1

CET PHYSICS 2014

VERSION CODE: B 1

1. A person is driving a vehicle at uniform speed of 5 ms-1 on a level curved track of radius 5 m.

The coefficient of static friction between tyres and road is 0.1. Will the person slip while taking the turn with the same speed? Take g = 10 ms-2.

(1) A person will slip if v2 = 5m2s-2 (2) A person will slip if v2 > 5m2s-2 (3) A person will slip if v2 < 5m2s-2 (4) A person will not slip if v2 > 5m2s-2 Ans: (2)

vmax = rg vmax = 0.1 5 10 5 = or 5 m2maxv = 2/s2 Person or vehicle will slip if the velocity is more than 5 m/s 2. A stone is thrown vertically at a speed of 30 ms-1 taking an angle of 45o with the horizontal.

What is the maximum height reached by the stone? Take g = 10 ms-2. (1) 30 m (2) 22.5 m (3) 15 m (4) 10 m Ans: (2)

2 2

2 2

sin2

30 sin (45)2 10

22.5

vHg

H

H m

=

= =

3. A force 5 2 5j k= + JG F i acts on a particle whose position vector is 2r i j k= +G . What is the

torque about the origin? (1) 8 1 (2)0 12i j k+ + 8 10 12i j+ k (3) 8 10 8i j k (4) 10 10i j k

Ans: (1)

1 2 15 2 5

= =

GG G i j kr F (10 2) ( 5 5) (2 10) 8 10 12= + + = + + i j k i j k

4. What is a period of revolution of earth satellite? Ignore the height of satellite above the

surface of earth. Given: (1) The value of gravitational acceleration g = 10 ms-2. (2) Radius of earth RE = 6400 km. Take = 3.14. (1) 85 minutes (2) 156 minutes (3) 87.73 minutes (4) 90 minutes Ans: (3)

36400 102 2

10RTg

= = T = 5024 s = 83.73 min

2

5. A period of geostationary satellite is

(1) 24 h (2) 12 h (3)30 h (4) 48 h Ans: (1) 6. What is the source temperature of the Carnot engine required to get 70% efficiency? Given

sink temperature = 27oC. (1) 1000 oC (2) 90 oC (3) 270 oC (4) 727 oC Ans: (4)

2

1

1

10

1

1

273 27 3000.7 1 1

300 0.3

1000 727

= += =

== =

TT

T

TT K C

1T

7. A 10 kg metal block is attached to a spring of spring constant 1000 Nm-1. A block is displaced

from equilibrium position by 10 cm and released. The maximum acceleration of the block is (1) 10 ms-2 (2) 100 ms-2 (3) 200 ms-2 (4) 0.1 ms-2

Ans: (1)

2 2max

2max

1000 10 /10

10 0.1

10 /

k rad sm

a Aa m s

= = == = =

8. A metallic wire of 1 m length has a mass of 10 x 10-3 kg. If a tension of 100 N is applied to a

wire, what is the speed of transverse wave? (1) 100 ms-1 (2) 10 ms-1 (3) 200 ms-1 (4) 0.1 ms-1 Ans: (1)

Linear density 3

310 10 10 10 /1

massm klength

= = = g m

3

100 100 /10 10

Tv m sm

= = = 9. A train is approaching towards a platform with a speed of 10 ms-1 while blowing a whistle of

frequency 340 Hz. What is the frequency of whistle heard by s stationary observer on the platform? Given speed of sound = 340 ms-1.

(1) 330 Hz (2) 350 Hz (3) 340 Hz (4) 360 Hz Ans: (2)

|340 340 350.3

340 10s

V f HzV V = = =

f

3

10. A rotating wheel changes angular speed from 1800 rpm to 3000 rpm in 20 s. What is the angular acceleration assuming to be uniform? (1) 60 rad s-2 (2) 90 rad s-2 (3) 2 rad s-2 (4) 40 rad s-2 Ans: (3)

1 1

2 2

18002 2 60 /6030002 2 100 /60

20

= = = = = =

=

f rad s

f rad s

t s

22 1100 60 40 2 /

20 20 = = = = rad s

t

11. A flow of liquid is streamline if the Reynold number is (1) less than 1000 (2) greater than 1000 (3) between 2000 to 3000 (4) between 4000 to 5000 Ans: (1) 12. A pipe of 30 cm long and open at both the ends produces harmonics. Which harmonic mode

of pipe resonates a 1.1 kHz source? Given speed of sound in air = 330 ms-1. (1) Fifth harmonic (2) Fourth harmonic (3) Third harmonic (4) Second harmonic Ans: (4)

1

23301,100

2 0.302

n

n

f n fvf n

n

n

= =

= =

A

13. In anomalous expansion of water, at what temperature, the density of water is maximum? (1) 4oC (2) < 4oC (3) > 4oC (4) 10oC Ans: (1) 14. An aeroplane executes a horizontal loop at a speed of 720 kmph with its wings banked at

45o. What is the radius of the loop? Take g = 10 ms-2. (1) 4 km (2) 4.5 km (3) 7.2 km (4) 2 km Ans: (1) v = 720 km/hr = 200 m/s

tan = 2vrg

or2 2200 4tan 10 1vr k

g = = = m . 15. A body having a moment of inertia about its axis of rotation equal to 3 kg m2 is rotating with

angular velocity of 3 rad s-1. Kinetic energy of this rotating body is same as that of a body of mass 27 kg moving with a velocity v. The value of v is

(1) 1 ms-1 (2) 0.5 ms-1 (3) 2 ms-1 (4) 1.5 ms-1 Ans: (1)

2 2

2 2

1 12 21 127 3 32 2

1 /

mv I

v

v m s

=

= =

4

16. A cycle tyre bursts suddenly. What is the type of this process? (1) Isothermal (2) Adiabatic (3) Isochoric (4) Isobaric Ans: (2) 17. An object is placed at 20 cm in front of a concave mirror produces three times magnified real

image. What is the focal length of the concave mirror? (1) 15 cm (2) 6.6 cm (3) 10 cm (4) 7.5 cm Ans: (1)

3( 20)

f fmf u f

= = ( all real images are inverted) 3 60f f + = 15f cm=

f 15cm= Since mirror is concave 18. A focal length of a lens is 10 cm. What is power of a lens in dioptre? (1) 0.1 D (2) 10 D (3) 15 D (4) D Ans: (2)

1 1 10

0.1P D

f= = =

19. A microscope is having objective of focal length 1 cm and eyepiece of focal length 6 cm. If

tube length is 30 cm and image is formed at the least distance of distinct vision, what is the magnification produced by the microscope? Take D = 25 cm.

(1) 6 (2) 150 (3) 25 (4) 125 Ans: (2)

0

1

30 251 155 1501 6

e

L DMf f = + = + =

20. A fringe width of a certain interference pattern is = 0.002 cm. What is the distance of 5th dark fringe from centre?

(1) 1 x 10-2 cm (2) 11 x 10-2 cm (3) 1.1 x 10-2 cm (4) 3.28 x 106 cm Ans: (None of the above answers are correct)

(2 1) (2 1)2 2nDx n nd

= + = + For 5th dark fringe, n = 4

35

3

9 9 2 102 2

9 10

x

cm

= = =

21. Diameter of the objective of a telescope is 200 cm. What is the resolving power of a

telescope? Take wavelength of light = 5000 0A .

(1) 6.56 x 106 (2) 3.28 x 105 (3) 1 x 106 (4) 3.28 x 106 Ans: (4)

RP = 6 662 4 10 3.28 10

1.22 1.22 0.5 10 1.22 = = = D

= 0.002 cm = 2 x 10-3 cm

5

22. A polarized light of intensity I0 is passed through another polarizer whose pass axis makes an

angle of 60o with the pass axis of the former. What is the intensity of emergent polarized light from second polarizer?

(1) I = I0 (2) I = I0/6 (3) I = I0/5 (4) I0/4 Ans: (4)

2 2 00 0cos cos 60 4II I I= = =

23. What is the de Broglie wavelength of the electron accelerated through a potential difference

of 100 volt?

