# Recent questions tagged gateme-2016-set2

The binary operation $\square$ is defined as $a \square b = ab+(a+b)$, where $a$ and $b$ are any two real numbers. The value of the identity element of this operation, defined as the number $x$ such that $a \square x = a$, for any $a$, is $0$ $1$ $2$ $10$.
Find the missing sequence in the letter series. B, FH, LNP, _ _ _ _. SUWY TUVW TVXZ TWXZ
A smart city integrates all modes of transport, uses clean energy and promotes sustainable use of resources. It also uses technology to ensure safety and security of the city, something which critics argue, will lead to a surveillance state. Which of the following can be logically inferred from the above ... promote surveillance. $(i)$ and $(iv)$ only $(ii)$ and $(iii)$ only $(iv)$ only $(i)$ only
Students taking an exam are divided into two groups, P and Q such that each group has the same number of students. The performance of each of the students in a test was evaluated out of $200$ marks. It was observed that the mean of group P was $105$, while that of ... Most students of group Q scored marks in a narrower range than students in group P. The median of the marks of group P is $100$.
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 $(iv)$.
Choose the statement $(s)$ where the underlined word is used correctly: A prone is a dried plum. He was lying prone on the floor. People who eat a lot of fat are prone to heart disease. $(i)$ and $(iii)$ only $(iii)$ only $(i)$ and $(ii)$ only $(ii)$ and $(iii)$ only
Which of the following curves represents the function $ln(|e^{[|\sin(|x|)]}|)$ for $\mid x\mid< 2\pi$? Here, $x$ represents the abscissa and $y$ represents the ordinate.
A window is made up of a square portion and an equilateral triangle portion above it. The base of the triangular portion coincides with the upper side of the square. If the perimeter of the window is $6$ $m$, the area of the window in $m^2$ is ___________. $1.43$ $2.06$ $2.68$ $2.88$
The unruly crowd demanded that the accused be _____________ without trial. hanged hanging hankering hung
The volume of a sphere of diameter $1$ unit is ________ than the volume of a cube of side $1$ unit. least less lesser low
The surface irregularities of electrodes used in an electrochemical machining (ECM) process are $3 \: μm$ and $6 \: μm$ as shown in the figure. If the work-piece is of pure iron and $12V \: DC$ is applied between the electrodes, the largest feed rate is ___________$mm/min$. ... $F_e^{+2}$ and the Faraday constant to be $96500$ Coulomb.
For the situation shown in the figure below the expression for $H$ in terms of $r$, $R$ and $D$ is $H=D+\sqrt{r^2+R^2}$ $H=(R+r)+(D+r)$ $H=(R+r)+\sqrt{D^2-R^2}$ $H=(R+r)+\sqrt{2D(R+r)-D^2}$
A project consists of $14$ activities, $A$ to $N$. The duration of these activities (in days) are shown in brackets on the network diagram. The latest finish time (in days) for node $10$ is __________
A food processing company uses $25,000 \:kg$ ... charge on an annual basis is $20\%$ of the purchase price of the corn flour per $kg$. The optimal order quantity (in $kg$) is _____________
For a certain job,the cost of metal cutting is $Rs$. $18C/V$ and the cost of tooling is $Rs$. $270C/(TV)$,where $C$ is a constant,$V$ is the cutting speed in $m/min$ and $T$ is the tool life in minutes.The Taylor's tool life equation is $VT^{0.25}$-$150$.The cutting speed (in $m/min$) for the minimum tool cost is
The Voltage-length characteristics of a direct current arc in an arc welding process is $V=(100+40l)$ ,where $l$ is the length of arc in $mm$ and $V$ is arc voltages in volts.during a welding process,the arc length varies between $1$ and $2 \: mm$ and welding current is in range $200-250 \: A$.Assuming a linear power source,the short circuit current is_____$A$
Gray cast iron blocks of size $100mm\times 50mm\times 10mm$ with a central spherical cavity of diameter $4 \:mm$ are sand cast.The shrinkage allowance for the pattern is $3\%$.The ratio of the volume of the pattern to the volume of casting is
A piston-cylinder device initially contains $0.4 \: m^3$ of air (to be treated as an ideal gas) at $100 \: kPa$ and $80^ \circ C$. The air is now isothermally compressed to $0.1 \: m^3$. The work done during this process is ________ $kJ$.
The large vessel shown in the figure contains oil and water. A body is submerged at the interface of oil and water such that $45$ percent of its volume is in oil while the rest is in water. The density of the body is _________ $kg/m^3$. The specific gravity of oil is $0.7$ and density of water is $1000$ $kg/m^3$. Acceleration due to gravity $g$ = $10$ $m/s^2$.
In a binary system of $A$ and $B$, a liquid of $20\% A (80\% \: B)$ is coexisting with a solid of $70\% \: A (30 \% B)$. For an overall composition having $40\% \: A$, the fraction of solid is $0.40$ $0.50$ $0.60$ $0.75$
The partial pressure of the water vapour in a moist air sample of relative humidity $70\%$ is $1.6 \: kPa$,the total pressure being $101.35 \: kPa$.moist air may be treated as an ideal gas mixture of water vapour and dry air.the relation between saturation temperature ($T_s$ ... $p_o=101.325 \: kPa$. The dry bulb temperature of the moist air sample (in $_{}^{\circ}\textrm{C}$) is
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 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 __________
Two cylindrical shafts $A$ and $B$ at the same initial temperature are simultaneously placed in a furnace. The surfaces of the shafts remain at the furnace gas temperature at all times after they are introduced into the furnace. The temperature variation in the axial direction of ... time required (in hours) for the centerline of the shaft B to attain the temperature of $400^ \circ C$ is _______ .
