Instruction
- Total number of questions : 20
- Time allotted : 30:00 Minutes:Seconds.
- Each question carry 1 mark, no negative marks.
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Quantitative Aptitude [ Question No: 1 To 6 ] :
Two vessels A and B contain milk and water mixed in the ratio 5 : 2 and 8 : 5 respectively. Find the ratio in which the contents of vessels A and B should be mixed to get a new mixture containing milk and water in the ratio 9 : 4.
A library has an average of 510 visitors on Sundays and 240 on other days. The average number of visitors per day in a month of 30 days beginning with a Sunday is:
A data set can have:
If a pole 6 m high casts a shadow 2√3 m long on the ground, then the sun's angle of elevation is:
During monsoon clearance sale, Amit buys a shirt at double discount of 20% and 10%. At what price he bought the shirt if marked price was Rs. 1000?
A boat running downstream covers a distance of 20 km in 2 hours while for covering the same distance upstream, it takes 5 hours. What is the speed of the boat in still water?
Reasoning [ Question No: 7 To 11 ] :
Direction for [ Question No: 7 To 7 ] :
Study the following information carefully and answer the questions given below:
A, B, C, D, E, F, G, Hand K are sitting around a circle facing the centre. F is fourth to the right of A, who is third to the right of B. K is fourth to the left of B and third to the right of D. C is third to the right of H. E is second to the left of G.
Who is fourth to the left of G?
Direction for [ Question No: 8 To 8 ] :
A team of five is to be selected from amongst five boys A, B, C, D and E and four girls P, Q, R and S. Some criteria for selecation are :
A and S have to be together.
P cannot be put with R.
D and Q cannot be together.
C and E have to be together.
R cannot be put with B.
Unless otherwise stated, these criteria are applicable to all the question below :
If two of the members are girls and D is one of the members, the members of the team other than D are :
Direction for [ Question No: 9 To 9 ] :
Four youngmen Raj, Prem, Ved and Ashok are friendly with four girls Sushma, Kushum, Vimla and Poonam.
Sushma and Vimla are friends.
Ved's girl friend does not like Sushma and Vimla.
Kusum does not care for Ved.
Prem's girl friend is friendly with Sushma. Sushma does not like Raj.
Who is Raj's girl friend ?
Which one of the following is odd pair of the words ?
The letters L, M, N, O, P, Q, R, S, and T in their order are substituted by nine integers 1 to 9 but not in that order. 4 is assigned to P. The difference between P and T is 5. The difference between N and T is 3. What is the integer assigned to N?
General Awareness / General Knowledge (GK) [ Question No: 12 To 15 ] :
Lines drawn on a map joining places of equal atmospheric pressure are called
The Number of members included in the Constitution Drafting Committee was:
Engineering Mathematics [ Question No: 16 To 16 ] :
For any real symmetric matrix \(A\), the transpose of \(A\) is ____ .
Fluid Mechanics [ Question No: 17 To 17 ] :
If the stream function (\(\psi(x, y)\)) for a two-dimensional incompressible flow field is given as \(2y(x^{2} - y^{2})\), the corresponding velocity field is
Machine Tool Design [ Question No: 18 To 18 ] :
Angle plate is made of
Manufacturing Technology [ Question No: 19 To 19 ] :
Match the additive manufacturing technique in Column I with its corresponding input material in Column II.
