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Recent questions tagged gateme-2017-set1

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What is the sum of the missing digits in the subtraction problem below? $\begin{array}{llllll} {} &5 & \text{_} & \text{_} & \text{_} & \text{_} \\ – &4 & 8 & \text{_}& 8 & 9 \\ \hline & & 1 & 1 &1 &1 \end{array}$ $8$ $10$ $11$ Cannot be determined.
asked Feb 27, 2017 in Analytical Aptitude Arjun 24.6k points
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"Here, throughout the early $1820$s, Stuart continued to fight is losing battle to allow his sepoys to wear their caste-marks and their own choice of facial hair on parade, being again reprimanded by the commander-in-chief. His retort that 'A stronger instance ... sepoys to wear caste-marks. The commander-in-cheif was exempt from the Europeans prejudice that dictated how the sepoys were to dress.
asked Feb 27, 2017 in Verbal Ability Arjun 24.6k points
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$P$, $Q$ and $R$ talk about $S's$ car collection. $P$ states that $S$ has at least $3$ cars. $Q$ believes that $S$ has less than $3$ cars. $R$ indicates that to its knowledge, $S$ has at least one car. Only one of $P, Q$ and $R$ is right. The number of cars owned by $S$ is. $0$ $1$ $3$ Cannot be determined.
asked Feb 27, 2017 in Analytical Aptitude Arjun 24.6k points
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Two very famous sportsmen Mark and Steve happened to be brothers and played for country $K$. Mark teased James, an opponent from country $E$, "There is no way you are good enough to play for your country." James replied, "Maybe not, but at least I am the ... known to play better than James. Steve was known to play better than Mark. James and Steve were good friends. James played better than steve.
asked Feb 27, 2017 in Verbal Ability Arjun 24.6k points
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Let $S_{1}$ be the plane figure consisting of the points $(x, y)$ given by the inequalities $\mid x - 1 \mid \leq 2$ and $ \mid y+2 \mid \leq 3$. Let $S_{2}$ be the plane figure given by the inequalities $x-y \geq -2, y \geq 1$, and $x \leq 3$. Let $S$ be the union of $S_{1}$ and $S_{2}$. The area of $S$ is. $26$ $28$ $32$ $34$
asked Feb 27, 2017 in Numerical Ability Arjun 24.6k points
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The growth of bacteria (lactobacillus) in milk leads to curd formation. A minimum bacterial population density of $0.8$ (in suitable units) is needed to form curd. In the graph below, the population density of lactobacillus in $1$ litre of milk is plotted as a function of time, at two ... Which one of the following options is correct? Only $i$. Only $ii$. Both $i$ and $ii$. Neither $i$ nor $ii$
asked Feb 27, 2017 in Numerical Ability Arjun 24.6k points
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In a company with $100$ employees, $45$ earn $Rs. 20,000$ per month, $25$ earn $Rs. 30000$, $20$ earn $Rs. 40000$, $8$ earn $Rs. 60000$, and $2$ earn $Rs. 150,000$. The median of the salaries is $Rs. 20,000$ $Rs. 30,000$ $Rs. 32,300$ $Rs. 40,000$
asked Feb 27, 2017 in Numerical Ability Arjun 24.6k points
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A right-angled cone (with base radius $5$ cm and height $12$ cm), as shown in the figure below, is rolled on the ground keeping the point $P$ fixed until the point $Q$ (at the base of the cone, as shown) touches the ground again. By what angle (in radians) about $P$ does the cone travel? $\dfrac{5\pi}{12} \\$ $\dfrac{5\pi}{24} \\$ $\dfrac{24\pi}{5} \\$ $\dfrac{10\pi}{13}$
asked Feb 27, 2017 in Numerical Ability Arjun 24.6k points
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As the two speakers become increasingly agitated, the debate became _________. lukewarm poetic forgiving heated
asked Feb 27, 2017 in Verbal Ability Arjun 24.6k points
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He was one of my best _______ and I felt his loss ________. friend, keenly friends, keen friend, keener friends, keenly
asked Feb 27, 2017 in Verbal Ability Arjun 24.6k points
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Two cutting tools with tool life equations given below are being compared: Tool $1$: $VT^{0.1}=150$ Tool $2$: $VT^{0.3}=300$ where $V$ is cutting speed in m/minute and $T$ is tool life in minutes. The breakeven cutting speed beyond which Tool $2$ will have a higher tool life is ________ m/minute.
