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GATE2016-1-31
A two-member truss $PQR$ is supporting a load $W$. The axial forces in members $PQ$ and $QR$ are respectively $2W$ tensile and $\sqrt{3}W$ compressive $\sqrt{3}W$ tensile and $2W$ compressive $\sqrt{3}W$ compressive and $2W$ tensile $2W$ compressive and $\sqrt{3}W$ tensile

A two-member truss $PQR$ is supporting a load $W$. The axial forces in members $PQ$ and $QR$ are respectively$2W$ tensile and $\sqrt{3}W$ compressive$\sqrt{3}W$ tensile a...

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GATE2015-3-36
A Prandtl tube (Pitot-static tube with $C$=$1$) is used to measure the velocity of water. The differential manometer reading is $10$ $mm$ of liquid column with a relative density of $10$. Assuming $g$ = $9.8$ $m$/$s^2$, the velocity of water (in $m/s$) is ________

A Prandtl tube (Pitot-static tube with $C$=$1$) is used to measure the velocity of water. The differential manometer reading is $10$ $mm$ of liquid column with a relative...

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GATE2016-3-54
The demand for a two-wheeler was $900$ units and $1030$ units in April $2015$ and May $2015$, respectively. The forecast for the month of April $2015$ was $850$ units. Considering a smoothing constant of $0.6$, the forecast for the month of June $2015$ is $850$ units $927$ units $965$ units $970$ units

The demand for a two-wheeler was $900$ units and $1030$ units in April $2015$ and May $2015$, respectively. The forecast for the month of April $2015$ was $850$ units. Co...

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GATE2016-3-34
Two circular shafts made of same material, one solid (S) and one hollow (H), have the same length and polar moment of inertia. Both are subjected to same torque. Here, $\theta _S$ is the twist and $\tau _S$ ... $\theta _S<\theta _H$ and $\tau _S<\tau _H$ $\theta _S=\theta _H$ and $\tau _S<\tau _H$

Two circular shafts made of same material, one solid (S) and one hollow (H), have the same length and polar moment of inertia. Both are subjected to same torque. Here, $\...

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GATE Mechanical 2015 Set 3 | GA Question: 7
Given below are two statements followed by two conclusions. Assuming these statements to be true, decide which one logically follows: Statements: No manager is a leader. All leaders are executives. Conclusions: No manager is an ... Only conclusion I follows Only conclusion II follows Neither conclusion I nor II follows Both conclusion I and II follows

Given below are two statements followed by two conclusions. Assuming these statements to be true, decide which one logically follows:Statements:No manager is a leader.All...

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GATE2015-1-1
If any two columns of a determinant $P=\begin{bmatrix} 4 & 7 & 8\\ 3 & 1 & 5\\ 9 & 6 & 2 \end{bmatrix}$ are interchanged, which one of the following statements regarding the value of the determinant is CORRECT? ... . Both absolute value and sign will change. Absolute value will change but sign will not change. Both absolute value and sign will remain unchanged.

If any two columns of a determinant $P=\begin{bmatrix} 4 & 7 & 8\\ 3 & 1 & 5\\ 9 & 6 & 2 \end{bmatrix}$ are interchanged, which one of the following statements regarding ...

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GATE2016-3-29
Three cards were drawn from a pack of $52$ cards. The probability that they are a king, a queen, and a jack is $\dfrac{16}{5525} \\$ $\dfrac{64}{2197} \\$ $\dfrac{3}{13} \\$ $\dfrac{8}{16575}$

Three cards were drawn from a pack of $52$ cards. The probability that they are a king, a queen, and a jack is$\dfrac{16}{5525} \\$$\dfrac{64}{2197} \\$$\dfrac{3}{13} \\$...

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GATE2015-2-50
The flow stress (in $MPa$) of a material is given by $\sigma =500\varepsilon ^{0.1}$, where $ε$ is true strain. The Young’s modulus of elasticity of the material is $200$ $GPa$. A block of thickness $100$ $mm$ made of this material is compressed to $95$ $mm$ thickness and then the load is removed. The final dimension of the block (in $mm$) is _________

The flow stress (in $MPa$) of a material is given by $\sigma =500\varepsilon ^{0.1}$,where $ε...

