# Recent questions tagged gateme-2015-set3

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? $110$ $1100$ $9900$ $10000$
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_____
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
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
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? $20$ $10$ $8$ $5$
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
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
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.
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
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
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 ________
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 $88$ $110$ $128$ $160$
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
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 $\displaystyle{\frac{1-e^{-2s}}{s}} \\$ $\displaystyle{\frac{1-e^{-s}}{2s}} \\$ $\displaystyle{\frac{2-2e^{-s}}{s}} \\$ $\displaystyle{\frac{1-2e^{-s}}{s}}$
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 ________
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 $P=\displaystyle{\frac{1}{24}}\begin{bmatrix} 4-3i & i\\ -i & 4+3i \end{bmatrix} \\$ ... $P=\displaystyle{\frac{1}{25}}\begin{bmatrix} 4+3i & -i\\ i & 4-3i \end{bmatrix} \\$
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 ________
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)
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 $cm$ ...
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 $14.46 \: mm$
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 ________
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 ________
For the overhanging beam shown in figure, the magnitude of maximum bending moment (in $kN$-$m$) 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 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 ________
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 ________
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 $1/12$ $1/2$ $2$ $12$
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 ________
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 ________
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 ________
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 ________
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$10$
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 $5.19$
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 ________
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 ________
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 ________
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 ________
The number of degrees of freedom of the linkage shown in the figure is -$3$ $0$ $1$ $2$
The value of $\displaystyle{\lim_{x\rightarrow 0}\left(\frac{-\sin x}{2\sin x+x\cos x}\right)}$ is ________
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 $f_n=\displaystyle{\frac{1}{2\pi }\sqrt{\frac{k}{4m}}} \\$ ... $f_n=\displaystyle{\frac{1}{2\pi }\sqrt{\frac{k}{m}}} \\$ $f_n=\displaystyle{\frac{1}{2\pi }\sqrt{\frac{2k}{m}}}$
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 ________