IIT-JEE 2011 - Nov 2009

XtraEdge Test Series # 7

Based on New Pattern

Time : 3 Hours

Syllabus :

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

Instructions : Section - I

• Question 1 to 8 are multiple choice questions with only one correct answer. +3 marks will be awarded for correct answer and -1 mark for wrong answer.

• Question 9 to 12 are multiple choice questions with multiple correct answer. +4 marks and -1 mark for wrong answer.

• Question 13 to 18 are passage based single correct type questions. +4 marks will be awarded for correct answer and -1 mark for wrong answer.

Section - II

• Question 19 to 20 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.

7. The distance of centres of mass of two square plates system a shown from point O. If masses of plates are 2m and m is (their edges are 'a' and '2a' respectively)

m a 2m

(A) 2

a (B) a (C)

2 a

3 (D)

3 a 2

8. A particle is moving in a circular path and its acceleration vector is making an angle of 30° with the velocity vector, then the ratio of centripetal acceleration to its tangential acceleration is –

(A) 2

1 (B)

3 (C)

1 (D) 3

Questions 9 to 12 are multiple choice questions. Each question has four choices (A), (B), (C) and (D), out of which MULTIPLE (ONE OR MORE) is correct.

9. Figure shows cyclic process. From c to b 40 J is transferred as heat from b to a, 130 J is transferred as heat, and work done is 80 J from a to c, 400 J is transferred as heat then –

a b

P c

(A) work done in process a to c is 310 J V (B) Net work done in cycle is 230

10. Two identical ideal springs of spring constant 1000 N/m as connected by an ideal pulley as shown and system is arranged in vertical plane. At equilibrium θ is 60º and masses m1 and m2 are 2kg and 3kg respectively. Then elongation in each spring when θ is 60º is –

θ θ

(A) 1.6 3 cm (B) 1.6 cm (C) 4.8 cm (D) none of these 11. A projectile is thrown from point P on horizontal

ground at angle θ with horizontal then -

(A) the projectile moves always from point P for any values of θ

(B) the projectile moves always from point P for some values of θ

(D) none of these

12. As shown in figure pulley is ideal and strings are massless. If mass m of hanging block is the minimum mass to set the equilibrium of system then –

(g = 10 m/s²)

20 kg

θ= 37º θ= 37º

µ = 0.5 θ = 37º

(A) m = 2.5 kg (B) m = 5 kg

(D) force applied by 20 kg block on inclined plane is 223 N

This section contains 2 paragraphs; each has 3 multiple choice questions. (Questions 13 to 18) Each question has 4 choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

Passage : I (No. 13 to 15)

One mole of monoatomic gas is taken through above cyclic process. TA = 300 K

Process AB is defined as PT = constant.

B C

P₀ A 3P₀ P

T 13. Work done in process AB is

(A) 400 R (B) – 400 R

14. Change in internal energy in process CA

(A) 900 R (B) 300 R (C) 1200 R (D) zero 15. Heat transferred in the process BC is

(A) 1000 R (B) 500 R

Passage : II (No. 16 to 18)

An external force F is applied at an angle θ with the horizontal as shown on the block of mass 'm'. The coefficient of friction between block and wall is µ.

16. The minimum value of force f required to keep the block at rest is –

θ m

rough (µ)

(A) θ cos µ

mg (B)

θ + θ µcos sin

(C)

− θ µcos sin

mg (D)

θ tan µ

17. The maximum value of force F up to which block remains at rest is -

(A) cosθ µ

mg (B)

θ + θ µcos sin

(C)

− θ µcos sin

mg (D)

tanθ µ

18. The value of force F for which friction force between block and wall is zero -

(A) mg (B)

θ sin

mg (C) θ cos

mg (D)

θ tan

This section contains 2 questions (Questions 19 to 20).

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

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

19. In the equation, y = A sin 2π (ax + bt + π/4) match the following :

Column-I Column-II

(A) Frequency of wave (P) a (B) Wavelength of wave (Q) b (C) Phase difference (R) π between two points

1/4a distance apart

(D) Phase difference of a (S) π/2 point after a time

interval of 1/8b

(T) none

20. Capillary rise and shape of droplets on a plate due to surface tension are shown in column II.

Column-I Column-II

(A) Adhesive forces is (P)

B A

greater than cohesive forces

(B) Cohesive forces is (Q)

greater than adhesive forces

two parallel plates of glass

^B ^A (D) Pressure at B > Pressure (S) ^B ^A

at A

(T) none

CHEMISTRY

Questions 1 to 8 are multiple choice questions. Each question has four choices (A), (B), (C) and (D), out of which ONLY ONE is correct.

