GATE 2011 Mechanical Engineering
34 questions across 1 session
An unbiased coin is tossed five times. The outcome of each loss is either a head or a tail. Probability of getting at least one head is _______.
A pipe of $$25$$ $$mm$$ outer diameter carries steam. The heat transfer coefficient between the cylinder and surrounding is $$5$$ $$W/{m^2}K.$$ It is propsed to reduce the heat los...
One unit of product $${P_1}$$ requires $$3$$ $$kg$$ of resource $${R_1}$$ and $$1$$ $$kg$$ of resource $${R_2}$$. One unit of product $${P_2}$$ requires $$2$$ $$kg$$ of resource $$...
Which one among the following welding processes uses non-consumable electrode?
Two identical ball bearings $$P$$ and $$Q$$ are operating at loads $$30kN$$ and $$45kN$$ respectively. The ratio of the life of bearing $$P$$ to the life of bearing $$Q$$ is
The ratios of the laminar hydrodynamic boundary layer thickness to thermal boundary layer thickness of flows of two fluids $$P$$ and $$Q$$ on a flat plate are $${1 \over 2}$$ and $...
A series expansion for the function $$\sin \theta $$ is _______.
Consider the following system of equations $$2{x_1} + {x_2} + {x_3} = 0,\,\,{x_2} - {x_3} = 0$$ and $${x_1} + {x_2} = 0.$$ This system has
A streamline and an equipotential line in a flow field
Cars arrive at a service station according to Poisson's distribution with a mean rate of $$5$$ per hour. The service time per car is exponential with a mean of $$10$$ minutes. At s...
One unit of product $${P_1}$$ requires $$3$$ $$kg$$ of resource $${R_1}$$ and $$1$$ $$kg$$ of resource $${R_2}$$. One unit of product $${P_2}$$ requires $$2$$ $$kg$$ of resource $$...
Heat and work are
A hole is dimension $$\phi {9^{\matrix{ { + 0.015} \cr { + 0\,\,\,\,\,\,\,\,\,\,} \cr } }}\,mm.$$ The corresponding shaft is of dimension $$\phi {9^{\matrix{ { + 0.010} \cr { + 0.0...
A single-point cutting tool with $${12^0}$$ rake angle is used to machine a steel work-piece. The depth of cut, $$i.e$$ uncut thickness is $$0.81$$ $$mm.$$ The chip thickness under...
The shear strength of a sheet metal is $$300MPa.$$ The blanking force required to produce a blank of $$100$$ $$mm$$ diameter from a $$1.54$$ $$mm$$ thick sheet is close to
In a condenser of a power plant, the steam condenses at a temperature of $${60^ \circ }C.$$ The cooling water enters at $${30^ \circ }C$$ and leaves at $${45^ \circ }C.$$ The logar...
In an experimental set-up, air flows between two stations $$P$$ and $$Q$$ adiabatically. The direction of flow depends on the pressure and temperature conditions maintained at $$P$...
A pump handling a liquid raises its pressure from $$1$$ bar to $$30$$ $$bar.$$ Take the density of the liquid as $$990$$ $$kg/{m^3}$$. The isentropic specific work done by the pump...
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...
The contents of a well-insulated tank are heated by a resistor of $$23\Omega $$ in which $$10A$$ current is flowing. Consider the tank along with its contents as a thermodynamic sy...
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 $$P$...
Consider the differential equation $${{dy} \over {dx}} = \left( {1 + {y^2}} \right)x\,\,.$$ The general solution with constant $$'C'$$ is
Eigen values of a real symmetric matrix are always
The coefficient of restitution of a perfectly plastic impact is
A cubic casting of $$50mm$$ side undergoes volumetric solidification shrinkage and volumetric solid contraction of $$4\% $$ and $$6\% $$ respectively. No riser is used. Assume unif...
The word Kanban is most appropriately associated with
Green sand mould indicates that
The integral $$\,\int\limits_1^3 {{1 \over x}\,\,dx\,\,\,} $$ when evaluated by using simpson's $$1/{3^{rd}}$$ rule on two equal sub intervals each of length $$1,$$ equals to
The maximum possible draft in cold rolling of sheet increases with the
What is $$\mathop {Lim}\limits_{\theta \to 0} {{\sin \theta } \over \theta }\,\,$$ equal to ?
The product of two complex numbers $$1 + i\,\,\,\,\& \,\,\,\,2 - 5\,i$$ is
If $$f(x)$$ is even function and a is a positive real number , then $$\int\limits_{ - a}^a {f\left( x \right)dx\,\,} $$ equals ________.
A spherical steel ball of $$12mm$$ diameter is initially at $$100K.$$ It is slowly cooled in a surrounding of $$300K.$$ The heat transfer coefficient between the steel ball and the...
A column has a rectangular cross-section of 10 mm $$ \times $$ 20 mm and a length of 1 m. The slenderness ratio of the column is close to