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GATE2015-1-4
The value of $\displaystyle{} \lim_{x\rightarrow 0}\dfrac{1- \cos(x^2)}{2x^4}$ is $0 \\$ $\dfrac{1}{2} \\$ $\dfrac{1}{4} \\$ undefined

The value of $\displaystyle{} \lim_{x\rightarrow 0}\dfrac{1- \cos(x^2)}{2x^4}$ is$0 \\$$\dfrac{1}{2} \\$$\dfrac{1}{4} \\$undefined

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GATE2015-1-46
A horizontal plate has been joined to a vertical post using four rivets arranged as shown in the figure. The magnitude of the load on the worst loaded rivet (in $N$) is _______

A horizontal plate has been joined to a vertical post using four rivets arranged as shown in the figure. The magnitude of the load on the worst loaded rivet (in $N$) is _...

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GATE2016-1-22
The part of a gating system which regulates the rate of pouring of molten metal is pouring basin runner choke ingate

The part of a gating system which regulates the rate of pouring of molten metal ispouring basinrunnerchokeingate

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GATE Mechanical 2014 Set 1 | Question: 37
An offset slider-crank mechanism is shown in the figure at an instant. Conventionally, the Quick Return Ratio (QRR) is considered to be greater than one. The value of QRR is _______

An offset slider-crank mechanism is shown in the figure at an instant. Conventionally, the Quick Return Ratio (QRR) is considered to be greater than one. The value of QRR...

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GATE2016-1-34
A simply-supported beam of length $3L$ is subjected to the loading shown in the figure. It is given that $P=1\: N$, $L=1\:m$ and Young's modulus $E=200\:GPa$. The cross-section is a square with dimension $10\:mm\times10\:mm$. The ... at a distance of $1.5L$ from the left end is _____________ (Indicate compressive stress by a negative sign and tensile stress by a positive sign.)

A simply-supported beam of length $3L$ is subjected to the loading shown in the figure.It is given that $P=1\: N$, $L=1\:m$ and Young’s modulus $E=200\:GPa$. The cross-...

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GATE2016-1-51
A cylindrical job with diameter of $200$ $mm$ and height of $100$ $mm$ is to be cast using modulus method of riser design. Assume that the bottom surface of cylindrical riser does not contribute as cooling surface. If the diameter of the riser is equal to its height, then the height of the riser (in $mm$) is $150$ $200$ $100$ $125$

A cylindrical job with diameter of $200$ $mm$ and height of $100$ $mm$ is to be cast using modulus method of riser design. Assume that the bottom surface of cylindrical r...

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GATE2016-3-38
A bolted joint has four bolts arranged as shown in figure. The cross sectional area of each bolt is $25$ $mm^2$. A torque $T$ = $200N-m$ is acting on the joint. Neglecting friction due to clamping force, maximum shear stress in a bolt is ______ $MPa$.

A bolted joint has four bolts arranged as shown in figure. The cross sectional area of each bolt is $25$ $mm^2$. A torque $T$ = $200N-m$ is acting on the joint. Neglectin...

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GATE2015-3-45
A bullet spins as the shot is fired from a gun. For this purpose, two helical slots as shown in the figure are cut in the barrel. Projections $A$ and $B$ on the bullet engage in each of the slots. Helical slots are such that one turn of helix is completed over a ... $m$. If velocity of bullet when it exits the barrel is $20$ $m/s$, its spinning speed in $rad/s$ is ________

A bullet spins as the shot is fired from a gun. For this purpose, two helical slots as shown in the figure are cut in the barrel. Projections $A$ and $B$ on the bullet en...

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GATE2015-3-35
In a CNC milling operation, the tool has to machine the circular arc from point $(20, 20)$ to $(10, 10)$ at sequence number $5$ of the CNC part program. If the center of the arc is at $(20, 10)$ ... R$10$ N $05$ G$90$ G$03$ X$20$ Y$20$ R$10$ N $05$ G$91$ G$02$ X$20$ Y$20$ R$10$

In a CNC milling operation, the tool has to machine the circular arc from point $(20, 20)$ to $(10, 10)$ at sequence number $5$ of the CNC part program. If the center of ...

