The maximum shear stress developed in the bar subjected to tensile stress (2σ) as shown in the figure will be_______.

A coin is tossed 3 times. The probability of getting head and tail alternatively is

If A and B are 3 × 3 real matrices such that rank (AB) = 1, then rank (BA) cannot be

If ω and ω² are cube roots of unity, then (2 - ω + 2ω²)(2 + 2ω - ω²) is

A vibrating system consists of a mass of 200 kg, spring stiffness of 80 N/mm. The natural frequency of vibration of the system is

A sine bar has a length of 250 mm. Each roller has a diameter of 20 mm. During taper angle measurement of a component, the height from the surface plate to the centre of roller is 110 mm. The calculated taper angle (in degrees) is ______.

Which of the following characteristics regarding fluid kinematics is/are correct?

1. Streamline represents an imaginary curve in the flow field so that the tangent to the curve at any point represents the direction of instantaneous velocity at that point.

2. Path lines, streamlines and streak lines are identical in steady flow. 

The value of t so that $\left[\begin{array}{c}4\\ -1\end{array}\right]$ is an eigen vector of $\left[\begin{array}{cc}3& 4\\ 2& t\end{array}\right]$ is ______

The room-temperature stress (σ) -strain (ϵ) curves of four materials P, Q, R, and S are shown in the figure below. The material that behaves as a rigid perfectly plastic material is

Tension in the cable supporting a lift of weight ‘W’ and having an acceleration of ‘a’ while going upward is (g is acceleration due to gravity)

Degree of freedom of given kinematic linkage is

A coin is tossed and a dice is rolled. The probability that the coin shows the head and the dice shows 6 is

In a machine tool the range of cutting speeds used is 10 m/min to 200 m/min and range of diameters of jobs used is 100 mm to 500 mm. The speed range ratio of the machine tool is

In a Pelton wheel, the bucket peripheral speed is 12 m/s, the water jet velocity is 24 m/s. If the defection angle is 135° and the flow is ideal, the maximum hydraulic efficiency will be ______ (in percentage)

A flange coupling is used

When water at 0°C is heated, its specific volume under standard atmosphere

Which one of the following symbols is used to represent welding activity on an operation process chart?

If the wire diameter of a compressive helical spring is increased by 5%, the change in deflection of the spring (in %) is_______.

The grinding wheel is considered better, if the grinding ratio is

The interpolator in a CNC machine controls

A solid round bar 3 m long and 5 cm in diameter is used a strut with both the ends hinged. Determine the crippling load (in kN). Take E = 2 × 10⁵ N/mm²

The current period forecast becomes equal to last period forecast for the value of smoothing constant equal to

Which of the following is correct sequence of the crystal structure with respect to percentage of voids (SCC – Simple Cubic Cell, FCC – Face Centred Cubic, BCC – Body Centred Cubic).

A circular column of length 'l' and diameter 'd' has has Euler crippling load of P₁ kN. If the diameter is reduced by 20 %, then the new criplling load becomes P₂ kN. What is the relation between P₁ and P₂?

A liquid flows downward through at tapered vertical portion of a pipe. At the entrance and exit of the pipe, the static pressures are equal. If for a vertical height ‘h’ the velocity becomes four times, then the ratio of ‘h’ to the velocity head at enterance will be

Obtain the root after first iteration using Newton Raphson method for the function f(x) = x² + e^x + 7x wit initial guess of x₀ = 1. _______

In a game, there are three rooms- I, Il and IIl. Room I contain 2 boxes having gift items and 3 empty boxes, room II contains 3 boxes having gift items and 2 empty boxes, and room III contains 4 boxes having gift items and one empty box respectively. There is an equal probability of each room being chosen by a player. Mr John selects one box from a room chosen at random. The probability that Mr John wins a box having gift items is:

If the conditions of maximum possible percentage reduction prevail in a drawing operation, what is the final area of cross-section (cm²) if the initial area of cross section is 230 cm².

The flow rate of material is given as σ = 1400 ϵ^0.3.

The Engineering strain at maximum load is ______

An elastomeric bearing pad is subjected to a shear force V during a static loading test. The pad has dimensions a = 150 mm and b = 225 mm, and thickness t = 55 mm. The lateral displacement of the top plate with respect to the bottom place is 14 mm under a load P = 16 kN. The shear modulus of elasticity G of the elastomer (upto 2 decimal places) is ………… MPa.

A rectangle beam 60 mm wide and 150 mm deep is simply supported over a span of 4 m. If the beam is subjected to uniformly distributed load of 4.5 kN/m, then the maximum bending stress induced in the beam is _____ MPa.

In a bi-axial state of stress, principal stresses are 200 MPa and 100 MPa respectively. Let τ₁ be the maximum shear stress in-plane and τ₂ be the maximum shear stress at the given point. Determine, which of the following options is/are true? 

What is the value of f(t) whose Laplace transform is given by $F\left(s\right)=\frac{\left(2s+4\right)}{\left(s^2+4s+3\right)}$ at t = 3^-1?

Find the blanking force (in kN) required to punch 10 mm diameter holes in a steel sheet of 3 mm thickness. Given shear strength of material = 400 MPa, penetration = 30% and shear provided on the punch = 2.5 mm.

