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Recent questions tagged gateme-2015-set3

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Right triangle $PQR$ is to be constructed in $xy$-plane so that the right angle is at $P$ and line $PR$ is parallel to $x$-axis.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? $110$ $1100$ $9900$ $10000$
asked Feb 24, 2017 in Numerical Ability Arjun 24.6k points
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In the given figure $Q$ is a right triangle, $PS:QS = 3:1$ $RT:QT = 5:2$ $PU:UR = 1:1$ If area of triangle $QTS$ is $20$ $cm^2$, then the area of triangle $PQR$ in $cm^2$ is_____
asked Feb 24, 2017 in Numerical Ability Arjun 24.6k points
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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
asked Feb 24, 2017 in Analytical Aptitude Arjun 24.6k points
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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
asked Feb 24, 2017 in Verbal Ability Arjun 24.6k points
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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? $20$ $10$ $8$ $5$
asked Feb 24, 2017 in Numerical Ability Arjun 24.6k points
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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
asked Feb 24, 2017 in Numerical Ability Arjun 24.6k points
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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
asked Feb 24, 2017 in Analytical Aptitude Arjun 24.6k points
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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.
asked Feb 24, 2017 in Verbal Ability Arjun 24.6k points
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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
asked Feb 24, 2017 in Verbal Ability Arjun 24.6k points
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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
asked Feb 24, 2017 in Verbal Ability Arjun 24.6k points
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A mixture of ideal gases has the following composition by mass: $\begin{array}{|c|c|c|} \hline N_2 & O_2 & CO_2 \\ \hline 60\% & 30\% & 10 \% \\ \hline \end{array}$ If the universal gas constant is $8314 \: J/kmol-K$, the characteristic gas constant of the mixture (in $J/kg-K$) is ________
asked Feb 24, 2017 in Thermodynamics Arjun 24.6k points
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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 $−5^\circ C$ ... convective resistance of the air inside the room, the heat loss, in $\displaystyle{\frac{W}{m^2}}$, is $88$ $110$ $128$ $160$
asked Feb 24, 2017 in Heat Transfer Arjun 24.6k points
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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 ________
asked Feb 24, 2017 in Applications Arjun 24.6k points
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For the linear programming problem: $\begin{array}{ll} \text{Maximize} & Z = 3X_1 + 2X_2 \\ \text{Subject to} &−2X_1 + 3X_2 \leq 9\\ & X_1 − 5 X_2 \geq −20 \\ & X_1, X_2 \geq 0 \end{array}$ The above problem has unbounded solution infeasible solution alternative optimum solution degenerate solution
asked Feb 24, 2017 in Numerical Methods Arjun 24.6k points
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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 ________
asked Feb 24, 2017 in Numerical Methods Arjun 24.6k points
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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 ________
asked Feb 24, 2017 in Applications Arjun 24.6k points
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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 $15^\circ 32′$ and $12.16 \: mm$ $18^\circ 32′$ and $15.66 \: mm$ $11^\circ 22′$ and $10.26 \: mm$ $10^\circ 32′$ and $14.46 \: mm$
asked Feb 24, 2017 in Applied Mechanics and Design Arjun 24.6k points
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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 $25^\circ C$. Assuming no generation of heat within the wall, the irreversibility (in $W$) due to heat transfer through the wall is ________
asked Feb 24, 2017 in Heat Transfer Arjun 24.6k points
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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 $\displaystyle{\frac{1-e^{-2s}}{s}} \\$ $\displaystyle{\frac{1-e^{-s}}{2s}} \\$ $\displaystyle{\frac{2-2e^{-s}}{s}} \\$ $\displaystyle{\frac{1-2e^{-s}}{s}}$
asked Feb 24, 2017 in Differential Equations Arjun 24.6k points
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The dimensions of a cylindrical side riser (height = diameter) for a $25 \: cm \times 15 \: cm \times 5 \: cm$ steel casting are to be determined. For the tabulated shape factor values given below, the diameter of the riser (in $cm$ ...
