 70

(T) None of these

11. A single conservative force acts on a body of mass 1 kg that moves along the x-axis.

The potential energy U(x) is given by U(x) = 20 + (x–2)² where x is in meters. At x = 5.0 m the particle has a kinetic energy of 20 J then –

Column-I Column-II

(A) minimum value (P) 29 of x in meters (B) maximum value (Q) 7.38 of x in meters

(D) maximum kinetic (S) – 3.38 Energy in joules

(T) None of these This section contains 8 questions (Q.12 to 19).

+4 marks will be given for each correct answer and –1 mark for each wrong answer. The answer to each of the questions is a SINGLE-DIGIT INTEGER, ranging from 0 to 9. The appropriate bubbles below the respective question numbers in the OMR have to be darkened. For example, if the correct answers to question numbers X, Y, Z and W (say) are 6, 0, 9 and 2, respectively, then the correct darkening of bubbles will look like the following :

0 1 2 3 4 5 6 7 8 9

0 1 2 3 4 5 6 7 8 9 X Y Z W

12. A particle moves in a straight line with its retardation proportional to its displacement 'x'. Change in kinetic energy is proportional to n^th power of x, where n is - 13. A particle of mass 10^–2 kg is moving along the

positive x-axis under the influence of a force F(x) = – K/(2x²) where K = 10 Nm². At time t = 0 it is at x = 1.0 m and its velocity is v = 0. Find its velocity when it reaches x = 0.50 m.

14. An artillery gun is mounted on a railway truck standing on straight horizontal rails. The total mass of the truck with gun shells and crew is M = 50 tons and the mass of each shell is m = 25 kg. The gun fires in a horizontal direction along the railway. The initial velocity of the shells is V0 = 1000 m/s. What will the speed of truck after the second shot? Disregard friction and air resistance.

15. A stationary body explodes into four identical fragments such that three of them fly off mutually perpendicular to each other, each will same K.E. E0. The energy of explosion will be K times of E₀, then the value of K is -

16. A cubical block of mass 6kg and side 16.1 cm is placed on frictionless horizontal surface. If is hit by a cue at the top as to impart-impulse in horizontal direction. Minimum impulse imparted to topple the block must be greater than.

17. A disc is rotating freely its axis. Percentage change in angular velocity of disc if temperature decreases by 20ºC is (coefficient of linear expansion of material of disc is 5 × 10^–4/ºC )

18. A glass capillary sealed at the upper end is of length 0.11 m and internal diameter 2 × 10^–5 m. This tube is immersed vertically into a liquid of surface tension 5.06 × 10^–2N/m. When the length x × 10^–2. m of the tube is immersed in liquid then the liquid level inside and outside the capillary tube becomes the same, then the value of x is : (Assume atmospheric pressure is 1.01 × 10⁵ ₂

m N )

19. A wire of length '2m' is clamped horizontally between two fixed support. A mass m = 5 kg is hanged from middle of wire. The vertical and depression in wire (in cm) in equilibrium is (Young modulus of wire = 2.4 × 10⁹ N/m², cross-sectional area = 1 cm²)

C HEMISTRY

1. Given that H2O (l) → H2O(g) ; ∆H = + 43.7 kJ H2O (s) → H₂O (l) ; ∆H = + 6.05 kJ

∆Hsublimation of ice is -

(A) 49.75 kJ mol^–1 (B) 37.65 kJ mol^–1 (C) 43.7 kJ mol^–1 (D) – 43.67 kJ mol^–1

2. A real gas of molar mass 60 g mol^–1 has density at critical point equal to 0.80 g/cm³ and its critical temperature is given by Tc =

821 10 4× ⁵

K. Then the van der Waal's constant 'a' (atm L² mol^–2) will be (A) 0.025 (B) 0.325

3. Adiabatic reversible expansion of a monoatomic gas (M) and a diatomic gas (D) at an initial temperatrue Ti has been carried out independently from initial volume V₁ to final volume V₂. The final temperature (TM for monoatomic gas and TD for diatomic gas) attained will be :

(A) TM = TD > Ti (B) TM < TD < Ti

4. What volume of 2N K2Cr2O7 solution is require to oxidise 0.81 g of H2S in acid medium -

(A) 47.8 (B) 23.8

5. 20 volume of H2O2 is equal to - (A) 20 % H2O2 by mass (B) 6 % H2O2 by mass

6. Which of the following is/are state function ? (A) q (B) q – w (C) q + w (D) q / w 7. According to kinetic theory of gases :

(A) the pressure exerted by a gas is proportional to mean square velocity of the molecules

(B) the pressure exerted by the gas is proportional to the root mean square velocity of the molecules (C) the root mean square velocity is inversely

proportional to the temperature

(D) the mean translational K.E. of the molecule is directly proportional to the absolute temperature

8. According to Charles' law : (A) V ∝

1 (B)

dT P

dV



 



 = K

dT



 



 = K (D)

2 P

T – V T

1 



 



 = 0

9. Consider in Redox reaction 2S2O32– + I² → S4O62– + 2I^– (A) S2O32– gets reduced to S4O62–

(B) S2O32– gets oxidised to S4O62–

This section contains 2 questions (Questions 10, 11).

