gate 2013 test series -2

GATE-2013 (Full Length)

S K Mondal’s Test Series -2

For any query E-mail: [email protected]

All India Test Series Mechanical Engineering

Duration: 3 Hrs Maximum Marks: 100 Read the following instructions carefully: There are total 65 questions carrying 100 marks: Q.1 to Q.25 (25 questions) will carry one mark each (sub-total 25 marks). Q.26 to Q.55 (30 questions) will carry two marks each (sub-total 60 marks).Question pairs (Q.48,Q 49) and (Q. 50, Q 51) are common data questions and question pairs (Q.52, Q.53) and (Q.54, Q.55) are linked answer questions. The answer to the second question of the last two pairs will depend on the answer to the first question of the pair. If the first question in the linked pair is wrongly answered or is un-attempted, then the answer to the second question in the pair will not be evaluated. Q 56 to Q 60 (5 questions) will carry one mark each (sub-total 5 marks). Q 61 to Q 65 (5 questions) will carry two marks each ( sub-total 10 marks). Negative Marking: For Q.1 to Q.25, 1/3 mark will be deducted for each wrong answer. For Q.26 to Q.55, 2/3 mark will be deducted for each wrong answer. The question pairs (Q.52, Q.53), and (Q.54, Q.55) are questions with linked answers. There will be negative marks only for wrong answer to the first question of the linked answer question pair i.e. for Q.52 and Q.54, 2/3 mark will be deducted for each wrong answer. There is no negative marking for Q.53 and Q.55. For Q.56 to Q.60, 1/3 mark will be deducted for each wrong answer. For Q.61 to Q.65, 2/3 mark will be deducted for each wrong answer. Fill Objective Response Sheet (ORS) using a soft HB pencil. Do not use the ORS for any rough work. You may like to use the Answer Book for any rough work, if needed. Answer All Questions

Last Test Series will be uploaded on 1 feb




Q1 to 25 carry 1 mark each Q.1 Find correct statement : In matrices

(a) ( )2 2 2A B A 2AB B+ = + + (b) ( )2 2 2A B A B+ = +

(c) ( )2 2 2A B A 2AB B+ ≠ + + (d) ( ) ( )2 2A B A B 4AB+ = − +

Q.2 The degree and order of the differential equation

2/32 2

2dy d y1dx dx

⎡ ⎤⎛ ⎞+ =⎢ ⎥⎜ ⎟⎝ ⎠⎢ ⎥⎣ ⎦

(a) 3, 2 (b) 2, 3 (c) 4, 1 (d) 1, 4 Q.3 Let A be an nxn matrix st. A2 = I and Y be an n- dimensional vector. Then the

linear system of equations Ax = y has (a) No solutions (b) Unique nsol s. (c) More than one but infinity many independent nsol s. (d) Infinitely many independent solutions.

Q.4 Let X be a Poisson variable st. 2p(x = 0) = p(x = 2) then the mean of the poisson

distribution is (a) 4 (b) 2 (c) 2 (d) 2−

Q.5 Let X be a non singular matrix. Then the inverse of the matrix tAA is

(a) Equals ( )t1 1A A− − (b) Does not exists

(c) Symmetric (d) Skew symmetric Q.6 A Cantilever AB of length l has a moment M applied at free end. The

deflection at the free end B is given as: (a) 2M L

EI (b) 2ML2EI (c) ML

2EI (d) 3ML2EI

Q.7 What is neutral plane in rolling?

(a) Where velocity of roller and work piece become equal (b) Where maximum deformation takes place (c) Where minimum deformation takes place (d) No plane is neutral

Q.8 Fettling is an operation performed (a) Before casting (b) After casting

(c) Before heat treatment (d) before machinery





Q.9 How many properties are independently required to fix state of pure substance in equilibrium conditions?

