Two vessels contain mixtures of spirit and water. In the first vessel, the ratio of spirit to water is 8 : 3 and in the second, the ratio is 5 : 1. A 35 litre cask is filled from these vessels, so as to contain a mixture of spirit to water in the ratio of 4 : 1. How much mixture is taken from the first vessel?

In a transportation problem given below in table, the cell contains the transportation cost. The transportation cost is

A vapour absorption refrigeration system is a heat pump with three thermal reservoirs, as shown in the figure. A refrigeration effect of 100 W is required at 250 K when the heat source available is at 400 K. Heat rejection occurs at 300 K. The minimum value of heat required (in W) is (Answer up to the nearest integer)

A body rotating at 20 rad/s is acted upon by a constant torque providing it a deceleration of 2 rad/s². The time (in s) at which the body have same kinetic energy as the initial if the torque continues to act is

The correct statements are:

A spur gear system having 20° full depth involute profile is transmitting 50 kW at 30 rev/s. The normal pressure between teeth is 35 N/mm of face width. The base circle radius of gear is 188 mm. The necessary face width of the gear tooth (in mm) is

The resultant force acting at a tool point is 1200 N and its angle of inclination to the horizontal is 58°. The plan approach angle to which it acts perpendicularly is 28°. The required feed force to turn the component (in N) is

Which one of the following is the correct expression for one-dimensional, steady-state, constant thermal conductivity heat conduction equation for a cylinder with heat generation?

If a² + b² + c² = 1, then ab + bc + ac lies in the interval

A bag contains 30 tickets numbered 1,2,3, ......... up to 30. Among them 5 are drawn at random and arranged in ascending order t₁ < />₂ < />₃ < />₄ < />₅. The probability of t₄ being 25 (Up to two decimal places) is . (Up to three decimal places)

A cantilever beam of length is subjected to a concentrated load P at a distance of l/3 from the free end. What is the deflection of the free end of the beam? (EI is the flexural rigidity)

A thin cylindrical vessel of mean diameter 1 m is made of plates 20 mm thickness. The joints are formed by welding along helical seams that make an angle of 45° with the axis of the cylinder. If the joint has an internal pressure of 2 MPa, then

Take E = 200 GPa and μ = 0.3

The fraction change in speed is

A ball is dropped to a smooth floor from the top of a tower, which has height 50 m, and the ball rebounds to a height of 20 m after the first bounce of the ball. What is coefficient of restitution between the floor and the ball?

In the isothermal transformation diagram for a 0.45 wt% C steel alloy, when we rapidly cool a small austenite specimen to 200°C and keep it there for about 1000 s, the major constituent in the final micro structure is

The total number of instantaneous centres for a mechanism consisting of 'n' links is

The mass flow rate of the steam is

What if the rigid beam is to remain horizontal?

The magnitude of radial force acting on a ball bearing varies as  while the direction remains fixed. The amplitude of the force is 1800 N and speed of rotation is 720 rpm. What will be the dynamic load capacity of the bearing for the expected life of 7000 hr?

A plate shaped frozen food has a thickness of 20 mm, average thermal conductivity of 2.58 W/mK, density of 1080 kg/m3, specific heat of 3550J/kgK and a uniform temperature of —20°C. The food material is suddenly immersed in a well stirred hot water maintained at a constant temperature of 90°C. The heat transfer coefficient between the food material and hot water is 25 W/m2K. The time required for the centre temperature of the food material to reach 30°C (in min) is _______.

What will be the flow rate (in m³/s)? (Answer up to four decimal places)

A 20º full depth involute spur pinion of 4 mm module and 21 teeth is to transmit 15 kW at 960 rpm. Its face width is 25 mm. The tangential force (in N) transmitted is (Answer up to two decimal places)

What will be the percentage change in cutting speed required to give an 80% reduction in tool life (i.e. to reduce tool life to one-fifth of its former value), when the value of n = 0.12. (Answer up to one decimal places)

By application of tensile force, the cross-sectional area of a bar P is first reduced by 30% and then by an additional 20% of initial original area. Another bar Q of the same material is reduced in cross-sectional area by 50% in a single step by applying tensile force. After deformation, the true strains in bar P and bar Q will respectively be

Match List I (Details of process of the cycle) with List II (Name of the cycle) and select correct answer using the codes given below the lists:

In an orthogonal cutting, cutting force is 350 N and the thrust force is 250 N. Rake angle is 10°. The effective coulomb's coefficient is . (Round off to two decimal places)

For the stability of a floating body, under the influence of gravity alone, which of the following is TRUE?

