ALL INDIA TEST SERIES FOR IIT-JEE

CRASH COURSE for IIT-JEE / AIEEE / PMT Intensive Crash Course by IITians & NITians

Course Features

59, Niti Khand – 3 Indirapuram (GZB.) cont. 9910817866 , 9990495952

TEST ID

00030403

AIEEE FULL TEST - 1 Ti m e : 3 ho ur s

M a xi m u m m ar k s: 4 3 2

Please read the instructions carefully. You are allotted 5 minutes specifically for this purpose.

INSTRUCTIONS A.

General: (i)

The Test Booklet consists of 90 questions. The maximum marks are 432.

(ii)

There are three sections in this paper consisting of Mathematics, Physics & Chemistry having 30 questions each. Part A –

CHEMISTRY (144 marks) – Question No. 4 to 9 and 13 to 30 consist of FOUR (4) marks each and Question No. 1 to 3 and 10 to 12 consist of EIGHT (8) marks each for each correct response.

Part B –

PHYSICS (144 marks) – Questions No.33 to 49 and 54 to 60 consist of FOUR (4) marks each and Question No. 31 to 32 and 50 to 53 consist of EIGHT (8) marks each for each correct response.

Part C –

MATHEMATICS (144 marks) – Question No. 61 to 69, 73 to 81 and 85 to 90 consist of FOUR (4) marks each and Question No. 70 to 72 and 82 to 84 consist of EIGHT (8) marks each for each correct response.

(iii)

Candidates will be awarded marks as stated above in instruction No. (ii) for correct response of each question 1/4 (one fourth) marks will be deducted for indicating incorrect response of each question. No deduction from the total score will be made if no response is indicated for an item in the answer sheet.

(iv)

Mark only one correct answer out of four alternatives.

(v)

Use Blue/Black Ball Point Pen only for writing particulars/ or any marking.

(vi)

Use of calculator is not allowed.

(vii)

Darken the circles in the space provided only.

(viii) Use of white fluid or any other material which damages the answer sheet, is not permitted.

B.

Filling the OMR SHEET: Please read carefully the instructions printed on the OMR SHEET before marking your response.

AIEEE Full Test - 1

PART A: CHEMISTRY 1.

The two particles A and B have de-Broglie wavelengths 1 nm and 5 nm respectively. If mass of A is four times the mass of B, the ratio of kinetic energy of A and B would be (a) 5 : 1 (b) 25 : 4 (c) 20 : 1 (d) 1 : 5

2.

For a radioactive element, a graph of log (b) −

(a) +2.303λ 3.

N vs time has a slope equal to N0

λ 2.303

(c) +

λ 2.303

(d) −2.303λ

n – Butane reacts with Br2 at 130°C to give mainly (b) H 3C

(a)

CH 2 CH 2 CH 2 Br

CH3 (c) H3C

C

CH3

(d) None of these

Br 4.

An oxide of nitrogen is reddish brown and paramagnetic at room temperature but it decolourises and also loses its paramagnetism on freezing it. The oxide at room temperature is (b) Pure N 2 O 4 (a) Pure NO 2 (c) equilibrium mixture of N 2 O 4 and NO 2

5.

The following data were obtained at a certain temperature for the decomposition of ammonia in contact with tungsten: P (mm) → 50 100 200 Relative t1/2 → 3.64

1.82

The order of the reaction is? (a) 2 (b) 1 6.

7.

8.

(d) N 2 O5

0.91 (c) 3

(d) zero

In sodium nitroprusside, the oxidation number, co-ordination number and EAN of iron are respectively (a) + 3, 6, 36 (b) +3, 6, 35 (c) +3, 3, 36 (d) +6, 3, 35 Which carbocation among the following is most stable? (a) ( C6 H 5 )2 CH +

(b)

(c) ( CH 3 )2 CH +

(d) ( CCl3 )2 CH +

Consider the species NO3− , NO2+ and NO −2 . Pick up the correct statement (a) The hybrid state of N in all the species is same. (b) The shapes of both NO +2 and NO −2 is bent while NO3− is planer. (c) The hybrid state of N in NO3− and NO −2 is same. (d) The hybrid state of N in NO +2 is sp2. 1

AIEEE Full Test - 1

Which of the following is not true about B2 H 6 ?

