Past Questions — 2010

To determine which alloy does not contain copper, let's analyze the composition of each option: 1. **Delta metal**: This is a high-strength alloy primarily composed of Copper (Cu), Silver (Ag), and Gold (Au). It contains copper. 2. **Monel metal**: This is a group of nickel-copper alloys. The most common form is approximately 67% Nickel (Ni) and 30% Copper (Cu). It contains copper. 3. **Nichrome**: This is an alloy consisting primarily of Nickel (Ni) and Chromium (Cr), often with small amounts of iron. It is widely used in heating elements due to its high electrical resistance and oxidation resistance. It does NOT contain copper. 4. **Silicon bronze**: As the name suggests, it is a type of bronze. Bronze is an alloy of Copper (Cu) and Tin (Sn), and silicon bronze specifically adds silicon to improve corrosion resistance and strength. It contains copper. Therefore, Nichrome is the only alloy among the choices that does not have copper as a constituent.

1. Definition: A point of contra-flexure (or point of inflection) is a point in a structural element where the bending moment changes sign (from positive to negative or vice versa). At this point, the curvature of the beam changes, and the bending moment is zero. 2. Analysis of Options: - Cantilever Beams: In a standard cantilever beam loaded from the free end, the bending moment is typically negative (hogging) throughout the entire length. Since the sign does not change, there is no point of contra-flexure. - Simply Supported Beams: For a simply supported beam with downward loads, the bending moment is typically positive (sagging) throughout the span. Since the sign does not change, there is no point of contra-flexure. - Overhanging Beams: An overhanging beam is a beam that extends beyond its supports. In such beams, the portion between the supports typically experiences sagging (positive moment), while the overhanging portion experiences hogging (negative moment). Therefore, there must be a point between the support and the span where the bending moment is zero and changes sign. This is the point of contra-flexure. 3. Conclusion: Among the given options, only overhanging beams (and fixed beams or continuous beams, which are not listed) can exhibit a point of contra-flexure.

In arc welding (specifically Shielded Metal Arc Welding - SMAW), the electrode consists of a metal core wire coated with a chemical material known as 'flux'. 1. Why 'flux' is correct: The flux coating serves several critical purposes: it melts to create a gaseous shield (protecting the molten weld pool from atmospheric contamination like oxygen and nitrogen), it stabilizes the electric arc, and it forms a layer of slag on top of the weld to slow the cooling rate and prevent oxidation. 2. Why other options are incorrect: - 'Protective layer' is a general term, but the specific technical name for the coating material in welding is flux. - 'Binder' is a component within the flux coating that holds the flux chemicals to the core wire, but it is not the name of the coating itself. - 'Slag' is the byproduct (the solidified waste) that forms after the flux has reacted and cooled; it is the result of the coating, not the coating material itself.

Creep in a belt drive is the relative motion between the belt and the pulley surface. It occurs because the belt is subjected to different tensions at the tight side and the slack side of the drive. As the belt moves from the tight side to the slack side, it undergoes a slight contraction; conversely, as it moves from the slack side to the tight side, it undergoes a slight extension. This continuous cycle of extension and contraction causes the belt to 'slip' slightly relative to the pulley, even if there is no gross slippage. - Option (a) and (b) are incorrect because while the material properties (elasticity) allow creep to happen, the 'cause' of the motion is the tension differential, not the material itself. - Option (c) is incorrect because simple expansion (like thermal expansion) does not describe the cyclic process of creep during operation.

In thick cylinder hoop stress varies hyperbolically through thickness, longitudinal stress remains uniform.

In structural engineering, members are classified based on the type of internal forces they are primarily designed to resist: 1. **Column**: A vertical structural member designed to support an axial compressive load. While 'strut' also carries compression, a column is the general term for a primary structural member subjected to axial compression. 2. **Beam**: A structural member primarily subjected to transverse loads, which causes bending and shear stresses, rather than axial compression. 3. **Strut**: A strut is also a member subjected to axial compression, but it is typically a shorter, secondary member used in bracing or trusses. In the context of general structural members subjected to axial compressive forces, 'column' is the standard technical term. Therefore, a structural member subjected to an axial compressive force is most accurately defined as a column.