1. Kinetic energy and potential energy of an electron in an orbit and the centrifugal force experienced by it are respectively -

(A) 2r Ze²

,– r Ze²

, r mv²

(B) – r 2 Ze²

, r Ze²

, r mv²

r 2 Ze² ,

mv² (D) – r Ze² ,

r 2 Ze² ,

r mv²

2. 3 L of a gas mixture consisting of propane and butane on complete combustion produced 10 dm³(cubic decimeter) CO2 under identical conditions. The volume of propane in the mixture is

-(A) 2L (B) 1L (C) 1.5 L (D) 0.5 L 3. Chloropicrin CCl3NO2 can be made cheaply for use

as an insectiside by a process which utilizes the reaction

CH3NO2 + 3Cl2 ––→ CCl3NO2 + 3HCl

How much nitromethane, CH3NO2 is needed to form 300 g of chloropicrin -

(A) 55 g (B) 111g

lone pairs is present on the central atom ? (A) ClO ⁻₃ (B) XeF4

(A) ^N

+ + O

–

O ^– (B) ^N

– + O

O ^–

+ O

–

O^–

⊕ (D) ^N

+ O O^–

–

6. 2 mole each of SO3, CO, SO2 and CO2 is taken in one litre vessel. If Kc for

SO3 + CO SO2 + CO2 is 1/9 then -

(A) total no. of moles at equilibrium are less than 8 (B) n(SO3) + n(CO2) = 4

7. Which of the following statements is correct for a solution saturated with AgCl and AgBr if their solubilities in moles per litre in separate solutions are x and y respectively ?

(A) [Ag⁺] = x + y (B) [Ag⁺]=[Br^–]+[Cl^–] (D) [Br^–] = y (D) [Cl^–] > x

8. The entropy change accompanying the heating of one mole of Helium gas, assuming ideal behaviour from a temperature of 300 K to a temperature of 1000 K at constant pressure.

(A) 25.17 J K^–1 mol^–1 (B) 20 kJ K^–1 mol^–1 (C) 2.517 J K^–1 mol^–1 (D) 0.2517 J K^–1 mol^–1 Questions 9 to 12 are multiple choice questions. Each question has four choices (A), (B), (C) and (D), out of which MULTIPLE (ONE OR MORE) is correct.

9. Pick up the correct statement(s)

(A) Pb⁴⁺ salts are better oxidising agents (B) As⁵⁺ salts are oxidising agents (C) Tl³⁺ salts are oxidising agents (D) Ga⁺ salts are reducing agents

10.

+ KOH (alc) —→

Which of the following can be formed.

(A) (B)

Br (C)

Br Br

(D) Br 11. Reduction of But-2-yne with Na and liquid NH3

gives an alkene which upon catalytic hydrogenation with D2 / Pt gives an alkane. The alkene and alkane formed respectively are - (A) cis-but-2-ene and

recemic-2, 3-dideuterobutane (B) trans-but-2-ene and

meso-2, 3-dideuterobutane (C) trans-but-2-ene and

recemic-2, 3-dideuterobutane (D) cis-but-2-ene and

meso-2, 3-dideuterobutane

12. Which of the following methods yield saturated hydrocarbons -

(A) RCH = CH2

COOH CH ) ii (

BH ) i (

3



 →

 (B) R–CH=CH2 ^CH →∆²^N²

(D) ^COONa

∆



 →

^NaOH^/^CaO

This section contains 2 paragraphs; each has 3 multiple choice questions. (Questions 13 to 18) Each question has 4 choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

Passage : I (No. 13 to 15)

Photoelectric effect is the phenomenon in which the surface of alkali metals like potassium and cesium emit electrons when a beam of light with high frequency is made to fall on them. The ejected electrons are called photoelectrons

Energy of photon = Work function + Maximum kinetic energy of ejected electrons.