(1) 12.27 0A (2) 1.227

0A (3) 0.1227

0A (4) 0.001227

0A

Ans: (2)

012.27 12.27 1.227

100A

V = = =

24. The maximum kinetic energy of the photoelectrons depends only on (1) potential (2) frequency (3) incident angle (4) pressure Ans: (2) 25. Which of the following spectral series of hydrogen atom is lying in visible range of

electromagnetic wave? (1) Paschen series (2) Pfund series (3) Lyman series (4) Balmer series Ans: (4) 26. What is the energy of the electron revolving in third orbit expressed in eV? (1) 1.51 eV (2) 3.4 eV (3) 4.53 eV (4) 4 eV Ans: (1)

2 213.6 13.6 1.51

(3)nE eV

n= = =

27. The relation between half life (T) and decay constant () is (1) T = 1 (2) T = 1

2 (3) T = loge 2 (4) = log 2T

Ans: (3)

0.693 0.693 log 2eT T T = = =

28. A force between two protons is same as the force between proton and neutron. The nature of

the force is (1) Weak nuclear force (2) Strong nuclear force (3) Electrical force (4) Gravitational force Ans: (2) 29. In n type semiconductor, electrons are majority charge carriers but it does not show any

negative charge. The reason is (1) electrons are stationary (2) electrons neutralize with holes (3) mobility of electrons is extremely small (4) atom is electrically neutral

6

Ans: (4) 30. For the given digital circuit, write the truth table and identify the logic gate it represents: (1) OR-Gate

A (2) NOR-Gate (3) NAND-Gate

Y (4) AND-Gate B

AAns: (4) A

B

A B A.B+ =

Y

B 31. If -current gain of a transistor is 0.98. What is the value of -current gain of the transistor? (1) 0.49 (2) 49 (3) 4.9 (4) 5 Ans: (2)

0.98 49

1 0.02 = = =

32. A tuned amplifier circuit is used to generate a carrier frequency of 2 MHz for the amplitude

modulation. The value of LC is

(1) 61

2 10 (2) 61

2 10 (3) 61

3 10 (4) 61

4 10 Ans: (4)

6 6

1 1 1 12 2 2 10 4 102

f LCfLC = = = =

33. If a charge on the body is 1 nC, then how many electrons are present on the body? (1) 1.6 1019 (2) 6.25 109 (3) 6.25 1027 (4) 6.25 1028Ans: (2)

9

99

1 10 6.25 101.6 10

+= = = =

qq ne ne

34. Two equal and opposite charges of masses m1 and m2 are accelerated in an uniform electric

field through the same distance. What is the ratio of their accelerations if their ratio of

masses is mm1

2 = 0.5?

(1) aa1

20.5= (2) a

a1

21= (3) a

a1

22= (4) a

a1

23=

Ans: (3) Force is same in magnitude for both

1 1 2

2 2 1

/ 2/

a F m ma F m m

= = =

7

35. What is the nature of Gaussian surface involved in Gauss law of electrostatic? (1) Scalar (2) Electrical (3) Magnetic (4) Vector Ans: (4) Area vector 36. What is the electric potential at a distance of 9 cm from 3 nC? (1) 270 V (2) 3 V (3) 300 V (4) 30 V Ans: (3)

99 10 qvr

=

9 9

2

9 10 3 10 3009 10

v V

= =

37. A voltmeter reads 4V when connected to a parallel plate capacitor with air as a dielectric. When a dielectric slab is introduced between plates for the same configuration, voltmeter reads 2V. What is the dielectric constant of the material?

(1) 0.5 (2) 2 (3) 8 (4) 10 Ans: (2)

r = am

V 42

V 2= =

38. A spherical conductor of radius 2 cm is uniformly charged with 3 nC. What is the electric field

at a distance of 3 cm from the centre of the sphere? (1) 3 206 V m-1 (2) 3 V m-1 (3) 3 104 V m-1 (4) 3 10-4 V m-1 Ans: (3)

9 29 10qEr

=

9 9

42 2

9 10 3 10 3 10(3 10 )

E

= = V/m

39. A carbon film resistor has colour code Green Black Violet Gold. The value of the resistor is (1) 50 M (2) 500 M (3) 500 5% M (4) 500 10% M Ans: (3) 50 x 107 5% = 500 x 106 5% = 500 5% M 40. Two resistors of resistances 2 and 6 are connected in parallel. This combination is then

connected to a battery of emf 2V and internal resistance 0.5 . What is the current flowing through the battery?

(1) 4 A (2) 43

A (3) 417

A (4) 1 A

Ans: (4)

1 2

1 2

R RR R+

2 6 1.5(2 6)

2 11.5 0.5

p

p

R

EI AR r

= = += = =+ +

8

41. The equivalent resistance of two resistors connected in series is 6 and their parallel

equivalent resistance is 43. What are the values of resistances?

(1) 4, 6 (2) 8, 1 (3) 4, 2 (4) 6, 2 Ans: (3) R1 + R2 = 6

1 2 1 2 1 21 2

4 8 2, 43

R R R R R RR R

= = = = + 42. In a potentiometer experiment of a cell of emf 1.25 V gives balancing length of 30 cm. If the

cell is replaced by another cell, balancing length of 30 cm. If the cell is replaced by another cell, balancing length is found to be 40 cm. What is the emf of second cell?

(1) 1.57 V (2) 1.67 V (3) 1.47 V (4) 1.37V Ans: (2) E1 L1 E1 L2 1 1 2

2 2 2

1.25 30 5 1.6740 3

E L EE L E

= = = = V 43. A charged particle experiences magnetic force in the presence of magnetic field. Which of the

following statement is correct? (1) The particle is moving and magnetic field is perpendicular to the velocity (2) The particle is moving and magnetic field is parallel to velocity (3) The particle is stationary and magnetic field is perpendicular (4) The particle is stationary and magnetic field is parallel Ans: (1) No force acts in other cases. 44. If a velocity has both perpendicular and parallel components while moving through a

magnetic field, what is the path followed by a charged particle? (1) Circular (2) Elliptical (3) Linear (4) Helical Ans: (4) Parallel component drags the particle to side and perpendicular component gives circular

path. Hence the path is helical. 45. A solenoid has length 0.4 cm, radius 1 cm and 400 turns of wire. If a current of 5 A is passed

through this solenoid, what is the magnetic field inside the solenoid? (1) 6.28 x 10-4T (2) 6.28 x 10-3 T (3) 6.28 x 10-7 T (4) 6.28 x 10-6 T Ans: (None of the above answers are correct)

0

72

( / )4004 3.14 10 5

0.4 100.628

B nI n N L

T

= == =

(No correct answer available)

9

46. A gyromagnetic ratio of the electron revolving in a circular orbit of hydrogen atom is 8.8 x 1010 C kg-1. What is the mass of the electron? Given charge of the electron = 1.6 x 10-19C.

(1) 1 x 10-29 kg (2) 0.1 x 10-29 kg (3) 1.1 x 10-29 kg (4) 111

x 10-29 kg

Ans: (4)

1929

10

21.6 10 1 10

2( / ) 2 8.8 10 11

eL m

em kgL

== = =

47. What is the value of shunt reistance required to convert a galvanometer of resistance 100

into an ammeter of range 1A? Given: Full scale deflection of the galvanometer is 5 mA.

(1) 59.95

(2) 9.955

(3) 0.5 (4) 0.05 Ans: (1)

3 2

3 3

5 10 10 0.5 5 51 5 10 1 5 10 10 0.05 9.95

g

g

I GS

I I

= = = = = 48. A circular coil of radius 10 cm and 100 turns carries a current 1 A. What is the magnetic

moment of the coil? (1) 3.142 x 104 A m2 (2) 104 A m2 (3) 3.142 A m2 (4) 3 A m2

Ans: (3) M = NIA = NIr2 = 102 x 1 x 3.142 x 10-2 = 3.142 Am2 49. A susceptibility of a certain magnetic material is 400. What is the class of the magnetic

material? (1) Diamagnetic (2) Paramagnetic (3) Ferromagnetic (4) Ferroelectric Ans: (3) 50. A solenoid of inductance 2H carries a current 1 A. What is the magnetic energy stored in a

solenoid? (1) 2 J (2) 1 J (3) 4 J (4) 5 J Ans: (2)

U = 21 1 2 1 12 2LI J= =

51. A multimeter reads a voltage of a certain A.C. source as 100 V. What is the peak value of

voltage of A.C. source? (1) 200 V (2) 100 V (3) 141.4 V (4) 400 V Ans: (3)

0 2 1.414 100 141.4rmsV V= = = V 52. A series LCR circuit contains inductance 5 mH, capacitance 2 F and resistance 10 . If a

frequency A.C. source is varied, what is the frequency at which maximum power is dissipated?

(1) 510

Hz (2) 510

Hz (3) 2 x 10

5 Hz (4) 5 x 10

3 Hz

10

Ans: (4)

4 3

0 3 6

1 1 10 522 2 5 10 2 10

10f HzLC

= = = =

53. A step down transformer has 50 turns on secondary and 1000 turns on primary winding. If a

transformer is connected to 220 V 1 A A.C. source, what is output current of the transformer?

(1) 120

A (2) 20 A (3) 100 A (4) 2 A

Ans: (2)

501000 220

11

11 220 120

s s

p p

s

s

s s p p

s

s

N VN V

V

V VV I V I

II A

=

===

= =

54. The average power dissipated in A.C. circuit is 2 watt. If a current flowing through a circuit is

2 A impedance is 1 , what is the power factor of the AC circuit? (1) 0.5 (2) 1 (3) 0 (4)

12

Ans: (1)

2

2

cos Zcos2cos 0.5

4 1

= == = =

P VI IPI Z

55. A plane electromagnetic wave of frequency 20 MHz travels through a space along x direction.

If the electric field vector at a certain point in space is 6 V m-1, what is the magnetic field vector at that point?