asked Feb 27, 2017 in Materials, Manufacturing and Industrial Engineering Arjun 24.6k points
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A sprue in a sand mould has a top diameter of $20 \: mm$ and height of $200$ mm. The velocity of the molten metal at the entry of the sprue is $0.5 \: m/s$. Assume acceleration due to gravity as $9.8 \: m/s^{2}$ and neglect all losses. If the mould is well ventilated, the velocity (upto $3$ decimal points accuracy) of the molten metal at the bottom of the sprue is _________ $m/s$
asked Feb 27, 2017 in Materials, Manufacturing and Industrial Engineering Arjun 24.6k points
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A block of length $200$ mm is machined by a slab milling cutter $34$ mm in diameter. The depth of cut and table feed are set at $2$ mm and $18$ mm/minute, respectively. Considering the approach and the over travel of the cutter to be same, the minimum estimated machining time per pass is ________ minutes.
asked Feb 27, 2017 in Materials, Manufacturing and Industrial Engineering Arjun 24.6k points
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Following data refers to the jobs $(P, Q, R, S)$ which have arrived at a machine for scheduling. The shortest possible average flow time is __________ days. $\begin{array}{|l|l|} \hline \text{Job} & \text{Processing Time (days)} \\ \hline P & 15 \\ \hline Q & 9 \\ \hline R & 22 \\ \hline S & 12 \\ \hline \end{array}$
asked Feb 27, 2017 in Materials, Manufacturing and Industrial Engineering Arjun 24.6k points
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Two models, $P$ and $Q$, of a product, earn profits of Rs.$100$ and Rs. $80$ per piece, respectively. Production times for $P$ and $Q$ are $5$ hours and $3$ hours, respectively, while the total production time available is $150$ hours. For a total batch size of $40$, to maximise profit, the number of units of $P$ to be produced is ________.
asked Feb 27, 2017 in Materials, Manufacturing and Industrial Engineering Arjun 24.6k points
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Assume that the surface roughness profile is triangular as shown schematically in the figure. If the peak to valley height is $20 \mu m$, the central line average surface roughness $R_{a}$ (in $\mu m$) is $5$ $6.67$ $10$ $20$
asked Feb 27, 2017 in Materials, Manufacturing and Industrial Engineering Arjun 24.6k points
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A $10$ mm deep cylindrical cup with diameter of $15$ mm is drawn from a circular blank. Neglecting the variation in the sheet thickness, the diameter (upto $2$ decimal points accuracy) of the blank is _________ mm.
