IIT-JEE 2011

ω (B)

t 2 MR²

∆ ω

∆

ω (D) Zero

4. Select the incorrect statement -

(A) The velocity of the centre of mass of an isolated system must stay constant

(B) Only a net external force can change the velocity of the center of mass of a system (C) A system have non-zero kinetic energy but zero

linear momentum (D) F^→_ext= m

dt v d^→+^→v

dmis true for all situation

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.

5. Velocity of a particle moving on straight line varies as 2

1th power of displacement. Then - (A) K.E. ∝ S (B) P ∝ S^1/2

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

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

Section - II

• Question 10 to 11 are Column Matching type questions. +8 marks will be awarded for the complete correctly matched answer and No Negative marks for wrong answer. However, +2 marks will be given for a correctly marked answer in any row.

Section - III

• Question 12 to 19 are numerical response type questions. +4 marks will be awarded for correct answer and -1 mark for wrong answer.

6. A block of density ρ is floating in a liquid X kept in container. A liquid Y of density ρ′ (< ρ) is slowly poured into container –

(A) The block will move up if liquid X and Y are immiscible

(B) The block will sink more if liquid X and Y are immiscible

(D) The block will not move if liquid X and Y are miscible

7. Six identical rod are connected as shown in figure and temperature difference of 100ºC is maintained across P and Q –

P A B Q

C (A) Temperature of point 'A' is 50ºC (B) Temperature of point A is

3 200ºC (C) Thermal current passing through B is zero (D) Thermal current passing through A is twice of

that through C

8. A solid iron cylinder A rolls down a ramp and an identical iron cylinder B slides down the same ramp without friction –

(A) B reaches the bottom first

(B) A and B have the same kinetic energy

(D) Linear speed of centre of mass of B is greater than that of A

9. A mass and spring system oscillates with amplitude A and angular frequency ω –

(A) The average speed during one complete cycle of oscillation is

π ω A 2 (B) Maximum speed is ωA

(D) Average acceleration of particle during one complete cycle of oscillation is zero

This section contains 2 questions (Questions 10 to 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

A B C D

P P P P

Q Q Q Q

R R R R

S S S S

T T T T P Q R S T

10. There are four identical rod having thermal resistance 10 Ω, each column I contains various arrangement of rod. Column II contains current flowing across point C when a temperature difference of 100ºC is maintained across A & B.

Match them.

Column-I Column-II

(A) ^A

C B (P) 2 J/sec

(B) A

B (Q) 4 J/sec

C B (R) 6 J/sec

(D) A

C B (S)

7 20J/sec

(T) None 11. A car of mass 500 kg is moving in a circular road

of radius 35/ 3. Angle of banking of road is 30º. Coefficient of friction between road and tyres is µ =

3 2

1 . Match the following:

Column-I Column-II (A) Maximum speed (in m/s) of (P) 5 2

car for safe turning

(B) Minimum speed (in m/s) of (Q) 12.50 car for safe turning

is zero

(D) Friction force (in 10² Newton) (S) 3 350 between tyres and road if

speed is

6 350m/s

(T) None

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

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. Pulley 'P' shown in figure is pulled upward with F = 2t N, where t is time in sec. Velocity of block of mass 1 at the time block 2 is about to lift is (in cm/sec). (Ans. in ... × 10¹)

F = 2t

2 1 m1 = 0.5 kg m2 = 1 kg

13. The upper edge of a gate in a dam runs along the water surface. The gate is 2.00 m high and 4.00 m wide and is hinged along a horizontal line through its center. The torque about the hinge arising from the force due to the water is (n × 10⁴ Nm). Find value of n.

2 m

14. A longitudinal wave of frequency 220 Hz travels down a copper rod of radius 8.00 mm. The average power in the wave is 6.50 µW. The amplitude of the wave is n × 10^–8m. Find n.

15. A piston-cylinder device with air at an initial temperature of 30ºC undergoes an expansion process for which pressure and volume are related as given below

P (kPa) 100 25 6.25

V (m³) 0.1 0.2 0.4

The work done by the system is n × 10³ J. Find n.

16. The block connected with spring is pushed to compress the spring by 10 cm and then released. All surfaces are frictionless and collision are elastic.

Time period of the motion in sec (mass of block = 9 kg and spring constant 4π² N/m).

5 cm

17. RMS velocity of gas at 27ºC is 300×381m/s.

RMS velocity (in m/s) when temperature is increased four times is. (Ans. in ... × 10²) 18. A block of mass 2 kg is placed on a wedge of mass

10 kg kept on a horizontal surface. Coefficient of friction between all surfaces is µ = 0.2. If block is slipping down the wedge with constant speed then friction force on wedge due to horizontal surface is (in Newton) :

19. A particular quantity 'y' varies as 'x' as shown in figure. RMS value of y with respect to x for large values of 'x' is.

