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#GATE QUESTION BANK
The minimum number of equal length subintervals needed to approximate $\int_{1}^{2}xe^xdx$ to an accuracy of atleast (10^(-6))/3 using trapezoidal rule is __________.

The minimum number of equal length subintervals needed to approximate $\int_{1}^{2}xe^xdx$ to an accuracy of atleast (10^(-6))/3 using trapezoidal rule is __________.

160 points

Gokulan K asked Jul 15, 2020

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GATE2016-3-50
In a sheet metal of $2$ $mm$ thickness a hole of $10$ $mm$ diameter needs to be punched. The yield strength in tension of the sheet material is $100$ $MPa$ and its ultimate shear strength is $80$ $MPa$. The force required to punch the hole (in $kN$) is __________

In a sheet metal of $2$ $mm$ thickness a hole of $10$ $mm$ diameter needs to be punched. The yield strength in tension of the sheet material is $100$ $MPa$ and its ultima...

28.7k points

Arjun asked Feb 24, 2017

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GATE2016-2-46
A refrigerator uses $R-134a$ as its refrigerant and operates on an ideal vapour-compression refrigeration cycle between $0.14 \: MPa$ and $0.8 \: MPa$.if the mass flow rate of refrigerant is $0.05 \: kg/s$,the rate of heat rejection to the environment is_______$kW$ ... $\text{At } P=0.8 \: MPa, \: h=93.42 \: kJ/kg, \: \text{ (saturated liquid) }$

A refrigerator uses $R-134a$ as its refrigerant and operates on an ideal vapour-compression refrigeration cycle between $0.14 \: MPa$ and $0.8 \: MPa$.if the mass flow ra...

28.7k points

Arjun asked Feb 24, 2017

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GATE2016-2-45
A reversible cycle receives $40 \: kJ$ of heat from one heat source at a temperature of $127^ \circ C$ and $37 \: kJ$ from another heat source at $97^ \circ C$. The heat rejected (in $kJ$) to the heat sink at $47^ \circ C$ is __________

A reversible cycle receives $40 \: kJ$ of heat from one heat source at a temperature of $127^ \circ C$ and $37 \: kJ$ from another heat source at $97^ \circ C$. The heat ...

28.7k points

Arjun asked Feb 24, 2017

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GATE2016-2-3
Laplace transform of $\cos( \omega t)$ is $\dfrac{s}{s^2+\omega ^2} \\$ $\dfrac{\omega }{s^2+\omega ^2} \\$ $\dfrac{s}{s^2-\omega ^2} \\$ $\dfrac{\omega }{s^2-\omega ^2}$

Laplace transform of $\cos( \omega t)$ is$\dfrac{s}{s^2+\omega ^2} \\$$\dfrac{\omega }{s^2+\omega ^2} \\$$\dfrac{s}{s^2-\omega ^2} \\$$\dfrac{\omega }{s^2-\omega ^2}$

28.7k points

Arjun asked Feb 24, 2017

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GATE2015-3-26
The value of moment of inertia of the section shown in the figure about the axis-XX is $8.5050×10^6$ $mm^4$ $6.8850×10^6$ $mm^4$ $7.7625×10^6$ $mm^4$ $8.5725×10^6$ $mm^4$

The value of moment of inertia of the section shown in the figure about the axis-XX is$8.5050×10^6$ $mm^4$$6.8850×10^6$ $mm^4$$7.7625×10^6$ $mm^4$$8.5725×10^6$ $mm^4$...

28.7k points

Arjun asked Feb 24, 2017

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GATE2015-2-38
A hollow shaft ($d_o$ = $2d_i$ where $d_o$ and $d_i$ are the outer and inner diameters respectively) needs to transmit $20$ $kW$ power at $3000$ $RPM$. If the maximum permissible shear stress is $30$ $MPa$, do is $11.29$ $mm$ $22.58$ $mm$ $33.87$ $mm$ $45.16$ $mm$

A hollow shaft ($d_o$ = $2d_i$ where $d_o$ and $d_i$ are the outer and inner diameters respectively) needs to transmit $20$ $kW$ power at $3000$ $RPM$. If the maximum per...

28.7k points

Arjun asked Feb 24, 2017

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GATE2015-2-22
Which one of the following statements is TRUE? The ‘GO’ gage controls the upper limit of a hole The ‘NO GO’ gage controls the lower limit of a shaft The ‘GO’ gage controls the lower limit of a hole The ‘NO GO’ gage controls the lower limit of a hole

Which one of the following statements is TRUE?The ‘GO’ gage controls the upper limit of a holeThe ‘NO GO’ gage controls the lower limit of a shaftThe ‘GO’ gag...