9.

(a) It contains two types of B − H bonds (c) It is an electron deficient molecule

(b) It contains on B − B bond (d) It contains multicentre bonds

In the accompanied diagram indicating E R , E T and E P as the energies of reactants, activated complex and products respectively. Which of the following is correct?

10.

(a) Forward reaction is slow (c) Reaction is exothermic Given

11.

(b) Backward reaction is fast (d) Reaction is endothermic



 NCl3 g + 3HCl g ; −∆H1 NH3( g ) + 3Cl2( g ) 

( ) ( )



 2NH3( g ) ; +∆H 2 N 2( g ) + 3H 2( g ) 



 2HCl g ; ∆H3 H 2( g ) + Cl2( g ) 

( ) The heat of formation of NCl3( g ) in the terms of ∆H1 , ∆H 2 and ∆H3 is ?

∆H 2 3 − ∆H3 2 2 ∆H 2 3 (c) ∆H f = ∆H1 − − ∆H3 2 2 (a) ∆H f = −∆H1 +

(b) ∆H f = ∆H1 +

∆H 2 3 − ∆H3 2 2

(d) None of these

The conductivity of the saturated solution of some bivalent salt XY is 3.06 × 10−6 ohm −1cm −1

12.

and its equivalent conductivity is 1.53ohm -1cm 2equivalent -1 . The value of K sp of XY is ? (b) 2.5 × 10−9

(a) 4 × 10-6

(c) 2.5 × 10−13 (d) 1× 10−6 3- Methyl -1- butene on oxymercuration – demercuration yields …………… as the major product? (a) 3-Methyl-2-butanol (b) 2-Methyl – 2- butanol (c) 3-methyl -1-butanol (d) 2-Methyl-1-butanol

13.

14.

Amongst the following, the compound that is both paramagnetic and coloured is? (b) ( NH 4 )2 [ TiCl6 ]

(a) K 2Cr2 O7

(d) K 4  Fe ( CN )6  The number of sigma and pi bonds in the structure given below are (c) VOSO 4

15.

(NC)2C (a) 17, 9 (c) 15, 6 2

C

N(CO)2 C2H 5 (b) 17, 7 (d) 17, 5

AIEEE Full Test - 1

16.

The major role of fluorspar CaF2 , which is added in small quantities in the electrolytic reduction of alumina dissolved in fused cryolite, is (a) to act as catalyst (b) to make the fused electrolyte less conducting (c) to lower the temperature of melt (d) to decrease the rate of oxidation of carbon at the electrode

17.

Which carbohydrate cannot be metabolized by human body? (a) Amylose (b) Cellulose (c) Maltose (d) Amylopectin

18.

( X → Z(K

)

X → Y K1 = 1010.e −500/T ; 2

= 1012.e−1000/T

)

At what T both K1 and K 2 are equal ? (a) 500 K 19.

20.

21.

22.

(b)

500 K 4.606

(c)

4.606 K 500

(d)

2.303 K 5000

Which among the following is hydrolysed most easily? (a) CH3COOC2 H5 (b) CH3CONH 2 (c) CH3COCl

(d) (CH3CO)2 O

The correct order of acid – strength is? (a) Cl2O7 > SO2 > P4O10

(b) CO2 > N 2O5 > SO3

(c) Na 2 O > MgO > Al2 O3

(d) K 2O > CaO > MgO

A compound is made by mixing cobalt (III) nitrite and potassium nitrite solutions in the ratio of 1 : 3. The aqueous solution of the compound showed 4 particles per molecule whereas molar – conductivity reveals the presence of six – electrical charges. The formula of the compound is? (a) Co ( NO2 )3 .2KNO2

(b) Co ( NO2 )3 .3KNO2

(c) K 3 Co ( NO 2 )6 

(d) K Co ( NO 2 )4 

What is true about the gas that diffuses through the porous plug at

1 th of the rate of diffusion of 6

dihydrogen gas? (a) The molar – mass of the gas is 72 kg mol–1 (b) It is one of the structural isomer of C5 H12 (c) The V.D. of the gas is 72 (d) The gas is lighter than dihydrogen 23.

