# Multiple choice question for engineering

## Set 1

1. Which data structure can be used suitably to solve the Tower of Hanoi problem?

a) Tree

b) Heap

c) Priority queue

d) Stack

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2. Select the appropriate code for the recursive Tower of Hanoi problem.(n is the number of disks)

a)

public void solve(int n, String start, String auxiliary, String end) { if (n == 1) { System.out.println(start + " -> " + end); } else { solve(n - 1, start, end, auxiliary); System.out.println(start + " -> " + end); solve(n - 1, auxiliary, start, end); } }

b)

public void solve(int n, String start, String auxiliary, String end) { if (n == 1) { System.out.println(start + " -> " + end); } else { solve(n - 1, auxiliary, start, end); System.out.println(start + " -> " + end); } }

c)

public void solve(int n, String start, String auxiliary, String end) { if (n == 1) { System.out.println(start + " -> " + end); } else { System.out.println(start + " -> " + end); solve(n - 1, auxiliary, start, end); } }

d) None of the mentioned

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3. Which among the following is not a palindrome?

a) Madam

b) Dad

c) Malayalam

d) Maadam

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4. Which data structure can be used to test a palindrome?

a) Tree

b) Heap

c) Stack

d) Priority queue

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5. Select the appropriate code which tests for a palindrome.

a)

public static void main(String[] args) { System.out.print("Enter any string:"); Scanner in=new Scanner(System.in); String input = in.nextLine(); Stack<Character> stk = new Stack<Character>(); for (int i = 0; i < input.length(); i++) { stk.push(input.charAt(i)); } String reverse = ""; while (!stk.isEmpty()) { reverse = reverse + stk.pop(); } if (input.equals(reverse)) System.out.println("palindrome"); else System.out.println("not a palindrome"); }

b)

public static void main(String[] args) { System.out.print("Enter any string:"); Scanner in=new Scanner(System.in); String input = in.nextLine(); Stack<Character> stk = new Stack<Character>(); for (int i = 0; i < input.length(); i++) { stk.push(input.charAt(i)); } String reverse = ""; while (!stk.isEmpty()) { reverse = reverse + stk.peek(); } if (input.equals(reverse)) System.out.println("palindrome"); else System.out.println("not a palindrome"); }

c)

public static void main(String[] args) { System.out.print("Enter any string:"); Scanner in=new Scanner(System.in); String input = in.nextLine(); Stack<Character> stk = new Stack<Character>(); for (int i = 0; i < input.length(); i++) { stk.push(input.charAt(i)); } String reverse = ""; while (!stk.isEmpty()) { reverse = reverse + stk.pop(); stk.pop(); } if (input.equals(reverse)) System.out.println("palindrome"); else System.out.println("not a palindrome"); }

d) None of the mentioned

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6. What is the number of moves required in the Tower of Hanoi problem for k disks?

a) 2k – 1

b) 2k + 1

c) 2^{k} + 1

d) 2^{k} – 1

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7. Select the appropriate code which reverses a word.

a)

public String reverse(String input) { for (int i = 0; i < input.length(); i++) { stk.push(input.charAt(i)); } String rev = ""; while (!stk.isEmpty()) { rev = rev + stk.peek(); } return rev; }

b)

public String reverse(String input) { for (int i = 0; i < input.length(); i++) { stk.push(input.charAt(i)); } String rev = ""; while (!stk.isEmpty()) { rev = rev + stk.pop(); } return rev; }

c)

public String reverse(String input) { for (int i = 0; i < input.length(); i++) { stk.push(input.charAt(i)); } String rev = ""; while (!stk.isEmpty()) { rev = rev + stk.pop(); } }

d)

public String reverse(String input) { for (int i = 0; i < input.length(); i++) { stk.push(input.charAt(i)); } String rev = ""; while (!stk.isEmpty()) { rev = rev + stk.pop(); stk.pop(); } return rev; }

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## Set 2

1. Differentiation of function f(x,y,z) = Sin(x)Sin(y)Sin(z)-Cos(x) Cos(y) Cos(z) w.r.t `y` is

a) f’(x,y,z) = Cos(x)Cos(y)Sin(z) + Sin(x)Sin(y)Cos(z)

b) f’(x,y,z) = Sin(x)Cos(y)Sin(z) + Cos(x)Sin(y)Cos(z)

c) f’(x,y,z) = Cos(x)Cos(y)Cos(z) + Sin(x)Sin(y)Sin(z)

d) f’(x,y,z) = Sin(x)Sin(y)Sin(z) + Cos(x)Cos(y)Cos(z)

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2. In euler theorem x ^{∂z}⁄_{∂x} + y ^{∂z}⁄_{∂y} = nz, here `n` indicates

a) order of z

b) degree of z

c) neither order nor degree

d) constant of z

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^{∂z}⁄

_{∂x}+ y

^{∂z}⁄

_{∂y}= nz ”.