28.7k points

Arjun asked Feb 24, 2017

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GATE2015-1-11
Air enters a diesel engine with a density of $1.0$ $kg$/$m^3$. The compression ratio is $21$. At steady state, the air intake is $30 × 10^{-3}$ $kg/s$ and the net work output is $15$ $kW$. The mean effective pressure (in $kPa$) is ____________

Air enters a diesel engine with a density of $1.0$ $kg$/$m^3$. The compression ratio is $21$. At steady state, the air intake is $30 × 10^{-3}$ $kg/s$ and the net work o...

28.7k points

Arjun asked Feb 24, 2017

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GATE Mechanical 2014 Set 3 | Question: 29
The real root of the equation $5x − 2 \cos x −1 = 0$ (up to two decimal accuracy) is _______

The real root of the equation $5x − 2 \cos x −1 = 0$ (up to two decimal accuracy) is _______

28.7k points

Arjun asked Feb 19, 2017

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GATE Mechanical 2014 Set 2 | Question: 14
For an incompressible flow field, $\overrightarrow{V}$, which one of the following conditions must be satisfied? $\bigtriangledown \cdot \overrightarrow{V}=0$ $\bigtriangledown \times \overrightarrow{V}=0$ ... $\frac{\partial \overrightarrow{V}}{\partial t}+(\overrightarrow{V} \cdot \bigtriangledown) \overrightarrow{V}=0$

For an incompressible flow field, $\overrightarrow{V}$, which one of the following conditions must be satisfied?$\bigtriangledown \cdot \overrightarrow{V}=0$$\bigtriangle...

28.7k points

Arjun asked Feb 19, 2017

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GATE Mechanical 2024 | Question: 50
A cutting tool provides a tool life of $60$ minutes while machining with the cutting speed of $60 \mathrm{~m} / \mathrm{min}$. When the same tool is used for machining the same material, it provides a tool life of $10$ ... material combination, the tool life computed using Taylor's tool life model is ________ minutes (rounded off to $2$ decimal places).

A cutting tool provides a tool life of $60$ minutes while machining with the cutting speed of $60 \mathrm{~m} / \mathrm{min}$. When the same tool is used for machining th...

4.4k points

admin asked Feb 16

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GATE2017 ME-1: 19
Consider the schematic of a riveted lap joint subjected to tensile load $F$, as shown below. Let $d$ be the diameter of the rivets, and $S_{f}$ be the maximum permissible tensile stress in the plates. What should be the minimum value for the thickness of the plates to guard against tensile failure of ... $\dfrac{F}{S_{f}W} \\$ $\dfrac{F}{S_{f}(W-d)} \\$ $\dfrac{2F}{S_{f}W}$

Consider the schematic of a riveted lap joint subjected to tensile load $F$, as shown below. Let $d$ be the diameter of the rivets, and $S_{f}$ be the maximum permissible...

28.7k points

Arjun asked Feb 26, 2017

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GATE Mechanical 2016 Set 1 | GA Question: 2
The policeman asked the victim of a theft, “What did you __________?” loose lose loss louse

The policeman asked the victim of a theft, “What did you __________?”looseloselosslouse

28.7k points

Arjun asked Feb 24, 2017

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GATE2015-2-26
The chance of a student passing an exam is $20 \%$. The chance of a student passing the exam and getting above $90 \%$ marks in it is $5 \%$. GIVEN that a student passes the examination, the probability that the student gets above $90 \%$ marks is $\dfrac{1}{18} \\ $ $\dfrac{1}{4} \\$ $\dfrac{2}{9} \\$ $\dfrac{5}{18}$

The chance of a student passing an exam is $20 \%$. The chance of a student passing the exam and getting above $90 \%$ marks in it is $5 \%$. GIVEN that a student passes ...

28.7k points

Arjun asked Feb 24, 2017

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GATE2015-2-24
Annual demand of a product is $50000$ units and the ordering cost is $Rs$. $7000$ per order. Considering the basic economic order quantity model, the economic order quantity is $10000$ units. When the annual inventory cost is minimized, the annual inventory holding cost (in $Rs$.) is _______

Annual demand of a product is $50000$ units and the ordering cost is $Rs$. $7000$ per order. Considering the basic economic order quantity model, the economic order quant...

