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GATE20153GA10
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,which one of the following statement is TRUE? X and Y are not independent Y and Z are dependent Y and Z are independent X and Z are independent
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GATE20153GA9
Right triangle PQR is to be constructed in xyplane so that the right angle is at P and line PR is parallel to xaxis.The x and y coordinates of P,Q and R are to be integers that satisfies the inequalities:$4\leq x\leq 5$ and $6\leq y\leq 16$. How many different triangles could be constructed with these properties? $110$ $1100$ $9900$ $10000$
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GATE20153GA8
In the given figure Q is a right triangle,PS:QS = $3:1$, RT:QT = $5:2$ and PU:UR = $1:1$. If area of triangle QTS is $20$ $cm^2$, then the area of triangle PQR in $cm^2$ is_____
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GATE20153GA7
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 executive. No executive is a manager Only conclusion I follows Only conclusion II follows Neither conclusion I nor II follows Both conclusion I and II follows
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GATE20153GA6
Select the option in place of underlined parts of sentence. Increased productivity necessary reflects greater efforts made by the employees. Increase in productivity necessary Increase productivity is necessary Increase in productivity necessarily No improvement required
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GATE20153GA5
Five teams have to compete in a league,with every team playing every other team exactly once,before going to the next round.How many matches will have to held to complete the league round of matches? $20$ $10$ $8$ $5$
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gate20153
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GATE20153GA3
Choose the statement where underlined word is used correctly When the teacher eludes to different authors,he is being elusive. When the thief keeps eluding the police, he is being elusive Matters that are difficult to understand,identify or remember are allusive Mirages can be allusive,but a better way to express them is illusory.
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GATE20153GA4
Tanya is older than Eric. Cliff is older than Tanya. Eric is older than Cliff. If the first two statements are true ,then the third statement is : True False Uncertain Data insufficient
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GATE20153GA2
Fill the blank with the correct idiom/phrase. That boy from the town was____in the sleepy village. dog out of heard sheep from the heap fish out of water bird from the flock
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GATE20153GA1
Choose the appropriate word/phrase, out of the four options given below, to complete the following sentence: Apparent lifelessness_________dormant life. harbours leads to supports affects
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GATE2015355
A mixture of ideal gases has the following composition by mass: $N_2$ $O_2$ $CO_2$ $60%$ $30%$ $10%$ If the universal gas constant is $8314$ $J/kmol$$K$, the characteristic gas constant of the mixture (in $J/kg$$K$) is ________
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GATE2015354
A brick wall $(k=0.9\frac{W}{m.k})$ 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 $−5^oC$ and the room needs to be maintained at $27^oC$. The heat transfer ... Neglecting the convective resistance of the air inside the room, the heat loss, in $\frac{W}{m^2}$, is $88$ $110$ $128$ $160$
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GATE2015350
The dimensions of a cylindrical side riser (height = diameter) for a $25$ $cm$ × $15$ $cm$ × $5$ $cm$ steel casting are to be determined. For the tabulated shape factor values given below, the diameter of the riser (in $cm$) is ________ Shape factor 2 4 6 8 10 12 Riser volume/Casting volume 1.0 0.70 0.55 0.50 0.40 0.35
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GATE2015352
Which of the following statements are TRUE, when the cavitation parameter $\sigma =0$? the local pressure is reduced to vapor pressure cavitation starts boiling of liquid starts cavitation stops (i), (ii) and (iv) only (ii) and (iii) only (i) and (iii) (i), (ii) and (iii)
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GATE2015353
One side of a wall is maintained at $400$ $K$ and the other at $300$ $K$. The rate of heat transfer through the wall is $1000$ $W$ and the surrounding temperature is $25^oC$. Assuming no generation of heat within the wall, the irreversibility (in $W$) due to heat transfer through the wall is ________
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GATE2015351
For the linear programming problem: Maximize $Z = 3X_1 + 2X_2$ Subject to $−2X_1 + 3X_2 ≤ 9$ $X_1 − 5 X_2 ≥ −20$ $X_1, X_2 ≥ 0$ The above problem has unbounded solution infeasible solution alternative optimum solution degenerate solution
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GATE2015349
A shaft of length $90$ $mm$ has a tapered portion of length $55$ $mm$. The diameter of the taper is $80$ $mm$ at one end and $65$ $mm$ at the other. If the taper is made by tailstock set over method, the taper angle and the set over respectively are $15^o32′$ and $12.16$ $mm$ $18^o32′$ and $15.66$ $mm$ $11^o22′$ and $10.26$ $mm$ $10^o32′$ and $14.46$ $mm$
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GATE2015348
A cantilever bracket is bolted to a column using three M$12×1.75$ bolts P, Q and R. The value of maximum shear stress developed in the bolt P (in $MPa$) is ________
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GATE2015347
The torque (in $N$$m$) exerted on the crank shaft of a two stroke engine can be described as $T$ =$10000$+$1000$ sin $2θ$−$1200$ cos $2θ$, where $θ$ is the crank angle as measured from inner dead center position. Assuming the resisting torque to be constant, the power (in $kW$) developed by the engine at $100$ $rpm$ is ________