60º 60º

x y

1 2 3 4

CHEMISTRY

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.

1. An ideal gaseous mixture of ethane (C2H6) and ethene (C2H4) occupies 28 litre at STP. The mixture reacts completely with 128 gm O2 to produce CO2

and H2O. Mole fraction of C2H4 in the mixture is - (A) 0.6 (B) 0.4 (C) 0.5 (D) 0.8 2. A bulb of constant volume is attached to a

manometer tube open at other end as shown in figure.

The manometer is filled with a liquid of density (1/3^rd) that of mercury. Initially h was 228 cm.

Gas h

Through a small hole in the bulb gas leaked assuming pressure decreases as

dp= – kP.

If value of h is 114 cm after 14 minutes. What is the value of k (in hour^–1) ?

[Use : ln(4/3) = 0.28 and density of Hg = 13.6 g/mL]

(A) 0.6 (B) 1.2

3. When 300 mL of 0.2 M HCl is added to 200 mL of 0.1 M NaOH. Resultant solution require how many equivalent of Ba(OH)2 ?

(A) 0.06 (B) 0.12 (C) 0.3 (D) 0.04 4. The dipole moment of HCl is 1.03D, if H–Cl bond

distance is 1.26Å, what is the percentage of ionic character in the H–Cl bond ?

(A) 60% (B) 29% (C) 17% (D) 39%

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.

5. Consider the following carbides CaC2, BeC2, MgC2

and SrC2 which of the given carbides on hydrolysis yield same product -

(A) CaC2 (B) Be2C (C) MgC2 (D) SrC2

6. Which of the following is/are correct regarding the periodic classification of elements ?

(A) The properties of elements are the periodic function of their atomic number

(B) Non metals are lesser in number than metals

(D) For transition elements the d-subshells are filled with electrons monotonically with the increase in atomic number

7. Which of the following statements regarding hydrogen peroxide is/are correct ?

(A) Hydrogen peroxide is a pale blue viscous liquid (B) Hydrogen peroxide can act as oxidising as well

as reducing agent

(D) In the crystalline phase, H2O2 is paramagnetic 8. Which of the following is/are state function ?

(A) q (B) q – w (C) q + w (D) q / w 9. The IUPAC name of the following compound is -

Br CN

(A) 3-Bromo-3-cyano phenol

(B) 3-Bromo-5-hydroxy benzonitrile (C) 3-Cyano-3-hydroxybromo benzene

(D) 5-Bromo-3-hydroxy benzonitrile

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

A B C D

P P P P

Q Q Q Q

R R R R

S S S S

T T T T P Q R S T

10. Column-I Column-II

(A) 5.4 g of Al (P) 0.5 NA electrons (B) 1.2 g of Mg²⁺ (Q) 15.9994 amu (C) Exact atomic weight (R) 0.2 mole atoms of mixture of oxygen

isotopes

(D) 0.9 mL of H2O (S) 0.05 moles

(T) 3.1 × 10²³ electrons

11. Column-I Column-II (Ionic species) (Shapes)

(A) XeF5+ (P) Tetrahedral (B) SiF5– (Q) Square planar (C) AsF4+ (R) Trigonal bipyramidal (D) ICl4– (S) Square pyramidal

(T) Octahedral

This section contains 8 questions (Questions 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. How much volume (in mL) 0.001 M HCl should we add to 10 cm³ of 0.001 M NaOH to change its pH by one unit ?

13. The stopcock, connecting the two bulbs of volumes 5 litres and 10 litres containing an ideal gas at 9 atm and 6 atm respectively, is opened. What is the final presure (in atm) in the two bulbs if the temperature remained the same ?

14. An acid type indicator, HIn differs in colour from its conjugate base (In^–). The human eye is sensitive to colour differences only when the ratio [In^– ] / [HIn] is greater than 10 or smaller than 0.1. What should be the minimum change in the pH of the solution to osberve a complete colour change ? (Ka = 1.5 × 10^–5) 15. What is the sum of total electron pairs (b.p. + l.p.)

present in XeF6 molecule ?

16. The number of geometrical isomers of CH3CH=CH–CH=CH–CH=CHCl is.

17. At 200ºC, the velocity of hydrogen molecule is 2.0 × 10⁵ cm/sec. In this case the de-Broglie wavelength (in Å) is about.

18. The equivalent weight of a metal is 4.5 and the molecular weight of its chloride is 80. The atomic weight of the metal is.

19. No. of π bond in the compound H2CSF4 is.

MATHEMATICS

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.