asked Feb 27, 2017 in Applied Mechanics and Design Arjun 24.6k points
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For an inline slider-crank mechanism, the lengths of the crank and connecting rod are $3$ m and $4$ m, respectively. At the instant when the connecting rod is perpendicular to the crank, if the velocity of the slider is $1$ m/s, the magnitude of angular velocity (upto $3$ decimal points accuracy) of the crank is ________ radian/s
asked Feb 27, 2017 in Applied Mechanics and Design Arjun 24.6k points
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Two disks $A$ and $B$ with identical mass $(m)$ and radius $(R)$ are initially at rest. They roll down from the top of identical inclined planes without slipping. Disk $A$ has all of its mass concentrated at the rim, while Disk $B$ has its mass uniformly distributed. At the bottom of the plane, the ... the centre of disk $B$ is $\sqrt{\dfrac{3}{4}} \\$ $\sqrt{\dfrac{3}{2}} \\$ $1 \\$ $\sqrt{2}$
asked Feb 27, 2017 in Theory of Machines Arjun 24.6k points
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A thin uniform rigid bar of Length $L$ and mass $M$ is hinged at point $O$, located at a distance of $\dfrac{L}{3}$ from one of its ends. The bar is further supported using springs, each of stiffness $k$, located at the two ends. A particle of mass $m=\dfrac{M}{4}$ is fixed at one end of ... is $\sqrt{\dfrac{5k}{M}} \\$ $\sqrt{\dfrac{5k}{2M}} \\$ $\sqrt{\dfrac{3k}{2M}} \\$ $\sqrt{\dfrac{3k}{M}}$
asked Feb 27, 2017 in Applied Mechanics and Design Arjun 24.6k points
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In an epicyclic gear train, shown in the figure, the outer ring gear is fixed, while the sun gear rotates counterclockwise at $100$ rpm. Let the number of teeth on the sun, planet and outer gears to be $50, 25$ and $100$, respectively. The ratio of magnitudes of angular velocity of the planet gear to the angular velocity of the carrier arm is ________.
asked Feb 27, 2017 in Applied Mechanics and Design Arjun 24.6k points
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A horizontal bar, fixed at one end $(x=0)$, has a length of $1$ m, and cross-sectional area of $100 mm^{2}$. Its elastic modulus varies along its length as given by $E(x)=100 e^{-x}$ GPa, where $x$ is the length coordinate (in m) along the axis of the bar. An axial tensile load of $10$ kN is applied at the free end $(x=1)$. The axial displacement of the free end is _________ mm
asked Feb 27, 2017 in Applied Mechanics and Design Arjun 24.6k points
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A machine element has an ultimate strength $(\sigma _{u})$ of $600 N/mm^{2}$, and endurance limit $(\sigma _{en})$ of $250 N/mm^{2}$. The fatigue curve for the element on a $\log-\log$ plot is shown below. If the element is to be designed for a finite life of $10000$ cycles, the maximum amplitude of a completely reversed operating stress is _________ $N/mm^{2}$.
asked Feb 27, 2017 in Applied Mechanics and Design Arjun 24.6k points
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A rectangular region in a solid is in a state of plane strain. The $(x, y)$ coordinates of the corners of the undeformed rectangle are given by $P(0, 0), Q(4, 0), R(4, 3), S(0, 3)$. The rectangle is subjected to uniform strains, $\varepsilon _{xx}=0.001, \varepsilon _{yy}=0.002,\gamma _{xy}=0.003$. The deformed length of the elongated diagonal, up to three decimal places is _______ units.
asked Feb 27, 2017 in Applied Mechanics and Design Arjun 24.6k points
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A point mass of $100$ kg is dropped onto a massless elastic bar (cross-sectional area $= 100 mm^{2}$, length $= 1$ m, Young's modulus$=100$ GPa) from a height $H$ of $10$ mm as shown (Figure is not to scale). If $g= 10 m/s^{2}$, the maximum compression of the elastic bar is _______ mm
asked Feb 27, 2017 in Applied Mechanics and Design Arjun 24.6k points
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An initially stress-free massless elastic beam of length $L$ and circular cross-section with diameter $d$ $(d << L)$ is held fixed between two walls as shown. The beam material has Young's modulus $E$ and coefficient of thermal expansion $a$. If the beam is slowly and uniformly heated, the temperature rise required to cause the beam to buckle is proportional to $d$ $d^{2}$ $d^{3}$ $d^{4}$
asked Feb 27, 2017 in Mechanics of Materials Arjun 24.6k points
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Heat is generated uniformly in a long solid cylindrical rod (diameter$=10$ mm) at the rate of $4 \times 10^{7} W/m^{3}$. The thermal conductivity of the rod material is $25 W/m.K$. Under steady state conditions, the temperature difference between the centre and the surface of the rod is ______ $^{\circ} C$.
