IIT-JEE 2011

γ (D)

1 PV

− γ γ

4. 1 g of water on evaporation at atmospheric pressure forms 1671 cm³ of steam. Heat of vaporisation at this pressure is 540 calg^–1. The increase in internal energy is

(A) 250 cal (B) 500 cal (C) 1000 cal (D) 1500 cal

5. A motion is described by y = 3e^x.e^–3t where y, x are in metre and t is in second.

(A) This represents equation of progressive wave propagating along –x direction with 3 ms^–1. (B) This represents equation of progressive wave

propagating along +x direction with 3 ms^–1 (C) This does not represent a progressive wave

equation

(D) Data is insufficient to arrive at any conclusion of this sort.

6. A tuning fork A of frequency as given by the manufacture is 512 Hz is being tested using an accurate oscillator. It is found that they produce 2 beats per second when the oscillator reads 514 Hz and 6 beats per second when it reads 510 Hz. The actual frequency of the fork in Hz is

(A) 508 (B) 512 (C) 516 (D) 518

7. The speed of longitudinal wave is 100 times the speed of transverse wave in a taut brass wire. If the Young's modulus of wire is 10¹¹ Nm^–2, then the stress in the wire is

(A) 10⁵ Nm^–2 (B) 10⁶ Nm^–2 (C) 10⁷ Nm^–2 (D) 10⁸ Nm^–2

XtraEdge Test Series # 6

Based on New Pattern

Time : 3 Hours

Syllabus : Physics : Calorimetry, K.T.G., Thermodynamics, Heat Transfer, Thermal expansion, Transverse wave, Sound wave, Doppler's effect. Chemistry : Chemical Equilibrium, Acid Base, Ionic Equilibrium, Classification &

Nomenclature, Isomerism, Hydrogen Family, Boron Family & Carbon Family, S-block elements. Mathematics:

Point, Straight line, Circle, Parabola, Ellipse, Hyperbola, Vector, 3-D Instructions :

Section - I

• Question 1 to 9 are multiple choice questions with only one correct answer. +3 marks will be awarded for correct answer and -1 mark for wrong answer.

• Question 10 to 13 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 14 to 19 are passage based single correct type questions. +4 marks will be awarded for correct answer and -1 mark for wrong answer.

Section - II

• Question 20 to 22 are Column Matching type questions. +6 marks will be awarded for the complete correctly matched answer and No Negative marks for wrong answer. However, 1 mark will be given for a correctly marked answer in any row.

8. Two sounding bodies are producing progressive waves given by y1 = 4 sin(400πt) and y2 = 3 sin(404πt), where t is in second which superpose near the ears of a person. The person will hear.

(A) 2 beats per second with intensity ratio 4/3 between maxima and minima

(B) 2 beats per second with intensity ratio 49 between maxima and minima

(D) 4 beats per second with intensity ratio 4/3 between maxima and minima.

9. An air bubble doubles in radius on rising from the bottom of a lake to its surface. Assuming that the bubble rises slowly and the atmospheric pressure to be equal to a column of water of height H, the depth of the lake is

(A) 4H (B) 5H

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

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.

10. Assertion : Sound produced by an open organ pipe is more melodious than that produced by a closed organ pipe.

Reason : Air can flow in a better way in an open organ pipe.

11. Assertion : Two tuning forks having frequencies 410 Hz and 524 Hz are kept close and made to vibrate.

Beats will not be heard.

Reason : Sound waves superimpose only when the frequencies of superposing waves are equal or nearly equal.

12. Assertion : A blue star is hotter than a red star.

Reason : According to Stefan's law, a black body at a higher temperature radiates more power per unit area.

13. Assertion : A hot body is kept in some surrounding.

As it cools, its temperature falls from 80ºC to 78ºC in a time duration t1 and from 50ºC to 48ºC in time duration t2. The temperature of surrounding is constantly 20ºC, then t1 > t2.

Reason : According to Newton's law of cooling, rate of cooling depends on the difference of temperature of the body and the surrounding.

This section contains 2 paragraphs; each has 3 multiple choice questions. (Question 14 to 19) Each question has 4 choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

Passage : I (No. 14 to 16)

Many waveforms are described in terms of combinations of travelling waves. Superposition principle is used to analyse such wave combinations.

