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# 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

Answer: d [Reason:] The Tower of Hanoi involves moving of disks ‘stacked’ at one peg to another peg with respect to the size constraint, it is conveniently done using stacks, although it is also possible using priority queues. Since stack approach is widely used, the more suitable option would be ‘d’ stack.

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

Answer: a [Reason:] First transfer all the diska to the auxiliary and then to the end peg, this is achieved by making auxiliary peg as the end peg in the first recursive call, in the second recursive call, the auxiliary becomes the start peg from where the disks are transferred to the end peg.

3. Which among the following is not a palindrome?
c) Malayalam

Answer: d [Reason:] By definition, a palindrome is a string which is the same forward and backward, here, option d doesn’t adhere to this definition.

4. Which data structure can be used to test a palindrome?
a) Tree
b) Heap
c) Stack
d) Priority queue

Answer: c [Reason:] Stack is a convenient option as it involves pushing and popping of characters.

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

Answer: a [Reason:] Push all the characters in the input string to a stack, now pop them and append to a new string which is checked for equality with the original string.

6. What is the number of moves required in the Tower of Hanoi problem for k disks?
a) 2k – 1
b) 2k + 1
c) 2k + 1
d) 2k – 1

Answer: d [Reason:] Tracing of the moves in the above ToH problem will prove this result, instead you can simply add a count for each recursive call to check the number of moves.

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;
}```

Answer: b [Reason:] Although, it is possible to reverse the string without using stack, it is done by looping through the string from the end character by character. In Java, it is also possible to use the StringBuilder and StringBuffer classes which have a built-in method ‘reverse’. Note its similarity to PalindromeTest.

## 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)

Answer: b [Reason:] f(x,y,z) = Sin(x)Sin(y)Sin(z)-Cos(x) Cos(y) Cos(z) Since the function has 3 independent variables hence during differentiation we have to consider x and z as constant and differentiate it w.r.t. y, f’(x,y,z) = Sin(x)Cos(y)Sin(z) + Cos(x)Sin(y)Cos(z).

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

Answer: a [Reason:] Statement of euler theorem is “if z is an homogeneous function of x and y of order `n` then x ∂z∂x + y ∂z∂y = nz ”.

3. If z = xn f(yx) 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

Answer: c [Reason:] Since the given function is homogeneous of order n , hence by euler’s theorem x ∂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

Answer: a [Reason:] Answer `a` is correct as statement of euler’s theorem is “if z is an homogeneous function of x and y of order `n` then x ∂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+yy , x ∂z∂x + y ∂z∂y = ?
a) 0
b) 1
c) 2
d) 3

6. Does function can be solved by euler’ s theorem
a) True
b) False

Answer: b [Reason:] No this function cannot be written in form of xn f(yx) 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

Answer: a [Reason:] Since the function can be written as,

8. If u = xx + yy + zz , find dudx + dudy + dudz at x = y = z = 1
a) 1
b) 0
c) 2u
d) u

Answer: d [Reason:] dudx = xx (1+log⁡(x) ) dudy = yy (1+log⁡(x)) dudz = zz (1+log⁡(x)) At x = y = z = 1, dudx + dudy + dudz = u.

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

Answer: a [Reason:] Since f satisfies euler’s theorem,

11. Find the approximate value of [0.982 + 2.012 + 1.942 ](12)
a) 1.96
b) 2.96
c) 0.04
d)-0.04

Answer: b [Reason:] Let f(x,y,z) = (x2 + y2 + z2 )(12) ……………..(1) Hence, x = 1, y = 2, z = 2 so that, dx = -0.02, dy = 0.01, dz = -0.06 From (1), ∂f∂x = xf ∂f∂y = yf ∂f∂z = zf

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)=400mh2 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-h2 ). Find the time spend by him with his family so that the happiness of a person is maximum.
a) √(13)
b) √(23)
c) √(43)
d) 0

Answer: b [Reason:] Given,H=400mh2 and m=√(1-h2 ) Let, ϑ=m2 + h2 + 1 = 0, hence By lagrange’s method, ∂H∂m + α∂v∂m = 0 400h2 + 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=-600mh2 Now from eq. 1 and 2 we get putting value of α, m = 1√3 and h = √(23) . Hence, total time spend by a person with his family is √(23).

