MOCK TEST - AIEEE PATTERN - Xtraedge April 2010

7. Experimental verification of Newton's law of cooling is valid for -

(A) large temperature difference i.e.

30°C to 85°C between hot liquid and surrounding (B) very large temperature difference i.e. 5°C to 95°C

between hot liquid and surrounding

(D) any temperature difference

8. While studying the dissipation of energy of a simple pendulum by plotting a graph between square of amplitude and time which of the following apparatus is not essential ?

(A) Ticker timer (B) Meter scale (C) Vernier calliper (D) Stop watch

9. An object is weighed on a balance whose pans are not equal in masses when placed in the left pan, the object appears to weigh 10.30g but when placed in the right pan, it appears to weigh 12.62g. What is the correct mass of the object ?

(A) 10.30 g (B) 12.62 g (C) 11.46 g (D) Can not find

10. When jockey is put at two ends of the potentiometer wire, the galvanometer gives diflections in opposite directions. It means that apparatus can -

(A) not give a null point

(B) give a null point (C) be faulty

(D) be used after making some changes in the circuit 11. A student performs an experiment to determine the

Young's modulus of a wire exactly 2cm long, by Searle's method. In a particular reading, the student measures the extension in the length of the wire to be 0.8 mm with an uncertainty of ± 0.05 mm at a load of exactly 1.0 kg.

The student also measures the diameter of the wire to be 0.4 mm with an uncertainty of ± 0.01 mm. Take g = 9.8 m/s² (exact). The Young's modulus obtained from the reading is -

(A) (2.0 ± 0.3) × 10¹¹ N/m² (B) (2.0 ± 0.2) × 10¹¹ N/m² (C) (2.0 ± 0.1) × 10¹¹ N/m² (D) (2.0 ± 0.05) × 10¹¹ N/m²

12. A student measures the focal length of a convex lens by putting an object pin at a distance 'u' from the lens and measuring the distance 'v' of the image pin. The graph between 'u' and 'v' plotted by the student should look like -

(A)

v(cm)

O u(cm)

(B)

O v(cm)

u(cm)

(C)

v(cm)

O u(cm)

(D)

v(cm)

O u(cm)

13. Two concave mirror each of focal length f. A point source is placed at a point midway between two mirror. The minimum value of d for which only one image of s is formed –

d s

(A) f (B) 2f

14. In YDSE, if the intensity of central maxima is IO then the y-coordinate of point where the intensity is

2 I_O

, d = 0.1 mm, D = 1m,

λ = 5000A°

y O

(A) 1.5 mm (B) 2 mm (C) 1.75 mm (D) 1.25 mm

15. Two charges of –4µC and +4µC are placed at points A (1,0,4) and B (2, –1,5) located in an electric field

→E = 0.20 iˆ V/cm. The torque acting on the dipole is-

(A) 8 × 10^–5 N-m (B) 8/ 2 × 10^–5 N-m (C) 8 2 × 10^–5 N-m (D)2 2 × 10^–5 N-m

16. Three concentric spherical metallic shells A, B and C of radii a, b and c (a < b < c) have surface charge densities σ, – σ and σ respectively. If the shells A and C are at same potential, then the correct relation between a, b and c is -

(A) a + c = b (B) b + c = a (C) a – b = c (D) a + b = c

17. Five identical plates of equal area A are placed parallel to and at equal distance d from each other as shown in figure. The effective capacity of the system between the terminals A and B is -

(A) 5 3

∈ (B)

4 5

o A

∈

o A

∈ (D)

5 4

o A

∈

18. Read the following statements carefully :

Y : The resistivity of semiconductor decreases with increase of temperature.

Z : In a conducting solid, the rate of collision between free electrons and ions increases with increase of temperature.

