# Recent questions tagged gateme-2014-set3

A man can row at $8$ $km$ per hour in still water. If it takes him thrice as long to row upstream, as to row downstream, then find the stream velocity in $km$ per hour.
In which of the following options will the expression $P < M$ be definitely true? $M < R > P > S$ $M > S < P < F$ $Q < M < F = P$ $P = A < R < M$
'Advice' is ________________. a verb a noun an adjective both a verb and a noun
The next term in the series $81, 54, 36, 24,\ldots$ is ________
A batch of one hundred bulbs is inspected by testing four randomly chosen bulbs. The batch is rejected if even one of the bulbs is defective. A batch typically has five defective bulbs. The probability that the current batch is accepted is ________
A firm producing air purifiers sold $200$ units in $2012$. The following pie chart presents the share of raw material, labour, energy, plant & machinery, and transportation costs in the total manufacturing cost of the firm in $2012$. The expenditure on labour in $2012$ ... If the company registered a profit of Rs. $10$ lakhs in $2012$, at what price (in $Rs$.) was each air purifier sold?
The multi-level hierarchical pie chart shows the population of animals in a reserve forest. The correct conclusions from this information are: Butterflies are birds There are more tigers in this forest than red ants All reptiles in this forest are either snakes or crocodiles Elephants are the largest mammals in this ... (i), (ii), (iii) and (iv) (i), (iii) and (iv) only (i), (ii) and (iii) only
Find the next term in the sequence: $7G, 11K, 13M$,____ $15Q$ $17Q$ $15P$ $17P$
The value of one U.S. dollar is $65$ Indian Rupees today, compared to $60$ last year. The Indian Rupee has ____________. depressed depreciated appreciated stabilized
“India is a country of rich heritage and cultural diversity.” Which one of the following facts best supports the claim made in the above sentence? India is a union of $28$ states and $7$ union territories. India has a population of over $1.1$ billion. India is home to $22$ official languages and thousands of dialects. The Indian cricket team draws players from over ten states.
Consider the given project network, where numbers along various activities represent the normal time. The free float on activity $4$-$6$ and the project duration, respectively, are $2$, $13$ $0$, $13$ $-2$, $13$ $2$, $12$
For spot welding of two steel sheets (base metal) each of $3$ $mm$ thickness, welding current of $10000$ $A$ is applied for $0.2$ $s$. The heat dissipated to the base metal is $1000$ $J$. Assuming that the heat required for melting $1$ $mm^3$ volume of steel is $20$ $J$ and interfacial contact resistance between sheets is $0.0002$ $Ω$, the volume (in $mm^3$) of weld nugget is _______
Which pair of following statements is correct for orthogonal cutting using a single-point cutting tool? P. Reduction in friction angle increases cutting force Q. Reduction in friction angle decreases cutting force R. Reduction in friction angle increases chip thickness S. Reduction in friction angle decreases chip thickness P and R P and S Q and R Q and S
The diameter of a recessed ring was measured by using two spherical balls of diameter $d_2$ = $60$ $mm$ and $d_1$ = $40$ $mm$ as shown in the figure. The distance $H_2$ = $35.55$ $mm$ and $H_1$ = $20.55$ $mm$. The diameter ($D$, in $mm$) of the ring gauge is _______
A cylindrical blind riser with diameter d and height h , is placed on the top of the mold cavity of a closed type san d mold as shown in the figure. If the riser is of constant volume, then the rate of solidification in the riser is the least when the ratio h:d is $1:2$ $2:1$ $1:4$ $4:1$
