GATE PI 2008

## GATE PI

In hollow cylindrical parts made by centrifugal casting, the density of the part is

View Question
In sand casting of hallow part of lead, a cylindrical core of diameter $$120mm$$ and height $$180mm$$ is placed inside t

View Question
The eigen vector pair of the matrix $$\left[ {\matrix{
3 & 4 \cr
4 & { - 3} \cr
} } \right]$$ is

View Question
The inverse of matrix $$\left[ {\matrix{
0 & 1 & 0 \cr
1 & 0 & 0 \cr
0 & 0 & 1 \cr

View Question
The value of the integral $$\,\,\int\limits_{ - \pi /2}^{\pi /2} {\left( {x\,\cos \,x} \right)dx\,\,} $$ is

View Question
The value of the expansion $$\mathop {Lim}\limits_{x \to 0} \left[ {{{\sin \left( x \right)} \over {{e^x}X}}} \right]\,\

View Question
If $$\overrightarrow r $$ is the position vector of any point on a closed surface $$S$$ that encloses the volume $$V$$

View Question
In a game, two players $$X$$ and $$Y$$ toss a coin alternately. Whoever gets a 'head' first, wins the game and the game

View Question
For a random variable $$\,x\left( { - \infty < x < \infty } \right)\,\,$$ following normal distribution, the mean

View Question
The solutions of the differential equation $${{{d^2}y} \over {d{x^2}}} + 2{{dy} \over {dx}} + 2y = 0\,\,$$ are

View Question
The value of the expression $${{ - 5 + 10i} \over {3 + 4i}}$$ is

View Question
Laplace transform of $$8$$ $${t^3}$$ is

View Question
Laplace transform of $$sin$$ $$ht$$ is

View Question
Two pipes of uniform section but different diameters carry water at the same volumetric flow rate. Water properties are

View Question
Oil is being pumped through a straight pipe, the pipe length, diameter and volumetric flow rate are all doubled in a new

View Question
Two pipes of inner diameter $$100mm$$ and outer diameter $$110mm$$ each are joined by flash butt welding using $$30V$$ p

View Question
Aluminium strips of $$2mm$$ thickness are joined together by resistance spot welding process by applying an electric cur

View Question
Which of the following powders should be fed for effective oxy-fuel cutting of stainless steel

View Question
Which pair among the following solid state welding processes uses heat from an external source
$$P$$- Diffusion welding

View Question
Diamond cutting tools are not recommended for machining of ferrous metals to

View Question
In an orthogonal cutting experiment, an $$HSS$$ tool having the following tool signature in the orthogonal reference sys

View Question
In an orthogonal cutting experiment, an $$HSS$$ tool having the following tool signature in the orthogonal reference sys

View Question
Brittle materials are machined with tools having zero or negative rake angles because it

View Question
During machining, the wear land $$(h)$$ has been plotted against machining time $$(T)$$ as given in the following figure

View Question
The quick return mechanism used in shaper has rocker arm drive of length $$200mm.$$ If the crank radius is $$50mm$$ and

View Question
A stepper motor has $$150$$ steps. The output shaft of the motor is directly coupled to a lead screw of pitch $$4mm,$$ w

View Question
Suppose point $$P1$$ in $$APT$$ (Automatically programmed Tool) programming is coded by statement
$$P1 = POINT/XSMALL,\

View Question
In a $$CNC$$ feed drive, a stepper motor with step angle of $$1.8deg$$ drives a lead screw with pitch of $$2mm.$$ The ba

View Question
In a rolling process, thickness of a strip is reduced from $$4mm$$ to $$3mm$$ using $$300mm$$ diameter rolls rotating at

View Question
A $$10mm$$ diameter annealed steel wire is drawn through a die at a speed of $$0.5/sec$$ to reduce the diameter by $$20\

View Question
By application of tensile force, the cross sectional area of bar $$' P '$$ is first reduced by $$30\% $$ and then by an

View Question
A $$10mm$$ diameter annealed steel wire is drawn through a die at a speed of $$0.5/sec$$ to reduce the diameter by $$20\

View Question
Match the following

View Question
A blank of $$50$$ $$mm$$ diameter is to be sheared from a sheet of $$2.5$$ $$mm$$ thickness. The required radial clearan

View Question
The following data are given for calculating limits of dimensions and tolerances for a hole: Tolerance unit $$'i'$$ (mic

View Question
An experimental setup is planned to determine the taper of work piece as shown in the figure. If the two precision rolle

View Question