(1) 2 x 10-3 T (2) 12

x 10-8 T (3) 2 T (4) 12

T

Ans: (1) E/B = C

B = E/C = 886 2 10

3 10T=

56. Two capacitors of 10 PF and 20 PF are connected to 200 V and 100 V sources respectively. If they are connected by the wire, what is the common potential of the capacitors? (1) 133.3 volt (2) 150 volt (3) 300 volt (4) 400 volt Ans: (1)

1 1 2 2

1 2

10 200 20 100 133.310 20

CV C VV VC C+ + = = =+ +

11

57. A physical quantity Q is found to depend on observables x, y and z, obeying relation

Q = x yz

3 2. The percentage error in the measurements of x, y and z are 1%, 2% and 4%

respectively. What is percentage error in the quantity Q? (1) 4% (2) 3% (3) 11% (4) 1% Ans: (3)

3 2 3 1 2 2 4 11%Q x y zQ x y z = + + = + + =

58. What of the following is not a vector quantity? (1) Weight (2) Nuclear spin (3) Momentum (4) Potential energy Ans: (4) 59. A car moves form A to B with a speed of 30 kmph and from B to A with a speed of 20 kmph.

What is the average speed of the car? (1) 25 kmph (2) 24 kmph (3) 50 kmph (4) 10 kmph Ans: (2)

1 2

1 2

2 2 30 20 2430 20av

v vv kmphv v

= = =+ + 60. A body starts from rest and moves with constant acceleration for t s. It travels a distance x1

in first half of time and x2 in next half of time, then (1) x2 = x1 (2) x2 = 2x1 (3) x2 = 3x1 (4) x2 = 4x1 Ans: (3)

a = 2 21x x

t

------ (1)

2112

x at= ( 0)u =1 2

In (1) 3x x=

1

CET CHEMISTRY 2014

VERSION CODE: C 2

1. Match the reactant in Column I with the reaction in Column II.

I II

(i) Acetic acid (a) Stephen

(ii) Sodium phenate (b) Friedel Crafts

(iii) Methyl cyanide (c) HVZ

(iv) Toluene (d) Kolbes

(1) i c, ii a, iii d, iv b (2) i d, ii b, iii c, iv a (3) i b, ii c, iii a, iv d (4) i c, ii d, iii a, iv b Ans: (4) Acetic acid HVZ, sodium phenate Kolbes, Methyl cyanide Stephen, Toluene Fridel-

crafts. 2. The statement that is NOT correct is (1) Hypophosphorous acid reduces silver nitrate to silver (2) In solid state PCl5 exists as [PCl4]

+ [PCl6]-

(3) Pure phosphine is non-inflammable (4) Phosphorous acid on heating disproportionates to give metaphosphoric acid and

phosphine Ans: (3) Pure phosphine is non inflameable. It catches fire when heated to 423 K. 3. In which one of the pairs of ion given, there is an ion that forms a co-ordination compound

with both aqueous sodium hydroxide and ammonia and an other ion that forms a co-ordination compound only with aqueous sodium hydroxide?

(1) Pb+2, Cu+2 (2) Zn+2, Al+3 (3) Cu+2, Zn+2 (4) Al+3, Cu+2

Ans: (2) Zn+2 forms coordination compound with NaOH to give Na2[Zn(OH)4] and with ammonia it

gives [Zn(NH3)4]2+ while Aluminium only forms complex with NaOH to give Na[Al(OH)4]

4. A crystalline solid X reacts with dil HCl to liberate a gas Y. Y decolourises acidified KMnO4.

When a gas Z is slowly passed into an aqueous solution of Y, colloidal sulphur is obtained X and Z could be, respectively

(1) Na2S, SO3 (2) Na2SO4, H2S (3) Na2SO3, H2S (4) Na2SO4, SO2 Ans: (3) Na2SO3 + 2HCl 2NaCl + H2O + SO2 H2O + SO2 H2SO3 H2SO3 + 2H2S 3S + 3H2O

2

CH2 - NH2

5. An aromatic compound A (C7H9N) on reacting with NaNO2/HCl at 0

o C forms benzyl alcohol and nitrogen gas. The number of isomers possible for the compound A is

(1) 5 (2) 7 (3) 3 (4) 6 Ans: (1)

The Aromatic compound is C6H5CH2NH2 oNaNO HCl

C2 /

0 C6H5CH2OH + N2

The isomers of benzyl zmine are

,

CH3

NH2

CH3

NH2

CH3

H2N

andNH - CH3

6. The statement that is NOT correct is (1) A furnace lined with Haematitie is used to convert cast iron to wrought iron (2) Collectors enhance the wettability of mineral particles during froth flotation (3) In vapour phase refining, metal should form a volatile compound (4) Copper from its low grade ores is extracted by hydrometallurgy Ans: (2) Collectors enhance the non wettability of mineral acids during froth floatation. 7. A solution of 1.25 g of P in 50 g of water lowers freezing point by 0.3o C. Molar mass of P is

94. Kf (water) = 1.86 K kg mol-1. The degree of association of P in water is

(1) 80% (2) 60% (3) 65% (4) 75% Ans: (1) 1.25 g of P in 50 g of H2O 25g in 1000 g of H2O Molality = 25/94 t = i Kp m 0.3 = i 1.86 25

94

i = 94 0.31.86 25

= 0.6064

= i

n

1 0.6064 1 0.39361 1 0.51 1

2

= = = 0.787 = 78.7%

8. Volume occupied by single CsCl ion pair in a crystal is 7.014 10-23 cm3. The smallest Cs

Cs internuclear distance is equal to length of the side of the cube corresponding to volume of one CsCl ion pair. The smallest Cs to Cs internuclear distance is nearly

(1) 4.4 oA (2) 4.3

oA (3) 4

oA (4) 4.5

oA

Ans: (3) a3 = 7.014 10-23

a = 2414 103 70. = 4.124 10-8 cm = 4.124 oA

9. For Cr + 14HO22 7 + + 6e- 2Cr+3 + 7H2O; Eo = 1.33 V At [Cr2O 27 ] = 4.5 millimole, [Cr+3] =

15 millimole, E is 1.067 V. The pH of the solution is nearly equal to (1) 2 (2) 3 (3) 5 (4) 4

3

Ans: (1)

For Cr + 14HO22 7 + + 6e- 2Cr+3 + 7H2O

E = Eo - RT

nF2.303

log Cr H OCr O H

3 2 72

2 142 7

[ ] [ ][ ][ ]

+ +

1.067 = 1.33 - 0.0596

log H

3 2 7

3 14(15 10 ) (1)(4.5 10 )[ ]

+

-0.263 = -0.0596

log H

6

3 14225 10

(4.5 10 )( )

+

-0.263 = -0.0098 [log 50 log (H+)14]

0.2630.0098 = 1.6990 + 14 pH 26.83 1.6990 =

25.137714

= 1.7955

10. 1.78 g of an optically active L-amino acid (A) is treated with NaNO2/HCl at 0

o C. 448 cm3 of nitrogen was at STP is evolved. A sample of protein has 0.25% of this amino acid by mass. The molar mass of the protein is

(1) 36,500 g mol-1 (2) 34,500 g mol-1 (3) 35,400 g mol-1 (4) 35,600 g mol-1 Ans: (4) 1.78 g - 448 cm3

? - 22400 cm3

Mol mass of L-amino acid = 1.78 22400

448

= 89

Mol mass of protein is 100 - 0.25 ? - 89

= 100 890.25

= 35,600 g/mol

11. 10 g of a mixture of BaO and CaO requires 100 cm3 of 2.5 M HCl to react completely. The

percentage of calcium oxide in the mixture is approximately (Given : molar mass of BaO = 153) (1) 52.6 (2) 55.1 (3) 44.9 (4) 47.4 Ans: (1) Let the mass of CaO = xg and BaO = 10 xg

x x10 100 2.576.5 28 1000 + =

[As the Eq mass of BaO = 1532

= 76.5 CaO = 562

= 28]

280 28X + 76.5X = 0.25 (76.5) (28) 48.5x = 535.5 280 48.5x = 255.5

x = 255.548.5

= 5.26

Percentage of CaO = 5.26 10010

= 52.6

4

12. The ratio of heats liberated at 298 K from the combustion of one kg of coke and by burning

water gas obtained from kg of coke is (Assume coke to be 100% carbon). (Given enthalpies of combustion of CO2, CO and H2 as 393.5 kJ, 285 kJ, 285 kJ respectively

all at 298 K). (1) 0.79 : 1 (2) 0.69 : 1 (3) 0.86 : 1 (4) 0.96 : 1 Ans: (2)

1 kg of coke = 100012

= 83.33 moles

C + O2 CO2 = 83.33 393.5 kJ C + H2O CO + H2 CO + H2 + O2 CO2 + H2O 83.33 285 + 83.33 285 = 83.33 (570) The ratio is 83.33 393.5 : 83.33 570 393.5 : 570 1 : 1.44 0.69 : 1 13. Impure copper containing Fe, Au, Ag as impurities is electrolytically refined. A current of 140

A for 482.5 s decreased the mass of the anode by 22.26 g and increased the mass of cathode by 22.011 g. Percentage of iron in impure copper is

(Given molar mass Fe = 55.5 g mol-1, molar mass Cu = 63.54 g mol-1) (1) 0.95 (2) 0.85 (3) 0.97 (4) 0.90 Ans: (4) The amount of impurity = 22.26 22.011 = 0.259 g Amount of Cu should have been deposited by a current of 140 a & 482.5 s current = 140 482.5 = 67,550 C ? Cku 96,500 C 31.77 g of Cu 67,500 C 22.239 g pure Cu But only 22.011 of cathode mass has increased 22.239 22.011 =0.228 g Instead of 0.228 g of Cu the amount of Fe oxidised 0.228 31.77 ? - 27.75