A B C D

Q R S T

T S P

P P Q R

R R Q Q

S S T

T P Q R S T

10. Column-I Column-II (A) If force of attraction (P) 



 

 + ₂ V

P a (V–b)= RT

among the gas molecules be negligible

(B) If the volume of the (Q) PV = RT –a/V gas molecules be

negligible

(T) PV/RT = 1–a/VRT 11. Match of the following :

Column-I Column-II

(A) A process carried (P) Adiabatic out infinitesimally

slowly

(B) A process in which (Q) ∆G = 0 no heat enters or

leaves the system

temperature

(D) A process in (S) Reversible equilibrium

(T) Isothermal

This section contains 8 questions (Q.12 to 19).

0 1 2 3 4 5 6 7 8 9

0 1 2 3 4 5 6 7 8 9 X Y Z W

12. Oxidation number of Fe in Na2[Fe(CN)5NO] is 13. The number of moles of KMnO4 reduced by one

mole of KI in alkaline medium is.

14. How many mole of electrons are needed to convert one mole of nitrate ion to hydrazine.

15. Calculate the volume occupied by 8.8 g of CO2 at 31.1ºC and 1 bar pressure. (R = 0.083 bar litre K^–1 mol^–1)

16. A compound exists in the gaseous phase both as monomer (A) and dimer (A2). The molecular weight of A is 48. In an experiment 96 g of the compound was confined in a vessel of volume 33.6 litre and heated to 273º C. Calculate the pressure developed if the compound exists as dimer to the extent of 50% by weight under these conditions.

17. The haemoglobin from the red blood corpuscles of most mammals contains approximately 0.33% of iron by weight. The molecular weight of haemoglobin as 67,200. The number of iron atoms in each molecule of haemoglobin is (atomic weight of iron = 56) : 18. 0.7 g of Na2CO3.xH2O were dissolved in water and

the volume was made to 100 mL, 20 mL of this solution required 19.8 mL of N/10 HCl for complete neutralisation. The value of x is

19. The temperature of a 5 mL of strong acid increases by 5ºC when 5 ml of a strong base is added to it. If 10 mL of each are mixed, temperature should increase by

MATHEMATICS

1. The set of {x : log1/3 log4(x² – 5) > 0} is equal to

4. If three positive real numbers a, b, c are in A.P. such that abc = 4, then the minimum possible value of b is (A) 2^3/2 (B) 2^2/3

number

(B) all the terms of the A.P. must be rational (C) all the terms of the A.P. must be integers

(D) sum to any number of terms of the A.P. must be

This section contains 2 questions (Questions 10, 11).

10. z lies on ……… if

11. The value of

This section contains 8 questions (Q.12 to 19).

+4 marks will be given for each correct answer and –1 mark for each wrong answer. The answer to each of the questions is a SINGLE-DIGIT INTEGER, ranging from 0 to 9. The appropriate bubbles below the respective question numbers in the OMR have to be darkened. For example, if the correct answers to question numbers X, Y, Z and W (say) are 6, 0, 9 and 2, respectively, then the correct darkening of bubbles will look like the following :

13. The number of real values of x which satisfy the equation which he may not select all of them is 255, then value of n is…

17. If 1, x1, x2, x3 are the roots of x⁴ – 1 = 0 and ω is a complex cube root of unity, find the value of

)

18. If the lengths of the sides of a right triangle ABC right angled at C are in A.P., find 5 (sin A + sin B).

19. A class contains 4 boys and g girls. Every Sunday five students, including at least three boys go for a picnic to Appu Ghar, a different group being sent every week. During, the picnic, the class teacher gives each girl in the group a doll. If the total number of dolls distributed was 85, then value of g is…

• William Bottke at Cornell University in the US has calculated that at least 900 asteroids of a kilometre or more across regularly sweep across Earth's path.

• The Dutch astronomer Christiaan Huygens (1629 - 1695) drew Mars using an advanced telescope of his own design. He recorded a large, dark spot on Mars, probably Syrtis Major. He noticed that the spot returned to the same position at the same time the next day, and calculated that Mars has a 24 hour period. (It is actually 24 hours and 37 minutes)

• Space debris travels through space at over 18,000 mph.

• The nucleus of Comet Halley is approximately 16x8x8 kilometers. Contrary to prior expectations, Halley's nucleus is very dark: its albedo is only about 0.03 making it darker than coal and one of the darkest objects in the solar system.

• A car travelling at a constant speed of 60 miles per hour would take longer than 48 million years to reach the nearest star (other than our Sun), Proxima Centauri.

This is about 685,000 average human lifetimes

• Scientists estimate that the contents of our universe consists of 4 percent ordinary atoms (baryons) in stars, nebulae and diffuse intergalactic gas. Dark Matter provides about 30 percent; and Dark Energy provides the rest of about 66% percent.

• One parsec is equal to 19.2 million million miles.

• The coldest known star is an unnamed star about 160 light years from Earth. Its surface temperature is only 2600F which is 7400F cooler than the Sun!

• Venus is the second closest planet to the Sun, and the sixth largest overall.

• The first manned space flight happened on the 12th April 1961, when Yuri Gagarin made a complete orbit of the Earth before landing safely back in Russia.

XtraEdge Test Series

In document XtraEdge_2010_09 (Page 69-76)