The most unlikely representation of resonance structures of p-nitrophenoxide ion is?

(a)

(b)

(c)

(d)

3

AIEEE Full Test - 1

24.

A molecule of white phosphorus does not have (a) Six P – P single bonds (b) Four P – P single bonds (c) Four lone – pair of electrons (d) PPP bond angle of 60° What electronic transition in Li ++ produces the radiation of the same wavelength as the first line in the lyman series of hydrogen? (a) n = 4 to n = 2 (b) n = 9 to n = 6 (c) n = 9 to n = 3 (d) n = 6 to n = 3

25.

The permissible values of '  ' for electron belonging to fourth energy level are

26.

1 2

(a) 0, , 2

(b) ±1, ±2, ±3

(c) 0, 1, 2, 3

(d) 1, 2, 3, 4

27.

5.6 litres of an unknown gas at NTP requires 12.5 calories to raise its temperature by 10°C at constant volume. Then atomicity of the gas is ? (a) Monoatomic (b) Diatomic (c) Triatomic (d) None of these

28.

Which of the following has highest value of van’t Hoff factor? (b) KBr (50% ionised) (a) K 2SO 4 (40% Ionised) (c) K 4  Fe ( CN )6  (20% ionised)

29.

(d) FeCl3 (30% ionized)

In the sequence of reactions,

, The product B is ? (a) Benzyl alcohol (c) 1-phenyl ethanol 30.

(b) 2-phanyl ethanol (d) Quinol

The maximum kinetic energy of photoelectron ejected from a metal is ‘x’ when it is irradiated with radiation having frequency twice the threshold frequency. If the frequency of the incident radiation is doubled. The maximum K.E. of the photoelectrons would become (a) x (b) 2 x (c) 3 x (d) 4 x

PART B: PHYSICS 31.

A solid sphere of mass 2kg is resting inside a cube as shown in figure. The cube is moving with a  ˆ m/s. The sphere is at rest with respect to cube. Total force exerted by velocity v = (tiˆ + 2tj) sphere on the cube [g = 10 m/s2] (a)

488

(c) 26 N

4

(b)

260 N

(d)

580 N

AIEEE Full Test -1

32.

33.

34.

Three rods made of same material and having the same cross-section have been joined as shown in figure. Each rod is of the same length. The left and right ends are kept at 0°C, 90°C & 60°C. The temperature of the junction of the rods will be

(a) 45°C (b) 50°C (c) 55°C (d) 60° A body is moving with a speed 1 m/s and a force F is needed to stop it in a distance x. If the speed of the body is 3 m/s the force needed to stop it in the same distance x will be (a) 1.5 F (b) 3 F (c) 6 F (d) 9 F Two perfect gases at absolute temperatures T1 & T2 are mixed. There is no loss of energy. The temperature of the mixture if the masses of the molecules are m1 & m 2 and the

number of

molecules in the gases are n1 & n 2 (both gases are of same nature)

T1 + T2 2 n T + n 2T1 (c) 1 2 n1 + n 2 (a) T =

35.

(b) T = T1T2 (d) none of these

An ideal gas is taken through the cycle A → B → C → A as shown in figure. If the heat supplied to the gas in the cycle is 5J. The work done by the gas in the process C → A is

(a) – 25 J (c) – 15 J

(b) – 10 J (d) – 20 J

36.

Light from source consists of two wavelength λ1 = 6500Å & λ 2 = 3900Å . If D = 2m and d = 6.5 mm. The minimum value of y where the minima of both the wave lengths coincide. (a) 0.1 mm (b) 0.2 mm (c) 0.3 mm (d) 0.4 mm

37.

Figure shows on irregular block of material of refractive index 2 . A ray of light strikes the face AB at an angle of 45° with normal. Where will the final image formed (AB = 3m)

38. 39.