A blast furnace is used for the smelting of iron ore to produce iron. In this process, iron oxides (ore) are reduced by carbon monoxide (derived from coke) at very high temperatures. The resulting molten metal is saturated with carbon (typically 3.5% to 4.5%) and other impurities like silicon and phosphorus. This crude, high-carbon iron is called 'pig iron' because it is cast into molds (called pigs and sows) as it cools. Why other options are incorrect: - Cast iron (a): While pig iron is a type of cast iron, 'cast iron' usually refers to pig iron that has been remelted and refined for specific casting purposes. - Wrought iron (c): This is the purest form of iron (very low carbon), produced by removing carbon from pig iron through processes like puddling. - White iron (d): This is a specific type of cast iron where all carbon is present as cementite, usually achieved through rapid cooling or specific alloying, not as the primary direct output of a blast furnace.

Young's Modulus (E) is a measure of the stiffness of a solid material. It is defined as the ratio of tensile or compressive stress to the corresponding longitudinal strain. 1. Formula: E = Stress / Strain 2. Stress is defined as Force per unit Area. Its SI unit is Pascal (Pa), which is equivalent to Newton per square meter (N/m²) or Newton per square millimeter (N/mm²). 3. Strain is the ratio of change in length to original length (ΔL/L), making it a dimensionless quantity (it has no units). 4. Therefore, the unit of Young's Modulus is the same as the unit of stress. Evaluating the options: - (a) Newton: This is the unit of Force, not modulus. - (b) Newton/mm²: This is a standard unit of pressure/stress (1 N/mm² = 1 MPa), which is the correct unit for Young's Modulus. - (c) Newton/cm²: While technically a unit of stress, in the context of engineering and technical exams for Strength of Materials, N/mm² (MPa) is the standard convention used for material properties. - (d) Newton-cm²: This is a product of force and area, which does not represent stress or modulus.

A Gantt chart is a type of bar chart that illustrates a project schedule. In Industrial Engineering and Project Management, it is primarily used to plan and track the progress of tasks over time. 1. Why 'production schedule' is correct: A Gantt chart maps out the start and finish dates of various elements of a project or production process. It allows managers to see which tasks are happening simultaneously, the duration of each task, and the overall timeline for production, making it a fundamental tool for production scheduling. 2. Why 'determining selling price' is incorrect: Selling price is determined by cost analysis, market research, and profit margin calculations, not by a scheduling tool. 3. Why 'material handling layout' is incorrect: Material handling layouts are represented by flowcharts, string diagrams, or plant layout drawings (CAD), which focus on spatial arrangement and movement rather than time-based scheduling.

CPM (Critical Path Method) and PERT (Program Evaluation and Review Technique) are the two primary network analysis techniques used in project management. 1. CPM (Critical Path Method) is an 'activity-oriented' technique. In CPM, the focus is on the activity itself (the work being performed), and the arrows in the network diagram represent the activities. It is typically used for deterministic projects where activity durations are known with certainty (e.g., construction projects). 2. PERT (Program Evaluation and Review Technique) is an 'event-oriented' technique. In PERT, the focus is on milestones or events (the start or completion of an activity), and the nodes represent these events. It is typically used for probabilistic projects where durations are uncertain (e.g., R&D projects). Therefore, option (c) is correct. Option (b) describes PERT, and options (a) and (d) are not standard classifications for these network techniques.

Step-by-step reasoning: 1. Elasticity refers to the ability of a material to return to its original shape after the removal of an applied load. 2. For most metals and ceramics, the relationship between stress and strain is linear (follows Hooke's Law) within the elastic limit. 3. Rubber is an elastomer. Elastomers consist of long-chain polymers that are cross-linked. When stretched, these chains uncoil, allowing for very large deformations. 4. The stress-strain curve for rubber is characterized by a non-linear relationship; it does not follow a straight line (Hooke's Law) even though the deformation is reversible (elastic). 5. Therefore, while rubber is elastic, its stress-strain behavior is non-linear. Option (a) is incorrect because rubber does not follow a linear relationship. Option (c) is incorrect because plastic behavior refers to permanent deformation, whereas rubber is primarily known for its elasticity.