## 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

Answer: a [Reason:] It was first developed as an idea which was later fabricated for industrial purpose.

2. What is the mesh size of coal used in winker gas generator?
a) <8
b) >8
c) <16
d) >16

Answer: a [Reason:] Since it provides better fluidization than the other ranges.

3. What is the gas used for fluidizing the coal feed?
a) Steam
b) Air
c) Oxygen
d) All of the mentioned

Answer: d [Reason:] The mixture of Steam-air-oxygen is utilized for generating the required conditions.

4. After having a hot environment in the chamber, what is released?
a) Carbon dioxide
b) Volatile matter
c) Oxygen
d) Water vapour

Answer: b [Reason:] Materials with low boiling point get evaporated in the furnace.

5. Where is the volatile matter used as raw gas?
a) Chemical synthesis
b) Cracking
c) Pyrolysis
d) All of the mentioned

Answer: a [Reason:] Used to produce ammonia and methyl alcohol.

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

Answer: a [Reason:] To prevent sintering of ash.

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

Answer: a [Reason:] Oxygen is not sufficient for cracking hence reducing 5 to 7 vol%.

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

Answer: a [Reason:] Secondary oxygen is injected just above the bed, causing combustion.

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

Answer: a [Reason:] Increasing the temperature will help in cracking methane.

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

Answer: a [Reason:] 20 to 30% of carbon is being lost by entrainment.

## Set 4

1. Which kind of fluid is included to obtain smooth fluidization?
a) Water
b) Air
c) Oxygen
d) Nitrogen

Answer: a [Reason:] Since water doesnt bubble, it simply fills up the bed with causing any disturbance in the bed.

2. Air is introduced in the bed to fluidize the bed in the bubble form, true or false?
a) True
b) False

Answer: a [Reason:] Air forms bubbles while passing through the bed.

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

Answer: d [Reason:] More the number of holes better is the distribution of air or fluid in the bed.

4. In case of a heavy bed, which type of distributor can withstand its weight?
a) Flat
b) Convex
c) Concave
d) Concavo-convex

Answer: c [Reason:] Weight is distributed among the plate without getting concentrated on any portion of distributor.

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

Answer: d [Reason:] More the number of holes better is the distribution of air or fluid in the bed, hence less channelling and slugging.

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

Answer: a [Reason:] In order to lop pressure drop and best efficiency, this range is selected.

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

Answer: a [Reason:] Nozzles generally have very small diameter holes in order to provide high velocity gas.

8. What is the approximate pressure drop across the orifice distributor?
a) 10%
b) 15%
c) 20%
d) 5%

Answer: a [Reason:] From the experimental studies, it was found that pressure drop was 10% across the distributor.

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

Answer: b [Reason:] Nozzle is a cap like structure which prevents the passage of solids through the distributor.

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

Answer: a [Reason:] Based on the pilot plant study, the velocity was decided.

## 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

Answer: a [Reason:] Fritz winker developed it.

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

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.

Answer: c [Reason:] Due to its inefficient design, it leads to high oxygen consumption and large carbon loss by entrainment.

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

Answer: d [Reason:] It provides smooth circulation of the reactants.

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

Answer: c [Reason:] All the elements are present in the process, no need to remove any part of it.

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

Answer: b [Reason:] Prevent the dust to reach the dust collectors by flowing them downwards.

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

Answer: a [Reason:] In fluidized bed, the air passing through the distributor, distributes the air throughout the reactor which indeed helps in uniform distribution of temperature.

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

Answer: d [Reason:] All the above processes use solid circulation principle.

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