28.7k points

Arjun asked Feb 24, 2017

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GATE Mechanical 2014 Set 4 | Question: 18
The total number of decision variables in the objective function of an assignment problem of size $n × n$ ($n$ jobs and $n$ machines) is $n^2$ $2n$ $2n-1$ $n$

The total number of decision variables in the objective function of an assignment problem of size $n × n$ ($n$ jobs and $n$ machines) is$n^2$$2n$$2n-1$$n$

28.7k points

Arjun asked Feb 19, 2017

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GATE Mechanical 2014 Set 2 | Question: 17
The difference in pressure (in $N/m^2$) across an air bubble of diameter $0.001$ $m$ immersed in water (surface tension $= 0.072$ $N/m$) is _______

The difference in pressure (in $N/m^2$) across an air bubble of diameter $0.001$ $m$ immersed in water (surface tension $= 0.072$ $N/m$) is _______

28.7k points

Arjun asked Feb 19, 2017

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GATE Mechanical 2014 Set 1 | Question: 48
A reversible heat engine receives $2$ $kJ$ of heat from a reservoir at $1000$ $K$ and a certain amount of heat from a reservoir at $800$ $K$. It rejects $1$ $kJ$ of heat to a reservoir at $400$ $K$. The net work output (in $kJ$) of the cycle is $0.8$ $1.0$ $1.4$ $2.0$

A reversible heat engine receives $2$ $kJ$ of heat from a reservoir at $1000$ $K$ and a certain amount of heat from a reservoir at $800$ $K$. It rejects $1$ $kJ$ of heat ...

28.7k points

Arjun asked Feb 19, 2017

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GATE Mechanical 2024 | Question: 16
Which one of the following failure theories is the most conservative design approach against fatigue failure? Soderberg line Modified Goodman line Gerber line Yield line

Which one of the following failure theories is the most conservative design approach against fatigue failure?Soderberg lineModified Goodman lineGerber lineYie...

4.4k points

admin asked Feb 16

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GATE Mechanical 2022 Set 1 | Question: 49
The product structure diagram shows the number of different components required at each level to produce one unit of the final product $P$. If there are $50$ units of on-hand inventory of component $A$, the number of additional units of component $A$ needed to produce 10 units of product $P$ is ______________ (in integer).

The product structure diagram shows the number of different components required at each level to produce one unit of the final product $P$. If there are $50$ units of on-...

28.7k points

Arjun asked Feb 15, 2022

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GATE Mechanical 2021 Set 2 | Question: 54
The torque provided by an engine is given by $T(\theta) =12000+ 2500 \sin(2 \theta) \text{N.m}$, where $\theta$ is the angle turned by the crank from inner dead center. The mean speed of the engine is $\text{200 rpm}$ and it ... minimum mass moment of inertia of the flywheel should be _______ $\text{kg.m}^{2} (\textit{round off to the nearest integer}$).

The torque provided by an engine is given by $T(\theta) =12000+ 2500 \sin(2 \theta) \text{N.m}$, where $\theta$ is the angle turned by the crank from inner dead center. T...

5.0k points

go_editor asked Mar 1, 2021

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GATE2020-ME-1: 42
A slot of $25\:mm\times 25\:mm$ is to be milled in a workpiece of $300\: mm$ length using a side and face milling cutter of diameter $100\: mm$, width $25\: mm$ and having $20$ teeth.For a depth of cut $5\: mm$ ... and approach and over travel distance of $5\: mm$ each, the time required for milling the slot is ________ minutes (round off to one decimal place).

A slot of $25\:mm\times 25\:mm$ is to be milled in a workpiece of $300\: mm$ length using a side and face milling cutter of diameter $100\: mm$, width $25\: mm$ and havin...

5.0k points

go_editor asked Feb 19, 2020

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GATE2016-3-53
A point P $(1, 3,−5)$ is translated by $2\hat{i}+3\hat{j}-4\hat{k}$ and then rotated counter clockwise by $90^\circ $ about the $z$-axis. The new position of the point is $(−6, 3,−9)$ $(−6,−3,−9)$ $(6, 3,−9)$ $(6, 3, 9)$

A point P $(1, 3,−5)$ is translated by $2\hat{i}+3\hat{j}-4\hat{k}$ and then rotated counter clockwise by $90^\circ $ about the $z$-axis. The new position of the point...

