GATE 2008 Production & Industrial
33 questions across 1 session
A blank of $$50$$ $$mm$$ diameter is to be sheared from a sheet of $$2.5$$ $$mm$$ thickness. The required radial clearance between the die and the punch is $$6\% $$ of sheet thickn...
The value of the integral $$\,\,\int\limits_{ - \pi /2}^{\pi /2} {\left( {x\,\cos \,x} \right)dx\,\,} $$ is
The value of the expansion $$\mathop {Lim}\limits_{x \to 0} \left[ {{{\sin \left( x \right)} \over {{e^x}X}}} \right]\,\,$$ is
The value of the expression $${{ - 5 + 10i} \over {3 + 4i}}$$ is
The solutions of the differential equation $${{{d^2}y} \over {d{x^2}}} + 2{{dy} \over {dx}} + 2y = 0\,\,$$ are
The inverse of matrix $$\left[ {\matrix{ 0 & 1 & 0 \cr 1 & 0 & 0 \cr 0 & 0 & 1 \cr } } \right]$$ is
The eigen vector pair of the matrix $$\left[ {\matrix{ 3 & 4 \cr 4 & { - 3} \cr } } \right]$$ is
For a random variable $$\,x\left( { - \infty < x < \infty } \right)\,\,$$ following normal distribution, the mean is $$\,\mu = 100\,\,.$$ If the probability is $$\,\,P = \alpha \,\...
In a game, two players $$X$$ and $$Y$$ toss a coin alternately. Whoever gets a 'head' first, wins the game and the game is terminated. Assuming that players $$X$$ starts the game t...
Laplace transform of $$8$$ $${t^3}$$ is
Laplace transform of $$sin$$ $$ht$$ is
If $$\overrightarrow r $$ is the position vector of any point on a closed surface $$S$$ that encloses the volume $$V$$ then $$\,\,\int {\int\limits_s {\left( {\overrightarrow r \,....
Oil is being pumped through a straight pipe, the pipe length, diameter and volumetric flow rate are all doubled in a new arrangement. The pipe friction factor, however, remains con...
Two pipes of uniform section but different diameters carry water at the same volumetric flow rate. Water properties are the same in the two pipes. The Reynolds number, based on the...
A $$10mm$$ diameter annealed steel wire is drawn through a die at a speed of $$0.5/sec$$ to reduce the diameter by $$20\% $$. The yield stress of the material is $$800MPa.$$ The po...
By application of tensile force, the cross sectional area of bar $$' P '$$ is first reduced by $$30\% $$ and then by an additional $$20\% $$. Another bar $$'Q'$$ of the same materi...
A $$10mm$$ diameter annealed steel wire is drawn through a die at a speed of $$0.5/sec$$ to reduce the diameter by $$20\% $$. The yield stress of the material is $$800MPa.$$ Neglec...
Diamond cutting tools are not recommended for machining of ferrous metals to
Brittle materials are machined with tools having zero or negative rake angles because it
In hollow cylindrical parts made by centrifugal casting, the density of the part is
In sand casting of hallow part of lead, a cylindrical core of diameter $$120mm$$ and height $$180mm$$ is placed inside the mould cavity. The densities of core material and lead are...
In a rolling process, thickness of a strip is reduced from $$4mm$$ to $$3mm$$ using $$300mm$$ diameter rolls rotating at $$100rpm.$$ The velocity of the strip (in $$m/sec$$) at the...
Which pair among the following solid state welding processes uses heat from an external source $$P$$- Diffusion welding $$Q$$- Friction welding $$R$$- Ultrasonic welding $$S$$- For...
Aluminium strips of $$2mm$$ thickness are joined together by resistance spot welding process by applying an electric current $$6000$$$$A$$ for $$0.15sec$$. The heat required for me...
Two pipes of inner diameter $$100mm$$ and outer diameter $$110mm$$ each are joined by flash butt welding using $$30V$$ power supply. At the interface, $$1mm$$ of material melts fro...
Which of the following powders should be fed for effective oxy-fuel cutting of stainless steel
The following data are given for calculating limits of dimensions and tolerances for a hole: Tolerance unit $$'i'$$ (microns) $$=0.45$$ $${\left( D \right)^{1/3}} + 0.001D.$$ The u...
A stepper motor has $$150$$ steps. The output shaft of the motor is directly coupled to a lead screw of pitch $$4mm,$$ which drives a table. If the frequency of pulse supply to the...
Suppose point $$P1$$ in $$APT$$ (Automatically programmed Tool) programming is coded by statement $$P1 = POINT/XSMALL,\,\,\,INTOF,\,\,\,LN1,\,\,CR1$$ The coded geometric situation...
In a $$CNC$$ feed drive, a stepper motor with step angle of $$1.8deg$$ drives a lead screw with pitch of $$2mm.$$ The basic length unit $$(BLU)$$ for this drive is
The quick return mechanism used in shaper has rocker arm drive of length $$200mm.$$ If the crank radius is $$50mm$$ and the offset between crank center and rocker arm pivot is $$20...
In an orthogonal cutting experiment, an $$HSS$$ tool having the following tool signature in the orthogonal reference system $$(ORS)$$ has been used: $$0-10-7-7-10-75-1$$ Given : Wi...
In an orthogonal cutting experiment, an $$HSS$$ tool having the following tool signature in the orthogonal reference system $$(ORS)$$ has been used: $$0-10-7-7-10-75-1$$ Given : Wi...