A simply supported beam PQ is loaded by a moment of 1 kN-m at the mid-span of the beam as shown in the figure. The reaction forces P R and Q R at supports P and Q respectively are

A column has a rectangular cross-section of 10 mm x 20 mm and a length of 1 m. The slenderness ratio of the column is close to

The crystal structure of austenite is

For the four-bar linkage shown in the figure, the angular velocity of link AB is 1 rad/s. The length of link CD is 1.5 times the length of link AB. In the configuration shown, the angular velocity of link CD (in rad/s) is

A mass of 1 kg is attached to two identical springs each with stiffness k = 20 kN/m as shown in the figure. Under frictionless condition, the natural frequency of the system in Hz is close to

A torque T is applied at the free end of a stepped rod of circular cross-sections as shown in the figure. The shear modulus of the material of the rod is G. The expression for d to produce an angular twist $\theta$at the free end is

The sheer strength of a sheet metal is 300 MPa. The blanking force required to produce a blank of 100 mm diameter from a 1.5 mm thick sheet is close to

Which of the following options is the closest in the meaning to Inexplicable?

A triangular-shaped cantilever beam of uniform-thickness is shown in the figure. The Young's modulus of the material of the beam is E. A concentrated load P is applied at the free end of the beam.

The area moment of inertia about the neutral axis of a cross-section at a distance x measured from the free end is

Few school curricula include a unit on how to deal with bereavement and grief, and yet all students at some point in their lives suffer from losses through death and parting. Based on the above passage, which topic would not be included in a unit on bereavement?

A triangular-shaped cantilever beam of uniform-thickness is shown in the figure. The Young's modulus of the material of the beam is E. A concentrated load P is applied at the free end of the beam.

The maximum deflection of the beam is

If Log (P) = (1/2) Log (Q) = (1/3) Log (R), which of the following options is TRUE?

Choose the most appropriate word(s) from the options given below to complete the following sentence. I contemplated________Singapore for my vacation but decided against it.

A container originally contains 10 litres of pure spirit. From this container, 1 litre of spirit is replaced with 1 litre of water. Subsequently, 1 litre of the mixture is again replaced with 1 litre of water and this process is repeated one more time. How much spirit is now left in the container?

Choose the most appropriate word from the options given below to complete the following sentence. If you are trying to make a strong impression on your audience, you cannot do so by being understated, tentative or_____________.

The variable cost (V) of manufacturing a product varies according to the equation V = 4q, where q is the quantity produced. The fixed cost (F) of production of same product reduces with q according to the equation F = 100/q. How many units should be produced to minimize the total cost (V+F)?

A transporter receives the same number of orders each day. Currently, he has some pending orders (backlog) to be shipped. If he uses 7 trucks, then at the end of the 4th day he can clear all the orders. Alternatively, if he uses only 3 trucks, then all the orders are cleared at the end of the 10th day. What is the minimum number of trucks required so that there will be no pending order at the end of the 5th day?

P, Q, R and S are four types of dangerous microbes recently found in a human habitat. The area of each circle with its diameter printed in brackets represents the growth of a single microbe surviving human immunity system within 24 hours of entering the body. The danger to human beings varies proportionately with the toxicity, potency and growth attributed to a microbe shown in the figure below:

A pharmaceutical company is contemplating the development of a vaccine against the most dangerous microbe. Which microbe should the company target in its first attempt?

Which one among the following welding processes uses non-consumable electrode?

Match the following criteria of material failure, under biaxial stresses $\sigma_1$ and $\sigma_2$ and yield stress $\sigma_y$, with their corresponding graphic representations: P. Maximum-normal-stress criterion

Q. Maximum-distortion-energy criterion R. Maximum-shear-stress criterion

A thin cylinder of inner radius 500 mm and thickness 10 mm is subjected to an internal pressure of 5 MPa. The average circumferential (hoop) stress (in MPa) is

A disc of mass m is attached to a spring of stiffness k as shown in the figure. The disc rolls without slipping on a horizontal surface. The natural frequency of vibration of the system is

A double – parallelogram mechanism is shown in the figure. Note that PQ is a single link. The mobility of the mechanism is

The values of enthalpy of steam at the inlet and outlet of a steam turbine in a Rankine cycle are 2800 kJ/kg and 1800 kJ/kg respectively. Neglecting pump work, the specific steam consumption (in kg/kW-hour) is