asked Feb 24, 2017 in Mechanics of Materials Arjun 24.6k points
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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 ________
asked Feb 24, 2017 in Applied Mechanics and Design Arjun 24.6k points
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For a given matrix $P=\begin{bmatrix} 4+3i & -i\\ i & 4-3i \end{bmatrix}$, where $i=\sqrt{-1}$, the inverse of matrix $P$ is $P=\displaystyle{\frac{1}{24}}\begin{bmatrix} 4-3i & i\\ -i & 4+3i \end{bmatrix} \\$ ... $P=\displaystyle{\frac{1}{25}}\begin{bmatrix} 4+3i & -i\\ i & 4-3i \end{bmatrix} \\$
asked Feb 24, 2017 in Linear Algebra Arjun 24.6k points
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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)
asked Feb 24, 2017 in Applications Arjun 24.6k points
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The value of $\int_{C}^{ }[(3x-8y^2)dx+(4y-6xy)dy]$, (where $C$ is the boundary of the region bounded by $x$ = $0$, $y$ = $0$ and $x+y$ = $1$) is ________
asked Feb 24, 2017 in Calculus Arjun 24.6k points
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A solid sphere $1$ of radius ‘$r$’ is placed inside a hollow, closed hemispherical surface $2$ of radius ‘$4r$’. The shape factor $F_{2-1}$ is $1/12$ $1/2$ $2$ $12$
asked Feb 24, 2017 in Heat Transfer Arjun 24.6k points
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Air in a room is at $35^\circ C$ and $60 \%$ relative humidity (RH). The pressure in the room is $0.1 \: MPa$. The saturation pressure of water at $35^ \circ C$ is $5.63 kPa$. The humidity ratio of the air (in $gram/kg$ of dry air) is ________
asked Feb 24, 2017 in Applications Arjun 24.6k points
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Steam enters a turbine at $30$ bar, $300^\circ C \: (u = 2750 \: kJ/kg$, $h = 2993 \: kJ/kg)$ and exits the turbine as saturated liquid at $15 \: kPa \: (u = 225 \: kJ/kg$, $h = 226 \: kJ/kg)$. Heat loss to the surrounding is ... $kJ/kg$ of steam) is ________
asked Feb 24, 2017 in Applications Arjun 24.6k points
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Refrigerant vapor enters into the compressor of a standard vapor compression cycle at −$10^\circ C \:(h = 402 \: kJ/kg)$ and leaves the compressor at $50^\circ C \: (h = 432 \: kJ/kg)$. It leaves the condenser at $30^\circ C \: (h = 237 \: kJ/kg)$. The COP of the cycle is ________
asked Feb 24, 2017 in Applications Arjun 24.6k points
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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 ________
asked Feb 24, 2017 in Fluid Mechanics Arjun 24.6k points
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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 $(20, 10)$ and the machine has incremental mode of defining position coordinates, the correct tool path command is N $05$ G$90$ ... $10$ 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$10$
asked Feb 24, 2017 in Materials, Manufacturing and Industrial Engineering Arjun 24.6k points
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Orthogonal turning of a mild steel tube with a tool of rake angle $10^\circ $ 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 $28^\circ 20′$ and $2.19$ $22^\circ 20′$ and $3.53$ $24^\circ 30′$ and $4.19$ $37^\circ 20′$ and $5.19$
asked Feb 24, 2017 in Materials, Manufacturing and Industrial Engineering Arjun 24.6k points
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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 ________
asked Feb 24, 2017 in Materials, Manufacturing and Industrial Engineering Arjun 24.6k points
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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 ________
asked Feb 24, 2017 in Applied Mechanics and Design Arjun 24.6k points
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The value of $\displaystyle{\lim_{x\rightarrow 0}\left(\frac{-\sin x}{2\sin x+x\cos x}\right)}$ is ________
asked Feb 24, 2017 in Calculus Arjun 24.6k points
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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 $f_n=\displaystyle{\frac{1}{2\pi }\sqrt{\frac{k}{4m}}} \\$ ... $f_n=\displaystyle{\frac{1}{2\pi }\sqrt{\frac{k}{m}}} \\$ $f_n=\displaystyle{\frac{1}{2\pi }\sqrt{\frac{2k}{m}}}$
asked Feb 24, 2017 in Vibrations Arjun 24.6k points
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Figure shows a wheel rotating about $O_2$. Two points $A$ and $B$ located along the radius of wheel have speeds of $80$ $m/s$ and $140$ $m/s$ respectively. The distance between the points $A$ and $B$ is $300$ $mm$. The diameter of the wheel (in $mm$) is ________
asked Feb 24, 2017 in Applied Mechanics and Design Arjun 24.6k points
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