= 0.228 27.75

31.77

= 0.199 g

% of Fe = 0.199 10022.26

= 0.89 0.90 14. 25 cm3 of oxalic acid completely neutralised 0.064 g of sodium hydroxide. Molarity of the

oxalic acid solution is (1) 0.064 (2) 0.045 (3) 0.015 (4) 0.032 Ans: (4) Oxalic acid

N25 0.064

1000 40 =

N = 0.064 100040 25

= 0.064 Molarity =

0.0642

= 0.032

5

CH3 C

O

CH2 C

O

CH3 > CH3 CO

CH2 C

O

OC2H5 > O CO

CH2 C

O

OC2H5H5C2

15. The statement that is NOT correct is (1) Angular quantum number signifies the shape of the orbital (2) Energies of stationary states in hydrogen like atoms is inversely proportional to the

square of the principal quantum number (3) Total number of nodes for 3s orbital is three. (4) The radius of the first orbit of He+ is half that of the first orbit of hydrogen atom. Ans: (3) Total number of nodes for 3s orbital = n 1 = 2 16. For the equilibrium:

CaCO3 (s) U CaO (s) + CO2 (g) ; Kp = 1.64 atm at 1000 K 50 g of CaCO3 in a 10 litre closed vessel is heated to 1000 K. Percentage of CaCO3 that

remains unreacted at equilibrium is (Given R = 0.082 L atm K-1 mol-1) (1) 40 (2) 50 (3) 60 (4) 20 Ans: (3)

CaCO3 U CaO + CO2 Kp = pCO2 No. of moles = n 1.64 10 = 0.082 1000 n n =

1.64 100.082 1000

= 0.2

No of moles of CO2 = 0.2 50 g of CaCO3 = 0.5 mole of CaCO3 gives 0.2 mole of CO2 percentage of CaCO3 unreacted = 0.3 mole = 60% 17. Conversion of oxygen into ozone is non-spontaneous at (1) all temperature (2) high temperature (3) room temperature (4) low temperature Ans: (2) Ozone is not stable at high temperature. It decomposers to give 2O3 3O2. Hence, the reverse reaction is non spontaneous at high temperature. 18. Density of carbon monoxide is maximum at (1) 2 atm and 600 K (2) 0.5 atm and 273 K (3) 6 atm and 1092 K (4) 4 atm and 500 K Ans: (4)

d = PMRT

as M R are count PT

ratio decides density PT

ratio is highest for 4 atm 500 K 19. The acid strength of active methylene group in (a) CH3COCH2COOC2H5 (b) CH3COCH2COCH3 (c) C2H5OOCCH2COOC2H5 decreases as (1) a > c > b (2) a > b > c (3) b > a > c (4) c > a > b Ans: (2) The acid strength of active methylene group is Because ester group has O R group which decreases electron withdrawing nature of

carbonyl group.

6

20. A metallic oxide reacts with water to from its hydroxide, hydrogen peroxide and also liberates

oxygen. The metallic oxide could be (1) CaO (2) KO2 (3) Li2O (4) Na2O2 Ans: (2) 2KO2 + 2H2O 2KOH + H2O2 + O2

21. X Ozonolysiductive(Re )

Y + Z Y can be obtained by Etards reaction, Z undergoes disproportionation reaction with

concentrated alkali. X could be CH CH2C CH (1) (2)

CH C

CH3

CH3

CH CH CH3 (3) (4) Ans: (2) CHO As Y is obtained from Etards reaction, Y is , Z undergoes Cannizzaros reaction. Hence Z is HCHO X is

CH = CH2 CHO O3

H2O/Zn HCHO 22. Gold Sol is not (1) a macro molecular colloid (2) a lyophobic colloid (3) a multimolecualr colloid (4) negatively charged colloid Ans: (1) Gold sol is not a macromolecular colloid. Eg: Polymers, Starch, proteins enzymes etc. 23. Carbocation as an intermediate is likely to be formed in the reaction:

(1) Propene + Cl2 hv 2 chloropropane

(2) Acetone + HCN OH acetonecyanohydrin (3) Ethylbromide + Aq KOH ethyl alcohol (4) Hexane Anhy AlCl HCl3. /

Hexane

2-methyl pentane

Ans: (4)

An. AlCl3/HCl CH3 CH

CH3

CH 2 CH 2 CH3 (2-methyl pentane)

This involves hydride shift and methyl shift resulting in more stable carbocation. 24. For an ideal binary liquid mixture (1) S(mix) = 0; G(mix) = 0 (2) H(mix) = 0; S(mix) < 0 (3) V(mix) = 0; G(mix) > 0 (4) S(mix) > 0; G(mix) < 0

7

CH3 C N

Ans: (4) For an ideal binary mixture Hmix = 0, Vmix = 0 But G < 0 and S > 0 25. For hydrogen oxygen fuel cell at one atm and 298 K

CH3MgBr CH3 C N MgBr

CH3

H3O+

CH3 C O

CH3

dil. NaOH CH3 C CH

CH3C

O

CH3

CH2 CH O CH2 CH3

H ICH2 CH OH CH3 CHO CH3CH2I

og gH O H O G kJ2( ) 2( ) 2 ( )1 ; 2402

+ = A Eo for the cell is approximately, (Given F = 96,500 C) (1) 2.48 V (2) 1.24 V (3) 2.5 V (4) 1.26 V Ans: (2) Go = -nFEo -240 kJ = -2 96500 Eo

Eo = 240000193000

= 1.24 V

26. Which one of these is not known? (1) CuCl2 (2) CuI2 (3) CuF2 (4) CuBr2 Ans: (2) 2CuI2 Cu2I2 + I2 Cupric iodide changes to Cu2I2 and I2 27. The correct statement is (1) The earlier members of lanthanoid series resemble calcium in their chemical properties. (2) The extent of actinoid contraction is almost the same as lanthanoid contraction. (3) In general, lanthanoid and actinoids do not show variable oxidation states (4) Ce+4 in aqueous solution is not known Ans: (2)

The extent of Lanthanoid Contraction ( 1.4 pm) which is almost similar to actinoid contraction ( 17 pm)

R dil NaOH1. .2. 4-methylpent-3-en-2-one 28. P

CH MgBrH O3

3

1.2. +

P is (1) propanone (2) ethanamine (3) ethanenitrile (4) ethanal Ans: (3) 29. When CH2 = CH O CH2 CH3 reacts with one mole of HI, one of the products formed is (1) ethane (2) ethanol (3) iodoethene (4) ethanal Ans: (4)

8

C3 CH CH2 CH

OH

30. 0.44 g of a monohydric alcohol when added to methylmagnesium iodide in ether liberates at

S.T.P., 112 cm3 of methane. With PCC the same alcohol forms a carbonyl compound that answers silver mirror test. The monohydric alcohol is

H 3 (1) (2) (CH3)3C CH2OH

CH 23 CH CH2 CH

OH

CH3

H

O

+ CH3MgBr ether 'A'H3O

+B

CH3MgI ROH CH4 MgOR

I

0.44 g 112 cm3

? 22400 cm3

H

O

+ CH3MgBr ether CH3 C

H

CH3

C

CH3

O

H

MgBrH2O/H

+

CH3 C

H

CH3

C

CH3

OH

H

CH3 CH

CH3

CH

OH

CH31234

3-methylbutan-2-ol

(3) (4) (CH3)2CH CH2OH Ans: (3)

Molecular mass of alcohol = 0.44 22400112

= 88

If the alcohol with PCC gives a carbonyl compound, the alcohol must be 2o alcohol. Hence, answer is either (1) or (3). But as the molecular mass is 88, the answer is (3).

31. The IUPAC name of B is (1) 3-methylbutan-2-ol (2) 2-methylbutan-3-ol (3) 2-methylbutan-2-ol (4) Pentan-2-ol Ans: (1)

32. For Freundilich isotherm a graph of log xm

is plotted against log P. The slope of the line and

its y-axis intercept, respectively corresponds to

(1) 1 ,kn

(2) 1log ,kn

(3) 1 , log kn

(4) 1log , log k n

Ans: (3)

log P

log x/m

Intercept = log k

slope = n1

9

X

33. A plot of 1T

Vs k for a reaction gives the slope -1 x 104 K. The energy of activation for the

reaction is (Given R = 8.314 K-1 mol-1) (1) 8314 J mol-1 (2) 1.202 kJ mol-1 (3) 12.02 J mol-1 (4) 83.14 kJ mol-1

However question is wrong as the plot is T1

vs k instead of T1

vs ln k.