28.7k points

Arjun asked Feb 24, 2017

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GATE2016-3-37
A single degree of freedom spring-mass system is subjected to a harmonic force of constant amplitude. For an excitation frequency of $\sqrt{\dfrac{3k}{m}}$, the ratio of the amplitude of steady state response to the static deflection of the spring is __________

A single degree of freedom spring-mass system is subjected to a harmonic force of constant amplitude. For an excitation frequency of $\sqrt{\dfrac{3k}{m}}$, the ratio of ...

28.7k points

Arjun asked Feb 24, 2017

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GATE2016-3-8
T he state of stress at a point on an element is shown in figure (a). The same state of stress is shown in another coordinate system in figure (b). The components $(\tau _{xx},\tau_{yy},\tau _{xy})$ are given by $(p/\sqrt{2},-p/\sqrt{2},0)$ $(0,0,p)$ $(p,-p,p/\sqrt{2})$ $(0,0,p/\sqrt{2})$

T he state of stress at a point on an element is shown in figure (a). The same state of stress is shown in another coordinate system in figure (b).The components $(\tau _...

28.7k points

Arjun asked Feb 24, 2017

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GATE2016-2-16
Consider the radiation heat exchange inside an annulus between two very long concentric cylinders. The radius of the outer cylinder is $R_o$ and that of the inner cylinder is $R_i$ . The radiation view factor of the outer cylinder onto itself is $1-\sqrt{\dfrac{R_i}{R_o}}\\$ $\sqrt{1-\dfrac{R_i}{R_o}} \\$ $1-\dfrac{R_i}{R_o}^{1/3} \\$ $1-\dfrac{R_i}{R_o}$

Consider the radiation heat exchange inside an annulus between two very long concentric cylinders. The radius of the outer cylinder is $R_o$ and that of the inner cylinde...

28.7k points

Arjun asked Feb 24, 2017

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GATE2016-1-55
Maximize $Z = 15X_1 + 20X_2$ subject to $\begin{array}{l} 12X_1 + 4X_2 \geq 36 \\ 12X_1 − 6X_2 \leq 24 \\ X_1, X_2 \geq 0 \end{array}$ The above linear programming problem has infeasible solution unbounded solution alternative optimum solutions degenerate solution

Maximize $Z = 15X_1 + 20X_2$ subject to $$\begin{array}{l} 12X_1 + 4X_2 \geq 36 \\ 12X_1 − 6X_2 \leq 24 \\ X_1, X_2 \geq 0 \end{array}$$The above linear programming pr...

28.7k points

Arjun asked Feb 24, 2017

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GATE2016-1-54
The annual demand for an item is $10,000$ units. The unit cost is $Rs$. $100$ and inventory carrying charges are $14.4\%$ of the unit cost per annum. The cost of one procurement is $Rs$. $2000$. The time between two consecutive orders to meet the above demand is _______ month($s$).

The annual demand for an item is $10,000$ units. The unit cost is $Rs$. $100$ and inventory carrying charges are $14.4\%$ of the unit cost per annum. The cost of one proc...

28.7k points

Arjun asked Feb 24, 2017

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GATE2016-1-49
Heat is removed from a molten metal of mass $2$ $kg$ at a constant rate of $10$ $kW$ till it is completely solidified.The cooling curve is shown in the figure Assuming uniform temperature throughout the volume of the metal during solidification,the latent heat of fusion of metal ( in $kJ$/$kg$) is _________

Heat is removed from a molten metal of mass $2$ $kg$ at a constant rate of $10$ $kW$ till it is completely solidified.The cooling curve is shown in the figureAssuming uni...

28.7k points

Arjun asked Feb 24, 2017

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GATE2016-1-10
A car is moving on a curved horizontal road of radius $100$ $m$ with a speed of $20$ $m/s$. The rotating masses of the engine have an angular speed of $100$ $rad/s$ in clockwise direction when viewed from the front of the car. The combined moment of inertia of the rotating masses is $10$ $kg$-$m^2$. The magnitude of the gyroscopic moment (in $N$-$m$) is __________

A car is moving on a curved horizontal road of radius $100$ $m$ with a speed of $20$ $m/s$. The rotating masses of the engine have an angular speed of $100$ $rad/s$ in cl...

28.7k points

Arjun asked Feb 24, 2017

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GATE2015-3-43
Newton-Raphson method is used to find the roots of the equation, $x^3+3x^2+3x-1=0$. If the initial guess is $x_0=1$, then the value of $x$ after $2^{nd}$ iteration is ________

Newton-Raphson method is used to find the roots of the equation, $x^3+3x^2+3x-1=0$. If the initial guess is $x_0=1$, then the value of $x$ after $2^{nd}$ iteration is ___...