The Moment of Inertia (I) of an area about any axis is governed by the Parallel Axis Theorem, which is expressed as: I = I_centroid + Ad², where 'I_centroid' is the moment of inertia about the axis passing through the centroid (central axis), 'A' is the area, and 'd' is the perpendicular distance between the centroidal axis and the parallel axis in question. Since A and d² are always non-negative, the value of I is minimized when d = 0. This occurs when the axis of rotation is the centroidal axis (central axis). Therefore, the moment of inertia is always least with respect to the central axis compared to any other parallel axis (such as the bottom-most axis or other horizontal/vertical axes not passing through the centroid).

Grey cast iron is characterized by the presence of graphite in the form of thin, interconnected flakes. This occurs during the slow cooling of the molten metal, allowing carbon to precipitate out of the austenite as graphite rather than forming a chemical compound. These graphite flakes act as internal stress raisers, which gives grey cast iron its characteristic brittle nature but also provides excellent vibration damping and machinability. Analysis of other options: - a. Cementite (Fe3C) is a hard, brittle intermetallic compound found in white cast iron or steel; in grey cast iron, the carbon has mostly decomposed from cementite into graphite. - b. 'Free carbon' is a general term for graphite, but 'flakes' is the specific morphological form that defines 'Grey' cast iron. - d. Spheroids (or nodules) are the form carbon takes in Ductile (Nodular) cast iron, achieved by adding elements like magnesium or cerium to the melt.

The methods mentioned in the question are all techniques used to solve optimization problems within the field of Linear Programming (LP): 1. **Graphical Method**: Used to solve linear programming problems with only two decision variables by plotting constraints on a graph to find the feasible region and the optimal vertex. 2. **Simplex Method**: An iterative algebraic procedure used to solve linear programming problems with any number of variables and constraints. It moves from one basic feasible solution (vertex) to another to optimize the objective function. 3. **Transportation Method**: A specialized form of linear programming used to minimize the cost of distributing a product from several sources to several destinations. Common algorithms include the North-West Corner Rule, Vogel's Approximation Method, and the MODI method. Why other options are incorrect: - **Break-even analysis (a)**: Focuses on finding the point where total cost equals total revenue; it does not use simplex or transportation methods. - **Value analysis (b)**: A systematic method to improve the 'value' of a product by examining its functions; it is a qualitative and cost-reduction tool, not a mathematical optimization method. - **Queueing theory (d)**: The mathematical study of waiting lines (queues), involving stochastic processes and probability distributions, rather than linear optimization constraints.

In machine design, for a bolt and nut to assemble and function as a threaded fastener, they must have matching thread profiles. This means they must share three critical characteristics: 1) The same nominal diameter, 2) The same pitch (the distance between adjacent thread crests), and 3) The same direction of twist (handedness). - Right-hand (RH) threads are the standard; they tighten when turned clockwise. - Left-hand (LH) threads are used in specific applications (e.g., on rotating shafts to prevent loosening) and tighten when turned counter-clockwise. If a bolt has left-hand threads, a right-hand nut will not fit because the helical paths are mirrored. Therefore, the nut must also have left-hand threads with the exact same pitch to ensure the threads mesh correctly. Thus, option (b) is the only correct choice.

In a thin cylindrical shell subjected to internal pressure (P), two primary types of stresses are developed: 1. Hoop Stress (Circumferential Stress), given by σ_h = Pd / 2t 2. Longitudinal Stress (Axial Stress), given by σ_l = Pd / 4t Comparing the two formulas, it is evident that the hoop stress is exactly twice the magnitude of the longitudinal stress (σ_h = 2 * σ_l). Because the hoop stress is the maximum principal stress and the limiting factor that would cause the cylinder to fail (typically by splitting along its length), the design and thickness of thin cylindrical shells are governed by the hoop stress. - Option (b) is incorrect because longitudinal stress is only half of the hoop stress and thus not the governing factor. - Option (c) is incorrect as volumetric stress is not a standard term used for the primary design criteria of thin-walled pressure vessels.