Two pulses travelling on same string are described by y1 =

2 ) t 4 x 3 (

− , y2 =

2 ) 6 t 4 x 3 (

− +

−

14. The direction in which pulse is travelling is (A) y1 is in positive x-axis, y2 is in positive x-axis (B) y1 is in negative x-axis, y2 is in negative x-axis (C) y1 is in positive x-axis, y2 is in negative x-axis (D) y1 is in negative x-axis, y2 is in positive x-axis 15. The time when the two waves cancel everywhere –

(A) 1 sec (B) 0.5 sec (C) 0.25 sec (D) 0.75 sec 16. The point where two waves always cancel

(A) 0.25 m (B) 0.5 m (C) 0.75 m (D) 1 m Passage : II (No. 17 to 19)

One mole of diatomic gas is taken through following cyclic process. The process CA is P = (Constant)V.

Temperature at C is 100 K.

B A

P 3P0

V C

17. Temperature at A is

(A) 300 K (B) 900 K (C) 600 K (D) 1200 L 18. Molar heat capacity for process CA is

(A) R (B) 2R

19. Work done in the cycle is - (A) 200 R (B) – 200 R (C) 400 R (D) – 400 R

The section contains 3 questions (Questions 20 to 22).

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 matches are A-P, A-S, B-Q, B-R, C-P, C-Q and D-S, then the correctly 4 × 4 matrix should be as follows :

D C B A

P P P P

Q Q Q Q

R R R R

S S S S Q P R S

20. Match the standing waves formed in column-II due to plane progressive waves in Column-I and also with conditions in column-I.

Column -I Column-II

(A) Incident wave is

y = A sin(kx – ωt) (P) y = 2A cos kx sin ωt (B) Incident wave is

y = A cos(kx – ωt) (Q) y = 2A sin kx ωt (C) x = 0 is rigid

support (R) y = 2A sin kx cos ωt (D) x = 0 is flexible

support (S) y = 2A cos kx cos ωt 21. Match Columns-I and II

Column –I Column-II

(A)

Wien's

displacement law explains

(P) Why days are hot and night cold in deserts

(B) Planck's law explains

(Q) Why a blackened platinum wire, when gradually heated, appears first dull red and then blue

(R) The distribution of energy in black body spectrum at shorter as well as longer wavelengths

(D) Newton's second law explains

(S) Why some stars are hotter than others 22. The figures given below depict different processes for

a given amount of an ideal gas.

1/V P

V P Adiabatic

(i) (ii)

V P

(iii) (iv)

Column -I Column-II

(A) In fig. (i) (P) Heat is absorbed by the system

(B) In fig (ii) (Q) Work is done on the system

(D) In fig. (iv) (S) Work is done by the system

C ^HEMISTRY

Questions 1 to 9 are multiple choice questions. Each question has four choices (A), (B), (C) and (D), out of which ONLY ONE is correct.

1. At constant pressure P, A dissociates on heating according to the equation

A(g) B(g) + C(g)

The equilibrium partial pressure of A at T K is 1/9 P, the equilibrium Kp at TK is

(A) 9

8P (B) 9

64P (C) 9

16P (D) 9 P

2. Calculate the pH of 6.66 × 10^–3 M solution of Al(OH)3. Its first dissociation is 100% where as second dissociation is 50% and third dissociation is negligible.

(A) 2 (B) 12

3. pH of the blood in the body is maintained by buffer solution of

(A) glucose and salt concentration (B) protein and salt concentration (C) CO33–

and HCO3–

(D) Salt and carbonate ion

4. IUPAC name of the following compound is : OH

CH3

(A) 2-methyl-3-cyclohexenol (B) 3-methyl-1-cyclohexen-4-ol (C) 4-hydroxy-3-methyl-1-cyclohexene (D) 2-hydroxy-1-methylcyclohexene

5. Which will form geometrical isomers ?

(A)

(B) CH3CH = NOH

6. The dissolution of Al(OH)3 by a solution of NaOH results in the formation of

(A) [Al(H2O)4(OH)2]⁺ (B) [Al(H2O)3(OH)3] (C) [Al(H2O)2(OH)4]^– (D) [Al(H2O)6](OH)3

7. Helium-oxygen mixture is used by deep sea divers in preference to nitrogen-oxygen mixture because (A) helium is much less soluble in blood than

nitrogen

(B) nitrogen is highly soluble in water (C) helium is insoluble in water

(D) nitrogen is less soluble in blood than helium 8. SF4 + BF3 → (A). The compound 'A' is

(A) [SF5]^–[BF2]⁺ (B)[SF3]⁺[BF4]^– (C) SF6 (D) S2F4

9. Red lead on reaction with dil. HNO3 forms (A) PbO

(B) PbO2

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

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.