(a) inside the slab (b) at 6 m from CD (c) data insufficient (d) at infinity An isolated hydrogen atom emits a photon of 10.2 eV recoil speed of hydrogen atom (a) 3.25 m/s (b) 3 m/s (c) 6.2 m/s (d) 1 m/s Thermal energy of a thermal neutron is order of (a) 105 J (b) 10–5 J (c) 10–10 J

(d) 10–21 J 5

AIEEE Full Test - 1

40.

The ratio of time constant in charging and discharging in the circuit shown in figure is

41.

(a) 1 : 1 (b) 3 : 16 (c) 4 : 3 (d) 3 : 4 In an A.C. current given by I = I0 + I1 cos ωt then its r.m.s. value will be (a)

42.

I0 + I1 2

(b)

I0 2

(c)

I0 − I1 2

(d)

I02 +

I12 2

Reading of ammeter is 2A. The value R’ is

(a) 2Ω

(b) 3Ω

(c) 4Ω

(d) 6Ω

Positive charge in a one mole of Li + ion

43.

(a) +1.6 × 10−19 C

(b) 29 × 104 C

(d) None (c) 4.8 × 10−19 C A motor drives a body along circle with constant speed. The power ‘P’ developed by the motor must vary with time ‘t’ as

44.

45.

(a)

(b)

(c)

(d)

A particle of mass m is moving in a circular path of constant radius ‘r’ such that its centripetal acceleration a C is proportional to t n (where ‘t’ is time). Then the power ‘p’ is proportional to (a) t

n −1

(b) t°

(c)

n +2 t n

(d)

 3n   −1 t 2 

A uniform rod AB of mass m & length ' 2 ' is at rest on a smooth horizontal surface. An impulse P is applied to the end B. The time taken by the rod to turn through 180° is

46.

(a) 47.

mπ 6P

(b)

mπ 3P

(c)

2mπ 3P

(d)

mπ 12P

For what condition wave speed in sine wave is greater than the particle speed (a) A <

6

λ 2π

(b) A >

λ 2π

(c) A >

λ π

(d) A <

λ π

AIEEE Full Test -1

48.

49.

A circular coil of 100 turns and effective diameter 20 cm carries a current of 1A. It is to turned in a magnetic field B = 3T from a position in which θ equal zero. So one in which θ equal 180°. The work required in this process is (a) 0 J (b) 2π J (c) 4π J (d) 6π J A ring having mass ‘m’ radius ‘r’ is rolling on a rough horizontal plane. AN uniform horizontal magnetic field is exists in space as B = B0 ( − uˆ ) . Along which two points induced e.m.f. is maximum (here V is linear speed & w is angular speed)

50.

(a) AB (b) BC (c) BD (d) AC p q r If the energy, E = G h c , where G is the universal gravitational constant, h is the Planck’s constant and c is the velocity of light, then the values of p, q and r are, respectively

–1 , 2 –1 (c) , 2

(a)

51.

1 5 and 2 2 1 3 and 2 2

1 , 2 1 (d) , 2 (b)

–1 –5 and 2 2 –1 –3 and 2 2 A

A particle of mass m and charge q is fastened to one end of a string of length l. The other end of the string is fixed to the point O. The whole system lies on a frictionless horizontal plane. Initially, the mass is at rest at A. A uniform electric field in the direction shown is then switched on. Then (a) the speed of the particle when it reaches B is

(b) the speed of the particle when it reaches B is

2qEl m

E l 60º O

B

qEl m

(c) the tension in the string when particles reaches at B is qE. (d) the tension in the string when the particle reaches at B is zero. 52.

53.

Two identical conducting rods AB and CD are connected to a A B C D circular conducting ring at two diametrically opposite points B and 100 ºC 0 ºC C. The radius of the ring is equal to the length of rods AB and CD. The area of cross-section, and thermal conductivity of the rod and ring are equal. Points A and D are maintained at temperatures of 100 ºC and 0 ºC. Temperature of point C will be (a) 62 ºC (b) 37 ºC (c) 28 ºC (d) 45 ºC A double slit of separation 0.1 cm is illuminated by while light. A coloured interference pattern is formed on a screen 100 cm away. If a pin hole is located in this screen at a distance of 2 mm from the central fringe, the wavelengths in the visible spectrum which will be absent in the light transmitted through the pin-hole are (a) 5714 Å and 4444 Å (b) 6000 Å and 5000 Å (c) 5500 Å and 4500 Å (d) 5200 Å and 4200 Å 7

AIEEE Full Test - 1

54.