Magnetic tape is a sequential access storage medium, meaning that to reach a specific piece of data, the tape must be wound forward or backward to that point. This makes it inefficient for 'original' or 'active' data that requires frequent, random access (which is why hard drives or SSDs are used instead). However, magnetic tapes have several key advantages: 1) High Capacity: They can store massive volumes of data (terabytes) more cheaply than other media. 2) Durability: They are excellent for long-term archiving. 3) Cost-effectiveness: The cost per gigabyte is very low for high-volume storage. Therefore, they are ideal for 'backup' purposes (where data is written sequentially and rarely accessed unless a disaster occurs) and for 'high volume data' (where the sheer scale of information makes other media too expensive). Options (a) is incorrect because tapes are overkill for low volume data; options (c) and (d) are incorrect because tapes are unsuitable for original/active data due to slow sequential access speeds.

To simplify the Boolean expression (X + Y + XY)(X + Z), we follow these logical steps: 1. **Simplify the first term (X + Y + XY):** Using the Absorption Law, we know that Y + XY = Y. Therefore, (X + Y + XY) simplifies to (X + Y). 2. **Substitute the simplified term back into the expression:** The expression now becomes (X + Y)(X + Z). 3. **Apply the Distributive Law (FOIL method):** (X + Y)(X + Z) = X·X + X·Z + Y·X + Y·Z 4. **Apply Boolean Identities:** - Idempotent Law: X · X = X - The expression is now: X + XZ + XY + YZ 5. **Further simplify using the Absorption Law:** - X + XZ = X(1 + Z) = X - Now we have: X + XY + YZ - Again, X + XY = X(1 + Y) = X 6. **Final Result:** The expression simplifies to X + YZ. Comparing this result to the options: - Option (a) X + Y + Z is incorrect. - Option (b) XY + YZ is incorrect. - Option (c) X + YZ matches our result. - Option (d) XZ + Y is incorrect.

In the Theory of Computation, regular languages are closed under several operations, including union, concatenation, Kleene star, and intersection. This property is known as 'Closure Properties of Regular Languages'. Step-by-step reasoning: 1. Let L1 and L2 be two regular languages. 2. Since they are regular, there exist Deterministic Finite Automata (DFAs) M1 and M2 that recognize L1 and L2 respectively. 3. To find the intersection (L1 ∩ L2), we can construct a 'Product Automaton'. This is a new DFA where the states are pairs of states from M1 and M2. 4. A state in the product automaton is an accepting state if and only if both component states from M1 and M2 are accepting states. 5. Because we can construct a DFA that recognizes the intersection of any two regular languages, the resulting language must also be regular by definition. Therefore: - Option (a) is correct because the intersection of any two regular languages is guaranteed to be regular. - Option (b) is incorrect because the result is always regular. - Option (c) is incorrect because there is no case where the intersection of two regular languages results in a non-regular language.

The Intel 8085 is an 8-bit microprocessor designed using NMOS technology. According to its technical specifications and datasheet, the device requires a single, regulated +5V DC power supply (typically with a tolerance of ±0.25V) to operate its internal logic circuits. Analysis of options: - Option (a) +5V: Correct. This is the standard operating voltage for the 8085 CPU. - Option (b) -5V: Incorrect. Negative voltage is not used to power the logic of the 8085. - Option (c) +12V: Incorrect. While some peripheral components or clock generators in older systems might have used higher voltages, the microprocessor itself would be destroyed if supplied with +12V. - Option (d) -12V: Incorrect. This is not the operating voltage for the 8085.

In an RL (Resistor-Inductor) series circuit connected to an AC source, the total impedance (Z) is given by Z = R + jXL, where R is the resistance and XL is the inductive reactance. The inductor opposes changes in current, which causes the current to reach its peak value after the voltage has reached its peak. Mathematically, the phase angle φ is given by tan(φ) = XL/R. Since XL (inductive reactance) is positive, the phase angle φ is positive, meaning the voltage leads the current, or equivalently, the current lags the voltage by an angle between 0° (purely resistive) and 90° (purely inductive). Analysis of options: - Option (a) is incorrect because current leads voltage in a capacitive (RC) circuit. - Option (b) is correct because the inductive property of the coil causes the current to lag. - Option (c) is incorrect because current and voltage are only in phase in a purely resistive circuit.