(A) Both Y and Z are true and Z is correct explaination of Y

(B) Both Y and Z are true but Z is not correct explaination of Y

(D) Y is false but Z is true

19. A 1m long metallic wire is broken into two unequal parts A and B. The part A is uniformly extended into another wire C. The length of C is twice the length of A and resistance of C is equal to that of B. The ratio of resistances of parts A and C is -

(A) 4 (B)

4 1

2 1

20. A 600 cm long potentiometer wire is connected to a circuit as shown in figure. The resistance of potentiometer wire is 15r. The distance from point A at which the jockey should touch the wire to get zero deflection in the galvanometer is –

A B

E/2 r

(A) 320 cm (B) 230 cm (C) 160 cm (D) 460 cm

21. A rectangular loop of metallic wire is of length a and breadth b and carries a current i. The magnetic field at the centre of the loop is -

(A) π µ

4 0i

ab b a 8 ²+ ²

(B) π µ

4 0i

ab b a 4 ²+ ²

4 0i

ab b a 2 ²+ ²

(D) π µ

4 0i

ab b a²+ ²

22. A short magnet produces a deflection of 30° when placed at certain distance in tanA position of magnetometer. If another short magnet of double the length and thrice the pole strength is placed at the same distance in tanB position of the magnetometer, the deflection produced will be -

(A) 60° (B) 30°

23. A solenoid has 2000 turns wound over a length of 0.30 m.

Its area of cross-section is 1.2 × 10^–3 m². Around its central section a coil of 300 turns is wound. If an initial current of 2A in the solenoid is reversed in 0.25 sec, the emf induced in the coil is equal to - (A) 6 × 10^–4 Volt (B) 4.8 × 10^–2 Volt (C) 6 × 10^–2 Volt (D) 48 kV

24. A 100 volt AC source of frequency 500 Hz is connected to a L–C-R circuit with L = 8.1 mH, C = 12.5 µF and R = 10 Ω, all connected in series.

The potential difference across the resistance is - (A) 100 V (B) 200 V

(A) Resultant of two vectors of unequal magnitude can be zero

(B) Resultant of three non-coplanar vectors of equal magnitude can be zero

resultant can be zero is four.

26. A stone thrown with the velocity V0 = 14 m/s at an angle 45° to the horizontal, dropped to the ground at a distance 'S' from the point where it was thrown.

From what height should the stone be thrown in horizontal direction with the same initial velocity so that it fall at the same spot -

(A) 14.2 m (B) 16.9 m (C) 10.0 m (D) 9.6 m

27. A small body of mass 'm' is attached to one end of a light inelastic string of length l. The other end of the string is fixed. The string is held initially taut and horizontal and then body is released. The centripetal acceleration of the body and the tension in the string when the string reaches vertical position will be - (A) g, mg (B) 2g, 3 mg

28. Assertion : A rocket moves forward by pushing the surrounding air backwards.

Reason : It derives the necessary thrust to move forward, according to Newton's third law of motion.

(A) Both Assertion and Reason are true and Reason is a correct explanation of the Assertion

(B) Both Assertion and Reason are true but Reason is not a correct explanation of the Assertion

29. While slipping on rough spherical surface of radius 'R', block A of mass 'm' comes with velocity 1.4gR at bottom B. Work done in slipping the block from 'B' to 'C' is –

m A

(A) 4

mgR (B) mgR

4 5 mgR

30. A 2000 kg rocket in free space expels 0.5 kg of gas per second at exhaust velocity 400 ms^–1 for 5 seconds. What is the increase in speed of rocket in this time -

(A) 2000 ms^–1 (B) 200 ms^–1 (C) 0.5 ms^–1 (D) zero

CHEMISTRY

31. Which of the following can act as a both Bronsted acid & Bronsted base -

(A) Na2CO3 (B) OH^– (C) HCO3– (D) NH3

32. In which compound the oxidation No. of Oxygen is +2

1 -

(A) OF2 (B)O2F2 (C) O2[PtF6] (D) KO2

33. The favourable conditions for a spontaneous reactions are -

(A) T ∆S > ∆H, ∆H = ⊕ , ∆S = ⊕ (B) T ∆S > ∆H, ∆H = ⊕ , ∆S = Θ (C) T ∆S = ∆H, ∆H = Θ , ∆S = Θ (D) T ∆S = ∆H, ∆H = ⊕ , ∆S = ⊕

