GATE 2016 Production & Industrial
28 questions across 1 session
The ratio of press force required to punch a square hole of $$30$$ $$mm$$ side in a $$1$$ $$mm$$ thick aluminium sheet to that needed to punch a square hole of $$60$$ $$mm$$ side i...
For the two functions $$f\left( {x,y} \right) = {x^3} - 3x{y^2}\,\,$$ and $$\,\,g\left( {x,y} \right) = 3{x^2}y - {y^3}\,\,$$ Which one of the following options is correct?
$$\mathop {\lim }\limits_{x \to 0} \left( {{{{e^{5x}} - 1} \over x}} \right)$$ is equal to ________.
At $$x=0,$$ the function is $$f\left( x \right) = \left| {\sin {{2\pi x} \over L}} \right|\left( { - \infty < x < \infty ,L > 0} \right)$$
The range of values of $$k$$ for which the function $$\,\,f\left( x \right) = \left( {{k^2} - 4} \right){x^2} + 6{x^3} + 8{x^4}$$ has a local maxima at point $$x=0$$ is
The function $$f\left( z \right) = {{{z^2} + 1} \over {{z^2} + 4}}$$ is singular at
The eigen values of the matrix are $$\left[ {\matrix{ 0 & 1 \cr { - 1} & 0 \cr } } \right]$$
To solve the equation $$2sinx=x$$ by Newton- Raphson method, the initial guess was chosen to be $$x=2.0.$$ Consider $$x$$ in radian only. The value of $$x$$ (in radian) obtained af...
The number of solutions of the simultaneous algebraic equations $$y=3x+3$$ and $$y=3x+5$$ is
A normal random variable $$X$$ has the following probability density function $$${f_x}\left( x \right) = {1 \over {\sqrt {8\pi } }}e{}^{ - \left\{ {{{{{\left( {x - 1} \right)}^2}}...
A fair coin is tossed $$N$$ times. The probability that head does not turn up in any of the tosses is
In abrasive water jet machining, the velocity of water at the exit of the orifice, before mixing with abrasives, is 800 m/s. The mass flow rate of water is 3.4 kg/min. The abrasive...
A vertical cylindrical tank of $$1$$ $$m$$ diameter is filled with water up to a height of $$5$$ $$m$$ from its bottom. Top surface of water is exposed to atmosphere. A hole of $$5...
In a fully developed turbulent flow through a circular pipe, a head loss of ݄$${{h_1}}$$ is observed. The diameter of the pipe is increased by $$10\% $$ for the same flow rate and...
A helical gear with involute tooth profile has been machined with a disc-type form gear milling cutter. The helical gear has $$30$$ teeth and a helix angle of $${30^ \circ }$$. The...
In a single-pass rolling operation, a $$200$$ $$mm$$ wide metalic strip is rolled from a thickness $$10$$ $$mm$$ to a thickness $$6$$ $$mm.$$ The roll radius is $$100$$ $$mm$$ and...
Two solid cylinders of equal diameter have different heights. They are compressed plastically by a pair of rigid dies to create the same percentage reduction in their respective he...
The throughput rate of a production system is $$20$$ units per hour. The average flow time is $$30$$ minutes and the cycle time is $$3$$ minutes. The average inventory (in units) i...
Two flat steel sheets, each of $$2.5$$ $$mm$$ thickness, are being resistance spot welded using a current of $$6000$$ $$A$$ and weld time of $$0.2$$ $$s.$$ The contact resistance a...
Consider the following statements: (P) Hardness is the resistance of a material to indentation. (Q) Elastic modulus is a measure of ductility. (R) Deflection depends on stiffness....
A thin-walled cylindrical pressure vessel of internal diameter 2 m is designed to withstand an internal pressure of 500 kPa (gauge). If the allowable normal stress at any point wit...
An engine, connected with a flywheel, is designed to operate at an average angular speed of $$800$$ rpm. During operation of the engine, the maximum change in kinetic energy in a c...
Consider the following statements. $$(P)$$ Computer aided process planning $$(CAPP)$$ takes input from material requirement plan $$(MRP).$$ $$(Q)$$ Production flow analysis helps i...
A single axis $$CNC$$ table is driven by a $$DC$$ servo motor that is directly coupled to a lead screw of $$5$$ $$mm$$ pitch. The circular encoder attached to the lead screw genera...
A single point right handed turning tool is used for straight turning. The feed is $$0.25$$ $$mm/rev$$ and the uncut chip thickness is found to be $$0.25$$ $$mm.$$ The inclination...
A cylindrical bar of $$100$$ $$mm$$ diameter is orthogonally straight turned with cutting velocity, feed and depth of cut of $$120$$ $$m/min$$, $$0.25$$ $$mm/rev$$ and $$4$$ $$mm,$...
The limits of a shaft designated as $$100h5$$ are $$100.000$$ $$mm$$ and $$100.014$$ $$mm.$$ Similarly, the limits of a shaft designated as $$100h8$$ are $$100.000$$ $$mm$$ and $$1...
Two cast iron blocks $$P$$ and $$Q,$$ each of $$500$$ $$mm$$ length, have the same cross-sectional area. Block $$P$$ has rectangular cross-section of $$100\,\,mm \times 200\,\,mm.$...