A four stoke single-cylinder engine produces 24 kW power at the engine crank shaft at 2000 rpm. The mechanical efficiency of the engine is at 80%, swept volume of 800 cc and a stroke length of 9 cm. The indicated mean effective pressure of the engine will be

If a ball which is dropped from a height of 2.25 m on a smooth floor attains the height of bounce equal to 1.00 m, the coefficient of restitution between the ball & floor is equal to

A mass of 2500 kg is lowered at a velocity of 1.5 m/sec from the drum as shown in figure. The mass of the drum is 50 kg and its radius of gyration can be taken as 0.7 m and radius of drum is 0.75 m. On applying the brake, the mass is brought to rest in a distance of 0.5 m. Which of the following statements are true?

The value of ∫_s (x + z) dy dz + (y + z) dx dz + (x + y) dx dy, Where ‘s’ is the surface of sphere x² + y² + z² = 4 is

A wall of furnace is made up of inside layer of silica brick 150 mm thick covered with a layer of magnesite brick 300 mm thick. The temperature at the inside surface of silica brick wall and outside surface of magnesite brick wall are 800°C and 200°C respectively. The contact thermal resistance between the two walls at the interface is 0.0045 °C/W per unit wall area. If the thermal conductivity of silica and magnesite brick are 1.5 W/m°C and 5.2 W/m°C. The rate of heat loss per unit area of wall will be (in kW/m²)

An ideal gas expands in an adiabatic frictionless nozzle from the inlet condition of 30 bar, 800 K to the ambient pressure of 1 bar at the outlet. The specific heat c_p for the gas is 1 kJ/kgK and c_v for the gas is 0.718 kJ/kg K. Neglecting inlet kinetic energy, the velocity of the gas (in m/s) at the nozzle exit is________.

A damped mass spring system has mass of 10 kg, spring stiffness of 4000 N/m and damping coefficient of 40 Ns/m. The amplitude of forcing function, F₀ is 60 N and the forcing frequency is 40 rad/sec. Determine the transmissibility of the system. (round up to two decimal places)

In a reverted gear train, Gear A has 16 teeth, and driving Gear B which has 64 teeth. Gear C with 20 teeth which is compounded with Gear B and drives Gear D which is co-axial with A. If speed of D is 120 rpm, what is speed of A. (All gears are of same module)

A 18 cm diameter cane has 18 cm of water, overlaid with 15 cm of oil ($\rho =891\frac{kg}{m^3}$). It is rotated about the centre in rigid-body motion at 150 RPM as shown in the figure given below. Then,

A solid shaft of diameter 0.4 m rotates inside a sleeve at a speed of 190 rpm. The dynamic viscosity of the oil used between them is 6 poise and the thickness of oil film is 1.5 mm. Calculate the power lost in bearing for a sleeve length of 90 mm ________ (in W)

A lawn sprinkler has two nozzles of diameters 8 mm each at the end of a rotating arm and the velocity of flow of water from each nozzle is 12m/s. One nozzle discharges water in the downward direction, while other nozzle discharges water vertically up. The nozzles are at a distance of 40cm from the centre of rotating arm. The magnitude of torque (Nm) required to hold the rotating arm stationary is ________. (Correct up to 2 decimals)

The square element in the figure is subjected to a biaxial stress of 400 N/mm² as shown. What is the intensity of normal stress σ_n on the plane BD?

The orthogonal cutting of steel is performed with following observations:

Cutting force = 1500 N, Thrust force = 650 N, Tool rake angle = 10°

Using the Merchant’s analysis, the shear force (in N) along the shear plane with be ________

In an electrochemical machining process, the current density is 80 A/cm² and the cross sectional area of each electrode is 4 cm². If the current efficiency is 75% and atomic weight, valency and density of material is 30, 3, and 2600 kg/m³ respectively, then the MRR is _________ mm³/min. (Using 2 electrodes)

A cam gives SHM to the follower with a lift of 50 mm. the minimum radius of cam is 50 mm and the angle of ascent, descent and dwell are 100°, 70° and 50° respectively. The cam shaft rotates at 350 rpm, then

For the system shown, determine the magnitude of resultant (in N), if resultant of the three forces is to be vertical.

Two small orifices A and B of dia. 1 cm and 2 cm respectively, are placed on sides of a tank at depths of h₁ and h₂ below the open liquid surface. If discharges through A and B are equal, then ratio of h₁ and h₂ (assuming equal c_d values) will be

The ideal gas of mass 1 kg is initially occupying the volume of 0.20 m³ is heated at a constant pressure of 1150 kPa until it’s volume is doubled. (Cp = 1.05 kJ/kg.K, Cv­ = 0.750 kJ/kgK)

Consider the following linear programming (LP) model

Maximize, Z = 600x₁ + 700x₂

Subjected to

6x₁ + 10x₂ ≤ 60

7x₁ + 12x₂ ≤ 84

6x₁ + 8x₂ ≤ 48

X₁, x₂, ≥ 0

The optimal value of the solution is _______

A set of jobs are to be processed on a single machine using shortest processing time rule. Find the average tardiness per Job (in minutes).

A single row deep groove ball bearing is subjected to a radial force of 6 KN and an axial load of 4 kN. The shaft rotates at 900 rpm. The bearing dynamic load carrying capacity is 100 KN. Find the bearing of life (in hours). If radial load factor axial load factor is 0.56 & 1.5 respectively. Bearing is designed for inner race rotation.