3. If z = x^{n} f(^{y}⁄_{x}) then

a) y ^{∂z}⁄_{∂x} + x ^{∂z}⁄_{∂y} = nz

b) 1/y ^{∂z}⁄_{∂x} + 1/x ^{∂z}⁄_{∂y} = nz

c) x ^{∂z}⁄_{∂x} + y ^{∂z}⁄_{∂y} = nz

d) 1/x ^{∂z}⁄_{∂x} + 1/y ^{∂z}⁄_{∂y} = nz

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^{∂z}⁄

_{∂x}+ y

^{∂z}⁄

_{∂y}= nz.

4. Necessary condition of euler’s theorem is

a) z should be homogeneous and of order n

b) z should not be homogeneous but of order n

c) z should be implicit

d) z should be the function of x and y only

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^{∂z}⁄

_{∂x}+ y

^{∂z}⁄

_{∂y}= nz” Answer `b` is incorrect as z should be homogeneous. Answer `c` is incorrect as z should not be implicit. Answer `d` is incorrect as z should be the homogeneous function of x and y not non-homogeneous functions.

5. If f(x,y) = ^{x+y}⁄_{y} , x ^{∂z}⁄_{∂x} + y ^{∂z}⁄_{∂y} = ?

a) 0

b) 1

c) 2

d) 3

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6. Does function can be solved by euler’ s theorem

a) True

b) False

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^{n}f(

^{y}⁄

_{x}) hence it does not satisfies euler’s theorem.

7. Value of is ,

a) -2.5 u

b) -1.5 u

c) 0

d) -0.5 u

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8. If u = x^{x} + y^{y} + z^{z} , find ^{du}⁄_{dx} + ^{du}⁄_{dy} + ^{du}⁄_{dz} at x = y = z = 1

a) 1

b) 0

c) 2u

d) u

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^{du}⁄

_{dx}= x

^{x}(1+log(x) )

^{du}⁄

_{dy}= y

^{y}(1+log(x))

^{du}⁄

_{dz}= z

^{z}(1+log(x)) At x = y = z = 1,

^{du}⁄

_{dx}+

^{du}⁄

_{dy}+

^{du}⁄

_{dz}= u.

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10. If f(x,y)is a function satisfying euler’ s theorem then

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11. Find the approximate value of [0.98^{2} + 2.01^{2} + 1.94^{2} ]^{(1⁄2)}

a) 1.96

b) 2.96

c) 0.04

d)-0.04

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^{2}+ y

^{2}+ z

^{2})

^{(1⁄2)}……………..(1) Hence, x = 1, y = 2, z = 2 so that, dx = -0.02, dy = 0.01, dz = -0.06 From (1),

^{∂f}⁄

_{∂x}=

^{x}⁄

_{f}

^{∂f}⁄

_{∂y}=

^{y}⁄

_{f}

^{∂f}⁄

_{∂z}=

^{z}⁄

_{f}

12. The happiness(H) of a person depends upon the money he earned(m) and the time spend by him with his family(h) and is given by equation H=f(m,h)=400mh^{2} whereas the money earned by him is also depends upon the time spend by him with his family and is given by m(h)=√(1-h^{2} ). Find the time spend by him with his family so that the happiness of a person is maximum.

a) √(^{1}⁄_{3})

b) √(^{2}⁄_{3})

c) √(^{4}⁄_{3})

d) 0

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^{2}and m=√(1-h

^{2}) Let, ϑ=m

^{2}+ h

^{2}+ 1 = 0, hence By lagrange’s method,

^{∂H}⁄

_{∂m}+ α

^{∂v}⁄

_{∂m}= 0 400h

^{2}+ 2m(α) = 0 ……………………………..(1) Similarly,

^{∂H}⁄

_{∂h}+ α

^{∂h}⁄

_{∂v}=0 800mh + 2h(α) = 0…………………………………(2) Multiply by m and h in eq’1’ and eq’2’ respectively and adding them α=-600mh

^{2}Now from eq. 1 and 2 we get putting value of α, m =

^{1}⁄

_{√3}and h = √(

^{2}⁄

_{3}) . Hence, total time spend by a person with his family is √(

^{2}⁄

_{3}).