Ans: (4)

ln k Vs T1

-Slope = aER

1 104 = aE8.314

Ea = 8.314 104 = 83140 J = 83.14 kJ 34. The IUPAC name of the complex ion formed when gold dissolves in aquaregia is (1) tetrachloridoaurate (III) (2) tetrachloridoaurate (I) (3) tetrachloridoaurate (II) (4) dichloridoaurate (III) Ans: (1) H[AuCl4] Tetrachloridoaurate (III) 35. The correct sequence of reactions to be performed to convert benzene into m-bromoaniline is (1) nitration, reduction, bromination (2) bromination, nitration, reduction (3) nitration, bromination, reduction (4) reduction, nitration, bromination Ans: (3)

Y

OH

C6H5COCl/ base Nitration (major product)

COO NO2 COO OH NO2

COO O2N COO O2N NO2

HNO3 - H2SO4

Step 1NO2

Step - 2

Br2H2O NO2

Br

Sn/Conc. HCl

NH2

NO2

Step 1 Nitration Step 2 Bromination Step 3 Reduction 36. Y is (1) (2) (3) (4) Ans: (1)

OH

C6H5COCl/base

OOCC6H5

Nitration OOC O2N

10

37. ( ) ( ) ( ) ( )g g g gA P Q R

+ + , follows first order kinetics with a half life of 69.3 s at 500oC. Starting from the gas A enclosed in a container at 500oC and at a pressure of 0.4 atm, the total pressure of the system after 230 s will be

(1) 1.15 atm (2) 1.32 atm (3) 1.22 atm (4) 1.12 atm Ans: (4)

23069.3

= 3.33 half lives

90% completion A(g) P(g) + Q(g) + R(g) 1-0.9 0.9 0.9 0.9 = 0.1 Total pressure = 0.1 + 0.9 +0.9 + 0.9 = 2.8 1 - 0.4 2.8 - ? 2.8 0.4 = 1.12 atm 38. 2 ( )gMnO HCl A

+ 573

( ) 2( ) ( )

( ) ( ) ( ) ( )

KA g excess gl s g g

F BB U C D

+ + +

The gases A, B, C and D are respectively (1) Cl2, ClF, UF6, ClF3 (2) Cl2, ClF3, UF6, ClF (3) O2, OF2, U2O3, O2F2 (4) O2, O2F2, U2O3, OF2 Ans: (2)

Cl2 + MnCl2 + 2H2O MnO2 + 4HCl (A) Cl2 + F2 (excess) ClF3 (B) 3ClF3 + U(5) UF6 + 3ClF (C) (D) A = Cl2 B = ClF3 C = UF6 D = ClF 39. Acetophenone cannot be prepared easily starting from (1) C6H5CH(OH)CH3 (2) C6H5CH3 (3) C6H5C CH (4) C6H6 Ans: (2)

H5C6 CH CH3

OH(O) H5C6 C C 3

O

H

C6H5C CHHg+2, H2SO4 H5C6 C CH3

O

C6H5 CH3COClAnhy

AlCl3C6H5COCH3

11

40. One mole of ammonia was completely absorbed in one litre solution each of (a) 1 M HCl, (b) 1 M CH3COOH and (c) 1 M H2SO4 at 298 K. The decreasing order for the pH of the resulting solutions is (Given Kb(NH3) = 4.74) [pKb (NH3) 4.7 Question is wrong] (1) b > c > a (2) a > b > c (3) b > a > c (d) c > b > a Ans: (3) 41. 5.5 mg of nitrogen gas dissolves in 180 g of water at 273 K and one atm pressure due to

nitrogen gas. The mole fraction of nitrogen in 180 g of water at 5 atm nitrogen pressure is approximately

(1) 1 10-6 (2) 1 10-5 (3) 1 10-3 (4) 1 10-4 Ans: (4) 5.5 mg in 180 g 1 atm 5 atm pressure requires 5.5 mg 5 = 27.5 mg of N2

3

327.5 10

1028180 1018

=

= 1 10-4 Mole fraction of N2 =

42. 50 cm3 of 0.04 M K2Cr2O7 in acidic medium oxidizes a sample of H2S gas to sulphur. Volume of 0.03 M KMnO4 required to oxidize the same amount of H2S gas to sulphur, in acidic medium is

(1) 60 cm3 (2) 80 cm3 (3) 90 cm3 d) 120 cm3 Ans: (2) 0.04 M K2Cr2O7 = 0.24 N K2Cr2O7 0.03 M KMnO4 = 0.15 N KMn4 0.24 50 = 0.15 V2

NO2

Cl

NO2

Cl

NO2

Cl Cl

NO2

V2 = 0.24 50

0.15

= 80 ml

43. The compound that reacts the fastest with sodium methoxide is (1) (2) (3) (4)

Ans: (3) As electron withdrawing group strengthens C-Cl bond, the reaction rate decreases 44. The pair of compounds having identical shapes for their molecules is (1) CH4, SF4 (2) BCl2, ClF3 (3) XeF2, ZnCl2 (4) SO2, CO2 Ans: (3) In SN2 reaction, no rearrangement takes place as inversion of configuration takes place 45. Conductivity of a saturated solution of a sparingly soluble salt AB at 298 K is 1.85 10-5 S m-1.

Solubility product of the salt AB at 298 K is

Given = 140 10om(AB) -4 S m2 mol-1 (1) 5.7 10-12 (2) 1.32 10-12 (3) 7.5 10-12 (4) 1.74 10-12

12

Ans: (4)

So = o

S = m

k1000 =

5

41.85 10

1000 140 10

S = 1.3 10-6 Ksp = S

2 = (1.3 10-6)2 = 1.69 10-12 46. An incorrect statement with respect to SN1 and SN2 mechanisms for alkyl halide is (1) A strong nucleophile in an aprotic solvent increases the rate or favours SN2 reaction. (2) Competing reaction for an SN2 reaction is rearrangement. (3) SN1 reactions can be catalysed by some Lewis acids. (4) A weak nucleophile and a protic solvent increases the rate or favours SN1 reaction. Ans: (2) 47. Butylated hydroxyl toluene as a food additive acts as (1) antioxidant (2) flayouring agent (3) colouring agent (4) emulsifier Ans: (1) BHA and BHT are used as antioxidants 48. Terylene is NOT a (1) copolymer (2) polyester finbre (3) chain growth polymer (4) step growth polymer Ans: (3) Examples for chain growth polymer, Polyethylene, PVC polypropylene etc. 49. The correct statement is (1) Cyclohexadiene and cyclohexene cannot be isolated with ease during controlled

hydrogenation of benzene. (2) One mole each of benzene and hydrogen when reacted gives 1/3 mole of cyclohexane and

2/3 mole unreacted hydrogen. (3) Hydrogenation of benzene to cyclohexane is an endothermic process. (4) It is easier to hydrogenate benzene when compared to cyclohexene. Ans: (1) 50. Among the elements from atomic number 1 to 36, the number of elements which have an

unpaired electron in their s subshell is (1) (2) 7 (3) 6 (4) 9 Ans: (3) 1H 1s1 3Li 1s22s1 11Na 1s22s22p63s1 19K 1s22s22p63s23p64s1 24Cr 1s22s22p63s23p64s13d5 29Cu 1s22s22p63s23p64s13d10

13

51. The statement that is NOT correct is (1) Compressibility factor measures the deviation of real gas from ideal behaviour. (2) Van der Waals constant a measures extent of intermolecular attractive forces for real

gases. (3) Critical temperature is the lowest temperature at which liquefaction of a gas first occurs. (4) Boyle point depends on the nature of real gas. Ans: (3) 52. The correct arrangement for the ions in the increasing order of their radii is (1) Na+, Cl-1, Ca+2 (2) Ca+2, K+, S-2

(3) Na+, Al+3, Be+2 (4) Cl-, F-, S-2

Ans: (2) Ca+2, K+ and S-2 are isoelectronic species, size depends on number of protons.

S K Ca

Atomic No 16 19 20

No. of protons 16 19 20

No. of electrons 16 19 20

S-2 K+ Ca+2

No. of electrons 18 18 18

As the number of protons increases size decreases. 53. The correct arrangement of the species in the decreasing order of the bond length between

carbon and oxygen in them is

(1) CO, CO2, HC , (2) Ca2O

2O

23CO +2, K+, S-2

(3) , HC , CO23CO

2, CO (4) CO, 23CO , CO2, 2HCO

Ans: (3) The type of bond gives a relative measure of the bond length. Triple bond shortest bond Double bond Intermediate between single and double bond Single bond longest bond 54. The species that is not hydrolysed in water is (1) P4O10 (2) BaO2 (3) Mg3N2 (4) CaC2 Ans: (2) P4O10 + 6H2O 4H3PO4 Mg3N2 + 6H2O 3 Mg (OH)2 + 2NH3 CaC2 + 2H2O Ca (OH)2 + C2H2 55. For the properties mentioned, the correct trend for the different species is in (1) strength as Lewis acid BCl3 > AlCl3 > GaCl3 (2) inert pair effect Al > Ga > In (3) oxidising property Al+3 > In+3 > Tl+3

(4) first ionization enthalpy B > Al > Tl Ans: (4)

14

CH CH2

CH3

56. A correct statement is (1) [Co(NH3)6]

+2 is paramagnetic. (2) [MnBr4]-2 is tetrahedral

(3) [CoBr2(en)2]- exhibits linkage isomerism. (4) [Ni(NH3)6]

+2 is an inner orbital complex. Ans: (1) IN [Co(NH3)6]

+2 Co+2 - 4so3d7

CH3 COOH

C6H5COOH1. NH

2. P3 NaOB Qr

1. Conc. 2S

2. heat to 460 K

3 C

O

H O4 'R'

CH

COOH

NH3

COONH4

CONH2 NH2

NaOBr Conc. H2SO4

, 460 C

NH2

SO3H

Electronic configuration - 18Ar [Co(NH3)6]

+2 : [18Ar] 57. Iodoform reaction is answered by all, except

(1) (2) CH C3 HO

(2) CH3 CH2 OH (4) CH3 CH2 CH2OH Ans: (4)

CH3CH2CH2 OH O[ ]

CH3CH2CHO

Iodoform reaction is answered by carbonyl compounds having group. 58. A crystalline solid XY3 has ccp arrangement for its element Y. X occupies (1) 66% of tetrahedral voids (2) 33% of tetrahedral voids (3) 66% of octahedral voids (4) 33% of octahedral voids Ans: (4) In ccp arrangement, a unit cell has 4 particles of Y. To keep formula XY3, number of x

particles are 43

= 1.33. As ccp has 4 octahedral sites, the percentage of X partices occupying

octahedral sites = 1.33

1004

= 33% 59.