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GATE2015-3-2
For the same material and the mass, which of the following configurations of flywheel will have maximum mass moment of inertia about the axis of rotation OO’ passing through the center of gravity.

For the same material and the mass, which of the following configurations of flywheel will have maximum mass moment of inertia about the axis of rotation OO’ passing th...

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GATE2015-1-37
In a slab rolling operation, the maximum thickness reduction $(Δℎ_{max}$) is given by $Δ_{max}$ = $\mu^2R$ , where $R$ is the radius of the roll and $\mu$ is the coefficient of friction between the roll and the sheet. If $\mu$ = $0.1$, the maximum angle subtended by the deformation zone at the centre of the roll (bite angle in degrees) is _______

In a slab rolling operation, the maximum thickness reduction $(Δℎ_{max}$) is given by $Δ_{max}$ = $\mu^2R$ , where $R$ is the radius of the roll and $\mu$ is the coef...

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GATE2015-3-3
A gear train is made up of five spur gears as shown in the figure. Gear $2$ is driver and gear $6$ is driven member. $N_2$, $N_3$, $N_4$, $N_5$ and $N_6$ represent number of teeth on gears $2$, $3$, $4$, $5$, and $6$ respectively. The gear(s) which act(s) as idler(s) is/are Only $3$ Only $4$ Only $5$ Both $3$ and $5$

A gear train is made up of five spur gears as shown in the figure. Gear $2$ is driver and gear $6$ is driven member. $N_2$, $N_3$, $N_4$, $N_5$ and $N_6$ represent number...

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GATE Mechanical 2016 Set 3 | GA Question: 8
Two and a quarter hours back,when seen in the mirror,the reflection of the wall clock without number marking seemed to show $1:30$.what is the actual current time shown by the clock? $8:15$ $11:15$ $12:15$ $12:45$

Two and a quarter hours back,when seen in the mirror,the reflection of the wall clock without number marking seemed to show $1:30$.what is the actual current time shown b...

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GATE2016-1-41
A steady laminar boundary layer is formed over a flat plate as shown in the figure. The free stream velocity of the fluid is $U_o$. The velocity profile at the inlet $a-b$ is uniform, while that at a downstream location $c-d$ ... rate, $\dot{m}_{bd}$ leaving through the horizontal section $b-d$ to that entering through the vertical section $a-b$ is ___________

A steady laminar boundary layer is formed over a flat plate as shown in the figure. The free stream velocity of the fluid is $U_o$. The velocity profile at the inlet $a-b...

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GATE2016-1-32
A horizontal bar with a constant cross-section is subjected to loading as shown in the figure. The Young’s moduli for the sections $AB$ and $BC$ are $3E$ and $E$, respectively. For the deflection at $C$ to be zero, the ratio $\displaystyle{\frac{P}{F}}$ is ____________

A horizontal bar with a constant cross-section is subjected to loading as shown in the figure. The Young’s moduli for the sections $AB$ and $BC$ are $3E$ and $E$, respe...

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GATE2016-3-55
A firm uses a turning center, a milling center and a grinding machine to produce two parts. The table below provides the machining time required for each part and the maximum machining time available on each machine. The profit per unit on parts $I$ and $II$ are $Rs. 40$ ... minutes) I II Turning machine $12$ $6$ $6000$ Milling center $4$ $10$ $4000$ Grinding Machine $2$ $3$ $1800$

A firm uses a turning center, a milling center and a grinding machine to produce two parts. The table below provides the machining time required for each part and the max...

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GATE2016-3-51
In a single point turning operation with cemented carbide tool and steel work piece, it is found that the Taylor’s exponent is $0.25$. If the cutting speed is reduced by $50 \%$ then the tool life changes by ______ times.

In a single point turning operation with cemented carbide tool and steel work piece, it is found that the Taylor’s exponent is $0.25$. If the cutting speed is reduced b...