A manufacturer can produce $12000$ bearings per day. The manufacturer received an order of $8000$ bearings per day from a customer. The cost of holding a bearing in stock is $Rs$. $0.20$ per month. Setup cost per production run is $Rs$. $50 0$. Assuming $300$ working days in a year, the frequency of production run should be $4.5$ days $4.5$ months $6.8$ days $6.8$ months
A diesel engine has a compression ratio of $17$ and cut-off takes place at $10\%$ of the stroke.Assuming ratio of specific heats $(\gamma)$ as $1.4$, the air-standard efficiency (in percent) is _______
A double-pipe counter-flow heat exchanger transfers heat between two water streams. Tube side water at $19$ liter/s is heated from $10^{\circ} \: C$ to $38^{\circ} \: C$. Shell side water at $25$ $litre/s$ is entering at $46^{\circ} \: C$. Assume constant properties of water; density is $1000 \: kg/m^3$ and specific heat is $4186 \: J/kg.K$. The LM TD (in $^{\circ}C$) is _______
Consider an objective function $Z(x_1,x_2)=3x_1+9x_2$ and the constraints $x_1+x_2 \leq 8$ $x_1+2x_2 \leq 4$ $x_1 \geq 0$ , $x_2 \geq 0$ The maximum value of the objective function is _______
A solid sphere of radius $r_1 = 20$ $mm$ is placed concentrically inside a hollow sphere of radius $r_2 = 30$ $mm$ as shown in the figure. The view factor $F_{21}$ for radiation heat transfer is $\dfrac{2}{3} \\$ $\dfrac{4}{9} \\$ $\dfrac{8}{27} \\$ $\dfrac{9}{4}$
At the inlet of an axial impulse turbine rotor, the blade linear speed is $25 \: m/s$, the magnitude of absolute velocity is $100 \: m/s$ and the angle between them is $25^{\circ}$. The relative velocity and the axial component of velocity remain the same ... blades. The blade inlet and outlet velocity triangles are shown in the figure. Assuming no losses, the specific work (in $J/kg$) is _______
A fluid of dynamic viscosity $2 × 10^{−5}$ $kg/m.s$ and density $1$ $kg/m^3$ flows with an average velocity of $1$ $m/s$ through a long duct of rectangular ($25$ $mm$ × $15$ $mm$) cross-section. Assuming laminar flow, the pressure drop (in $Pa$) in the fully developed region per meter length of the duct is _______
Heat transfer through a composite wall is shown in figure. Both the sections of the wall have equal thickness $(l)$. The conductivity of one section is $k$ and that of the other is $2k$. The left face of the wall is at $600$ $K$ and the right face is at $300$ $K$. The interface temperature $T_i$ (in $K$) of the composite wall is _______
A siphon is used to drain water from a large tank as shown in the figure below. Assume that the level of water is maintained constant. Ignore frictional effect due to viscosity and losses at entry,and exit. At the exit of the siphon, the velocity of water is $\sqrt{2g(Z_Q-Z_R)} \\$ $\sqrt{2g(Z_P-Z_R)} \\$ $\sqrt{2g(Z_O-Z_R)} \\$ $\sqrt{2gZ_Q}$
An amount of $100 \: kW$ of heat is transferred through a wall in steady state. One side of the wall is maintained at $127^{\circ} \: C$ and the other side at $27^{\circ} \: C$. The entropy generated (in $W/K$) due to the heat transfer through the wall is _______
A certain amount of an ideal gas is initially at a pressure $p_1$ and temperature $T_1$. First, it undergoes a constant pressure process $1$-$2$ such that $T_2$ = $3T_1$/$4$. Then, it undergoes a constant volume process $2$-$3$ such that $T_3$ = $T_1$/$2$. The ratio of the final volume to the initial volume of the ideal gas is $0.25$ $0.75$ $1.0$ $1.5$
A mass-spring-dashpot system with mass $m = 10$ $kg$, spring constant $k = 6250$ $N/m$ is excited by a harmonic excitation of $10 cos(25t)$ $N$. At the steady state, the vibration amplitude of the mass is $40$ $mm$. The damping coefficient ($c$, in $N.s/m$) of the dashpot is _______