28.7k points

Arjun asked Feb 24, 2017

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GATE2015-1-8
For flow of viscous fluid over a flat plate, if the fluid temperature is the same as the plate temperature, the thermal boundary layer is thinner than the velocity boundary layer thicker than the velocity boundary layer of the same thickness as the velocity boundary layer not formed at all

For flow of viscous fluid over a flat plate, if the fluid temperature is the same as the plate temperature, the thermal boundary layer isthinner than the velocity boundar...

28.7k points

Arjun asked Feb 24, 2017

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GATE Mechanical 2014 Set 4 | Question: 12
As the temperature increases, the thermal conductivity of a gas increases decreases remains constant increases up to a certain temperature and then decreases

As the temperature increases, the thermal conductivity of a gas increasesdecreasesremains constantincreases up to a certain temperature and then decreases

28.7k points

Arjun asked Feb 19, 2017

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GATE Mechanical 2014 Set 3 | Question: 45
A fluid of dynamic viscosity $2 × 10^{−5}$ $kg/m.s$ and density $1$ $kg/m^3$ flows with an average velocity of $1$ $m/s$ through a long duct of rectangular ($25$ $mm$ × $15$ $mm$) cross-section. Assuming laminar flow, the pressure drop (in $Pa$) in the fully developed region per meter length of the duct is _______

A fluid of dynamic viscosity $2 × 10^{−5}$ $kg/m.s$ and density $1$ $kg/m^3$ flows with an average velocity of $1$ $m/s$ through a long duct of rectangular ($25$ $mm$ ...

28.7k points

Arjun asked Feb 19, 2017

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GATE Mechanical 2014 Set 3 | Question: 41
A certain amount of an ideal gas is initially at a pressure $p_1$ and temperature $T_1$. First, it undergoes a constant pressure process $1$-$2$ such that $T_2$ = $3T_1$/$4$. Then, it undergoes a constant volume process $2$-$3$ such that $T_3$ = $T_1$/$2$. The ratio of the final volume to the initial volume of the ideal gas is $0.25$ $0.75$ $1.0$ $1.5$

A certain amount of an ideal gas is initially at a pressure $p_1$ and temperature $T_1$. First, it undergoes a constant pressure process $1$-$2$ such that $T_2$ = $3T_1$/...

28.7k points

Arjun asked Feb 19, 2017

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GATE Mechanical 2014 Set 2 | Question: 13
The thermal efficiency of an air-standard Brayton cycle in terms of pressure ratio $r_p$ and $\gamma (= c_p /c_v)$ is given by $1-\dfrac{1}{{r_p}^{\gamma -1}} \\$ $1-\dfrac{1}{{r_p}^{\gamma }} \\$ $1-\dfrac{1}{{r_p}^{1/\gamma }} \\$ $1-\dfrac{1}{{r_p}^{(\gamma -1)/\gamma }}$

The thermal efficiency of an air-standard Brayton cycle in terms of pressure ratio $r_p$ and $\gamma (= c_p /c_v)$ is given by$1-\dfrac{1}{{r_p}^{\gamma -1}} \\$$1-\dfrac...

28.7k points

Arjun asked Feb 19, 2017

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GATE Mechanical 2014 Set 1 | Question: 53
For the given assembly: $25 \: H7/g8$, match Group $A$ with Group $B$ ... $P-I, Q-IV, R-III, S-II$ $P-II, Q-III, R-IV, S-I$ $P-II, Q-IV, R-III, S-I$

For the given assembly: $25 \: H7/g8$, match Group $A$ with Group $B$$$\begin{array}{|c|l|c|l|} \hline & \textbf{Group A} & & \textbf{Group B} \\ \hline P. & \text{H} & I...

28.7k points

Arjun asked Feb 19, 2017

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GATE Mechanical 2014 Set 1 | GA Question: 1
Choose the most appropriate phrase from the options given below to complete the following sentence. The aircraft _________ take off as soon as its flight plan was filed. is allowed to will be allowed to was allowed to has been allowed to

Choose the most appropriate phrase from the options given below to complete the following sentence.The aircraft _________ take off as soon as its flight plan was filed.is...

28.7k points

Arjun asked Feb 19, 2017

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GATE Mechanical 2024 | Question: 19
The "Earing" phenomenon in metal forming is associated with deep drawing rolling extrusion forging

The "Earing" phenomenon in metal forming is associated withdeep drawingrollingextrusionforging

4.4k points

admin asked Feb 16

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