34. The substance not likely to contains CaCO3 is - (A) Dolomite (B) A marble statue (C) Calcined Gypsum (D) Sea shells

35. On mixing 10ml of acetone with 50ml of CHCl3, the total volume of the solutions-

(A) < 60ml (B) > 60ml (C) = 60ml (D) unpredictable

36. On addition of He gas at constant volume to the reaction N2 + 3H2 2NH3 at equilibrium-

(A) The reaction stops

(B) Forward reactions is favoured (C) Reaction remains unaffected (D) Backward reactions is favoured

37. The half life of a reaction is 24 hours . If we start with 10gm of reactant, How many grams of it will reaction after 96 hours, (I order reaction)

(A) 0.625gm (B) 6.25gm (C) 1.25gm (D) 0.125gm

38. The current is passed in Ag2SO4 aqueous solution &

1.6 gm O2 is obtained. The amount of Ag deposited will be- [Ag = 108gm]

(A) 107.8g (B) 1.6g (C) 0.8g (D) 21.6g 39. In decinormal solution CH3COOH is ionized to the

extent of 1.3% find the pH of solution.

(A) 3.89 (B) 2.89 (C) 4.89 (D) 5.89 40. A FCC element (atomic wt.= 60) has a cell edge of

400pm. Its density is-

(A) 6.23 g/cm³ (B) 6.43 g/cm³ (C) 6.53 g/cm³ (D) 6.63 g/cm³ 41. Which set of quantum No. is not possible-

n l m s (A) 2 0 0 +1/2 (B) 4 2 –3 –1/2 (C) 3 2 –2 +1/2 (D) 2 1 0 +1/2

42. Give simplest formula of compound which containing 6gm C, 3.01×10²³ atom O and 2 mole H atoms-

(A) CH₂O (B) CH₄O (C) CHO (D) CH₃O

43. The IUPAC Name of

(A) 1,2-dimethyl Cyclohexene (B) 2,3-dimethyl Cyclohexene (C) 1,2-dimethyl Cyclohex-2-ene

(D) 5,6-dimethyl Cyclohex-1-ene

44. Which of the following reagent can make distinction between Pri. and Sec. amines ?

(A) NH3 (B) NaNO2/HCl (C) HCl (D) All

45. Toluene reacts with Cl2 in the presence of light to give -

(A) Benzyl chloride (B) Benzoyl chloride (C) p-chlorotoluene (D) o- chlorotoluene

46. Which compound is formed when excess of KCN is added to an aqueous solution of copper sulphate (A) Cu (CN)2 (B) K2 [Ca(CN)4] (C) K [Cu(CN)2] (D) K3 [Cu(CN)4] 47. The Blue Print Process involves the use of-

(A) Indigo dyes (B) Iron compound (C) Vat dyes (D) some other compounds 48. The ionic radii of N^3–, O^2–, F^–and Na⁺ follow the

order-

(A) N^3–> O^2– > F^– > Na⁺(B) N^3–> Na⁺ > O^2– > F^– (C) Na⁺> O^2–>N^3–> F^– (D) O^2–> F^–> Na⁺> N^3–

49. Reaction xy2 xy + y (g) (g) (g)

Initial pressure of xy2 is 600 mm Hg & total pressure at equilibrium is 800 mm Hg. Kp of reaction is - (A) 50 (B) 100 (C) 166.6 (D) 400 50. Cell: Zn|Zn⁺²|| Cu⁺²| Cu

If the correct reactions of Zn⁺² & Cu⁺² ions are doubled, the emf of the cells:

(A) doubled (B) halved (C) same (D) zero

51. What is the pH of buffer solution containing 12g CH3COOH & 16.4g CH3COONa in 500ml of solution (Ka for CH3COOH = 1.8×10^–5).