The value of focal length of a spherical mirror from the following observations. Object distance u = ( 50 ± 0.5 ) cm and image v = ( 20 ± 0.1) cm (a) 14.3 ± 0.343 (c) 14 ± 0.3

(b) 14.3 ± 0.024 (d) 14.3 ± 0.1

π   2π  t + φ  & y 2 = b sin  t + φ  . The phase difference 2   3 

Two SHMs are given by y1 = a sin 

55.

between there after 2 sec. (a) 56.

π 2

(b)

π 6

(c)

π 3

The maximum tension in the string of an oscillating What is its angular amplitude (a) 30°

57.

(b) 15°

(d) π pendulum is thrice the minimum tension.

2 3

2 5

(c) sin −1  

(d) cos −1  

The potential energy of a particle executing SHM varies sinusoidally. If the frequency oscillation of particle is n, that of potential energy is (a)

58.

n 2

(b)

n 2

(c) n

of

(d) 2 n

The following data was recorded for values of object distance and the corresponding value of image distance in the experiment on study of real image formation by a convex lens of power + 5D. One of these observation is incorrect, Identify this

S.No. 1 2 3 4 5 6 Object distance 25 30 35 45 50 55 Image distance 97 61 37 35 32 30 (a) observation 1 (c) observation 4

(b) observation 3 (d) observation 5

Suppose the potential energy between electron and proton at a distance r is given by –

59.

Ke2 . 3r 3

Application of Bohr’s theory to hydrogen atom in this case shows that (a) energy in the nth orbit is proportional to n6 (b) energy is proportional to m–6 (m : mass of electron) (c) Energy in the nth orbit is proportional to n–2 (d) energy is proportional to m3 (m = mass of electron) A particle moving in the positive x–direction has initial velocity v0. The particle undergoes retardation kv2, where v is its instantaneous velocity. The velocity of the particle as a function of time is given by

60.

(a) v = v0/(1 + kv0t)

(b) v =

v0 kt

(d) v =

(c) v =

8

2v0 1 + kt v0

(1 + k v t ) 2 2 0

AIEEE Full Test -1

PART C: MATHEMATICS 61.

Let f(x) = [x], the greatest integer less than or equal to x and g(x) = {x}, the fractional part of x. The solution of the equation 4g ( x ) = i ( x ) + f ( x ) ; x > 0, i being identity function is (a) 81/7 (c) 91/7

62.

(b) 5/3 (d) none of these

Let z1 and z 2 be two non – zero complex numbers such that

z1 z 2 + = 1 , then the origin and z 2 z1

points represented by z1 and z 2 (a) lie on a straight line (c) form an equilateral triangle

63.

64.

(b) form a right triangle (d) none of these

2 0 1   If A = 2 1 3 , then A 2 − 5A + 6I is equal to   1 −1 0  1 −1 −3    (a) −1 −1 −10    −5 4 4 

1 −5  1  (b) −1 −1 4    −3 −10 4 

(c) 0

(d) I

If

∫

tan 7 xdx = f ( x ) then

(a) f ( x ) is a polynomial of degree 8 in tan x (b) f ( x ) is a polynomial of degree 5 in tan x (c) f ( x ) =

1 1 1 tan 6 x − tan 4 x + tan 2 x + log cos x + C 6 4 2

(d) f ( x ) is a polynomial of degree 6 in tan x 65.

The curve satisfying the differential equation (1 − x 2 )y '+ xy = ax are (a) ellipses and hyperbolas (c) ellipses and straight lines

66.

The number of real solution of tan −1 x ( x + 1) + sin −1 x 2 + x + 1 = π / 2 is (a) 0 (c) 2

67.