10. Assertion : For a reaction at equilibrium, the free energy for the reaction is minimum.

Reason : The free energy for both reactants and products decreases and become equal.

11. Assertion : Tropylium cation is more stable than (CH3)3C^⊕

Reason : It is stabilized by both resonance effect and inductive effect.

12. Assertion : K2CO3 can be prepared by Solvay process like Na2CO3.

Reason : KHCO3 is highly water soluble.

13. Assertion : PbI4 does not exist although PbCl4 exist.

Reason : Both Pb⁴⁺ and I^–1 are strong oxidant and strong reductant respectively.

This section contains 2 paragraphs; each has 3 multiple choice questions. (Question 14 to 19) Each question has 4 choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

Passage : I (No. 14 to 16)

Lithium only forms monoxide when heated in oxygen. Sodium forms monoxide and peroxide in excess of oxygen. Other alkali metals form super oxide with oxygen i.e., MO2. The abnormal behaviour of lithium is due to small size. The larger size of nearer alkali metals also decides the role in formation of superoxides. The three ions related to each other as follows :

ion Oxide

O2⁻ ¹ →^/²^O²

ion Peroxide

O ⁻ →^O²

ion Superoxide2O2⁻

All the three ions abstract proton from water.

14. Consider the following reaction : M + O2 →

oxide) per su

( MO2 (M = alkali metal) Select the correct statement :

(A) M can not be Li and Na (B) M can not be Cs and Rb (C) M can not be Li and Rb (D) None of these

15. Lithium does not form stable peroxide because : (A) of its small size

(B) d-orbital are absent in it

(D) covalent nature of peroxide

16. Which compound will liberate oxygen when react with water :

(A) Na2O2 (B) KO2

Passage : II (No. 17 to 19)

All the boron trihalides except BI3 may be prepared by direct reaction between the elements. Boron trihalides consist of trigonalplanar BX3 molecules.

Unlike the halides of the other elements in the group they are monomeric in the gas, liquid and solid states, BF3 and BCl3 are gases, BBr3 is a volatile liquid and BI3 is a solid. Boron trihalides are Lewis acids because they form Lewis complexes with suitable bases.

BF3(g) + : NH3(g) → F3B – NH3(g)

However, boron chlorides, bromides and iodides are susceptible (sensitive) to protolysis by mild proton sources such as water, alcohols and even amines for example BCl3 undergoes rapid hydrolysis.

BCl3(g) + 3H2O(_l) → B(OH)3(aq.) + 3HCl(aq.)

It is supposed that the first step in the above reaction is the formation of the complex Cl3B ← OH2 which then eliminates HCl and reacts further with water.

17. Which of the following is the best order of Lewis acid strength of BF3, BCl3 and BBr3 ?

(A) BF3 > BCl3 > BBr3 (B) BF3 = BCl3 = BBr3

18. Which of the following reaction is incorrect ? (A) BF3(g) + F₍⁻_aq_.) →

[ ]

BF4 ⁻₍_aq_.)

(B) BCl3(g) + 3EtOH(_l) → B(OEt)3(_l) + 3HCl(g)

BF3(g) +Br3BN(CH3)3(g) (D) BCl3(g) +

Excess ) ( 5 5H N C

2 _l → Cl3B(C5H5N)2(s)

19. Which of the following is correct ?

(A) B(OCH3)3 is much weaker Lewis acid than BBr3

(B) B(OH)3(aq.) behave as a triprotic acid (C) [H2BO3](aq.)– is a conjugate base of H3BO3(aq.)

(D) BF3 does not react with ethers.

The section contains 3 questions (Questions 20 to 22).