## Set 3

1. Winker gas generator, was the first commercial application of the fluidized bed for chemical operations, true or false?

a) True

b) False

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2. What is the mesh size of coal used in winker gas generator?

a) <8

b) >8

c) <16

d) >16

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3. What is the gas used for fluidizing the coal feed?

a) Steam

b) Air

c) Oxygen

d) All of the mentioned

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4. After having a hot environment in the chamber, what is released?

a) Carbon dioxide

b) Volatile matter

c) Oxygen

d) Water vapour

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5. Where is the volatile matter used as raw gas?

a) Chemical synthesis

b) Cracking

c) Pyrolysis

d) All of the mentioned

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6. Why does winker gas generator does not produce enough amount of synthetic gas?

a) Temperature is kept below 1000 Celsius

b) Temperature is kept above 1000 Celsius

c) Pressure is kept at 1 atm

d) None of the mentioned

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7. When temperature is kept below 1000 Celsius, what happens in the process?

a) Leads to insufficient cracking of methane

b) Leads to sufficient cracking of methane

c) Leads to sufficient cracking of ethane

d) Leads to insufficient cracking of ethane

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8. What is done in order to prevent insufficient cracking of methane?

a) Secondary oxygen

b) Secondary nitrogen

c) Secondary carbon dioxide

d) All of the mentioned

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9. What happens when we inject secondary oxygen for combustion?

a) Raises temperature above 1000 Celsius

b) Maintains temperature at 1000 Celsius

c) Reduces further below 1000 Celsius

d) None of the mentioned

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10. What is another problem apart from methane cracking in winker gas generator?

a) Carbon loss

b) Corrosion

c) Insufficient air supply

d) All of the mentioned

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## Set 4

1. Which kind of fluid is included to obtain smooth fluidization?

a) Water

b) Air

c) Oxygen

d) Nitrogen

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2. Air is introduced in the bed to fluidize the bed in the bubble form, true or false?

a) True

b) False

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3. Which type of distributor provides the best quality for fluidization?

a) Single orifice plate

b) Multiple orifice plate

c) Nozzle plate

d) Sintered plate

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4. In case of a heavy bed, which type of distributor can withstand its weight?

a) Flat

b) Convex

c) Concave

d) Concavo-convex

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5. Which type of distributor reduces channelling and slugging to maximum extent?

a) Single orifice plate

b) Multiple orifice plate

c) Nozzle plate

d) Sintered plate

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6. What is range of orifice diameter in the distributor in FCC?

a) 3.8-5.1 cm

b) 1.2-3.5 cm

c) 5.5-7.9 cm

d) None of the mentioned

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7. What is the range of nozzle opening in the roasting of sulphide ore?

a) 0.4-0.6 cm

b) 1.2-1.5 cm

c) 3.8-5.1 cm

d) None of the mentioned

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8. What is the approximate pressure drop across the orifice distributor?

a) 10%

b) 15%

c) 20%

d) 5%

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9. Which arrangement is fabricated in order to prevent the solids pass through the distributor?

a) Orifice

b) Nozzle

c) Sintered

d) All of the mentioned

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10. What is the fluidizing velocity range for drying of fine coal with fluidized bed?

a) 3.7-4.3 m/s

b) 4.3-4.9 m/s

c) 4.9-5.5 m/s

d) 5.5-6-1 m/s

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## Set 5

1. First commercial fluidized bed for gasification of powdered coal which was awarded patent in 1922, was developed by?

a) Fritz Winker

b) Colburn Jake

c) Dolph Jagger

d) Cameron John

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2. In below fig, how is the presence of another inlet of steam and air in the middle of the reactor useful?

a) It results in proper distribution of particles

b) Resultant temperature leads to decomposition of methane

c) It has not much effect and can be excluded

d) For increasing the speed of solids exit

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3. Based on the current technology, do you consider Winkler gas producer efficient and is still better to use?

a) Yes, it can still be used

b) Depending on the process we should decide its efficiency

c) No, because of its high consumption of oxygen

d) No, because it is big in size.

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4. Which is the best suitable equipment to be introduced in the thermofor catalytic cracking?

a) Bucket elevator

b) Gas lift

c) Bucket and Lift elevator

d) Pneumatic conveying system

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5. In below fig, which part of the process should be removed for getting better efficiency of the process?

a) Cooler for spent catalyst

b) Electrostatic precipitation

c) No need of any removal

d) Whole process needs to be modified

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6. What is the best way to prevent load on the dust collectors in the fluidized bed reactor?

a) Up flow beds

b) Down flow beds

c) Side flow beds

d) None of the mentioned

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7. Which bed shown below, can provide with remarkable temperature uniformity for highly exothermic and temperature sensitive reactions?

a) Fluidized bed reactor

b) Spouted bed

c) Teeter bed

d) Batch reactor

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8. Mention few processes where the solids circulation principle, developed for the FCC process has been used?

a) In fluid hydro-forming for re-forming naphtha vapour

b) Fluid coking for the treatment of heavy oil

c) Sand cracking for thermal cracking

d) All of the mentioned

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9. In drying processes, how important is the inclusion of fluidized bed?

a) Most efficient drying

b) Somewhat better than spouted bed and less than teeter bed

c) Drying is best all the beds

d) Least efficient drying

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10. Efficiency in fluidized bed for any process is the highest when compared with any other beds, true or false?

a) True

b) False