Delta-Star: Z_star=Z_delta/3; three equal Z in delta give Z/3 per phase in star.

In graph theory, a tree is defined as a connected graph that contains no cycles (acyclic). 1. **Minimally Connected**: A graph is said to be minimally connected if it is connected, but the removal of any single edge results in the graph becoming disconnected. This is a fundamental property and an alternative definition of a tree. If a graph is connected and has no cycles, removing any edge must break the connectivity because there is only one unique path between any two vertices. 2. **Why other options are incorrect**: - **a. completely connected**: A completely connected graph (Complete Graph $K_n$) is one where every pair of distinct vertices is connected by a unique edge. While a tree with 2 vertices is complete, any complete graph with 3 or more vertices contains cycles (e.g., a triangle), which violates the definition of a tree. - **c. contains a circuit**: By definition, a tree is acyclic. If a graph contains a circuit (cycle), it cannot be a tree. - **d. is planar**: While it is true that all trees are planar (they can be drawn in a plane without edges crossing), being planar is not a sufficient condition. Many non-tree graphs (like a simple square or a complete graph $K_4$) are planar but are not trees because they contain cycles.

In a balanced three-phase system, the instantaneous power is the sum of the powers of the three individual phases. Let the voltages and currents be represented as: $v_1 = V_m \sin(\omega t)$, $i_1 = I_m \sin(\omega t - \phi)$ $v_2 = V_m \sin(\omega t - 120^\circ)$, $i_2 = I_m \sin(\omega t - 120^\circ - \phi)$ $v_3 = V_m \sin(\omega t - 240^\circ)$, $i_3 = I_m \sin(\omega t - 240^\circ - \phi)$ The instantaneous power for one phase is $p_1 = v_1 i_1 = V_m I_m \sin(\omega t) \sin(\omega t - \phi)$. Using the trigonometric identity $\sin A \sin B = \frac{1}{2}[\cos(A-B) - \cos(A+B)]$, we get: $p_1 = \frac{V_m I_m}{2} [\cos(\phi) - \cos(2\omega t - \phi)]$ Summing the powers for all three phases: $P_{total} = p_1 + p_2 + p_3$ $P_{total} = \frac{V_m I_m}{2} [3\cos(\phi) - (\cos(2\omega t - \phi) + \cos(2\omega t - 240^\circ - \phi) + \cos(2\omega t - 480^\circ - \phi))]$ The sum of three cosine waves of the same frequency displaced by $120^\circ$ is zero. Therefore, the oscillating components (which are at the second harmonic frequency $2\omega$) cancel each other out completely. $P_{total} = \frac{3 V_m I_m}{2} \cos(\phi) = 3 V_{rms} I_{rms} \cos(\phi)$ Since $V_{rms}$, $I_{rms}$, and $\phi$ are constants for a balanced system, the total instantaneous power is a constant. This is a primary advantage of three-phase systems over single-phase systems, as it eliminates power pulsations in motors and generators.

To convert a binary number (base 2) to a hexadecimal number (base 16), the binary digits are grouped into sets of four, starting from the right (least significant bit). 1. Given binary number: 11010011 2. Split into groups of four: (1101) and (0011) 3. Convert each group to its decimal equivalent: - 1101 = (1 × 2³) + (1 × 2²) + (0 × 2¹) + (1 × 2⁰) = 8 + 4 + 0 + 1 = 13 - 0011 = (0 × 2³) + (0 × 2²) + (1 × 2¹) + (1 × 2⁰) = 0 + 0 + 2 + 1 = 3 4. Map the decimal values to hexadecimal digits (where 10=A, 11=B, 12=C, 13=D, 14=E, 15=F): - 13 = D - 3 = 3 5. Combine the results: D3. Comparing with options: - a. D3 (Correct) - b. A3 (Incorrect, A represents 10) - c. B3 (Incorrect, B represents 11) - d. D2 (Incorrect, the second group 0011 equals 3, not 2)