(A) 4.7447 (B) 4.4774 (C) 4.4477 (D) None

52. How many moles of ferrous oxalate are completely oxidized by 1 mole KMnO4 in acidic medium-

(A) 3/5 (B) 5/3

53. In an irreversible process taking place at constant-T

&P and which only pressure-volume work is being done, than (dG) and (dS), satisfy the criteria-

(A) (dS)V, E > 0, (dG)T,P < 0 (B) (dS)V, E = 0, (dG)T,P = 0

54. 3,3-dimethylbutan-2-ol, on reaction with Conc.

H2SO4 at 443K will give…… as major product- (A) 3,3-dimethyl but-1-ene

(B) 2,3-dimethyl but-2-ene (C) 2,2-dimethyl but-2-ene

(D) 2,2-dimethyl-1- butene

55. Select the true statement about benzene from amongst the following-

(A) Because unsaturation benzene easily undergoes addition reaction

(B) There are two types of C-C bonds in benzene molecule

isomeric substances

56. OH __{ →}Zndust__ B

3 3

AlCl Cl C H 

 →

 ⁻ K

^alk^.^KMnO⁴→D. Identity ‘D’ ?

(A) ^CH³ (B)

57. In Lassaigne’s test, the organic compound is first fused with sodium metal. The sodium metal is used because

(A) The melting point of sodium metal is low

(B) Sodium metal reacts with elements present in organic compounds to form inorganic compounds

58. Concentrated hydrochloric acid when kept in open air sometimes produces a cloud at white fumes the explanation for it is that-

(A) Oxygen in air reacts with the emitted HCl gas to form a cloud of chlorine gas

(B) Strong affinity of HCl gas for moisture in air results in forming of droplets of liquid solution which appears like a cloudy smoke

(C) Due to strong affinity for water concentrated hydrochloric acid pulls moisture of air towards itself. This moisture forms droplets of water and hence the cloud.

(D) Concentrated hydrochloric acid emits strongly smelling HCl gas all the time

59. Consider the following complex [Co(NH3)5CO3]ClO4

The coordination number, oxidation number, number of d-electrons and number of unpaired electrons on the metal respectively-

(A) 6, 3, 6, 0 (B) 7, 2, 7, 1 (C) 7, 1, 6, 4 (D) 6, 2, 7, 3

60. Point out the incorrect statement about resonance (A) Resonance structure should have equal energy (B) In Resonance structure, the constituent atoms

should be in the same position

(D) Resonance structure should differ only in the location of electrons around the constituent atoms

MATHEMATICS

61. If the angles of elevation of an aeroplane from two points 1 km apart be 60º and 30º, then the height of the aeroplane is -

(A) 500m (B)

3 500 m

2000m (D) None

62. Suppose a population A has 100 observations 101, 102, ...200 and another population B has 100 observations 151, 152, ... 250. If VA and VB

represents the variances of the two population respectively then

B A

V V is -

(A) 4

9 (B)

9 4

2 (D) 1

63. If vertices of a triangle are (1, 0), (2, b) & (c², – 3) then centroid of triangle

(A) can lie on y axis (B) always lie on x axis (C) lie on x axis if a + b = 3

(D) lie on y axis if c = 3 only 64. The value of k in order that

f(x) = sinx – cosx – kx + b decreases for all real values is given by :

(A) k < 1 (B) k ≥ 1

65. _x^lim→₀ ₂

x x cos –

e ² is equal to -

(A) 3/2 (B) 1/2

66. If ∆ =

3 3 3

2 2 2

1 1 1

c b a

, then

3 3 3 3 3

2 2 2 2 2

1 1 1 1 1

c b c 3 b 2 a

− +

is equal to -

(A) ∆ (B) 2∆

67. In a ∆ABC, angle A is greater than angle B. If the measures of angles A and B satisfy the equation 3sin x – 4 sin³x – k = 0, 0 < k < 1, then the measure of angle C is -