⇒ 2

1 ₂

mvmax= h(ν – ν0)

13. Lithium does not show photoelectric effect due to - (A) small size and high charge density

(B) high ionization energy (C) low ionization energy

(D) None

14. The K.E. of photoelectrons depend on - (A) Wavelength of light (B) Frequency of light (C) Intensity of light (D) None of these 15. Electrons are emitted with zero velocity from a

metal surface when it is exposed to radiation of wavelength 6800Å. The threshold frequency (ν0) is-

(A) 2.92 × 10^–19 s^–1 (B) 4.41 × 10¹⁴ s^–1 (C) 7.18 × 10¹⁹ s^–1 (D) 5.84 × 10⁵ s^–1 Passage : II (No. 16 to 18)

Real gases deviate from ideal behaviour because of the following two faulty assumptions of kinetic theory:

(i) The actual volume occupied by molecules is negligible as compared to the total volume of the gas.

(ii) The forces of attraction and repulsion between molecules of the gas are negligible

The extent of deviation of a real gas from ideal behaviour is expressed in terms of compressibility factor (z).

Hence, suitable corrections were applied to the ideal gas equation so that it can also explain the behaviour of real gases. The equation obtained by applying the two corrections to the usual gas equations is known as van der Waal equation 1. Volume correction

Corrected (ideal) volume = (V – b)

where b is the effective volume of the molecules.

2. Pressure correction (intermolecular attraction correction)

Corrected (ideal pressure = P + p However, p = ₂

V a

∴ The van der Waal's equation becomes











 + ₂² V

P an (V – nb) = nRT

On the basis of the above work-up answer the following questions :

16. 0.5 value of compressibility factor (z) indicates that the gas :

(A) shows positive deviation from the ideal gas (B) negative deviation from the ideal gas behaviour (C) either of the two

(D) the factor is insufficient

17. van der Waal equation is obeyed by the real gases:

(A) over a wide range of temperature and pressure (B) over all temperatures

(D) over a specific temperature and specific pressure 18. At low pressure, the van der Waal's equation is -

(A) PV = RT+

a (B) PV = RT – V a

a (D) PV = RT – ₂ V

This section contains 2 questions (Questions 19 to 20).

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

19. Column-I Column-II

(A) No. of ion in 1 mole (P) NA K4[Fe(CN)6]

(B) No. of atoms in (Q) 5NA

Ca3(PO4)2 in 0.2 mole of this compound

(D) No. of protons in (S) 1.56 × 10²⁴ 0.1 mole CH4

(NA = 6.0 × 10²³)

(T) 0.3 × 10²⁵

20. Column-I Column-II

(A) Ratio of energy of (P) 4 : 3 electron in 3rd orbit

of H-atom and 4th orbit of Li²⁺ ion

(B) Ratio of de-Broglie (Q) 25 : 16 wavelengths of electron

in 2nd orbit of H-atom to 3rd orbit of He⁺ ion

for H-atom

(D) Ratio of frequencies (S) 4 : 9 of revolution of

electrons in 2nd orbit of H-atom and 3rd orbit of He⁺ ion

(T) 2 : 3

MATHEMATICS

Questions 1 to 8 are multiple choice questions. Each question has four choices (A), (B), (C) and (D), out of which ONLY ONE is correct.

1. If z1, z2, z3 are three distinct complex numbers and a, b, c are three positive real numbers such that

| z z

| a

2− =

| z z

| b

3− =

| z z

| c

1− , then value of

3 2

z z

− +

1 3

z z

− +

2 1

z z

− is

(A) 0 (B) w

(a – 2) (x – [x])² + 2(x – [x]) + a² = 0 (1) (where [x] denotes the greatest integer ≤ x) has no integral solution and has exactly one solution in (2, 3), then a lies in the interval -

(A) (–1, 2) (B) (0, 1) (C) (–1, 0) (D) (2, 3) 3. Value of

∑

− n

1 k

1 k k)(C ) C

( is -

(A) ²ⁿCn (B)

1(²ⁿ⁺²Cn+1) – ²ⁿCn

4. In a triangle with one angle 2π/3, the lengths of the sides form an A.P. If the length of the greatest side is 7 cm, the radius of the circumcircle of the triangle is - (A) 37 /3cm (B) 5 3/3cm

5. The value of cos^–1 x + cos^–1 



 