(a) 1 (b) 2 (c) 3 (d) 4 Q.10 In case of heat exchanger, the value of logarithmic mean temperature

difference should be (a) As small as possible. (b) As large as possible. (c) Constant. (d) None of the above. Q.11 The most suitable theory of failure for a brittle material is

(a) The maximum normal stress theory (b) The Coulomb-Mohr’s theory (c) The maximum shear stress theory (d) The maximum distortion energy theory

Q.12 Interference is inherently absent in the following type of gears. (a) Involute (b) Cycloidal (c) Stub (d) Hypocycloidal Q.13 Diametral quotient is defined as (a) Axial module/reference diameter (b) Pitch diameter/module

(c) Module/pitch diameter (d) Pitch/pitch diameter Q.14 The number of elements that comprise the signature of a single point lathe

cutting tool is (a) 4 (b) 5 (c) 6 (d) 7 Q.15 In case of a circular section the relation between maximum shear stress and

average shear stress (a) 3

max mean2τ = τ (b) max meanτ = τ (c) 2max mean3τ = τ (d) 4

max mean3τ = τ Q.16 The total average emissivity at a given temperature is given by

(a) b

0

b0

E d

E d

α

λ λ

α

λ

ε λ

λ

∫

∫ (b)

b0

b0

E d

E d

λ

λ λ

α

λ

ε λ

λ

∫

∫ (c)

b0

b0

E d

E d

α

λ λ

λ

λ

ε λ

λ

∫

∫ (d)

b0

b0

E d

E d

λ

λ λ

λ

λ

ε λ

λ

∫

∫

Q.17 In a flat belt tension in the tight side (T1) = 250 N, Tension in the slack side

(T2) = 226 N, centrifugal tension (Tc) = 534 N, then what should be the Initial tension in the belt?

(a) 250 N (b) 772 N (c) 277 N (d) 500 N Q.18 A weight W1 on a smooth table is connected by a light cord passing over a

smooth pulley to another wt W2 which is free to more vertically. The tension in card will be





W1

W2

(a) 1 2W W+ (b) 1 2W W2+

(c) 1 2

1 2

W WW W+

(d) 1 2

1 2

W WW W+

Q.19 There are two bars one prismatic and one conical length and specific weight

of both are same. Ratio of their elongation due to their own weight will be (a) 0. 5 : 1 (b) 1 : 1 (c) 2 : 1 (d) 3 : 1

Q.20 Value of Wahl stress factor for springs with increase in value of c

(a) Decrease (b) increase (c) Remain same (d) does not depend upon C

Q.21 Which is not a characteristic of product layout?

(a) Large volume of production (b) Less flexibility of product change (c) Maximum inspection (d) Possibility of time and motion studies

Q.22 A 40 mm thick sheet is rolled with 500 mm diameter rolls to reduce thickness

without any charge in its width. The friction coefficient at the work-roll interface is 0.2. The minimum possible thickness of the sheet that can be produced in a single pass is (a) 30 mm (b) 15 mm (c) 25 mm (d) 37 mm

Q.23 Which process is used for cutting thicker plates? (a) Gas cutting (b) Punching (c) Piercing (d) Hobbing Q.24 Which flame in oxy – acetylene gas welding has got 3 distinct colour zone? (a) Carburizing flame (b) Oxidizing flame (c) Neuter flame (d) No such flame Q.25 Which inert gas is commonly used for shielding in use of case of thin work

piece and low voltage applied? (a) Argon (b) Helium (c) CO2 (d) None

Q.26 to Q.55 carries two marks each Q.26 The value of integral 2n 1

c

cosz dz,z 1+ +∫ c : z 1= is

(a) 2 iπ (b) ( )n2 i 1π − (c) ( )n2 i 1n!

π − (d)

( )( )

n2 i 12n !

π −





Q.27 Which of the following sets of vector in 3R are linearly independent

1. ( ) ( ) ( )1,0,0 0,1,0 1,1,0⎡ ⎤⎣ ⎦

2. ( ) ( ) ( )1,0,0 0,1,0 0,0,1⎡ ⎤⎣ ⎦

3. ( ) ( ) ( )0,1,0 1,0,1 1,1,0⎡ ⎤⎣ ⎦

4. ( ) ( ) ( )0,0,1 0,1,0 0,1,1⎡ ⎤⎣ ⎦

Select the correct answer (a) 1 and 2 (b) 2 and 3 (c) 3 and 4 (d) 1 and 4

Q.28 For a scalar function f (x, y, z) = 2 2 2x 3y 2z+ + , the directional derivatives at

the point p (1, 2, -1) in the direction of vector i j 2k− + is

(a) -18 (b) 3 6− (c) 3 6 (d) 18

Q.29 The equation2 2

2 2xx xy yy x y

y xy 2xy xx yu u u u u− + − + is

(a) elliptic (b) parabolic (c) hyperbolic (d) None of the above

Q.30 Value of 3t

0te sin dt

∞−∫

(a) 1/50 (b) 3/50 (c) 3/25 (d) 1/25 Q.31 If the diameter of a finished round cornered cup is to be 4 cm and height 3

cm (radius of corner = 0.5 cm) then the diameter of blank should be (a) 5.5 cm (b) 6.5 cm (c) 7.5 cm (d) 9.5 cm Q.32 Two shafts are connected by a universal joint. The driving shaft rotator at a

uniform speed 120 rpm. Total fluctuation of speed does not exceed 10 rpm. Calculate minimum speed of shaft