(A) 3

π (B)

π (C)

3 2π

(D) 6 5π

68. If the p, q, r have truth values.

F, F, T then the statement (p ↔ q) ∨ ~ r → (p ∧ r) will be

(A) T (B) F (C) T, F (D) None 69. The statement (p ∨ q) ↔ (q ∧ ~ p) is a

(A) Tautology (B) Contradiction

70. If n^thterm of sequence 2 21,

13 17 ,

9 1 , 1

23 20, .... is

17 5 then value of n is -

(A) 20 (B) 10 (C) 5 (D) 13

71. The ratio in which plane 2x – k = 0 divides the line joining (–2, 4, 7) & (3, – 5, 8) is 9 : 1 then k equal to- (A) 4 (B) 5 (C) 6 (D) 7

72. If |a| = 2, |b| = 5 and |a × b| = 8 then |a – b| is equal to:

(A) 12 (B) 15 (C) 17 (D) 5 73. The extremities of a line segment of length 6 move in

two fixed perpendicular lines. If locus of a point P which divides this line segment in ratio 1 : 2 is an ellipse then eccentricity of this ellipse is -

(A) 2

1 (B)

1 (C)

3 (D)

4 3

74. The value of p such that the vertex of parabola y = x² + 2px + 13 is 4 units above x-axis & lies in first quadrant is :

(A) 3 (B) 4 (C) ± 3 (D) – 3

75. If the lines represented by x² + 2λx + 2y² = 0 & lines represented by (1 + λ)x² – 8xy + y² = 0 are equally inclined then λ equals :

(A) – 2 (B) + 2

76. locus of centre of a variable circle

tx² + ty² + 2(t² + 1)x – 2(t² – 1)y + t = 0 is a : (A) Straight line (B) Parabola

77. If

∫

− 4

1f(x)dx = 4 and ⁴(3 f(x))

∫

2 ⁻ dx = 7 then the value of

∫

2⁴f(x)dx is -

(A) 2 (B) – 3

78. Bisector of angle between lines 2x + y – 6 = 0 &

4x – 2y + 7 = 0 which contains origin is - (A) acute angle bisector ; x = 5/8 (B) acute angle bisector ; y = 19/4 (C) obtuse angle bisector ; x = 5/8 (D) obtuse angle bisector ; y = 19/4

79. The value of

∫

₁²

[

^f⁽^g⁽^x⁾⁾

]

^–¹^f 'g(x). g'(x) dx where g(1) = g(2) is equal to -

(A) 1 (B) 2

80. If f(x) =

∫

^x²₁⁺₊^sin_x²²^x ^sec²x dx and f(0) = 0 then f(1) =

(A) 1 – π/4 (B) π/4 – 1 (C) tan1 – π/4 (D) None of these

81. The domain of the function f(x) =

] x [ x

x sec^–¹

− is - (A) R (B) R – {(– 1, 1)I}

(A) Df = [– 1, 1] (B) Rf = {–π/2, π/2}

83. If z1, z2, z3 represents the vertices of an equilateral triangle such that

|z1| = |z2| = |z3| then -

(A) z1 + z2 = z3 (B) z1 + z2 + z3 = 0 (C) z1z2 = 1/z³ (D) z1 – z2 = z3 – z2

84. In a class of 100 students there are 70 boys whose average marks in a subject are 75.If the average marks of the complete class is 72, then what is the average of the girls.