(b) ellipses and parabola (d) circles and ellipses

(b) 1 (d) infinite

If z − 25i ≤ 15 , then |maximum arg (z) – minimum arg (z)| equals (a) 2 cos −1 ( 3 / 5 )

(b) 2 cos −1 ( 4 / 5 )

(c) π / 2 + cos −1 ( 3 / 5 )

(d) sin −1 ( 3 / 5 ) − cos −1 ( 3 / 5 )

9

AIEEE Full Test - 1

b+c a−b a

a

b c

If ∆1 = c + a

b − c b and ∆ 2 = b c a , then ∆1 − ∆ 2 equal to a+b c−a c c a b

68.

(a) 0

(b) 3abc

(c) 6abc

(d) 2(a 3 + b3 + c3 ) m

69.

The sum

10  20 

∑  i  m − i  (where i =0 





p   = 0 if p < q) is maximum where m is q

(a) 5 (b) 10 (c) 15 (d) 20 Let A be the set of all determinants of order 3 with entries 0 or 1 only, B be the subset of A consisting of all determinants with value 1, and C be the subset consisting of all determinants with value ‘– 1’. Then if n (B) and n(C) denote the number of elements in B and C, respectively, we have

70.

(a) C = φ

(b) n ( B ) = n ( C )

(c) A = B ∪ C

(d) n ( B ) = 2n ( C )

The value of lim

71.

(

1 − cos ax 2 + bx + c

( x − α)

x →α

(a) ( a − b )

2

2

 a ( α − β)   2  

) where α and β are the roots of ax (b)

2

+ bx + c = 0 is

( α − β )2 2

2

(c) 

(d) none of these

If f ( x ) = x 2 + 2bx + 2c2 and g ( x ) = − x 2 − 2cx + b 2 are such that min f ( x ) > max g ( x ) ,

72.

then relation between b and c, is (a) no relation (c) c <

b

(b) 0 < c < b/ 2 (d) c > 2 b

2

The greatest value of the term independent of x, as α varies over R, in the expansion of

73.

sin α    x cos α +  x   (a) 20C10

20

is (b) 20C15

(c) 20C19

(

The number of rational terms in the expansion of 1 + 2 + 3 5

74.

(a) 7

(b) 11

(d) none of these

)

6

(c) 12

(d) none of these

a + bx ( a + bx ) ( a + bx ) + + + .... + upto ∞ is 1! 2! 3! 2

Coefficient of x100 in the expression

75.

10

is

(a) ea b100 / 99!

(b) ea b100 / (100!)

(c) ea b98 / 100!

(d) none of these

3

AIEEE Full Test -1

76.

Let f be a function defined on R by f ( x ) = [ x ] + x − [ x ] then (a) f is not continuous at every x ∈ I (c) f is a continuous function

77.

78.

(b) f is not continuous at every x ∈ R ~ I (d) none of these

Let h(x) = min{x, x 2 } for x ∈ R . Then which of the following is not correct (a) h is continuous for all x (b) h is differentiable for all x (c) h '(x) = 1 for all x = 1 (d) h is not a differentiable function at least two points The image of the interval [-1, 3] under f ( x ) = 4x 3 − 12x is (a) [-2, 0] (c) [- 8, 0]

79.

∫

(b) [-8, 72] (d) [8, 72]

dx

= fog ( x ) + C then

2 − 3x − x 2

2x − 3 17 2x + 3 (c) f ( x ) = sin −1 x, g ( x ) = 17 (a) f ( x ) = sin −1 x, g ( x ) =

80.

81.

The value of

2

∫0

(d) none of these

dx , where [x] is the greatest integer less than or equal to x is

(

)

Let f ( x ) = Π cos ( 2k − 1) x + i sin ( 2k − 1) x then (a) n 2f ( x )

k =1

( Re f ( x ) ) ''+ i ( Im f ( x ) ) '' is equal to

(b) − n 4f ( x )

(c) − n 2f ( x ) 83.