(a) 511 (b) 105 (c) 115 (d) 15 Q.33 Hitesh products Ltd (HPL) produces an item, which requires shearing

operation first followed by punching operation. There are 5 different jobs to be processed, the processing times for which are given below:

Job

Punch Time

Shear Time

1

5

4

2

1

4

3

4

10

4

10

6

5

3

2

Using Johnson’s rule find the makes pan of the schedule? (a) 22 days (b) 10 days (c) 27 days (d) 72 days





Q.34 If there are two critical paths in a project with means 30 and variances of 9 and 16 respectively then according to PERT calculations the project duration is

(a) Normally distributed with mean 30 and standard deviation 3 (b) Normally distributed with mean 30 and standard deviation 4 (c) Beta distribution with mean 30 and standard deviation 4 (d) None of the above Q.35 Dry Saturated steam at 5 bar with negligible velocity expands isentropically

in a convergent nozzle to 1 bar dryness fraction 0.94. Determine the velocity of steam leaving the nozzle.

at P1 = 5 bar , hg = 2747.5 KJ / kg at P = 1 bar , hf = 417.5 KJ / kg, hg = 2258 KJ / kg (a) 444 m/s (b) 446 m/s (c) 644 m/s (d) 1000 m/s Q.36 A geometrically similar open channel model is constructed with 5:1 scale. If

model measure discharge of 0.2 m3/s, the corresponding discharge in prototype is

(a) 5 m3/s (b) 25 m3/s (c) 1 m3/s (d) 125 m3/s Q.37 How much heat would be generated in the spot welding of two sheets of 1 mm

thick steel that required a current of 10000 A for 0.1 seconds? An effective resistance of 100 μΩ is assumed.

(a) 1000 kJ (b) 5 kJ (c) 1 kJ (d) 2 kJ Q.38 Fig shows a hoisting apparatus in which span AB 5 m long is free to turn in a

vertical plane through A and B and is fastened by a cable BC 3 m long to a point C, 6 m vertically above. A weight of 1500 kg is supported by a cable at B. neglecting the weight of space and cable the force along AB and BC will be

A

B

C

3

51500 kg

6

Figure

(a) 1250 and 750 Kgf (b) 1500 and 1000 Kgf (c) 1000 and 1500 Kgf (d) 1500 and 1250 Kgf

Q.39 An engine with 80% mechanical efficiency develops b.p of 48 kW. Assuming

friction as constant, what will be mechanical efficiency at half load? (a) 40% (b) 53% (c) 67% (d) 80% Q.40 In a slab of thickness L there is internal heat generation of q (W/m3). The

temperature on two faces of slab (Tw) is

(a) aqLT2h

+ (b) aqLTh

+ (c) ahLTq

+ (d) aqhTL

+





Q.41 What is standard time for a article when total quantity produced was 60 in a time span of total observing time of 600 sec in which 80% of time was observed in working (Assume rating factor = 1 and allowance = 10% of normal time)

(a) 9 sec (b) 6 sec (c) 10 sec (d) 7 sec Q.42 Consider following statements

(1) Adiabatic saturation temperature and wet bulb temperature is same for air & water-vapour mixture at low pressure.

(2) Adiabatic saturation temperature is a thermodynamic property whereas wet bulb temperature is not a thermodynamic property

(a) Both are correct (b) Only 1 is correct (c) Only 2 is correct (d) None is correct

Q.43 Chemical dehumidification is associated with (a) Cooling (b) heating

(c) Neither cooling nor heating (d) No chemical dehumidification possible Q.44 A Casting 3200 200 70mm× × size solidifies in 10 min. Determine the

solidification time for 3200 100 10mm× × under similar conditions. (a) 0.734 min (b)0.846 min (c) 0.648 min (d) 0.648 min Q.45 To cut a blank of 25 mm wide and 30 mm long form a 1.5 mm thick metal strip,

if the ultimate shear stress of the material is 450 N/mm2. Determine the work done if the percentage of penetration is 25% of material thickness.

