Which one of the following equations is a correct identity for arbitrary $$3 \times 3$$ real matrices $$P,Q$$ and $$R$$

The value of the integral $$\int\limits_0^2 {{{{{\left( {x - 1} \right)}^2}\sin \left( {x - 1} \right)} \over {{{\left(

The value of the integral $$\,\int\limits_0^2 {\int\limits_0^x {{e^{x + y}}\,\,dy} } $$ $$dx$$ is

A nationalized bank has found that the daily balance available in its savings accounts follows a normal distribution wit

The number of accidents occurring in a plant in a month follows Poisson distribution with mean as $$5.2.$$ The probabil

The solution of the initial value problem $$\,\,{{dy} \over {dx}} = - 2xy;y\left( 0 \right) = 2\,\,\,$$ is

Consider an ordinary differential equation $${{dx} \over {dt}} = 4t + 4.\,\,$$ If $$x = {x_0}$$ at $$t=0,$$ the increme

If $$z$$ is a complex variable, the value of $$\int\limits_5^{3i} {{{dz} \over z}} $$ is

Laplace transform of $$\cos \,\left( {\omega t} \right)$$ is $${s \over {{s^2} + {\omega ^2}.}}$$. The Laplace transfor

In a statically determinate plane truss, the number of joints $$(j)$$ and the number of members $$(m)$$ are related by

For the truss shown in the figure, the forces F1 and F2 are 9 kN and 3 kN, respectively. The force (in kN) in the member

A uniform slender rod (8 m length and 3 kg mass) rotates in a vertical plane about a horizontal axis 1m from its end as

A wardrobe (mass 100 kg, height 4 m, width 2 m, depth 1 m), symmetric about the Y-Y axis, stands on a rough level floor

A ladder AB of length 5 m and weight (W) 600 N is resting against a wall. Assuming frictionless contact at the floor (B)

A flow field which has only convective acceleration is

A flow field which has only convective acceleration is

Consider the following statements regarding streamline(s): (i) It is a continuous line such that the tangent at any poin

Consider a velocity field $$\overrightarrow V = K\left( {y\widehat i + x\widehat k} \right),$$ where $$K$$ is a constan

As the temperature increases, the thermal conductivity of a gas

A plane wall has a thermal conductivity of $$1.15$$ $$W/m.K.$$ If the inner surface is at $${1100^ \circ }C$$ and the ou

Match Group $$A$$ with Group $$B$$ Group-A $$P:$$$$\,\,\,\,\,\,\,$$ Biot number $$Q:$$$$\,\,\,\,\,\,\,$$ Grashof numbe

Two infinite parallel plates are placed at a certain distance apart. An infinite radiation shield is inserted between th

Demand during lead time with associated probabilities is shown below: Expected demand during lead time is ___________

The precedence relations and duration (in days) of activities of a project network are given in the table. The total flo

At a work station, $$5$$ jobs arrive every minute. The mean time spent on each job in the work station is $$1/8$$ minute

A shaft is subjected to pure torsional moment. The maximum shear stress developed in the shaft is $$100$$ $$MPa.$$ The y

A bolt of major diameter $$12$$ $$mm$$ is required to clamp two steel plates. Cross sectional area of the threaded porti

Ball bearings are rated by a manufacturer for a life of $${10^6}$$ revolutions. The catalogue rating of a particular b

A cylindrical riser of $$6$$ $$cm$$ diameter and $$6$$ $$cm$$ height has to be designed for a sand casting mould for pro

In a rolling process, the maximum possible draft, defined as the difference between the initial and the final thickness

Within the Heat Affected Zone (HAZ) in a fusion welding process, the work material undergoes

A butt weld joint is developed on steel plates having yield and ultimate tensile strength of $$500$$ $$MPa$$ and $$700$$

Better surface finish is obtained with a large rake angle because

A cast iron block of $$200$$ $$mm$$ length is being shaped in a shaping machine with a depth of cut of $$4$$ $$mm,$$ fee

Two separate slab milling operations, $$1$$ and $$2,$$ are performed with identical milling cutters. The depth of cut in

A $$GO-No$$ $$GO$$ plug gauge is to be designed for measuring a hole of nominal diameter $$25$$ $$mm$$ with a hole toler

The number of independent elastic constants required to define the stress-strain relationship for an isotropic elastic s

If the Poisson's ratio of an elastic material is $$0.4$$, the ratio of modulus of rigidity to Young's modulus is _____ .

A frame is subjected to a load $$P$$ as shown in the figure. The frame has a constant flexural rigidity $$EI$$. The effe

A thin gas cylinder with an internal radius of 100 mm is subject to an internal pressure of 10 MPa. The maximum permissi

Torque and angular speed data over one cycle for a shaft carrying a flywheel are shown in the figures. The moment of ine

A point mass is executing simple harmonic motion with an amplitude of $$10$$ mm and frequency of $$4$$ Hz. The maximum a

A single degree of freedom system has a mass of 2kg, stiffness 8 N/m and viscous damping ratio 0.02. The dynamic magnifi

A reversed Carnot cycle refrigerator maintains a temperature of $$ - {5^ \circ }C.$$ The ambient air temperature is $${3

A closed system contains $$10$$ $$kg$$ of saturated liquid ammonia at $${10^ \circ }C.$$ Heat addition required to conve

Two identical metal blocks $$L$$ and $$M$$ (specific heat $$=0.4$$ $$kJ/kg.K$$), each having a mass of $$5$$ $$kg,$$ are

Steam with specific enthalpy $$\left( h \right)\,\,3214\,\,kJ/kg$$ enters an adiabatic turbine operating at steady state

Kaplan water turbine is commonly used when the flow through its runner is