R is (1) o-bromo sulphanilic acid (2) sulphanilamide (3) sulphanilic acid (4) p-bromo sulphanilamide Ans: (3) 60. The statement that is NOT correct is (1) Aldose or ketose sugars in alkaline medium do not isomerise. (2) Carbohydrates are optically active. (3) Penta acetate of glucose does not react with hydroxylamine. (4) Lactose has glycosidic linkage between C4 of glucose and C1 of galactose unit. Ans: (1)

sp3 d2

1

CET MATHEMATICS 2014

VERSION CODE: C 2

1. Which one of the following is not correct for the features of exponential function given by f

(x) = bx where b > 1? (1) For very large negative values of x, the function is very close to 0. (2) The domain of the function is R, the set of real numbers. (3) The point (1, 0) is always on the graph of the function. (4) The range of the function is the set of all positive real numbers. Ans: (3) Consider y = bx .. (1) Clearly (1, 0) doesnt satisfy (1)

2. If y = (1 + x) (1 + x2) (1 + x4), then dydx

at x = 1 is

(1) 20 (2) 28 (3) 1 (4) 0 Ans: (2)

dydx

= (1 + x) (1 + x2) 4x3 + (1 + x2) (1 + x4) + (1 + x4) (1 + x) 2x

x

dydx 1=

= (1 + 1) (1 + 12) 4 + (1 + 1) (1 + 1) + (1 + 1) (1 + 1) 2

= 16 + 4 + 8 = 28 [Aliter : use logarithmic differentiation] 3. If y = (tan1x)2, then (x2 + 1)2 y2 + 2x (x2 + 1) y1 is equal to (1) 4 (2) 0 (3) 2 (4) 1 Ans: (3)

y| = x

x

1

22tan1

+ y| (1 + x2) = 2 tan-1 x

(1 + x2) y|| + y| (2x) = x22

1 + (1 + x2)2 y|| + 2x (1 + x2) y| = 2 4. If f (x) = x3 and g (x) = x3 4x in 2 x 2, then consider the statements: (a) f (x) and g (x) satisfy mean value theorem (b) f (x) and g (x) both satisfy Rolles theorem (c) Only g (x) satisfies Rolles theorem. Of these statements (1) (a) and (b) are correct (2) (a) alone is correct (3) None is correct (4) (a) and (c) are correct Ans: (4) f (x) and g (x) are both continuous is [-2, 2] and differentiable is (-2, 2) f (x) and g (x) satisfy Mean Value Theorem Now f (-2) = -8, f (2) = 8 f (-2) f (2) | g(1) = g(-2) f (x) doesnt satisfy Rolles theorem 5. Which of the following is not a correct statement?

(1) Mathematics is interesting (2) 3 is a prime (3) 2 is irrational (4) The sun is a star

2

Ans: (2)

3 is prime is the false statement. Note that the question is not, which of the following is not a statement? in which case (1) would have been clearly the answer.

Here we have to identify a statement which is not correct. i.e., a statement whose truth value is false. Hence (2) is the answer.

( )6. If the function f (x) satisfies

x

f xlim

x2121

= , then f (x) = xlim1

(1) 1 (2) 2 (3) 0 (4) 3 Ans: (2) Method of inspection

Clearly if or 0 or 3, then x

f x1

lim ( ) 1 = xf xx21( ) 2lim

1 doesnt exist, contradicting

x

f xx21( ) 2lim

1 =

7. The tangent to the curve y = x3 + 1 at (1, 2) makes an angle with y axis, then the value of

tan is (1) 1

3 (2) 3 (3) 3 (4) 1

3

Ans: (1) Clearly = 90 + = 90 + tan = tan (90 + ) = - cot Now tan = dy x

dx2(1,2)

3= = 3

Required = - cot = - 13

In the diagram above, is to be considered as the angle made by tangent with y axis and not .[e.g When we say angle made by a line with x axis, it is the angle measured from x-axis to the line in anticlockwise direction, unless mentioned otherwise].

Here we consider as the angle made by the line with +ve x-axis and not |]

8. If the function f (x) defined by f (x) = x x x......... x+ + + + +100 99 2

1100 99 2

, then f (0) =

(1) 100 f (0) (2) 100 (3) 1 (4) 1 Ans: (3) f| (x) = 1 + x + x2 + . + x99

f| (0) = 1

O

y

x

|

)

x

y

3

9. If f (x) = f ( + e x) and ( )ef x dx

e

= + 2 , then dx is equal to ( )e x f x

(1) - e (2) e +2

(3) 1 (4) e

2

Ans: (3)

I = e exf x dx e x f e x dx( ) ( ) ( )

= + +

e ee x f x dx e f x I( ) ( ) ( ) ( )

= + = +

I e Ie22 ( ) 1 = + =+

10. If linear function f (x) and g (x) satisfy dx = f (x) cos x + g (x) sin x + C, then ( ) ( )x cosx x sinx + 3 1 1 2

+ = + + x x x dx f x x g x x C[(3 1)cos (1 2 )sin] ( )cos ( )sin + + x x x dx n x x dx3 1)sin sin .3 (1 2 )( cos ) cos ( 2)

(1) f (x) = 3 (x 1) (2) f (x) = 3x 5 (3) g (x) = 3 (x 1) (4) g (x) = 3 + x Ans: (3)

= ( = (3x 1) sin x + 3 cos x cos x + 2x cos x 2 sin x + C = (3x 1 2) sin x + (2 + 2x) cos x + C = 3 (x 1) sin x + 2 (x + 1) cos x + C f (x) = 2 (x + 1), g (x) = 3 (x 1) 11. The value of the integral ( )/

/log sec tan d

4

4 is

(1) 0 (2) 4

(3) (4) 2

d/4

/4g (sec tan ) 0

=

Ans: (1)

The value of lo log (sec - tan ) is an odd function if f () = log (sec - tan ) then, f (-) = log [sec + tan ] = -log (sec - tan ) = -f()

12. sin x

sin x cos x+ 2 222

dx =

(1) log (1 + sin2x) + C (2) log (1 + cos2 x) + C (3) log (1 + cos2 x) + C d) log (1 + tan2 x) + C Ans: (3)

x

x x2 2sin2

sin 2cos + = x dxx2

sin21 cos + sin

2 x = 1 cos2 x

put cos2x = t , 1 + cos2 x = t -2 cos x sin x dx = dt or sin 2x dx = -dt

= -dtt = - log t + c = - log (1 + cos

2 x) + C

4

13. Let S be the set of all real numbers. A relation R has been defined on S by aRb |a b|

1, then R is (1) symmetric and transitive but not reflexive (2) reflexive and transitive but not symmetric (3) reflexive and symmetric but not transitive (4) an equivalence relation Ans: (3) a R b |a b| 1, a R a = |a a| = 0 1 R is reflexive if a R b |a b| 1 then b R a |b a| 1, |a b| 1, which is true. R is symmetric But R is not transitive, take a = 1, b = 2 Then |a b| = |1 2| = 1= 1 Let b = 2 and c = 3 |b c| = |2 3|= 1

But a R c |a c| = |1 3| = 2 > 1 14. For any two real numbers, an operation defined by a b = 1 + ab is (1) neither commutative nor associative (2) commutative but not associative (3) both commutative and associative (4) associative but not commutative Ans: (2) a * b = 1 + ab Now a * b = 1 + ab b * a = 1 + ba = 1 + ab = a * b * is commutative (a * b) * c = (1 + ab) * c = 1 + (1 + ab) c = 1 + c + abc but a * (b * c) = a * (1 + bc) = 1 + a (1 + bc) = 1 + a + abc (a * b) * c a * (b * c) * is not associate