(a) 75 J (b) 72 J (c) 82 J (d)28 J Q.46 What is value of bulk modules of elasticity with value of v = 0.31, if E =

2.4× 106 Kg / cm2. (a) 2.1× 106 Kg / cm2 (b) 2.4× 106 Kg / cm2 (c) 0.74× 106 Kg / cm2 (d) 8× 106 Kg / cm2

Q.47 Calculate the available energy of 10 kg of water at 600 K w.r.t to surrounding

at 300 K [assume p = 1 atm, ln2 = 0.7 Cp = 4.2 kJ/kgK] (a) 3780 kJ (b) 6480 kJ (c) 12600 kJ (d) 1890 kJ

Common Data Questions 48 and 49 Find the air standard efficiencies for the Otto and Diesel cycle on the basis of equal compression ratio of 10 and equal heat rejection of 840 kJ/kg. The suction conditions are 1 bar and 328 K. Take Cp = 1 kJ / kgK. CV = 0.712 kJ / kgK, 1.4γ = Q.48 Efficiency of Otto cycle (a) 50% (b) 55% (c) 60% (d) 65% Q.49 The efficiency of Diesel cycle (a) 84% (b) 48.2% (c) 28.4% (d) None of the above.

Common Data Questions 50 and 51 A tyre is shrunk on a wheel 12 m diameter. After shrunken hoop stress in tyre is 120 N /mm2 and α for tyre is 11.7 ×10-6 /0C and E = 200 kN/m2

Q.50 Calculate internal diameter of tyre assuming wheel to be rigid. (a) 11.993 m (b) 10.993 m (c) 11.019 m (d) 10.019 m





Q.51 Find the least temperature to which tyre must be heated above that of wheel before it would be fitted.

(a) 51.3 0C (b) 41.3 0C (c) 30.9 0C (d) 69.1 0C

Linked Questions 52 and 53 Q.52 A store sells 5200 cases of a cold drink per year. The supplier charges Rs. 100

for each delivery and average carrying cost is Rs. 10.40 per unit per year. Calculate the economic order quantity. (a) 316 (b) 520 (c) 626 (d) 110

Q.53 What are the number of orders per year with overall annual sell of 5200? (a) 16 (b) 52 (c) 30 (d) cannot be calculated

Linked Questions 54 and 55 Consider a viscous damping in which damping force = 400 N and velocity =10m / s, mass of system = 40 kg and spring constant k 4000N m= Q.54 Calculate the critical damping coefficient

(a) Ns800m

(b) Ns400m

(c) Ns4000m

(d) Ns40000m

Q.55 Calculate damping factor or damping ratio

(a) 0.05 (b) 0.5 (c) 0.4 (d) 0.04

Q56 to 60 carry 1 mark each Q.56 For n 2≥ , n n 1 n 2P 2P P− −= − . Given that oP 1= and 1P 0= . Find 7 8 9 38P P P ....... P+ + + + = (a) 31 (b) 645 (c) 32 (d) 688 Q.57 Choose the word which is nearest in meaning to the given word. AUSTERE (a) Proud (b) Rigorous (c) Revered (d) Very poor Q.58 Fill in the blank with appropriate preposition. He died __________ over eating. (a) Of (b) For (c) From (d) In Q.59 The average age of 10 members of a committee is the same as it was 4 years

ago, because an old member has been replaced by a young member. Find how much younger is the new member?

(a) 44 (b) 40 (c) 30 (d) 35 Q.60 If n is a natural number greater than 1, then 11075 1075n n−− is not divisible by

which of the following (a) 15 (b) 23 (c) 43 (d) 179

Q61 to 65 carry 2 marks each Q.61 Some 480,000 immigrants were living in a certain country in 1999. Although

most of these immigrants were not employed in professional occupations,





many of them were. For instance, many of them were engineers and many of them were nurses. Very few of these immigrants were librarians, another professional occupation. From the information given above, it can be validly concluded that, in 1999, in the country described above, (a) Most immigrants were either engineers or nurses (b) It is not the case that some of the nurses were immigrants (c) None of the engineers were immigrants (d) Some of the engineers were immigrants