| Additive manufacturing technique (Column I) | Input material (Column II) | ||
|---|---|---|---|
| P | Fused deposition modelling | 1 | Photo sensitive liquid resin |
| Q | Laminated object manufacturing | 2 | Heat fusible powder |
| R | Selective laser sintering | 3 | Filament of polymer |
| 4 | Sheet of thermoplastic or green compacted metal sheet | ||
Thermodynamics [ Question No: 20 To 20 ] :
Direction for [ Question No: 20 To 20 ] :
Notation used:
P : pressure, V : volume, T : temperature, s : specific entropy, h : specific enthalpy, Cp : molar heat capacity at constant pressure, Cv : molar heat capacity at constant volume, R : universal gas constant
In an ideal Rankine cycle, steam enters the turbine at 10 MPa and 500 °C (h = 3375.1 kJ/kg, s = 6.5995 kJ/kg.K). It is cooled in the condenser at a pressure of 10 kPa. At 10 kPa, hf = 191.81 kJ/kg, sf = 0.6492 kJ/kg.K, hg = 2583.9 kJ/kg and sg = 8.1488 kJ/kg.K. The heat rejected in the condenser (in kJ/kg) is
Total number of questions : 20
Number of answered questions : 0
Number of unanswered questions : 20
Quantitative Aptitude [ Question No: 1 To 6 ] :
Two vessels A and B contain milk and water mixed in the ratio 5 : 2 and 8 : 5 respectively. Find the ratio in which the contents of vessels A and B should be mixed to get a new mixture containing milk and water in the ratio 9 : 4.
Your Answer : (Not Answered)
Correct Answer : D
The vessels should be mixed in the ratio 7 : 2.
Work with the fraction of milk in each. Vessel A has \(\frac{5}{7}\), vessel B \(\frac{8}{13}\), and the mixture must have \(\frac{9}{13}\). By the rule of alligation:
\[ \begin{aligned} A : B &= \left(\tfrac{9}{13} - \tfrac{8}{13}\right) : \left(\tfrac{5}{7} - \tfrac{9}{13}\right) \\ &= \tfrac{1}{13} : \tfrac{2}{91} \\ &= 7 : 2 \end{aligned} \]
Check: 7 litres of A give 5 of milk, 2 litres of B give \(\frac{16}{13}\), so milk is \(\frac{81}{13}\) of 9 litres, which is \(\frac{9}{13}\).
A library has an average of 510 visitors on Sundays and 240 on other days. The average number of visitors per day in a month of 30 days beginning with a Sunday is:
Your Answer : (Not Answered)
Correct Answer : D
If a month of 30 days begins with a Sunday, it will have 5 Sundays and 25 other days.
Total visitors on Sundays = 5 × 510 = 2550.
Total visitors on other days = 25 × 240 = 6000.
Total visitors in the month = 2550 + 6000 = 8550.
Average visitors per day = \(\frac{8550}{30} = 285\).
A data set can have:
Your Answer : (Not Answered)
Correct Answer : D
A data set's mode has the following properties:
- Unimodal: Has one mode (e.g., {1, 2, 2, 3}).
- Bimodal/Multimodal: Has two or more modes (e.g., {1, 1, 2, 3, 3}).
- No mode: If all values appear with the same frequency (e.g., {1, 2, 3, 4}).
Therefore, all of the above statements are possible.
If a pole 6 m high casts a shadow 2√3 m long on the ground, then the sun's angle of elevation is:
Your Answer : (Not Answered)
Correct Answer : C
Let the angle of elevation be θ.
\(\tan \theta = \frac{\text{Height of pole}}{\text{Length of shadow}} = \frac{6}{2\sqrt{3}}\).
\(\tan \theta = \frac{3}{\sqrt{3}} = \sqrt{3}\).
The angle whose tangent is √3 is 60°.
During monsoon clearance sale, Amit buys a shirt at double discount of 20% and 10%. At what price he bought the shirt if marked price was Rs. 1000?
Your Answer : (Not Answered)
Correct Answer : A
A "double discount" applies the second rate to the already-reduced price.
\[ 1000 \times (1 - 0.20) = \text{Rs. } 800 \]
\[ 800 \times (1 - 0.10) = \text{Rs. } 720 \]
The single equivalent discount is
\[ 1 - 0.80 \times 0.90 = 0.28 = 28\% \]
not 30%, so he pays Rs. 720 rather than Rs. 700. Rs. 800 is the price after the first discount only.