A slider-crank mechanism with crank radius $60$ $mm$ and connecting rod length $240$ $mm$ is shown in figure. The crank is rotating with a uniform angular speed of $10$ $rad/s$, counter clockwise. For the given configuration, the speed (in $m/s$) of the slider is _______
A four-wheel vehicle of mass $1000 \: kg$ moves uniformly in a straight line with the wheels revolving at $10 \: rad/s$. The wheels are identical, each with a radius of $0.2 \: m$. Then a constant braking torque is applied to all the wheels and the vehicle experiences a uniform deceleration. For the vehicle to stop in $10 \: s$, the braking torque (in $N.m$) on each wheel is______
Consider a rotating disk cam and a translating roller follower with zero offset. Which one of the following pitch curves, parameterized by $t$, lying in the interval $0$ to $2 \pi$ ... $x(t)$= $\dfrac{1}{2}$+$\cos t$ , $y(t)=\sin t$
A force $P$ is applied at a distance $x$ from the end of the beam as shown in the figure. What would be the value of $x$ so that the displacement at ‘$A$’ is equal to zero? $0.5L$ $0.25L$ $0.33L$ $0.66L$
An annular disc has a mass $m$, inner radius $R$ and outer radius $2R$. The disc rolls on a flat surface without slipping. If the velocity of the center of mass is $v$, the kinetic energy of the disc is $\dfrac{9}{16}mv^2 \\$ $\dfrac{11}{16}mv^2 \\$ $\dfrac{13}{16}mv^2 \\$ $\dfrac{15}{16}mv^2$
The real root of the equation $5x − 2 \cos x −1 = 0$ (up to two decimal accuracy) is _______
Consider two solutions $x(t)=x_1(t)$ and $x(t)=x_2(t)$ of the differential equation $\dfrac{d^2x(t)}{dt^2}+x(t)=0, \: t>0$ such that $x_1(0)=1, \dfrac{dx_1(t)}{dt} \bigg \vert_{t=0}=0$, $x_2(0)=0, \dfrac{dx_2(t)}{dt}\bigg \vert _{t=0}=1$. The Wronskian $W(t)=\begin{bmatrix} x_1(t) & x_2(t)\\ \\ \dfrac{dx_1(t)}{dt} & \dfrac{dx_2(t)}{dt} \end{bmatrix}$ at $t=\pi /2$ is $1$ $-1$ $0$ $\pi /2$
An analytic function of a complex variable $z = x + i y$ is expressed as $f (z) = u(x, y) + i v(x, y)$ , where $i=\sqrt{-1}$ . If $u(x, y) = x^2 − y^2$ , then expression for $v(x, y)$ in terms of $x$, $y$ and a general constant $c$ would be $xy + c \\$ $\dfrac{x^2+y^2}{2}+c \\$ $2xy+c \\$ $\dfrac{(x-y)^2}{2}+c$
The damping ratio of a single degree of freedom spring-mass-damper system with mass of $1 kg$, stiffness $100 N/m$ and viscous damping coefficient of $25 N.s/m$ is _______
Consider a simply supported beam of length, $50h$, with a rectangular cross-section of depth, $h$, and width, $2h$. The beam carries a vertical point load, P, at its mid-point. The ratio of the maximum shear stress to the maximum bending stress in the beam is $0.02$ $0.10$ $0.05$ $0.01$
A body of mass (M) $10$ $kg$ is initially stationary on a $45^{\circ}$ inclined plane as shown in figure. The coefficient of dynamic friction between the body and the plane is $0.5$. The body slides down the plane and attains a velocity of $20 m/s$. The distance traveled (in meter) by the body along the plane is _______
A drum brake is shown in the figure. The drum is rotating in anticlockwise direction. The coefficient of friction between drum and shoe is $0.2$. The dimensions shown in the figure are in $mm$. The braking torque (in $N.m$) for the brake shoe is _______
A machine produces $0$, $1$ or $2$ defective pieces in a day with associated probability of $1/6$, $2/3$ and $1/6$, respectively. The mean value and the variance of the number of defective pieces produced by the machine in a day, respectively, are $1$ and $1/3$ $1/3$ and $1$ $1$ and $4/3$ $1/3$ and $4/3$