Q.62 Let101010M 10= . If M ends with N zeros and N ends with P zeros, how many

digits are there in P? (a) 2 (b) 3 (c) 10 (d) 11

Q.63 If a is an integer , then for how many integer values of n can the quadratic

equation 2 nx (2a 3)x 4 0− + + = have real and equal roots for x ? (a) 0 (b) 1 (c) 2 (d) 3

Q.64 If the arithmetic mean of 11(39) 9and (62) is n(144) , then sum of 4 5(32) and (21) in a system with radix (base) n is (a) 140 (b) 110 (c) 100 (d) 50 Q.65 Two fair dice are thrown simultaneously. What is the probability that one die

shown up a number greater then “4” and then other number shown up a number less than “3”?

(a) 1/9 (b) 4/9 (c) 2/9 (d) 1/18




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ME Test-3 Answer 1. Ans. c Exp. AB BA≠ in general 2. Ans. a

Exp. 2 22 2

2dy d y1dx dx

⎡ ⎤ ⎛ ⎞⎛ ⎞+ =⎢ ⎥ ⎜ ⎟⎜ ⎟⎝ ⎠⎢ ⎥ ⎝ ⎠⎣ ⎦

Degree – 3 Order – 2 3. Ans. b Exp. 2A I= ( )det A.A det I⇒ =

( ) ( )2

det A . det A 1

(det A) 1det A 1

⇒ =

⇒ =⇒ = ±

By crammer’s rule system of equation has unique solution. 4. Ans. b. Exp. Here X is Poisson variable

( )m re mp x rr!

−

∴ = = , where m = means of the distribution. r = 0,1,2,3,……..

( ) ( )2p x 0 p x 2∴ = = =

m 0 m 2e m e m2.0! 2!

− −

⇒ =

2m 4⇒ = m 2⇒ = ± 5. Ans. c Exp. A is non singular ⇒ A is square matrix Now tAA is define.

∴ ( ) ( )t tt t t tAA A A AA= =

6. Ans. (b) 7. Ans. (a) 8. Ans. (b) Exp. Fettling is cleaning of cast 9. Ans. (b) Exp. For normal substance; 3 preparers and proper 2 properties. 10. Ans. (b) 11. Ans. (b) 12. Ans. (b) 13. Ans. (b) 14. Ans. (d)





15. Ans. (d) 16. Ans. (a) 17. Ans. (b)

Exp. 1 2 co

T T 2TT2

+ +=

18. Ans. (d) Exp. Friction = 0 (smooth pulley) T = W1 a W2 –T = W2 a Adding W2 = (W1 + W2) a

T

W1

W2

Ta

a Figure

2

1 2

WaW W

=+

1T W a=

1 2

1 2

W WTW W

=+

19. Ans. (d) Exp. Elongation of prismatic bar

2l

2Eγ

=

2lElongationof conical bar

6Eγ

=

ratio 3 : 1= 20. Ans. (a)

Exp. Wahl stress correction factor 4C 1 0.6154C 4 C

−= +

−

21. Ans. (c) Exp. Max inspection is required on production line is stress linked for man production 22. Ans. (a) Exp. (∆h)max = µ2R = 0.22x250 = 10 mm 23. Ans. (a) 24. Ans. (a) 25. Ans. (a) Exp. Argon thinwalled plate,Lowvoltage→ Helium thickwalled plate,Highvoltage→ 2CO UsedonlywithDECP(reversepolarity)→

26. Ans. d Exp. z = 0 is pole of order 2n + 1





Let ( ) 2n 1cos zf zz +=

( ) ( ) ( ) ( )2n

2n 12nz 0

1 dRes f ,0 lim z 0 f z2n ! dz

+

→

⎧ ⎫⎪ ⎪⎡ ⎤= −⎨ ⎬⎣ ⎦⎪ ⎪⎩ ⎭

( ) ( )

2n

2nz 0

1 dlim cos z2n ! dz→

=

( ) ( )n1 12n !

