GATE 2010 Production & Industrial

If $$f\left( x \right) = \sin \left| x \right|\,\,$$ then the value of $${{df} \over {dx}}\,\,$$ at $$\,\,x = {{ - \pi } \over 4}\,\,$$ is

The integral $$\,\,{1 \over {\sqrt {2\pi } }}\int\limits_{ - \infty }^\infty {{e^{{{ - {x^2}} \over 2}}}} dx\,\,$$ is equal to

The solution of the differential equation $${{dy} \over {dx}} - {y^2} = 1$$ satisfying the condition $$y(0)=1$$ is

If $$(1, 0, -1)$$$${}^T$$ is an eigen vector of the following matrix $$\left[ {\matrix{ 1 & { - 1} & 0 \cr { - 1} & 2 & { - 1} \cr 0 & { - 1} & 1 \cr } } \right]$$ then the corresp...

Which one of the following differential equations has a solution given by the function $$y = 5\sin \left( {3x + {\pi \over 3}} \right)$$

The value of $$q$$ for which the following set of linear equations $$2x+3y=0, 6x+qy=0$$ can have non-trivial solution is

The following algorithm computes the integral $$\,J = \int\limits_a^b {f\left( x \right)dx\,\,\,} $$ from the given values $${f_j} = f\left( {{x_j}} \right)$$ at equidistant points...

If a random variable $$X$$ satisfies the poission's distribution with a mean value of $$2,$$ then the probability that $$X > 2$$ is

Two white and two black balls, kept in two bins, are arranged in four ways as shown below. In each arrangement, a bin has to be chosen randomly and only one ball needs to be picked...

Cold shut (lap) may occur in products obtained by:

Hot die steel, used for large solid dies in drop forging, should necessarily have

During open die forging process using two flat and parallel dies, a solid steel disc of initial radius $$({R_{IN}})\,\,200mm$$ and Initial height $$({H_{IN}})\,\,50mm$$ attains a h...

In a rolling process, the roll separating force can be decreased by

Solidification time of a metallic alloy casting is

A small bore is designated as $$25H7.$$ The lower (minimum) and upper (maximum) limits of the bore are $$25.000mm$$ and $$25.021$$ respectively. When the bore is designated as $$25...

An industrial gas $$\left( {{C_p} = 1kJ/kgK} \right)$$ enters a parallel flow heat exchanger at $${250^ \circ }C$$ with a flow rate of $$2$$ $$kg/s$$ to heat a water stream. The wa...

During a steady gas metal arc welding with direct current electrode positive polarity, the welding current, voltage and weld speed are $$150A,$$ $$30V$$ and $$6m/min$$ respectively...

For a $$3$$-axes $$CNC$$ table, the slide along the vertical axis of the table driven by a $$DC$$ servo motor via lead screw nut mechanism. The lead screw has a pitch of $$5mm.$$ T...

Which of the following powder production methods produces spongy and porous particles?

During turning of a low carbon steel bar with TiN coated carbide insert, one needs to improve surface finish without sacrificing material removal rate. To achieve improved surface...

During the filling process of a given sand mould cavity by metal through a horizontal runner of circular $$C.S,$$ the frictional head loss of the molten metal in the runner will in...