15. Let f : N N defined by f (n) = +

n if n isodd

n if n is even

12

2

then f is

(1) onto but not one-one (2) one-one and onto (3) neither one-one nor onto (3) one-one but not onto Ans: (1) f : f : N N

n if n is odd

n if n is even

12

2

+ f (n) =

Now for n = 1, f (1) = 1 12+

= 1

And if n = 2, f (2) = 22

= 1

f (1) = f (2), But 1 2. f (x) is not one-one

5

f (x) = n 12+

if n is odd

if y = n 12+

then n = 2y 1, y

also, f (x) = n2

if n is even i.e., y = n2

or n = 2y y f (x) is onto 16. Suppose f (x) = (x + 1)2 for x 1. If g (x) is a function whose graph is the reflection of the

graph of f (x) in the line y = x, then g (x) =

(1) ( )x + 211

x > 1 (2) x - 1 (3) x + 1 (4) x 1

Ans: (4) f (x) = (x + 1)2 for x -1 g (x) is the reflection of f (x) in the line y = x, then g (x) is the

inverse of f (x) let y = (x + 1)2

y = x + 1 x = y 1 i.e., f -1 (y) = y 1 or g (x) = x 1

17. The domain of the function f (x) = cosx is

(1) , 3 22

(2) , 0 2 (3) , 2 2 (4) , ,

30 2

2 2Ans: (*)

xcos cos x 0 f (x) = 0 cos x 1 x is in I quad or IV quad i.e., x varies from 0 to

2

(in I quadrant)

also from 32

to 2, cos x is 0 In = 30, ,2

2 2 , cos x > 0

However, ,2 2

also is the domain of the function. Infact 3 ,22

and 0,2

are also

domains since cos x > 0 when x belongs to either of these two intervals. 18. In a class of 60 students, 25 students play cricket and 20 students play tennis and 10

students play both the games, then the number of students who play neither is (1) 45 (2) 0 (3) 25 (4) 35 Ans: (3) n () = 60 n (C) = 25 n (T) = 20 n (C T) = 10 then n (C T)| = ? n (C T) = n (C) + n (T) n (C T) = 25 + 20 10 = 35 n (C T)| = n (n) n (C T) = 60 35 = 25

6

19. Given 0 x 12

then the value of x xtan sin sin x +

21 11

2 2 is

(1) 1 (2) 3 (3) 1 (4) 13

Ans: (1)

x 102

tan x x x

21 11sin sin

2 2 +

is

= tan x x x

211sin sin

2 +

put sin-1 x = or x = sin given = tan 1 sin cossin

2 +

= tan 1sin sin4 +

tan tan 14 4 + = =

20. The value of sin (2 sin1 0.8) is equal to (1) 0.48 (2) sin 1.2o (3) sin 1.6o (4) 0.96 Ans: (4) The value of sin (2 sin-1 (0.8)) is Let sin-1 0.8 = sin = 0.8

21 sin cos =

0 2 12 0 21 2 0

0 2 12 0 21 2 0

= 0.6

given exp = sin 2 = 2 sin cos = 2 0.8 0.6 = 1.6 0.6 = 0.96 21. If A is 3 x 4 matrix and B is a matrix such that AB and BA are both defined, then B is of the

type (1) 4 x 4 (2) 3 x 4 (3) 4 x 3 (4) 3 x 3 Ans: (2)

22. The symmetric part of the matrix is A1 2 46 8 22 2 7

=

(1) (2) (3) (4) 1 4 32 8 03 0 7

1 4 34 8 03 0 7

Ans: (4)

A Symmetric part of A = A|1 ( )2

+

=

1 2 4 1 6 21 6 8 2 2 8 22 2 2 7 4 2 7

+

1 4 34 8 03 0 7

=

7

23. If A is a matrix of order 3, such that A (adj A) = 10 I, then |adj A| = (1) 1 (2) 10 (3) 100 (4) 10 I Ans: (3) We know A . Adj A = |A| I Clearly |A| = 10 |Adj A| = |A|3 1 = |A|2 = 102 = 100 24. Consider the following statements: (a) If any two rows or columns of a determinant are identical, then the value of the

determinant is zero (b) If the corresponding rows and columns of a determinant are interchanged, then the value

of determinant does not change. (c) If any two rows (or columns) of a determinant are interchanged, then the value of the

determinant changes in sign. Which of these are correct? (1) (a) and (c) (2) (a) and (b) (3) (a), (b) and (c) (4) (b) and (c) Ans: (3) Since each option is correct options (1), (2), (3), (4) are all correct answers.

25. The inverse of the matrix is A2 0 00 3 00 0 4

=

(1)

2 0 01 0 3 024 0 0 4

(2) (3)

2 0 00 3 00 0 4

1 0 01 0 1 024 0 0 1

(4)

1 0 02

10 03

10 04

ab

c

0 00 00 0

Ans: (4)

If A = , A-1 = a

b

c

1 0 0

10 0

10 0

When a 0, b 0, c 0 x x x ax x x bx x x c

2 34 56 7

+ + ++ + + is 26. If a, b and c are in A.P., then the value of + + +

R R R R R R1 11 1 2 2 2 3,= =

(1) 0 (2) x (a + b + c) (3) a + b + c (4) 9x2 + a + b + c Ans: (1)

a bb c

x x x

2 22 26 7

+ + + c

= R1 R2 since a b = b c ( a, b, c are in AP b a = c b)

8

27. The local minimum value of the function f| given by f (x) = 3 + |x|, x R is (1) -1 (2) 3 (3) 1 (4) 0 Ans: (1 & 3) or (2) Clearly when x > 0, local minimum = 1 When x < 0, local minimum = -1 option (1) and (3) both are true However, if the question was given as The local minimum value of the function f given by f (x) = 3 + |x|, x R is, then (3) is correct answer. It is clear from the graph of the

function y = |x| + 3. Eventhough it is not differentiable at x = 3, it still has a relative minimum.

28. A stone is dropped into a quiet lake and waves move in circles at the speed of 5 cm/sec. At

that instant, when the radius of circular wave is 8 cm, how fast is the enclosed area increasing?

(1) 6cm2/s (2) 8cm2/s (3) 83

cm2/s (4) 80cm2/s Ans: (4)

Given drdt

= 5 cm/sec

A = r2 dAdt

= .2r drdt

= 2.(8). 5 = 80cm2/sec 29. A gardener is digging a plot of land. As he gets tired, he works more slowly. After t minutes

he is digging at a rate of t2

square metres per minute. How long will it take him to dig an

area of 40 square metres? (1) 100 minutes (2) 10 minutes (3) 30 minutes (4) 40 minutes Ans: (1)

Given, dAdt t

2= dAt2= dt

A = 2.2 t + C Where t = 0, C = 0

4 t = 40 t = 100

xf x

1, 0( )1, 0>

9

30. The area of the region bounded by the lines y = mx, x = 1, x = 2, and x axis is 6 sq. units,

then m is (1) 3 (2) 1 (3) 2 (4) 4 Ans: (4) y = mx

Area = = 6 mxdx2

1

xm

22

1

62

= m (22 12) = 12 2 1

3m = 12 m = 4 31. Area of the region bounded by two parabolas y = x2 and x = y2 is

(1) 14

(2) 13

(3) 4 (4) 3

Ans: (2)

y2 = 4ax, x2 = 4by is a b4 .43

Required = 1.1 13 3

=

32. The order and degree of the differential equation y = xdy

dydxdx

2+ is

(1) 1, 2 (2) 1, 3 (3) 2, 1 (4) 1, 1 Ans: (1)

dy dyy xdx dx

2

2 = + order = 1, degree = 2

33. The general solution of the differential equation dy y xdx x

3+ = is

(1) cx

= y x (2) cy xx

= + (3) cy xx

2= (4) cy xx

2= + Ans: (4 & 3)

+ =

==

= += +

dyx y xdxdy xy xdxd xy x dxon egratexy x C

Cy xx

2

2

2

3

2

3

( ) 3

( ) 3 (*)int ,

Infact, after integrating (*) one may also write

3

2

xy x CCy xx

= =

10

34. The distance of the point P (a, b, c) from the x-axis is

(1) a b2 2+ (2) b c2 2+ (3) a (4) a c2 2+ Ans: (2) P (a, b, c), A (a, 0, 0)

Distance = b c b c2 2 2 2 2+ + = +0 35. Equation of the plane perpendicular to the line

x y z1 2 3= = and passing through the point

(2, 3, 4) is (1) 2x + 3y + z = 17 (2) x + 2y + 3z = 9 (3) 3x + 2y + z = 16 (4) x + 2y + 3z = 20 Ans: (4)

Since plane is perpendicular to x y z1 2 3= =

Direction ratio of normal to the plane is 1, 2, 3. Eq is 1x + 2y + 3z + d = 0. Passes through the point (2, 3, 4) 2 + 6 + 12 + d = 0 d = -20

Eq is x + 2y + 3z = 20

36. The line x y z2 3 43 4 5 = = is parallel to the plane

(1) 2x + 3y + 4z = 0 (2) 3x + 4y + 5z = 7 (3) 2x + y 2z = 0 (4) x + y + z = 2 Ans: (3) D.R of line = 3, 4, 5 Line and plane are parallel normal to plane and line are perpendicular a1a2 + b1b2 + c1c2 = 0 For plane 2x + y 2z = 0 3 (2) + 4(1) 2(5) = 0 2x + y 2z = 0 37. The angle between two diagonals of a cube is

(1) cos-1 13 (2) 30

o (3) cos-1 13

(4) 45 o

Ans: (1) Consider a diagonal with each side 1. Now BC and OA are diagonals.