A boat running downstream covers a distance of 20 km in 2 hours while for covering the same distance upstream, it takes 5 hours. What is the speed of the boat in still water?
Your Answer : (Not Answered)
Correct Answer : B
Write \( b \) for the boat's speed in still water and \( r \) for the stream's. Then
\[ \text{downstream} = b + r, \qquad \text{upstream} = b - r \]
\[ b + r = \frac{20}{2} = 10 \text{ km/h}, \qquad b - r = \frac{20}{5} = 4 \text{ km/h} \]
\[ b = \frac{10 + 4}{2} = 7 \text{ km/h} \]
The data are entirely sufficient, so "data inadequate" is a trap: two journey times over a known distance always determine both speeds.
Reasoning [ Question No: 7 To 11 ] :
Direction for [ Question No: 7 To 7 ] :
Study the following information carefully and answer the questions given below:
A, B, C, D, E, F, G, Hand K are sitting around a circle facing the centre. F is fourth to the right of A, who is third to the right of B. K is fourth to the left of B and third to the right of D. C is third to the right of H. E is second to the left of G.
Who is fourth to the left of G?
Your Answer : (Not Answered)
Correct Answer : A
Correct answer: C
Facing the centre, each person’s left is the next seat clockwise and their right the next seat anticlockwise. Fix B; A sits three to B’s right, F four beyond A, K four to B’s left and D three to K’s left. Of the four seats left, C three to H’s right fits in only one way, and E two to G’s left then fills the last two. Clockwise the circle reads B → G → F → E → K → C → A → D → H.
Counting four seats to G’s left - clockwise - gives F, E, K and then C. The arrangement is fully determined, so the data are not inadequate.
Direction for [ Question No: 8 To 8 ] :
A team of five is to be selected from amongst five boys A, B, C, D and E and four girls P, Q, R and S. Some criteria for selecation are :
A and S have to be together.
P cannot be put with R.
D and Q cannot be together.
C and E have to be together.
R cannot be put with B.
Unless otherwise stated, these criteria are applicable to all the question below :
If two of the members are girls and D is one of the members, the members of the team other than D are :
Your Answer : (Not Answered)
Correct Answer : C
Correct answer: P S A B
D is in and two members are girls, so the team is three boys and two girls. D bars Q, which eliminates the two options containing her. Of the remaining pair, P S C E puts S in the team without A, breaking the rule that they must be together. P S A B works: A is with S, P is not with R since R is absent, and neither the C-E pair nor the R-B restriction is engaged.
Direction for [ Question No: 9 To 9 ] :
Four youngmen Raj, Prem, Ved and Ashok are friendly with four girls Sushma, Kushum, Vimla and Poonam.
Sushma and Vimla are friends.
Ved's girl friend does not like Sushma and Vimla.
Kusum does not care for Ved.
Prem's girl friend is friendly with Sushma. Sushma does not like Raj.
Who is Raj's girl friend ?
Your Answer : (Not Answered)
Correct Answer : B
Sushma and Vimla are friends and Prem's girl friend is friendly with Sushma. This means that Prem's girl friend is Vimla.
Ved's girl friend does not like Sushma and Vimal. So, she is either Kusum or Poonam. But Kusum does not care for Ved. So, Ved's girl friend is Poonam.
Sushma does not like Raj. So, Raj's girl friend is Kusum.
Clearly, Ashok's girl friend is Sushma.
So, Raj's girl friend is Kusum.
Which one of the following is odd pair of the words ?
Your Answer : (Not Answered)
Correct Answer : D
The odd pair is Dengue : Fever.
In the other three pairs, the second word is the organ that the disease mainly affects: jaundice is a sign of liver disorder, rickets affects the bones, and tuberculosis most commonly attacks the lungs.
In Dengue : Fever, the second word is a symptom (dengue is itself called a fever), not an organ, so the relation is different.
