GATE PI 2016

## GATE PI

Two cast iron blocks $$P$$ and $$Q,$$ each of $$500$$ $$mm$$ length, have the same cross-sectional area. Block $$P$$ has

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The eigen values of the matrix are $$\left[ {\matrix{
0 & 1 \cr
{ - 1} & 0 \cr
} } \right]$$

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The number of solutions of the simultaneous algebraic equations $$y=3x+3$$ and $$y=3x+5$$ is

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At $$x=0,$$ the function is $$f\left( x \right) = \left| {\sin {{2\pi x} \over L}} \right|\left( { - \infty < x <

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The range of values of $$k$$ for which the function $$\,\,f\left( x \right) = \left( {{k^2} - 4} \right){x^2} + 6{x^3} +

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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}

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$$\mathop {\lim }\limits_{x \to 0} \left( {{{{e^{5x}} - 1} \over x}} \right)$$ is equal to ________.

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A normal random variable $$X$$ has the following probability density function
$$${f_x}\left( x \right) = {1 \over {\sqr

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A fair coin is tossed $$N$$ times. The probability that head does not turn up in any of the tosses is

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To solve the equation $$2sinx=x$$ by Newton- Raphson method, the initial guess was chosen to be $$x=2.0.$$ Consider $$x$

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The function $$f\left( z \right) = {{{z^2} + 1} \over {{z^2} + 4}}$$ is singular at

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In abrasive water jet machining, the velocity of water at the exit of the orifice, before mixing with abrasives, is 800

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A $$2m \times 2m$$ square operating in a vertical wall is covered with a metalic plate of the same dimensions as shown i

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A vertical cylindrical tank of $$1$$ $$m$$ diameter is filled with water up to a height of $$5$$ $$m$$ from its bottom.

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In a fully developed turbulent flow through a circular pipe, a head loss of ݄$${{h_1}}$$ is observed. The diameter of th

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A long slender metallic rod of length $$L$$ is used as a fin. As shown in the figure below, the left end of the fin is k

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The throughput rate of a production system is $$20$$ units per hour. The average flow time is $$30$$ minutes and the cyc

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Consider a network with nodes $$1, 2, 3, 4, 5$$ and $$6.$$ The nodes are connected with directed arcs as shown in the ta

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In linear gas tungsten arc welding of two plates of the same material, the peak temperature $$T$$ (in $$K$$) is given as

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Two flat steel sheets, each of $$2.5$$ $$mm$$ thickness, are being resistance spot welded using a current of $$6000$$ $$

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A helical gear with involute tooth profile has been machined with a disc-type form gear milling cutter. The helical gear

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A single point right handed turning tool is used for straight turning. The feed is $$0.25$$ $$mm/rev$$ and the uncut chi

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A cylindrical bar of $$100$$ $$mm$$ diameter is orthogonally straight turned with cutting velocity, feed and depth of cu

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A $$60$$ $$mm$$ wide block of low carbon steel is face milled at a cutting speed of $$120$$ $$m/min,$$ feed of $$0.1$$ $

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Consider the following statements.
$$(P)$$ Computer aided process planning $$(CAPP)$$ takes input from material requirem

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A single axis $$CNC$$ table is driven by a $$DC$$ servo motor that is directly coupled to a lead screw of $$5$$ $$mm$$ p

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In a single-pass rolling operation, a $$200$$ $$mm$$ wide metalic strip is rolled from a thickness $$10$$ $$mm$$ to a th

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Two solid cylinders of equal diameter have different heights. They are compressed plastically by a pair of rigid dies to

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The ratio of press force required to punch a square hole of $$30$$ $$mm$$ side in a $$1$$ $$mm$$ thick aluminium sheet t

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The limits of a shaft designated as $$100h5$$ are $$100.000$$ $$mm$$ and $$100.014$$ $$mm.$$ Similarly, the limits of a

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The roughness profile of a surface is depicted below.
The surface roughness parameter $${R_a}\,\,$$ (in $$\mu m$$) is

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A beam is subjected to an inclined concentrated load as shown in the figure below. Neglect the weight of the beam.
Th

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Consider the following statements:
(P) Hardness is the resistance of a material to indentation.
(Q) Elastic modulus is a

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A bar of rectangular cross-sectional area of $$50$$ mm2 is pulled from both the sides by equal forces of $$100$$ N as sh

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A 1 m × 10 mm $$ \times $$ 10 mm cantilever beam is subjected to a uniformly distributed load per unit length of 100 N/

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A thin-walled cylindrical pressure vessel of internal diameter 2 m is designed to withstand an internal pressure of 500

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An engine, connected with a flywheel, is designed to operate at an average angular speed of $$800$$ rpm. During operatio

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