Heat and work are

The crank radius of a single-cylinder I. C. engine is 60 mm and the diameter of the cylinder is 80 mm. The swept volume of the cylinder (in cm³) is

The contents of a well-insulated tank are heated by a resistor of 23 W in which 10 A current is flowing. Consider the tank along with its contents as a thermodynamic system. The work done by the system and the heat transfer tothe system are positive. The rates of heat (Q), work (W) and change in internal energy (DU) during the process (in kW) are

An ideal Brayton cycle, operating between the pressure limits of 1 bar and 6 bar, has minimum and maximum temperatures of 300 K and 1500 K. The ratio of specific heats of the working fluid is 1.4. The approximate final temperatures (in Kelvin) at the end of the compression and expansion processes are respectively

In an experimental set-up, air flows between two stations P and Q adiabatically. The direction of flow depends on the pressure and temperature conditions maintained at P and Q. The conditions at station P are 150 kPa and 350 K. The temperature at station Q is 300 K. The following are the properties and relations pertaining to air: Specific heat at constant pressure, C_p = 1.005 kJ/kgK; Specific heat at constant volume, C_v = 0.718 kJ/kgK; Characteristic gas constant, R = 0.287 kJ/kgK Enthalpy, h = c_p T Internal energy, u = C_v T

If the pressure at station Q is 50 kPa, the change in entropy (s_Q - s_P ) in kJ/kgK is

In an experimental set-up, air flows between two stations P and Q adiabatically. The direction of flow depends on the pressure and temperature conditions maintained at P and Q. The conditions at station P are 150 kPa and 350 K. The temperature at station Q is 300 K. The following are the properties and relations pertaining to air: Specific heat at constant pressure, C_p = 1.005 kJ/kgK; Specific heat at constant volume, C_v = 0.718 kJ/kgK; Characteristic gas constant, R = 0.287 kJ/kgK Enthalpy, h = c_p T Internal energy, u = C_v T

If the air has to flow from station P to station Q, the maximum possible value of pressure in kPa at station Q is close to

The temperature and pressure of air in a large reservoir are 400 K and 3 bar respectively. A converging-diverging nozzle of exit area 0.005 m² is fitted to the wall of the reservoir as shown in the figure. The static pressure of air at the exit section for isentropic flow through the nozzle is 50 kPa. The characteristic gas constant and the ratio of specific heats of air are 0.287 kJ/kgK and 1.4 respectively.

The density of air (in kg/m³) at the nozzle exit is

The temperature and pressure of air in a large reservoir are 400 K and 3 bar respectively. A converging-diverging nozzle of exit area 0.005 m² is fitted to the wall of the reservoir as shown in the figure. The static pressure of air at the exit section for isentropic flow through the nozzle is 50 kPa. The characteristic gas constant and the ratio of specific heats of air are 0.287 kJ/kgK and 1.4 respectively.

The mass flow rate of air through the nozzle in kg/s is

What is $\lim\limits_{\theta \rightarrow0} \frac{sin \theta}{\theta}$ equal to?

The integral $\int\limits_1^3 \frac{1}{x}$ when evaluated by using Simpson's 1/3 rule on two equal subintervals each of length 1, equals

A series expansion for the function sin$\theta$ is

The product of two complex numbers 1+i and 2-5i is

An unbiased coin is tossed five times. The outcome of each toss is either a head or a tail. The probability of getting at least one head is

If f(x) is an even function and a is a positive real number, then $\int\limits_{-a}^a f(x) dx$equals

Consider the following system of equations:
2x₁ + x₂ + x₃ = 0 x₂ - x₃ = 0
x₁ + x₂ = 0 This system has

Eigen values of a real symmetric matrix are always

Consider the differential equation $\frac{dy}{dx} = (1+y^2)x$. The general solution with constant c is

The coefficient of restitution of a perfectly plastic impact is

A stone with mass of 0.1 kg is catapulted as shown in the figure. The total force in N exerted by the rubber band as a function of distance x (in m) is given by F_x = 300 x². If the stone is displaced by 0.1 m from the un-stretched position (x = 0) of the rubber band, the energy stored in the rubber band is

A 1 kg block is resting on a surface with coefficient of friction ى = 0.1. A force of 0.8 N is applied to the block as shown in figure. The friction force is