2x + 3 17

(a) 2 (b) 8/3 (c) 4 (d) none of these If algebraic sum of distance of a variable line from points (2, 0), (0, 2) and (-2, -2) is zero, then the line passes through the fixed point (a) (-1, -1) (b) (0,0) (c) (1, 1) (d) (2, 2) n

82.

 x 2 +1 

x 

(b) f ( x ) = tan −1 x, g ( x ) =

(d) n 4f ( x )

The maximum and minimum value of f ( x ) = ab sin x + b 1 − a 2 cos x + c lie in the interval (assuming a < 1, b > 0 ) (a) [ b − c, b + c]

(b) ( b − c, b + c )

(c) [ c − b, b + c] 84.

The value of

16π +2 3 3 4 (c) π + 2 3 3 (a)

16

∫1

(d) none of these

tan −1

x − 1dx is 4 π−2 3 3 16 (d) π−2 3 3

(b)

11

AIEEE Full Test - 1

85.

Let 0 < α < π / 2 be a fixed angle. If P = (cos θ,sin θ) and Q = (cos(α − θ),sin(α − θ)) then Q is obtained from P by (a) clockwise rotation around the origin through an angle α (b) anticlockwise rotation around the origin through an angle α (c) reflection in the line through origin with slope tanα (d) reflection in the line through the origin with slope tan(α/2)

86.

If two lines represented by the equation ax 3 + bx 2 y + cxy 2 + dy3 = 0 are at right angles then

a 2 + d 2 + ac + bd is equal to (a) – 1 (c) 1

(b) 0 (d) ab + cd

An equation of the chord of the circle x 2 + y 2 = a 2 passing through the point (2,3) farthest from the centre is (a) 2x + 3y = 13 (b) 3x − y = 3

87.

(c) x − 2y + 4 = 0 88.

Equation

of

the

(d) x − y + 1 = 0 plane

through

three

ˆ 3iˆ − 2ˆj + 4k,5i ˆ ˆ + 7ˆj + 3kˆ is −6iˆ + 3jˆ + 2k,

( ) (c) rˆ. ( ˆi + ˆj − 7kˆ ) + 23 = 0

A,

B,

C

with

position

vectors

( ) (d) rˆ. ( ˆi − ˆj − 7kˆ ) = 23

(a) rˆ. ˆi − ˆj + 7kˆ + 23 = 0

89.

points

(b) rˆ. ˆi + ˆj + 7kˆ = 23

If the two regression coefficients are positive then (b) 1/ b YX + 1/ b XY < 2 / r (a) 1/ b YX + 1/ b XY > 2 / r (c) 1/ b YX + 1/ b XY < r / 2

90.

(d) none of these

The number of times a fair coin must be tossed so that the probability of getting at least one head is at least 0.95. (a) 5 (b) 6 (c) 7 (d) 12

***

12

AIEEE Full Test - 1

TEST ID

00030403

AIEEE FULL TEST - 1 ANSWERS KEY CHEMISTRY 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

(b) (b) (a) (c) (a) (b) (b) (c) (b) (c)

11. 12. 13. 14. 15. 16. 17. 18. 19. 20.

(a) (d) (a) (c) (a) (c) (b) (b) (c) (a)

21. 22. 23. 24. 25. 26. 27. 28. 29. 30.

(c) (b) (c) (b) (d) (c) (b) (d) (b) (c)

51. 52. 53. 54. 55. 56. 57. 58. 59. 60.

(b) (c) (a) (a) (c) (d) (d) (b) (a) (a)

81. 82. 83. 84. 85. 86. 87. 88. 89. 90.

(b) (b) (c) (d) (a) (b) (a) (a) (a) (a)

PHYSICS 31. 32. 33. 34. 35. 36. 37. 38. 39. 40.

(d) (b) (d) (c) (a) (c) (d) (a) (d) (c)

41. 42. 43. 44. 45. 46. 47. 48. 49. 50.

(d) (d) (b) (d) (a) (b) (a) (d) (d) (a)

MATHEMATICS 61. 62. 63. 64. 65. 66. 67. 68. 69. 70.

(b) (c) (a) (c) (a) (c) (b) (a) (c) (b)

71. 72. 73. 74. 75. 76. 77. 78. 79. 80.

(c) (d) (d) (a) (b) (c) (b) (b) (c) (d)

1