GATE PI 2012
GATE 2012 Previous Year
3 hDuration
39Total Marks
26Questions
7Sections
Instructions
General instructions for this test:
- Duration: 3 h. The timer starts as soon as you begin and cannot be paused.
- Total questions: 26 across 7 section(s); maximum marks: 39.
- You are allowed 1 attempt(s) at this test.
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Paper Structure
Machine Tools And Machining
Machine Tools And Machining
Q1.
mcq single
+1 / 0.3
A $$CNC$$ vertical milling machine has to cut a straight slot of $$10$$ $$mm$$ width and $$2$$ $$mm$$ depth by a cutter of $$10$$ $$mm$$ diameter between points $$(0, 0)$$ and $$(100, 100)$$ on the $$XY$$ plane (dimensions in $$mm$$). The feed rate used for milling is $$50$$ $$mm/min.$$ Milling time for the slot (in seconds) is
Q2.
mcq single
+2 / 0.6
In a shaping process, the number of double strokes per minute is $$30$$ and the quick return ratio is $$0.6,$$ If the length of the stroke is $$250mm,$$ the average cutting velocity in $$m/min$$ is
Q3.
mcq single
+2 / 0.6
In a single pass drilling operation, a through hole of $$15$$ $$mm$$ diameter is to be drilled in a steel plate of $$50mm$$ thickness. Drill spindle speed is $$500epm,$$ feed is $$0.2mm/rev$$ and drill point angle is $${118^ \circ }.$$ Assuming $$2mm$$ clearance at approach and exit, the total drill time (in seconds) is
Metrology
Metrology
Q1.
mcq single
+1 / 0.3
In an interchangeable assembly, shafts of size $${25.000^{\matrix{
{ + 0.040} \cr
{ - 0.010} \cr
} }}\,\,mm$$ mate with holes of size $${25.000^{\matrix{
{ + 0.030} \cr
{ + 0.020} \cr
} }}\,\,mm.$$
The maximum interference (in microns) in the assembly is
Q2.
mcq single
+2 / 0.6
A Sine bar has a length of $$250mm.$$ Each roller has a diameter of $$20mm.$$ During taper angle measurement of a component, the height from the surface plate to the center of a roller is $$100mm.$$ The calculated taper angle (in degrees) is
Metal Forming
Metal Forming
Q1.
mcq single
+2 / 0.6
In a single pass rolling process using $$410mm$$ diameter steel rollers, a strip of width $$140mm$$ and thickness $$8mm$$ undergoes $$10\% $$ reduction of thickness. The angle of bite in radians is
Q2.
mcq single
+1 / 0.3
A solid cylinder of diameter $$100$$ $$mm$$ and height $$50$$ $$mm$$ is forged between two frictionless flat dies to a height of $$25$$ $$mm.$$ The percentage change in diameter is
Q3.
mcq single
+2 / 0.6
Calculate the punch size in $$mm,$$ for a circular blanking operation for which details are given below.
Size of the blank $$25$$ $$mm$$
Thickness of the sheet $$2$$ $$mm$$
Radial clearance between punch and die $$0.06$$ $$mm,$$ Die allowance $$0.05$$ $$mm$$
Q4.
mcq single
+1 / 0.3
Match the following metal forming processes with their associated stresses in the Work-piece
Joining Of Materials
Joining Of Materials
Q1.
mcq single
+2 / 0.6
In a $$DC$$ $$arc$$ welding operating, the length characteristic was obtained as $${V_{arc}} = 20 + 5l$$ where the $$arc$$ length $$l$$ was varied between $$5mm$$ and $$7mm.$$ Here $${V_{arc}}$$ denotes the arc voltage in volts. The $$arc$$ current was varied from $$400A$$ to $$500A.$$ Assuming linear power source characteristic, the open circuit voltage and the short circuit current for the welding operation are
Heat Transfer
Heat Transfer
Q1.
mcq single
+1 / 0.3
For an opaque surface, the absorptivity $$\left( \alpha \right),$$ transmissivity $$\left( \tau \right)$$ and reflectivity $$\left( \rho \right)$$ are related by the equation:
Q2.
mcq single
+2 / 0.6
Consider two infinitely long thin concentric tubes of circular cross section as shown in the figure. If $${D_1}$$ and $${D_2}$$ are the diameters of the inner and outer tubes respectively, then the view factor $${F_{22}}$$ is given by
Q3.
mcq single
+1 / 0.3
Which one of the following configurations has the highest fin effectiveness?