= −

( ) ( )( )

n

c

2 i 1f z dz

2n !π × −

∴ =∫

27. Ans. b 28. Ans. b

Exp. ∇f 2xi 6y j 4zk− − −

= + +

∇f⎥ p 2i 12 j 4k− − −

= + −

Now unit vector in the direction of i j 2k− − −− + is

( )22 2

n (i j 2k)1 1 2

∧= − +

+ − +

1 (i j 2k)6

= − +

∴ Required directional derivative at p

= ∇ f .n∧

12i 12 j 4k . i j 2k6

− − − − − −⎛ ⎞ ⎛ ⎞= + − − +⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

( )1 2 12 86

= − −

186

−= 3 6= −

29. Ans. b

Exp. 2A = λ , B 2xy= − , 2C x= ,2yD

x−

= ,2xE

y= , F 0= , G 0=

2 2 2 2 2B 4AC 4x y 4y x 0− = − = The given equation represents parabola. 30. Ans. b

Exp. { }3t st2

0 0

d 1te dt te sintdt L tsintds s 1

∞ ∞− − − ⎛ ⎞= = = ⎜ ⎟+⎝ ⎠∫ ∫





( )2 22

2s 2 3 350s 1 3 1

×⎛ ⎞= = =⎜ ⎟+⎝ ⎠ +

31. Ans. (c) Exp. Diameter of blank ( ) 2D d 4dh r= + −

24 4 4 3 0.5= + × × − 16 48 0.5= + − 8 0.5 7.5cm= − = 32. Ans. (c) Exp. Letα = greatest permissible angle between the shaft axes then

( )( )

2o1 cos

10 120 or 16.4cos− α

= α=α

max oNN 125 rpm

cos16.4= =

ominN Ncos =120 cos16.4 115 rpm= α × =

33. Ans. (c) 34. Ans. (b) 35. Ans. (c) Exp. h2 = hf2 + X2hg2 = 2540 KJ / kg V = ( )1 22000 h h− 36. Ans. (b) Exp. (velocity ratio)

p p/T p

m m/T m

v L L5

v L L= α = = p prototype−

2

p p2

m m

A L25

A Lα = m-model

Discharg ratio p p p

m m m

Q A v25 5 125

Q A v= = × =

p mQ 125 Q= × 30.2 250125 25m / sec10 10

= × = =

37 Ans. (c) Exp. 2 2 6Q I Rt (10,000) (100 10 ) (0.1)J−= = × × × 38. Ans. (a) Exp. If we draw force triangle it will be similar to ABCΔ

A

B

C

Fac

Fbc

Fab

Figure

From similarly





BCAB FF 15005 3 6

= =

AB1500 fF 1250Kgf

6×

⇒ = =

BC1500 3F 750Kgf

6×

= =

39. Ans. (c)

Exp. m

bp 48I.P 10 60kW0.8

= = × =η

Friction power = I.P – B.P = 12 kW

At half load BP 48= but friction power will be same.2

` 24 24 66.67%24 12 36

= =+

40. Ans. (a) Exp. Where Ta atmospheric temperature

h heat transfer coefficient tΔ Surface heat transfer on one side

w a1Q q AL hA(T T )2

= = −

w aqLT T2h

= +

Tw Tw Ta

41. Ans. (a) Exp. Standard time

( )total timeof observance × percentageof working time

= Totalquantityproduced

×Rating factor+ Allowance

600 80= × ×1 +10%of this 60 100

⎡ ⎤⎧ ⎫⎨ ⎬⎢ ⎥⎩ ⎭⎣ ⎦

600 80=1.1× ×10 100

=8.8sec.

42. Ans. (a) 43. Ans. (b) 44. Ans. (d)

Exp. use

21

112

2 2

2

VAt

t VA

⎛ ⎞⎜ ⎟⎝ ⎠=

⎛ ⎞⎜ ⎟⎝ ⎠

45. Ans. (d) Exp. F P.t.= τ





W F punchtravel= × Punchtravel percentage penetration= 0.25 t= × 46. Ans. (a)

Exp. ( ) ( )

66E E 2.4 10K 2.1 10

3 1 2v 3 1 2v 3(1 0.62)×

= = = = ×− − −

47. Ans. (a)

Exp. 600

op

300

TAvailability mc 1 dTT

⎛ ⎞= −⎜ ⎟⎝ ⎠∫

( ) 60010 4.2 600 300 300ln300

⎡ ⎤= × × − −⎢ ⎥⎣ ⎦

( )= 10 4.2 600 210× × − 3780 kJ= 48. Ans. (c) 49. Ans. (b) 50. Ans. (a)