(A) 73 (B) 65

85. A letter is taken at random from the letters of word 'STATISTICS' and a another letter is taken at random from letters of word 'ASSISTANT'. The probability that they are the same letter is -

(A) 1/45 (B) 13/90 (C) 19/0 (D) 5/18 86. If A = {x : x ∈ I ; – 2 ≤ x ≤ 2}

Β = { x : x ∈ I ; 0 ≤ x ≤ 3}

C = {x : x ∈ N ; 1 ≤ x ≤ 2} and D = {(x, y) ∈ N × N; x + y = 8} then - (A) n(A ∪ (B ∪ C)) = 5 (B) n(D) = 6 (C) n(B ∪ C) = 5 (D) None of these

87. Solution of sec²y dx

dy + 2xtany = x³ is -

(A) tan y = ce⁻^x²+ (x²– 1) (B) tany = ce⁻^x²+ (x² – 1) (C) tany = ce⁻^x²– (x² – 1)

(D) None of these

88. The equation of common tangent to the curves y²= 8x and xy = –1 is -

(A) 3y = 9x + 2 (B) y = 2x + 1 (C) 2y = x + 8 (D) y = x + 2

89. Let f be twice differentiable function such that f"(x) = – f(x) and f'(x) = g(x)

h(x) = (f(x))²+ (g(x))². If h(5) = 11 then h(10) is equal to

(A) 22 (B) 11

90. We are required to from different words with the help of letter of the word INTEGER. Let m1, be the number of words in which I and N are never together and m2 be the number of words which begin with I and end with R. Then

2 1

m is given by -

(A) 30 (B) 1/30

PHYSICS

1. If the amplitude of a damped oscillator becomes half in 2 minutes, the amplitude of oscillation w.r.t. initial one after 6 minutes is

(A) 27

1 (B)

1 (C)

1 (D)

64 1

2. An infinite number of spring having force constants as k, 2k, 4k, 8k ... ∞ and respectively are connected in series; then equivalent spring constant is

(A) k (B) 2k (C) k/2 (D) ∞

3. A point particle of mass 0.1 kg is executing SHM of amplitude 0.1 m when the particle passes through the mean position. Its kinetic energy is 8 × 10^–3 J. The equation of motion of this particle when the initial phase of oscillation is 45º can be given by

(A) 0.1 cos 



 



 +π t 4

4 (B) 0.1 sin 



 



 +π t 4 4



 



 +π

t 4 (D) 0.2 sin 



 

 +π t 2 2

4. A mass m is moving with constant velocity along a line parallel to x-axis away from the origin. It angular momentum with respect to origin.

(A) is zero (B) remains constant (C) goes on increasing (D) goes on decreasing 5. A vessel containing oil (density = 0.8g/cm³) over

mercury (density = 13.6 g/cm³) has a homogeneous sphere floating with half of its volume immersed in mercury and other half in oil. The density of material of sphere in g/cm³ is

(A) 3.3 (B) 6.4 (C) 7.2 (D) 2.8

6. Two trains move towards each other with the same speed, speed of sound is 340 ms^–1. If the pitch of the tone of the whistle of one is heard on the other changes by 9/8 times then the speed of each train is

V V

(A) 2 ms^–1 (B) 2000 ms^–1 (C) 20 ms^–1 (D) 200 ms^–1

7. A sound level I differ by 4 dB from another sound of intensity 10 nW cm^–2. The absolute value of intensity of sound level I in Wm^–2 is

(A) 2.5 × 10^–4 (B) 5.2 × 10^–4 (C) 2.5 × 10^–2 (D) 5.2 × 10^–2

8. An ideal gas is taken through the cycle A → B → C

→ A as shown. If the net heat supplied to the gas in the cycle 5J, the work done by the gas in the process C → A

A 2 C

P(N/m²) 10 V(m³)

(A) – 5 J (B) – 15 J (C) – 10 J (D) –20 J 9. There are n electrons of charge e on a drop of oil of

density ρ. It is in equilibrium in an electric field E.

Then radius of drop is (A)

2 / 1

g 4

neE 2 

 





πρ (B)

2 / 1

g neE

 



 ρ (C)

3 / 1

g 4

neE 3 

 





πρ (D)

3 / 1

g neE 2 

 



 πρ

10. Two identical cells of emf 1.5 V and internal resistance 1 Ω are in series. A third cell of similar parameters is connected in parallel to the

In document Xtraedge April 2010 (Page 71-78)