Angle between diagonals = Angle between OAJJJG

and BCJJJG

. z

= (1, 1, 1) (0, 0, 0) = (1, 1,1) OAJJJG

BCJJJG

= (0, 1, 1) (1, 0, 0) = (-1, 1,1) C(0, 1, 1)

Now cos = 2 2 2 2 2 2

1( 1) 1(1) (1)(1) 131 1 1 ( 1) 1 1

+ + =+ + + +

x

y O

A(1, 1, 1)

B (1, 0, 0)

11

38. Lines x y z

K2 3

1 1 = =

4 and

x y zK1 4

2 1 = = 5 are coplanar if

(1) K = 2 (2) K = 0 (3) K = 3 (4) K = -1 Ans: (2)

2 1 2 1 2 1

1 1 1

2 2 2

0x x y y z za b ca b c

=

1 2 4 3 5 41 1

2 1k

k

= 0

1 1 11 1 0

2 1k

k =

k = 0 39. A and B are two events such that P (A) 0, P (B/A) if (i) A is a subset of B (ii) A B = are respectively (1) 1, 1 (2) 0 and 1 (3) 0, 0 (4) 1, 0 Ans: (4)

P(B | A) = ( )

( )P A BP A

P(B | A) = 0 Since P(A) 0, P(A) = 1 (Inspection) P(A) = 1, P(A =0 )B A B = 40. Two dice are thrown simultaneously. The probability of obtaining a total score of 5 is

(1) 19

(2) 118

(3) 136

(4) 112

Ans: (1) O (s) = 36 E = {(1, 4), (4, 1), (2,3) , (3, 2)} P(E) = 4/36 = 1/9 41. If the events A and B are independent if P (A|) =

23

and P (B|) = 27

, then P (A B) is equal to

(1) 421

(2) 521

(3) 121

(4) 321

Ans: (2) P (A = P(A) . P(B ) (independent events) )B = [1- P(A|)] [1- P(B|)] = [1 2/3] [1 2/7]

= 1 5 5.3 7 21

= 1 5 5.3 7 21

=

12

42. A box contains 100 bulbs, out of which 10 are defective. A sample of 5 bulbs is drawn. The

probability that none is defective is

(1) 910

(2) 51

10 (3)

5910 (4)

512

Ans: (3)

5 5

55 0 5

0

10 0.1 0.9 5100( ) (0.1) (0.9)

9(0) (0.1) (0.9)10

x xx

p q

p x C

p C

= = = =n =

= =

43. The area of the parallelogram whose adjacent sides are i k + and is i j k 2 + + (1) 3 (2) 2 (3) 4 (4) 3 Ans: (4)

Area = a bG G

1 0 12 1 1

i j ki j k= + +

=

area = 1 1 1+ + = 3 1 1 1 3+ + =

44. If a and are two unit vectors inclined at an angle

b

3

, then the value of a b + is

(1) equal to (2) greater than 1 (3) equal to 0 (4) less than 1 Ans: (2)

2 2 2

| | | | 1, / 3

| | | | | | 2(| |. | | cos )1 1 2.1.1.1/ 2 3

| | 3

| | 1

a b

a b a b a b

a b

a b

= = =+ = + +

= + + == + = + >

G GG G G G G G

G GG G

a b c

45. The value of is equal to a b b c c a

(1) 0 (2) 1 (3) 2

a b b a c a

(4) 2

Ans: (1)

= a b b c c a

a b b c b a c c c a = +

13

a b

a b b c b a c a = +

= 0 c c

a b c a b a a c a b b c b b a b c a. . . . . . + +

= - 0 + 0 0 + 0 - a b c

= 0 46. If x + y 2, x 0, y 0 the point at which maximum value of 3x + 2y attained will be (1) (0, 2) (2) (0, 0) (3) (2, 0) (4)

1 1,2 2

Ans: (3) Corner points are (0, 0), (2, 0) (0, 2) Max. of 2x + 3y is 6 at (2, 0) 47. If sin = sin , then (1)

2 +

is any multiple of 2

and 2

is any odd multiple of .

(2) 2

+ is any odd multiple of

2

and 2

is any multiple of .

(3) 2

+ is any multiple of

2

and 2

is any even multiple of .

(4) 2

+ is any even multiple of

2

and 2

is any odd multiple of .

Ans: (*) sin = sin sin - sin = 0 2cos sin 0

2 2 + =

It is not necessary that 2

+ is odd multiple of

2

and 2

is any multiple of should be

simultaneously hold good for the above equation to be true. Hence the correct answer should be

/ 2

2 2odd multiple of or anymultiple of + = =

48. If tan x = 34

, < x < 32

, then the value of cos x2

is

(1) - 110

(2) 310

(3) 110

(4) - 310

Ans: (1) Tan x = 3/4 cos x = - 4/5 1+ cos x = 2 cos2 (x/2) 1 4/5 = 2 cos2 (x/2)

21 cos ( / 2)10

x= cos (x/2) = - 110

110

14

49. In a triangle ABC, a [b cos C c cos B] = (1) 0 (2) a2 (3) b2 - c2 (4) b2

Ans: (3) a[b cos C c cos B] (b cos C + c cos B) (b cos C - c cos B) b2 cos2 C c2 cos2 B b2 (1 sin2 C) c2 (1 sin2 B)

b2 2 2

22 21 14 4

c bcR R

= b2 - 2 2 2 2

22 24 4

b c c bcR R

+2 2

22 21 14 4

c bcR R

= b2 c2

50. If and are two different complex numbers with || = 1, then 1

is equal to

(1) 12

(2) 0 (3) 1 (4) 1

Ans: (1) Take, = 0, = 1

Then 1 0 11 01

= =

51. The set A = {x :|2x + 3| < 7} is equal to the set (1) D = {x : 0 < x + 5 < 7} (2) B = {x : - 3 < x < 7} (3) E = {x : - 7 < x < 7} (4) C = {x : - 13 < 2x < 4} Ans: (1) |2x + 3| < 7 -7 < 2x +3 < 7 -10 < 2x < 4 -5 < x < 2 0 < x + 5 < 7 52. How many 5 digit telephone numbers can be constructed using the digits 0 to 9, if each

number starts with 67 and no digit appears more than once? (1) 335 (2) 336 (3) 338 (4) 337 Ans: (2) 3 digits from 0, 1, 2, 3, 4, 5, 8, 9 (arrangement of 8 digits taking 3 at a time 8P3 = 720 = 8 x 7 x 6 = 42 x 8 = 336 53. If 21st and 22nd terms in the expansion of (1 + x)44 are equal, then x is equal to

(1) 87

(2) 2122

(3) 78

(4) 2324

Ans: (3) 44

44 20 44 21 2020 21 44

21

(44 21)!21! 23! 21! 21 7.(44 20)!20! 24! 20! 24 8

CC x C x xC

= = = = =

15

54. Consider an infinite geometric series with first term a and common ratio r. If the sum is 4

and the second term is 34

, then

(1) a = 2, r = 38

(2) a = 47

, r = 37

(3) a = 32

, r = 12

(4) a = 3, r = 14

Ans: (4)

4 41

4 444 4

ar

ar a

= = =

check with options 55. A straight lien passes through the points (5, 0) and (0, 3). The length of perpendicular form

the point (4, 4) on the line is

(1) 1534

(2) 172

(3) 172

(4) 172

Ans: (4)

2 2

3 00 ( 5)5

5 3 15

3(4) 5(4) 15 17 172343 5

y x

y x

d

= =

+ = = =+

56. Equation of circle with centre (-a, -b) and radius a b2 2 is (1) x2 + y2 + 2ax + 2by + 2b2 = 0 (2) x2 + y2 - 2ax - 2by - 2b2 = 0 (3) x2 + y2 - 2ax - 2by + 2b2 = 0 (4) x2 + y2 - 2ax + 2by + 2a2 = 0 Ans: (1) Only (1) has centre (a, b) 57. The area of the triangle formed by the lines joining the vertex of the parabola x2 = 12y to the

ends of Latus rectum is (1) 20 sq. units (2) 18 sq. units (3) 17 sq. units (4) 19 sq. units Ans: (1)

2 12 4 12 3x y a a= = = area of triangle =

1 ( ) (2

base height)

1 1(4 | |)(| |) (12)(3) 182 2

a a = = 58. If the coefficient of variation and standard deviation are 60 and 21 respectively, the

arithmetic mean of distribution is (1) 60 (2) 30 (3) 35 (4) 21 Ans: (3)

coefficient of variation = 100x

2160 .100 35xx

= =

16

Y 59. The function represented by the following graph is (1) Continuous but not differentiable at x = 1 (2) Differentiable but not continuous at x = 1 (3) Continuous and differentiable at x = 1 (4) Neither continuous nor differentiable at x = 1 Ans: (1) ( ) | 1|f x x=

60. If f (x) = x x

xK x

3sin 052 0

= is continuous at x = 0, then the value of K is

(1) 10

(2) 310

(3) 32

(4) 35

Ans: (2)

0

0

3sinlim 25

3 sinlim 25

3 25

3 /10

x

x

x kx

x kx

k

k

= =

==

X 0

1

2

1 2