A streamline and an equipotential line in a flow field

Figure shows the schematic for the measurement of velocity of air (density = 1.2kg/m³) through a constant–area duct using a pitot tube and a water-tube manometer. The differential head of water (density = 1000 kg/m³) in the two columns of the manometer is 10 mm. Take acceleration due to gravity as 2 9.8 m/s² . The velocity of air (in m/s) is

In a condenser of a power plant, the steam condenses at a temperature of 60^oC. The cooling water enters at 30^oC and leaves at 45^oC. The logarithmic mean temperature difference (LMTD) of the condenser is

A spherical steel ball of 12 mm diameter is initially at 1000 K. It is slowly cooled in a surrounding of 300 K. The heat transfer coefficient between the steel ball and the surrounding is 5 W/m²K. The thermal conductivity of steel is 20 W/mK. The temperature difference between the centre and the surface of the steel ball is

A pipe of 25 mm outer diameter carries steam. The heat transfer coefficient between the cylinder and surroundings is 25 W/m K . It is proposed to reduce the heat loss from the pipe by adding insulation having a thermal conductivity of 0.05 W/mK. Which one of the following statements is TRUE?

Cars arrive at a service station according to Poisson's distribution with a mean rate of 5 per hour. The service time per car is exponential with a mean of 10 minutes. At steady state, the average waiting time in the queue is

One unit of product P₁ requires 3 kg of resource R₁ and 1 kg of resource R₂. One unit of product P₂ requires 2 kg of resource R₁ and 2 kg of resource R₂. The profits per unit by selling product P₁ and P₂ are Rs. 2000 and Rs. 3000 respectively. The manufacturer has 90 kg of resource R₁ and 100 kg of resource R₂.

The unit worth of resource R₂ i.e., dual price of resource R₂ (in Rs. per kg) is

One unit of product P₁ requires 3 kg of resource R₁ and 1 kg of resource R₂. One unit of product P₂ requires 2 kg of resource R₁ and 2 kg of resource R₂ . The profits per unit by selling product P₁ and P₂ are Rs.2000 and Rs.3000 respectively. The manufacturer has 90 kg of resource R₁ and 100 kg of resource R₂.

The manufacturer can make a maximum profit of Rs.

Two identical ball bearings P and Q are operating at loads 30 kN and 45 KN respectively. The ratio of the life of bearing P to the life of bearing Q is

Choose the word from the options given below that is most nearly opposite in meaning to the given word: Amalgamate

The word kanban is most appropriately associated with

Green sand mould indicates that

The maximum possible draft in cold rolling of sheet increases with the

A single-point cutting tool with 12⁰ rake angle is used to machine a steel work- piece. The depth of cut, i.e. uncut thickness is 0.81 mm. The chip thickness under orthogonal machining condition is 1.8 mm. The shear angle is approximately

Match the following non-traditional machining processes with the corresponding material removal mechanisms:

Mechanical process| Mechanism of material removal| | P. Chemical machining| 1. Erosion| | Q. Electro-chemical machining| 2. Corrosive reaction| | R. Electro - discharge machining| 3. Ion displacement| | S. Ultrasonic machining| 4. Fusion and vapourization|

A hole is dimension ^$\phi$^{$9 ^{\begin{matrix} \ +0.015 \ \ +0 \ \end{matrix}}$}mm. The corresponding shaft is of dimension ^{$\phi$$9 ^{\begin{matrix} \ +0.010 \ \ +0.001 \ \end{matrix}}$}mm. The resulting assembly has

A cubic casting of 50 mm side undergoes volumetric solidification shrinkage and volumetric solid contraction of 4% and 6% respectively. No riser is used. Assume uniform cooling in all directions. The side of the cube after solidification and contraction is

If a mass of moist air in an airtight vessel is heated to a higher temperature, then

A pump handling a liquid raises its pressure from 1 bar to 30 bar. Take the density of the liquid as 990 kg/m³. The isentropic specific work done by the pump in kJ/kg is

The operation in which oil is permeated into the pores of a powder metallurgy product is known as

The ratios of the laminar hydrodynamic boundary layer thickness to thermal boundary layer thickness of flows of two fluids P and Q on a flat plate are $\frac{1}{2}$ and 2 respectively. The Reynolds number based on the plate length for both the flows is 10⁴. The Prandtl and Nusselt numbers for P are $\frac{1}{8}$ and 35 respectively. The Prandtl and Nusselt numbers for Q are respectively