D C B A

P P P P

Q Q Q Q

R R R R

S S S S Q P R S

20. Match the following :

Column -I Column-II

(A) Na + Liq. NH3 (P) Paramagnetic (B) Li (Q) Blue coloured (C) KO2 (R) Strongest reducing

agent

(D) [e(NH3)x]^– (S) Highest ionisation energy

21. Match the following :

Column -I Column-II

(A) Enantiomers (P) meso-Tartaric acid (B) Enantiomerism (Q) CH3CH = C = CHC2H5

(R) Possess identical physical and chemical properties

(D) Diastereomerism (S) Possess different physical properties 22. Match the following :

Column -I Column-II

(A) Saturated solution of

AgCl (P) Common ion

effect (B) Unsaturated solition

of AgCl (Q) IP = SP (C) Supersaturated

solution of AgCl (R) IP > SP (D) Solution of AgCl in

presence of NaCl

(S) IP < SP

MATHEMATICS

Questions 1 to 9 are multiple choice questions. Each question has four choices (A), (B), (C) and (D), out of which ONLY ONE is correct.

1. Q, R and S are the points on the line joining the points P (a, x) and T (b, y) such that PQ = QR = RS =

ST, then 



 



 + +

8 y 3 x ,5 8

b 3 a

5 is the mid point of the segment

(A) PQ (B) QR (C)RS (D) ST

2. The line x + y = 1 meets x-axis at A and y-axis at B.P is the mid-point of AB (fig.) P1 is the foot of the perpendicular from P to OA; M1 is that from P1 to OP; P2 is that from M1 to OA; M2 is that from P2 to OP; P3 is that from M2 to OA and so on. If Pn denotes the nth foot of the perpendicular on OA from Mn–1, then OPn =

A x P

O P3 P2 P1

B y

(A) 1/2 (B) 1/2ⁿ

3. The angle between a pair of tangents drawn from a point P to the circle x² + y² + 4x – 6y + 9 sin²α + 13 cos²α = 0 is 2α. The equation of the locus of the point P is

(A) x² + y² + 4x – 6y + 4 = 0 (B) x² + y² + 4x – 6y – 9 = 0 (C) x² + y² + 4x – 6y – 4 = 0 (D) x² + y² + 4x – 6y + 9 = 0

4. The directrix of the parabola y² + 4x + 3 = 0 is (A) x –3/4 = 0 (B) x + 1/4 = 0 (C) x – 1/4 = 0 (D) x – 4/3 = 0

5. Equation of the locus of the pole with respect of the ellipse ₂

x + ₂

y = 1, of any tangent line to the auxiliary circle is the curve

4 2

a x + ₄

y = λ² where (A) λ² = a² (B) λ²= 1/a² (C) λ² = b² (D) λ² = 1/b²

6. If PQ is a double ordinate of the hyperbola

2 2

x – ₂

y = 1 such that OPQ is an equilateral triangle, O being the centre of the hyperbola. Then the eccentricity e of the hyperbola, satisfies

(A) 1 < e < 2/ 3 (B) e = 2/ 3 (C) e = 3 /2 (D) e > 2/ 3

7. Equation of the plane through (3, 4, – 1) which is parallel to the plane r.(2i – 3j + 5k) = 0 is

(A) r.(2i – 3j + 5k) + 11 = 0 (B) r.(3i – 4j + k) + 11 = 0 (C) r.(3i + 4j – k) + 7 = 0 (D) r.(2i – 3j + 5k) + 11 = 0

8. If a = λ(i + j – k), b = µ(i – j + k), and c are unit vectors perpendicular to the vector a and coplanar with a and b, then a unit vector d perpendicular to both a and c is

(A) 6

1 (2i – j + k) (B) 2 1 (j + k)

1 (i – 2j + k) (D) 2 1 (j – k)

9. If a, b, c are three non-coplanar vectors such that a + b + c = αd and b + c + d = βa then j + 4k then a + b + c + d is equal to

(A) 0 (B) αa

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

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.

10. Assertion : The points A(3, 4), B(2, 7), C(4, 4) and D(3, 5) are such that one of them lies inside the triangle formed by the other points.

Reason : Centroid of a triangle lies inside the triangle.

11. Assertion : The line 9x + y – 28 = 0 is a chord of contact of a point P with respect to the circle 2x² + 2y² – 3x + 5y – 7 = 0.