Which one of the following statements applicable to a perfect gas will also be true for an irreversible process? (Symbols have the usual meanings)

A bell-crank lever ABC is pivoted at B and carries a weight 14 kN at C as shown in figure. Take AB = 21 cm and BC = 30 cm. The horizontal force F (in kN) necessary to prevent turning of the lever, is _______. (Answer up to two decimal places)

What is the minimum height of cylindrical riser with h = d for steel casting with length 300 mm, width 150 mm and thickness 30 mm? Shrinkage of casting is fed by piping in riser. For shape factor of 15, volume of pipe is around 1/6 volume of riser and percentage shrinkage for steel as 7

Take V_R/V_C = 0.30 vc

Let the random variable X have uniform distribution on the interval (0,1) Y = -2 log X. Then E(Y) is_______.

1 kg of water had been heated from 273 K to 373 K by first bringing it in contact with a reservoir at 323 K and then with a reservoir at 373 K. The change in entropy of the universe (in J/K) is

Assume heating of water is a constant volume process.

Take CV of water at 273 K is 4.217 kJ/kgK and CV of water at 323 K is 4.180 kJ/kgK

If a force F → is derivable from a potential function V(r), where r is the distance from the origin of the coordinate system, it follows that

Which of the above are correct?

When a steel is heated in a furnace and then cooled in air at ordinary temperature, the process is one of

Consider the differential equation y" + 4y' + 3y = e' , with initial conditions y(0) = y'(0) = 1. Laplace transform of y is

A rimmed flywheel (mass density = 7000 kg/m³) is used on a punching press running at a mean speed of 250 rpm. The punching operation consists of one-quarter revolution during which the flywheel is required to supply 3000 Nm of energy. The coefficient of speed fluctuations is limited to 0.2. the rim which contributes 90% of the required moment of inertia has a mean radius of 0.45 m due to space limitation. The cross-section of the rim is square, its area will be ________________ x 10^-3m²

Size of a shaper is given by

If 'n' variables in a physical phenomenon contained 'm' fundamental dimensions, then the variables can be arranged into

When milling a slot 20 mm wide x 10 cm long in a rectangular plate 10 cm x 20 cm, the cutting speed = 60 m/min, diameter of end drill = 20 mm, number of flutes = 8, feed = 0.01 mm/flute and depth of cut = 3 mm. The cutting time for the operation to be completed in a single pass, is( Answer up to one decimal place)

A problem in mechanics is given to three students A, B and C whose chances of solving it are 1/2, 1/3 and 1/4 respectively. The probability that the problem will be solved, is

An incompressible flow field has u = xz3 and w = xe-Y . What form does continuity imply for the velocity component of y-direction i.e., V?

Inverse Laplace Transform of  is

A flat plate of 15 cm wide and 45 cm long placed longitudinally in a stream of oil of RD = 0.925 and kinematic viscosity of 0.9 stoke, flowing with a free stream velocity of 6 m/s. The friction drag on the plate (in N) is____________.

The roots of the equation are

The type of partial differential equation u_xx+xu_yy = 0, x>0 is

In a beam of circular cross-section, the shear stress variation across a cross - section

At a particular location, the atmospheric pressure was measured as 0.96 bar and the temperature was 30°C. The relative humidity of air at the location is 60%. Vapour pressure of water is correlated by the expression In Psat = 19.013 — 5325/T where P is in kPa and T is in K. The humidity ratio of air (in g/k-g) of dry air is ____________.

In a tool life test, doubling the cutting speed reduces the tool life to 1/8th of the original. The Taylor's tool life index is _____. (Answer up to two decimal places)

The rank of a 3 x 3 matrix C = AB found by multiplying a non-zero column matrix A of size 3 x 1 and a non-zero row matrix B of size 1 x 3 is

For an involute rack and pinion arrangement, the value of pressure angle and module is kept fixed at 20° and 5 mm. If the addendum of the rack is 6 mm, then minimum number of teeth on pinion to avoid interference is

Match List I (State of stress) with List II (Kind of loading) and select the correct answer using the codes given below the lists:

The quick return ratio of the mechanism is (Answer up to the nearest integer)

What will be the expected project completion time?