1. If 0 < r < s ≤ n and ⁿPr = ⁿPs, then value of r + s is - (A) 2n – 2 (B) 2n – 1

2. If sin x + sin² x + sin³ x = 1, then cos⁶ x – 4 cos⁴ x + 8 cos² x is equal to -

(A) 0 (B) 2 (C) 4 (D) 8 3. If x is real, and

k =

1 x x

2 2

+ +

− then

(A) 1/3 ≤ k ≤ 3 (B) k ≥ 5

4. A flagstaff stands in the centre of a rectangular field whose diagonal is 1200 m, and subtends angles 15º and 45º at the mid points of the sides of the field. The height of the flagstaff is -

(A) 200 m (B) 300 2+ 3m (C) 300 2− 3m (D) 400 m

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.

5. If a, b, c are the sides of the ∆ABC and a², b², c² are the roots of x³ – px² + qx – k = 0, then

(A) a

A cos +

b B cos +

c C cos =

k 2

(B) a cos A + b cos B + c cos C = k 2

p q 4 − ²

(D) sin A sin B sin C = k 8∆³

6. The coordinates of the feet of the perpendiculars from the vertices of a triangle on the opposite sides are (20, 25), (8, 16) and (8, 9). The coordinates of a vertex of the triangle are -

(A) (5, 10) (B) (50, –5) (C) (15, 30) (D) (10, 15)

7. Let E =  (A) E is divisible by exactly 2 primes

(B) E is prime (C) E ≥ 30 (D) E ≤ 35

8. If m is a positive integer, then[( 3+1)²^m] + 1, where [x] denotes greatest integer ≤ n, is divisible by-

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

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

12. Fifteen persons, among whom are A and B, sit down at random at a round table. if p is The probability that there are exactly 4 persons between A and B find 14 p.

13. If l is the length of the intercept made by a common the length of the perpendicular from the focus of the parabola on this normal; then

741 2p 3k³+ ²

is equal to 15. The volume of the tetrahedron whose vertices are

(0, 1, 2) (3, 0, 1) (4, 3, 6) (2, 3, 2) is equal to

17. Find the value of x which satisfy the equation log2 (x² – 3) – log2 (6x – 10) + 1 = 0

18. Find the coefficient of x²⁰⁰⁹ in the expansion of (1 – x)²⁰⁰⁸ (1 + x + x²)²⁰⁰⁷

19. Find the value of x satisfying 4¹^/^log²^x = 2.

PHYSICS

1. q =

2 2 0

c 1 v

−

is valid or not, q is the charge on

particle when it is moving with velocity v, q0 is the rest charge and c is the velocity of light .

2. A concave mirror is dipped inside the liquid of absolute refractive index 1.25. What will be the percentage change in its focal length.

3. Write the name of a compound semiconductor.

4. If one of the slit get closed in Young's Double slit experiment then fringe pattern will be observed or not on the screen.

5. Write one of the use of Zener Diode.

6. Name the experiment which proves the Dual Nature of electron.

7. If nuclear density d ∝ Aⁿ, where A is the atomic number then write the value of n.

8. Why standard resistors are made of alloys.

9. Name the quantities whose SI units are given below : 1. V – m 2. C-m

out of the two also name the vector quantity.

10. A transistor is shown in figure.

+2V +1V +3V

(i) Name the type of transistor . (ii) Is the transistor is properly biased.

11. A time variant current is given - i(t) = 1 + 3 2 sin (314 t + 30º) Find its root mean square value.

General Instructions : Physics & Chemistry

• Time given for each subject paper is 3 hrs and Max. marks 70 for each.

• All questions are compulsory.

• Marks for each question are indicated against it.

• Question numbers 1 to 8 are very short-answer questions and carrying 1 mark each.

• Question numbers 9 to 18 are short-answer questions, and carry 2 marks each.

• Question numbers 19 to 27 are also short-answer questions, and carry 3 marks each.

• Question numbers 28 to 30 are long-answer questions and carry 5 marks each.

• Use of calculators is not permitted.

General Instructions : Mathematics

• Time given to solve this subject paper is 3 hrs and Max. marks 100.

• All questions are compulsory.

• The question paper consists of 29 questions divided into three sections A, B and C.

Section A comprises of 10 questions of one mark each.

Section B comprises of 12 questions of four marks each.

Section C comprises of 7 questions of six marks each.

• All question in Section A are to be answered in one word, one sentence or as per the exact requirement of the question.

• There is no overall choice. However, internal choice has been provided in 4 questions of four marks each and 2 question of six marks each. You have to attempt only one of the alternatives in all such questions.

• Use of calculators is not permitted.

In document Dec 2009 (Page 65-71)