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GATE2015346
For the overhanging beam shown in figure, the magnitude of maximum bending moment (in $kN$$m$) is ________
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GATE2015345
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 distance of $0.5$ $m$. If velocity of bullet when it exits the barrel is $20$ $m/s$, its spinning speed in $rad/s$ is ________
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GATE2015344
Laplace transform of the function $f(t)$ is given by $F(s)=L\begin{Bmatrix} f(t) \end{Bmatrix}=\int_{0}^{\infty }f(t)e^{st}dt$ . Laplace transform of the function shown below is given by $\frac{1e^{2s}}{s}$ $\frac{1e^{s}}{2s}$ $\frac{22e^{s}}{s}$ $\frac{12e^{s}}{s}$
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gate20153
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GATE2015343
NewtonRaphson method is used to find the roots of the equation, $x^3+3x^2+3x1=0$. If the initial guess is $x_0=1$, then the value of $x$ after $2^{nd}$ iteration is ________
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GATE2015342
For a given matrix $P=\begin{bmatrix} 4+3i & i\\ i & 43i \end{bmatrix}$, where $i=\sqrt{1}$, the inverse of matrix P is $P=\frac{1}{24}\begin{bmatrix} 43i & i\\ i & 4+3i \end{bmatrix}$ ... $P=\frac{1}{25}\begin{bmatrix} 4+3i & i\\ i & 43i \end{bmatrix}$
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GATE2015341
The value of $\int_{C}^{ }[(3x8y^2)dx+(4y6xy)dy]$, (where $C$ is the boundary of the region bounded by $x$ = $0$, $y$ = $0$ and $x+y$ = $1$) is ________
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GATE2015340
A solid sphere $1$ of radius ‘$r$’ is placed inside a hollow, closed hemispherical surface $2$ of radius ‘$4r$’. The shape factor $F_{21}$ is $1/12$ $1/2$ $2$ $12$
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GATE2015339
Air in a room is at $35^oC$ and $60$% relative humidity (RH). The pressure in the room is $0.1$ $MPa$. The saturation pressure of water at $35^oC$ is $5.63$ $kPa$. The humidity ratio of the air (in $gram/kg$ of dry air) is ________
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GATE2015338
Steam enters a turbine at $30$ bar, $300^oC$ ($u$ = $2750$ $kJ/kg$, $h$ = $2993$ $kJ/kg$) and exits the turbine as saturated liquid at $15$ $kPa$ ($u$ = $225$ $kJ/kg$, $h$ = $226$ $kJ/kg$). Heat loss to the ... $kJ/kg$ of steam) is ________
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gate20153
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GATE2015337
Refrigerant vapor enters into the compressor of a standard vapor compression cycle at −$10^oC$ ($h$ = $402$ $kJ/kg$) and leaves the compressor at $50^oC$ ($h$ = $432$ $kJ/kg$). It leaves the condenser at $30^oC$ ($h$ = $237$ $kJ/kg$). The COP of the cycle is ________
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GATE2015336
A Prandtl tube (Pitotstatic 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 ________
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gate20153
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GATE2015335
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$10$
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gate20153
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GATE2015334
Orthogonal turning of a mild steel tube with a tool of rake angle $10^o$ is carried out at a feed of $0.14$ $mm/rev$. If the thickness of the chip produced is $0.28$ $mm$, the values of shear angle and shear strain will be respectively $28^o20′$ and $2.19$ $22^o20′$ and $3.53$ $24^o30′$ and $4.19$ $37^o20′$ and $5.19$
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gate20153
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GATE2015333
The annual requirement of rivets at a ship manufacturing company is $2000$ $kg$. The rivets are supplied in units of $1$ $kg$ costing $Rs$. $25$ each. If it costs $Rs$. $100$ to place an order and the annual cost of carrying one unit is $9$% of its purchase cost, the cycle length of the order (in days) will be ________
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GATE2015332
Ratio of solidification time of a cylindrical casting (height = radius) to that of a cubic casting of side two times the height of cylindrical casting is ________
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GATE2015331
In a rolling operation using rolls of diameter $500$ $mm$, if a $25$ $mm$ thick plate cannot be reduced to less than $20$ $mm$ in one pass, the coefficient of friction between the roll and the plate is ________
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GATE2015330
For ball bearings, the fatigue life $L$ measured in number of revolutions and the radial load $F$ are related by $FL^{1/3}$=$K$, where $K$ is a constant. It withstands a radial load of $2$ $kN$ for a life of $540$ million revolutions. The load (in $kN$) for a life of one million revolutions is ________
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GATE2015329
The number of degrees of freedom of the linkage shown in the figure is $3$ $0$ $1$ $2$
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GATE2015321
Which two of the following joining processes are autogeneous? Diffusion welding Electroslag welding Tungsten inert gas welding Friction welding (i) and (iv) (ii) and (iii) (ii) and (iv) (i) and (iii)
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GATE2015326
The value of moment of inertia of the section shown in the figure about the axisXX is $8.5050×10^6$ $mm^4$ $6.8850×10^6$ $mm^4$ $7.7625×10^6$ $mm^4$ $8.5725×10^6$ $mm^4$
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GATE2015328
Figure shows a single degree of freedom system. The system consists of a massless rigid bar OP hinged at O and a mass m at end P. The natural frequency of vibration of the system is $f_n=\frac{1}{2\pi }\sqrt{\frac{k}{4m}}$ $f_n=\frac{1}{2\pi }\sqrt{\frac{k}{2m}}$ $f_n=\frac{1}{2\pi }\sqrt{\frac{k}{m}}$ $f_n=\frac{1}{2\pi }\sqrt{\frac{2k}{m}}$
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