Reason : The line joining the points of contacts of the tangents drawn from a point P outside a circle to the circle is the chord of contact of P with respect to the circle.

12. Assertion : The line bx – ay = 0 will not meet the hyperbola ₂

a x – ₂

y = 1 (a > b > 0)

Reason : The line y = mx + c does not meet the hyperbola ₂

a x – ₂

y = 1if c² = a²m² – b²

13. Assertion : The lines 1

1 x−

= 1 y

− = 1

1 z+

and

2 1 x−

= 2 1 y+

= 3

z are coplanar and equation of the plane containing them is 5x + 2y – 3z – 8 = 0

Reason : the line 1

2 x−

= 2

1 y+

= 3 z is perpendicular to the plane 3x + 6y + 9z – 8 = 0 and parallel to the plane x + y – z = 0.

This section contains 2 paragraphs; each has 3 multiple choice questions. (Question 14 to 19) Each question has 4 choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

Passage : I (No. 14 to 16)

A(3, 7) and B(6, 5) are two points.

C : x² + y² – 4x – 6y – 3 = 0 is a circle.

14. The chords in which the circle C cuts the members of the family S of circles through A and B are concurrent at

(A) (2, 3) (B) (2, 23/3) (C) (3, 23/2) (D) (3, 2)

15. Equation of the member of the family S which bisects the circumference of C is

(A) x² + y² – 5x – 1 = 0 (B) x² + y² – 5x + 6y – 1 = 0 (C) x² + y² – 5x – 6y – 1 = 0 (D) x² + y² + 5x – 6y – 1= 0

16. If O is the origin and P is the centre of C, then difference of the squares of the lengths of the tangents from A and B to the circle C is equal to (A) (AB)² (B) (OP)²

a = 6i + 7j + 7k,

b = 3i + 2j – 2k, P(1, 2, 3).

17. The position vector of L, the foot of the perpendicular from P on the line r = a + λb is

(A) 6i + 7j + 7k (B) 3i + 2j – 2k (C) 3i + 5j + 9k (D) 9i + 9j + 5k

18. The image of the point P in the line r = a + λb is (A) (11, 12, 11) (B) (5, 2, –7)

19. If A is the point with position vector ar then Area of the ∆PLA in sq. units is equal to

(A) 3 6 (B) 7 17/2

The section contains 3 questions (Questions 20 to 22).

D C B A

P P P P

Q Q Q Q

R R R R

S S S S Q P R S

20. If P(x, y) is a point in the coordinate plane such that

Column -I Column-II

(A) P is equidistant from (a + b, a – b) and (a – b), (a + b)

(P) 3x² + 3y² – 2xy = 0

(B) P is at a distance a + b, from (a, b)

(Q) y – 2x = 0 (C) distance of P from

x-axis is twice its distance from y-axis

(R) x² + y² – 2ax – 2by – 2ab = 0

(D) distance of P from the origin is the mean of the its distances from the coordinate axes.

(S) x = y

21. Match the column.

Column -I Column-II

(A) y = mx + (a²+b²) 1+m² (P) ₂

a x + ₂

b y = 1

(B) y = mx + a²m²+b² (Q) ₂² a x – ₂

b y = 1

(C) y = mx + a²m²−b² (R) b²y² = 4ax (D) y = mx + a/b²x m (S) x² + y² = a² + b² 22. If a and b are two units vectors inclined at angle α to

each other then

Column –I Column-II

(A) |a + b| < 1 if (P) 3

2π < α < π (B) |a – b| = |a + b| if (Q) π/2 < θ ≤ π (C) |a + b| < 2 (R) α = π/2 (D) |a – b| < 2 (S) 0 ≤ θ < π/2

Honesty

• To be persuasive, You must be believable.

To be believable, You must be credible.

To be credible, You must be truthful.

• An honest man is the noblest work of God.

• If I am honesty in all my dealings, I can never experience fear.

• Prefer a loss to a dishonest gain; one brings pain for the moment, the other for all time.

XtraEdge Test Series

In document XtraEdge_2009_10 (Page 55-62)

IIT-JEE 2011

IIT-JEE 2011

XtraEdge Test Series # 6

C HEMISTRY

[ ]

MATHEMATICS

Honesty

XtraEdge Test Series

C ^HEMISTRY