Engineering Mathematics
Engineering Mathematics
Q1.
mcq single
+1 / 0.3
The inverse Laplace transform of the function $$F\left( s \right) = {1 \over {s\left( {s + 1} \right)}}$$ is given by
Q2.
mcq single
+1 / 0.3
For the spherical surface $${x^2} + {y^2} + {z^2} = 1,$$ the unit outward normal vector at the point $$\left( {{1 \over {\sqrt 2 }},{1 \over {\sqrt 2 }},0} \right)$$ is given by
Q3.
mcq single
+2 / 0.6
An automobile plant contracted to buy shock absorbers from two suppliers $$X$$ and $$Y$$. $$X$$ supplies $$60$$% and $$Y$$ supplies $$40$$% of the shock absorbers. All shock absorbers are subjected to a quality test. The ones that pass the quality test are considered reliable. Of $$X'$$ s shock absorbers, $$96$$% are reliable. Of $$Y'$$ s shock absorbers, $$72$$% are reliable. The probability that a randomly choosen shock absorber, which is found to reliable, is made by $$Y$$ is
Q4.
mcq single
+2 / 0.6
A box contains $$4$$ red balls and $$6$$ black balls. Three balls are selected randomly from the box one after another, without replacement. The probability that the selected set contains one red ball and two black balls is
Q5.
mcq single
+2 / 0.6
$$x+2y+z=4, 2x+y+2z=5, x-y+z=1$$
The system of algebraic equations given above has
Q6.
mcq single
+1 / 0.3
For the matrix $$A = \left[ {\matrix{
5 & 3 \cr
1 & 3 \cr
} } \right],$$ ONE of the normalized eigen vectors is given as
Q7.
mcq single
+2 / 0.6
Consider the differential equation $$\,\,{x^2}{{{d^2}y} \over {d{x^2}}} + x{{dy} \over {dx}} - 4y = 0\,\,\,$$ with the boundary conditions of $$\,\,y\left( 0 \right) = 0\,\,\,$$ and $$\,\,y\left( 1 \right) = 1.\,\,\,$$ The complete solution of the differential equation is
Q8.
mcq single
+1 / 0.3
$$\,\mathop {Lim}\limits_{x \to 0} \left( {{{1 - \cos x} \over {{x^2}}}} \right)$$ is
Q9.
mcq single
+1 / 0.3
The area enclosed between the straight line $$y=x$$ and the parabola $$y = {x^2}$$ in the $$x-y$$ plane is
Q10.
mcq single
+1 / 0.3
Consider the function $$f\left( x \right) = \left| x \right|$$ in the interval $$\,\, - 1 \le x \le 1.\,\,\,$$ At the point $$x=0, f(x)$$ is
Q11.
mcq single
+1 / 0.3
At $$x=0,$$ the function $$f\left( x \right) = {x^3} + 1$$ has
Q12.
mcq single
+2 / 0.6
A political party orders an arch for the entrance to the ground in which the annual convention is being held. The profile of the arch follows the equation $$y = 2x\,\,\, - 0.1{x^2}$$ where $$y$$ is the height of the arch in meters. The maximum possible height of the arch is
Casting
Casting
Q1.
mcq single
+2 / 0.6
A mold having dimensions $$100 \times 90 \times 20$$ (all in $$mm$$) is filled with molten metal througgh a gate with height $$'h'$$ and $$C.S$$ area $$A,$$ the mould filling time is $${t_1}$$. The height is now quadrupled and the cross sectional area is halved. The corresponding filling time is $${t_2}$$. The ratio $${t_2}/{t_1}$$ is