Consider a parallel-flow heat exchanger with area $A_p$ and a counter-flow heat exchanger with area $A_c$ . In both the heat exchangers, the hot stream flowing at $1 \: kg/s$ cools from $80^\circ C$ to $50^\circ C$. For the cold stream in both ... heat exchangers are of the same fluid. Also, both the heat exchangers have the same overall heat transfer coefficient. The ratio $A_c/A_p$ is _________
Consider a frictionless, massless and leak-proof plug blocking a rectangular hole of dimensions $2R \times L$ at the bottom of an open tank as shown in the figure. The head of the plug has the shape of a semi-cylinder of radius $R$. The tank is filled with a liquid of density $\rho$ up to the tip of the ... $2\rho R^2gL(1+\dfrac{\pi }{4}) \\$ $\pi R^2\rho gL \\$ $\dfrac{\pi }{2}\rho R^2gL$
Consider fluid flow between two infinite horizontal plates which are parallel (the gap between them being $50 \: mm$). The top plate is sliding parallel to the stationary bottom plate at a speed of $3\: m/s$. The flow between the plates is solely due to the motion of the top plate. The force per ... _________ $N/m^2$. Viscosity of the fluid $μ = 0.44 \:kg/m-s$ and density $\rho = 888 \: kg/m^3$.
In a structural member under fatigue loading, the minimum and maximum stresses developed at the critical point are $50$ $MPa$ and $150$ $MPa$, respectively. The endurance, yield, and the ultimate strengths of the material are $200$ $MPa$, $300$ $MPa$ and $400$ $MPa$, respectively. The factor of safety using modified Goodman criterion is $\dfrac{3}{2} \\$ $\dfrac{8}{5} \\$ $\dfrac{12}{7} \\$ $2$
The error in numerically computing the integral $\int_{0}^{\pi }(\sin x+\cos x)dx$ using the trapezoidal rule with three intervals of equal length between $0$ and $\pi$ is ___________
The probability that a screw manufactured by a company is defective is $0.1$. The company sells screws in packets containing $5$ screws and gives a guarantee of replacement if one or more screws in the packet are found to be defective. The probability that a packet would have to be replaced is _________
A scalar potential $\varphi$ has the following gradient: $\bigtriangledown \varphi =yz\hat{i}+xz\hat{j}+xy\hat{k}$ . Consider the integral $\int_{c}^{ }\bigtriangledown \varphi .d\overrightarrow{r}$ on the curve $\overrightarrow{r}=x\hat{i}+y\hat{j}+z\hat{k}$. The curve $C$ is ... . The value of the integral is ________
The value of $\oint_{\Gamma }^{ }\dfrac{3z-5}{(z-1)(z-2)}dz$ along a closed path $\Gamma$ is equal to $(4\pi i)$ , where $z=x+iy$ and $i=\sqrt{-1}$. The correct path $\Gamma$ is
The system shown in the figure consists of block A of mass $5$ $kg$ connected to a spring through a massless rope passing over pulley B of radius $r$ and mass $20$ $kg$. The spring constant $k$ is $1500$ $N/m$. If there is no slipping of the rope over the pulley, the natural frequency of the system is_____________ $rad/s$.
The rod $AB$, of length $1$ $m$, shown in the figure is connected to two sliders at each end through pins. The sliders can slide along $QP$ and $QR$. If the velocity $VA$ of the slider at $A$ is $2$ $m/s$, the velocity of the midpoint of the rod at this instant is ___________ $m/s$.
A circular metallic rod of length $250 \: mm$ is placed between two rigid immovable walls as shown in the figure. The rod is in perfect contact with the wall on the left side and there is a gap of $0.2 \: mm$ between the rod and the wall on the right side. If the temperature ... material of the rod is $200 \: GPa$ and the coefficient of thermal expansion is $10^{−5}$ per $_{}^{\circ}\textrm{C}$.
In the figure, the load $P=1 \: N$, length $L=1 \: m$, Young’s modulus $E=70 \: GPa$, and the cross-section of the links is a square with dimension $10 \: mm \times 10 \: mm$. All joints are pin joints. The stress (in $Pa$) in the link $AB$ is ___________ (Indicate compressive stress by a negative sign and tensile stress by a positive sign.)
A simply supported beam of length $2L$ is subjected to a moment $M$ at the mid-point $x = 0$ as shown in the figure. The deflection in the domain $0 \leq x \leq L$ is given by $w=\dfrac{-Mx}{12EIL}(L-x)(x+c)$ where $E$ is the Young's modulus, $I$ is the area moment of inertia ... $x$ = $0$ is $ML/(2EI)$ $ML/(3EI)$ $ML/(6EI)$ $ML/(12EI)$
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 system of particles in motion has mass center $G$ as shown in the figure. The particle $i$ has mass $m_i$ and its position with respect to a fixed point $O$ is given by the position vector $r_i$. The position of the particle with respect to $G$ is given by the vector $\rho _i$. ... $\sum _i\rho _i\times m_i\ddot{r_i}$ $\sum _ir _i\times m_i\ddot{r_i}$ $\sum _i\rho _i\times m_i\ddot{\rho _i}$
A mass of $2000$ $kg$ is currently being lowered at a velocity of $2$ $m/s$ from the drum as shown in the figure. The mass moment of inertia of the drum is $150$ $kg$-$m^2$. On applying the brake, the mass is brought to rest in a distance of $0.5$ $m$. The energy absorbed by the brake (in $kJ$) is __________