Exp. ( ) ( )D d DHoopstress E 1d d E− σ

σ = ⇒ − =

5D 120 1 1.0006 dd 2 10

⇒ = + = ⇒×

d 11.993m1.0006

= =

51. Ans. (a)

Exp. 4D d 6D d(1 t) Or t

d 10−

π = π + α α = =

04 6

6 1t 51.3 C10 11.7 10−= × =

×

52. Ans. (a)

Exp. 3

1

2c RQ=c 1c inventarycarrying cost→

3c ordering costperorder→

100×5200×2= =316.210.40

53. Ans. (a)

Exp. No. of order per year 5200 16.4 16316.2

= = =

54. Ans. (a) Exp. Critical damping coefficient C nC 2mw= =

(As critical damping, 2 2n na 0 whereω − = ω CCk , a

m 2m= = , C nC 2m= ω )

nk 10m

ω = =

CC 2 40 10 800N m= × × = 55. Ans. (a)

Exp. Damping ratio CC

C F 400C 40,C 800C v 10

= = = = =





40Damping ratio 0.05800

= =

56. Ans. (d) Exp. 2P 1= − , 3P 2= − , 4P 3= − and so on ( )nP n 1= − −

nP n 1= −

7 8 38P 6, P 7......... P 37= = = ∴ Sum 6 7 8 ... 37= + + + +

( )32 6 37 6882

= + =

57. Ans. (b) 58. Ans. (c) Exp. Die of a disease. Die From exertion/overwork. 59. Ans. (b) Exp. Let x and y be the present ages of the younger and the old member respectively. So, by the condition,

2 3 10x x x ........ x10

+ + + +

1 2 3 10(y 4) (x 4) (x 4) (x 4) .... (x 4)10

− + − + − + − + + −=

2 3 10x x x ........ x10

+ + + +⇒ 2 3 10y x x ........ x 40

10+ + + + −

=

y x 40⇒ − = 60. Ans. (b) Exp. 11075 (1075 1)n− − 11075 1074n−= × 11075 2 3 179n−= × × × 1(25 43) 2 3 179n−= × × × ×

The number is a multiple of 179,43and 15(multiple of 3 and 5). As it is not multiple of 23, it is not divisible by 23. 61. Ans. (d) Exp. Some of the engineers were immigrants

Response D is correct because it restates the third sentence in terms of the overlap between immigrants and engineers in the country described in the paragraph. Response A says that most immigrants are engineers or nurses, which are professional occupations. However, the second sentence says that most immigrants are not employed in professional occupations, so Response A is false. Response B is false because it denies that there is any overlap between immigrants and nurses, even though this overlap is clear from the third sentence of the paragraph. Response C is false because it denies the overlap between immigrants and engineers.

62. Ans. (d)

Exp. 101010M 10= Ends with

1010N 10= zeros N ends with 1010 zeroes. P = 1010 P ends with 10 zeroes i.e. it has total 11 digits.

63. Ans. (b) Exp. Let the roots be m and n. 2b 4ac 0⇒ − =





2 n 1(2a 3) 4 ++ = n 1 n 12a 3 2 or (2 )+ +⇒ + = −

Only possible solutions for (a, n) are (-1,-1) (-2,-1). So, only one possible value of n exists.

64. Ans. (c) Exp. ( )1139 = ( )1 o

103 11 9 11 42× + × =

( )962 = ( )o106 9 2 9 56× + × =

AM of ( )1139 and ( )962 is ( )1042 56 49

2+

=

By, the condition. ( ) ( )n 10144 49=

2 o1 n 4 n 4 n⇒ × + × + × 49= 2n 4n 45 0⇒ + − = ( ) ( )n 9 n 5 0⇒ + − = n 5⇒ = Now, ( ) ( )4 532 21+ = ( )o3 4 2 4× + × ( )o2 5 1 5+ × + × ( )1025=

Now, check (a), (b), (c), (d) (a) ( )5140 = ( )2 o

101 5 4 5 0 5 45× + × + × = Similarly check (b), (d)

Now, (c) ( )5100 = ( )2 1 o101 5 0 5 0 5 25× + × + × =

65. Ans. (c) Exp. Here sample space (S) = 6 × 6 = 36. Favorable Cases for the problem are 8 i.e.((5,1) ,(5,2), (6,1), (6,2), (1,5),( 2,5), (1, 6), (2, 6). Therefore, required probability = 8/36 = 2/9.


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