 + 3−3x² 2

1 2 x (1/2 ≤ x ≤ 1) is equal to -

(A) π/6 (B) π/3 (C) π (D) 0

6. Two rods of lengths a and b slide along the x-axis and y-axis respectively in such a manner that their ends are concyclic. The locus of the centre of the circle passing through the end points is -

(A) 4(x² + y²) = a² + b² (B) x² + y² = a² + b² (C) 4(x² – y²) = a² – b² (D) x² – y² = a² – b²

7. The locus of the mid-point of the line segment joining the focus to a moving point on the parabola y² = 4ax is another parabola with directrix -

(A) x = – a (B) x = – a/2 (C) x = 0 (D) x = a/2

8. If PQ is a double ordinate of the hyperbola

2 2

a 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

Questions 9 to 12 are multiple choice questions. Each question has four choices (A), (B), (C) and (D), out of which MULTIPLE (ONE OR MORE) is correct.

9. Let α be a repeated root of

p(x) = x³ + 3ax² + 3bx + c = 0, then - (A) α is a root of x² + 2ax + b = 0 (B) α =

) b a ( 2

ab c

2−

−

c ab

2−

−

(D) α is a root of ax² + 2bx + c = 0

10. Let N denote the number of ways in which n boys can be arranged in a line so that 3 particular boys are separated. Then -

(A) 3!|N (B) (n – 2)!|N (C) ^n–2C3|N (D) (n – 3)² (n – 4)²|N 11. The equation 3 sin² x+10 cos x – 6 = 0 is satisfied if-

(A) x = nπ + cos^–1 (1/3) (B) x = nπ – cos^–1 (1/3)

12. The Cartesian equation of the curve whose parametric equation is x = 2t – 3 and y = 4t² – 1 is given by -

(A) (x+3)² – y – 1 = 0 (B) x² + 6x – y + 8 = 0 (C) (y+1)² + x + 3 = 0 (D) y² + 6x – 2y + 4 = 0

This section contains 2 paragraphs; each has 3 multiple choice questions. (Questions 13 to 18) Each question has 4 choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

Passage : I (No. 13 to 15)

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.

13. AB is equal to -

(A) R sin θ (B) 2R sin (θ/2) (C) R cos θ (D) 2R cos (θ/2) 14. Area of the segment AMB is equal to -

(A) (1/2) R² θ (B) (1/2)R² sin θ (C) (1/2) R² (θ – sin θ) (D) none of these

15. If the area AMBECL is 1/nth 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 : II (No. 16 to 18)

A(x1, y1), B(x2, y2), C(x3, y3) are the vertices of a triangle ABC. lx + my + n = 0 is an equation of the line L.

16. If L intersects the sides BC, CA and AB of the triangle ABC at P, Q, R respectively then

PC BP×

QA CQ×

AR is equal to -

(A) – 1 (B) – 1/2

17. If the centroid of the triangle ABC is at the origin and algebraic sum of the lengths of the perpendiculars from the vertices of the triangle ABC on the line L is equal to 1 then sum of the squares of the intercepts made by L on the coordinate axes is equal to -

(A) 0 (B) 4

18. If P divides BC in the ratio 2 : 1 and Q divides CA in the ratio 1 : 3 then R divides AB in the ratio -

(A) 2 : 3 internally (B) 2 : 3 externally (C) 3 : 2 internally (D) 3 : 2 externally

This section contains 2 questions (Questions 19 to 20).

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

19. Let a1, a2, a3, ... be a geometric progression such that log10(am) =

1 and log10(an) = m

for two fixed positive integer m and n, with m < n, then

Column-I Column-II

(A) a2m+n (P) 10^1/m–1/n

(B) amn (Q) 10

20. Column-I Column-II

(A) Equation of the polar (P) 8x + 2y – 23 = 0 of (–7, –9) with

respect to the circle x²+y²–12x–8y–48 = 0

(B) Equation of the (Q) 13x + 13y – 30 = 0 common chord of the

circles x²+ y² + 2x + 2y + 1 = 0 and x²+y² +4x + 3y + 2 = 0

the circle x² + y² + 12x + 8y + 26 = 0

(D) Equation of the radical (S) x + 5y + 52 = 0 axis of the circles

2x² + 2y² + 4x + 4y + 9 = 0 and x² + y² + 6x+3y – 7 = 0

XtraEdge Test Series

In document Nov 2009 (Page 62-69)