The letters L, M, N, O, P, Q, R, S, and T in their order are substituted by nine integers 1 to 9 but not in that order. 4 is assigned to P. The difference between P and T is 5. The difference between N and T is 3. What is the integer assigned to N?
Your Answer : (Not Answered)
Correct Answer : C
The integer assigned to N is 6.
P is 4. T differs from P by 5, so T is 9 or −1; only 9 lies between 1 and 9, so T = 9.
N differs from T by 3, so N is 6 or 12. Only 6 is in range, so N = 6.
4 is already taken by P, so it cannot also belong to N. 5 and 7 differ from T = 9 by 4 and 2, not 3.
General Awareness / General Knowledge (GK) [ Question No: 12 To 15 ] :
Your Answer : (Not Answered)
Correct Answer : B
Michael Phelps won eight gold medals at the 2008 Beijing Olympics, the most at any single Games.
He beat Mark Spitz's seven from 1972, and set world records in seven of the eight events.
Your Answer : (Not Answered)
Correct Answer : B
The religious text of the Jews is the Torah.
It is the first five books of the Hebrew Bible - Genesis, Exodus, Leviticus, Numbers and Deuteronomy - and is read from a hand-written scroll in the synagogue. The Analects are Confucian, the Tripitaka Buddhist and the Zend Avesta Zoroastrian.
Lines drawn on a map joining places of equal atmospheric pressure are called
Your Answer : (Not Answered)
Correct Answer : B
Correct answer: Isobars
Isobars join points of equal pressure, and they are what gives a weather chart its familiar look. Their spacing carries the important information: closely packed isobars mean a steep pressure gradient and therefore strong winds, while widely spaced ones mean light winds. Closed rings mark centres of high or low pressure, and in the northern hemisphere air spirals anticlockwise into a low and clockwise out of a high. The prefix iso-, from the Greek for equal, generates a whole family of such lines. Isotherms join places of equal temperature, isohyets places of equal rainfall, and contours places of equal height above sea level.
The Number of members included in the Constitution Drafting Committee was:
Your Answer : (Not Answered)
Correct Answer : A
The Drafting Committee had seven members, with Dr B.R. Ambedkar as chairman.
The others were Alladi Krishnaswami Ayyar, N. Gopalaswami Ayyangar, K.M. Munshi, Mohammad Saadulla, N. Madhava Rau and T.T. Krishnamachari. It was appointed on 29 August 1947.
Engineering Mathematics [ Question No: 16 To 16 ] :
For any real symmetric matrix \(A\), the transpose of \(A\) is ____ .
Your Answer : (Not Answered)
Correct Answer : D
The transpose of a symmetric matrix is \(A\) itself.
A matrix is symmetric precisely when \(a_{ij} = a_{ji}\) for all i and j, which is the statement \(A^{T} = A\). Transposing swaps rows and columns, and for a symmetric matrix that swap changes nothing.
\(A^{T} = -A\) defines a skew-symmetric matrix, not a symmetric one. \(A^{T} = A^{-1}\) defines an orthogonal matrix, and a symmetric matrix need not be invertible at all. The transpose of A is the null matrix only when A itself is the null matrix.
Fluid Mechanics [ Question No: 17 To 17 ] :
If the stream function (\(\psi(x, y)\)) for a two-dimensional incompressible flow field is given as \(2y(x^{2} - y^{2})\), the corresponding velocity field is
Your Answer : (Not Answered)
Correct Answer : B
The velocity field is \(\vec{V} = 2(x^{2} - 3y^{2})\hat{i} - 4xy\,\hat{j}\).
With \(\psi = 2x^{2}y - 2y^{3}\) and the usual convention \(u = \partial\psi/\partial y\), \(v = -\partial\psi/\partial x\):
\[ \begin{aligned} u &= 2x^{2} - 6y^{2} = 2(x^{2} - 3y^{2}) \\ v &= -4xy \end{aligned} \]
Check: \(\partial u/\partial x + \partial v/\partial y = 4x - 4x = 0\), so the flow is incompressible, as it must be. The option with \(+4xy\) has the wrong sign on v and fails this continuity check. The two options with \(2x^{2}y\) for u are just the stream function's first term, not its derivative.