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GATE2016-3-21
Equal amounts of a liquid metal at the same temperature are poured into three moulds made of steel, copper and aluminum. The shape of the cavity is a cylinder with 15 mm diameter. The size of the moulds are such that the outside temperature of the moulds do ... , respectively.) Copper - Steel - Aluminum Aluminum - Steel - Copper Copper - Aluminum - Steel Steel - Copper - Aluminum

Equal amounts of a liquid metal at the same temperature are poured into three moulds made of steel, copper and aluminum. The shape of the cavity is a cylinder with 15 mm ...

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GATE2015-1-33
Following data refers to the activities of a project, where, node $1$ refers to the start and node $5$ ... (CP) in the network is $1$-$2$-$3$-$5$ $1$-$4$-$3$-$5$ $1$-$2$-$3$-$4$-$5$ $1$-$4$-$5$

Following data refers to the activities of a project, where, node $1$ refers to the start and node $5$ refers to the end of the project.$\begin{array}{|l|l|} \hline \text...

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GATE2016-3-49
For an orthogonal cutting operation, tool material is HSS, rake angle is $22^\circ $, chip thickness is $0.8 \: mm$, speed is $48 \: m/min$ and feed is $0.4 \: mm/rev$. The shear plane angle (in degrees) is $19.24$ $29.70$ $56.00$ $68.75$

For an orthogonal cutting operation, tool material is HSS, rake angle is $22^\circ $, chip thickness is $0.8 \: mm$, speed is $48 \: m/min$ and feed is $0.4 \: mm/rev$. T...

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GATE2015-1-36
The solidification time of a casting is proportional to $\left( \dfrac{V}{A} \right )^2$, where $V$ is the volume of the casting and $A$ is the total casting surface area losing heat. Two cubes of same material and size are cast using sand casting process. The top face of one of ... insulated to that of the other cube is $\dfrac{25}{36} \\$ $\dfrac{36}{25} \\$ $1 \\$ $\dfrac{6}{5}$

The solidification time of a casting is proportional to $\left( \dfrac{V}{A} \right )^2$, where $V$ is the volume of the casting and $A$ is the total casting surface area...

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GATE Mechanical 2016 Set 2 | GA Question: 4
Fact: If it rains, then the field is wet. Read the following statements: It rains The field is not wet The field is wet It did not rain Which one of the options given below is NOT logically possible, based on the given fact? If $(iii)$, then $(iv)$. If $(i)$, then $(iii)$. If $(i)$, then $(ii)$. If $(ii)$, then $(iv)$.

Fact: If it rains, then the field is wet.Read the following statements:It rainsThe field is not wetThe field is wetIt did not rainWhich one of the options given below is ...

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GATE2016-1-44
A fluid (Prandtl number, $P_r=1$) at $500\:K$ flows over a flat plate of $1.5\:m$ length, maintained at $300\: K$. The velocity of the fluid is $10 \: m/s$. Assuming kinematic viscosity,$v=30\times 10^{-6}$ $m^2/s$, the thermal boundary layer thickness (in $mm$) at $0.5 \:m$ from the leading edge is __________

A fluid (Prandtl number, $P_r=1$) at $500\:K$ flows over a flat plate of $1.5\:m$ length, maintained at $300\: K$. The velocity of the fluid is $10 \: m/s$. Assuming kine...

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GATE2016-1-19
The INCORRECT statement about regeneration in vapor power cycle is that it increases the irreversibility by adding the liquid with higher energy content to the steam generator heat is exchanged between the expanding fluid in the turbine and the compressed ... the principle is similar to the principle of Stirling gas cycle it is practically implemented by providing feed water heaters

The INCORRECT statement about regeneration in vapor power cycle is thatit increases the irreversibility by adding the liquid with higher energy content to the steam gener...

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GATE Mechanical 2015 Set 2 | GA Question: 10
Ms.X will be in Bagdogra from $01/05/2014$ to $20/05/2014$ and from $22/05/2014$ to $31/05/2014$.On the morning of $21/5/2104$, she will reach Kochi via Mumbai. Which of the statement below is logically valid and can be inferred from the above ... in May. Ms.X will be only in Kochi for one day,only in May. Only Ms.X will be in Kochi for one day in May.

Ms.X will be in Bagdogra from $01/05/2014$ to $20/05/2014$ and from $22/05/2014$ to $31/05/2014$.On the morning of $21/5/2104$, she will reach Kochi via Mumbai.Which of t...

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GATE2016-3-4
The area (in percentage) under standard normal distribution curve of random variable Z within limits from −$3$ to +$3$ is __________

The area (in percentage) under standard normal distribution curve of random variable Z within limits from −$3$ to +$3$ is __________

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GATE Mechanical 2014 Set 2 | Question: 33
Consider a flywheel whose mass $M$ is distributed almost equally between a heavy, ring-like rim of radius $R$ and a concentric disk-like feature of radius $R/2$. Other parts of the flywheel, such as spokes, etc, have negligible mass. The best ... for $α$, if the moment of inertia of the flywheel about its axis of rotation is expressed as $αMR^2$, is _______

Consider a flywheel whose mass $M$ is distributed almost equally between a heavy, ring-like rim of radius $R$ and a concentric disk-like feature of radius $R/2$. Other pa...

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GATE2015-3-54
A brick wall $\left(k=0.9\displaystyle{\frac{W}{m.k}}\right)$ of thickness $0.18$ $m$ separates the warm air in a room from the cold ambient air. On a particular winter day, the outside air temperature is $−5^\circ C$ ... resistance of the air inside the room, the heat loss, in $\displaystyle{\frac{W}{m^2}}$, is $88$ $110$ $128$ $160$

A brick wall $\left(k=0.9\displaystyle{\frac{W}{m.k}}\right)$ of thickness $0.18$ $m$ separates the warm air in a room from the cold ambient air. On a particular winter d...

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GATE2016-2-54
A food processing company uses $25,000 \:kg$ ... on an annual basis is $20\%$ of the purchase price of the corn flour per $kg$. The optimal order quantity (in $kg$) is _____________

A food processing company uses $25,000 \:kg$ of corn flour every year. The quantity-discount price of corn flour is provided in the table below:$$\begin{array}{|l|l|} \hl...

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GATE2016-2-32
A rigid horizontal rod of length $2L$ is fixed to a circular cylinder of radius $R$ as shown in the figure. Vertical forces of magnitude $P$ are applied at the two ends as shown in the figure. The shear modulus for the cylinder is $G$ and the Young’s modulus is $E$. The vertical deflection at point A is $PL^3/(\pi R^4G)$ $PL^3/(\pi R^4E)$ $2PL^3/(\pi R^4E)$ $4PL^3/(\pi R^4G)$

A rigid horizontal rod of length $2L$ is fixed to a circular cylinder of radius $R$ as shown in the figure. Vertical forces of magnitude $P$ are applied at the two ends a...

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GATE Mechanical 2014 Set 4 | Question: 55
A butt weld joint is developed on steel plates having yield and ultimate tensile strength of $500$ $MPa$ and $700$ $MPa$, respectively. The thickness of the plates is $8$ $mm$ and width is $20$ $mm$. Improper selection of ... $mm$ depth along the weld. The maximum transverse tensile load (in $kN$) carrying capacity of the developed weld joint is _______

A butt weld joint is developed on steel plates having yield and ultimate tensile strength of $500$ $MPa$ and $700$ $MPa$, respectively. The thickness of the plates is $8$...

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GATE Mechanical 2015 Set 3 | GA Question: 10
A coin is tossed thrice. Let C be the event that head occurs in each of first two tosses. Let Y be the event that tails occurs in third toss. Let Z be the event that two tails occur in three tosses. Based on the above information, ... statement is TRUE? X and Y are not independent Y and Z are dependent Y and Z are independent X and Z are independent

A coin is tossed thrice. Let C be the event that head occurs in each of first two tosses. Let Y be the event that tails occurs in third toss. Let Z be the event that two ...

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