Machine Tool Design [ Question No: 18 To 18 ] :
Angle plate is made of
Your Answer : (Not Answered)
Correct Answer : B
The key answer is spheroidal cast iron.
Angle plates are made as castings in cast iron, then accurately machined so that their two working faces are flat and at exactly 90° to each other. Cast iron is chosen because it is stable once stress-relieved, machines to a fine flat finish and damps vibration well. The spheroidal graphite (SG) form named in the key adds toughness, so the plate resists cracking if knocked.
High speed steel and tool steel are cutting-tool materials, far too costly for a bulky work-holding plate. Cast steel is not the usual choice because it lacks cast iron's vibration damping and dimensional stability.
Manufacturing Technology [ Question No: 19 To 19 ] :
Match the additive manufacturing technique in Column I with its corresponding input material in Column II.
| Additive manufacturing technique (Column I) | Input material (Column II) | ||
|---|---|---|---|
| P | Fused deposition modelling | 1 | Photo sensitive liquid resin |
| Q | Laminated object manufacturing | 2 | Heat fusible powder |
| R | Selective laser sintering | 3 | Filament of polymer |
| 4 | Sheet of thermoplastic or green compacted metal sheet | ||
Your Answer : (Not Answered)
Correct Answer : A
The match is P-3, Q-4, R-2.
- Fused deposition modelling melts a filament of polymer (such as ABS or PLA) in a heated nozzle and lays it down bead by bead (3).
- Laminated object manufacturing cuts and bonds sheets, paper, thermoplastic or green compacted metal sheet, one layer at a time (4).
- Selective laser sintering uses a laser to fuse a bed of heat fusible powder, layer by layer (2).
The unused material, photo sensitive liquid resin (1), belongs to stereolithography, which cures resin with ultraviolet light; it is not the input for any of the three techniques listed, so every option using 1 is wrong. 'P-4, Q-1, R-4' also uses item 4 twice.
Thermodynamics [ Question No: 20 To 20 ] :
Direction for [ Question No: 20 To 20 ] :
Notation used:
P : pressure, V : volume, T : temperature, s : specific entropy, h : specific enthalpy, Cp : molar heat capacity at constant pressure, Cv : molar heat capacity at constant volume, R : universal gas constant
In an ideal Rankine cycle, steam enters the turbine at 10 MPa and 500 °C (h = 3375.1 kJ/kg, s = 6.5995 kJ/kg.K). It is cooled in the condenser at a pressure of 10 kPa. At 10 kPa, hf = 191.81 kJ/kg, sf = 0.6492 kJ/kg.K, hg = 2583.9 kJ/kg and sg = 8.1488 kJ/kg.K. The heat rejected in the condenser (in kJ/kg) is
Your Answer : (Not Answered)
Correct Answer : A
The heat rejected is 1898 kJ/kg.
Expansion in the ideal turbine is isentropic, so the exit entropy is 6.5995 kJ/kg.K. At 10 kPa the dryness fraction and enthalpy are
\[ \begin{aligned} x &= \frac{6.5995 - 0.6492}{8.1488 - 0.6492} = 0.7934 \\ h_{2} &= 191.81 + 0.7934(2583.9 - 191.81) \\ &= 2089.7\ \text{kJ/kg} \end{aligned} \]
The condenser turns this wet steam into saturated liquid at \(h_{f}\), so it rejects \(h_{2} - h_{f} = 2089.7 - 191.8 = 1897.9 \approx 1898\) kJ/kg.
3796 is twice this value, 949 half of it and 2847 one and a half times it; none matches the isentropic exit state.
Marks
Total number of questions : 20
Number of answered questions : 0
Number of unanswered questions : 20