asked Feb 27, 2017 in Heat Transfer Arjun 24.6k points
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Two black surfaces, AB and BC, of lengths $5$ m and $6$ m, respectively, are oriented as shown. Both surfaces extend infinitely into the third dimension. Given that view factor $F_{12}=0.5, T_{1}=800 K, T_{2}=600 K, T_{\text{surrounding}}=300 K$ and Stefan-Boltzmann ... $2$ to the surrounding environment is _______ kW.
asked Feb 27, 2017 in Heat Transfer Arjun 24.6k points
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Air contains $79\%$ $N_{2}$ and $21\%$ $O_{2}$ on a molar basis. Methane $(CH_{4})$ is burned with $50\%$ excess air than required stoichiometrically. Assuming complete combustion of methane, the molar percentage of $N_{2}$ in the products is _______.
asked Feb 27, 2017 in Applications Arjun 24.6k points
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Moist air is treated as an ideal gas mixture of water vapour and dry air (molecular weight of air$= 28.84$ and molecular weight of water $=18$). At a location, the total pressure is $100$ kPa, the temperature is $30^{\circ}$ C and the relative humidity is $55\%$. ... the saturation pressure of water at $30^{\circ} C$ is $4246$ Pa, the mass of water vapour per kg of dry air is _________ grams.
asked Feb 27, 2017 in Applications Arjun 24.6k points
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For a steady flow, the velocity field is $\vec{V}=(-x^{2}+3y)\hat{i}+(2xy)\hat{j}$. The magnitude of the acceleration of a particle at $(1, -1)$ is $2$ $1$ $2\sqrt{5}$ $0$
asked Feb 27, 2017 in Fluid Mechanics Arjun 24.6k points
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$P(0, 3), Q (0.5, 4)$ and $R(1, 5)$ are three points on the curve defined by $f(x)$. Numerical integration is carried out using both Trapezoidal rule and Simpson's rule within limits $x=0$ and $x=1$ for the curve. The difference between the two results will be $0$ $0.25$ $0.5$ $1$
asked Feb 27, 2017 in Numerical Methods Arjun 24.6k points
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A parametric curve defined by $x= \cos \left ( \dfrac{\Pi u}{2} \right ), y= \sin \left ( \dfrac{\Pi u}{2} \right )$ in the range $0 \leq u \leq 1$ is rotated about the $X$-axis by $360$ degrees. Area of the surface generated is $\dfrac{\Pi }{2} \\$ $\pi \\$ $2 \pi \\$ $4 \pi$
asked Feb 27, 2017 in Calculus Arjun 24.6k points
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For the vector $\vec{V}=2yz\hat{i}+3xz \hat{j}+4xy \hat{k}$, the value of $\bigtriangledown$. $(\bigtriangledown \times \vec{V})$ is ________.
asked Feb 27, 2017 in Calculus Arjun 24.6k points
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Consider the matrix $P=\begin{bmatrix} \dfrac{1}{\sqrt{2}} & 0 &\dfrac{1}{\sqrt{2}} \\ 0 & 1 & 0\\ -\dfrac{1}{\sqrt{2}} &0 & \dfrac{1}{\sqrt{2}} \end{bmatrix}$ Which one of the following statements about $P$ is INCORRECT ? Determinant of P is equal to $1$. $P$ is orthogonal. Inverse of $P$ is equal to its transpose. All eigenvalues of $P$ are real numbers.
asked Feb 27, 2017 in Linear Algebra Arjun 24.6k points
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The pressure ratio across a gas turbine (for air, specific heat at constant pressure, $c_{p}=1040 J/kg.K$ and ratio of specific heats, $\gamma=1.4$) is $10$. If the inlet temperature to the turbine is $1200$ K and the isentropic efficiency is $0.9$, the gas temperature at turbine exit is ________ $K$
asked Feb 27, 2017 in Applications Arjun 24.6k points
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One kg of an ideal gas (gas constant, $R= 400 J/kg.K$; specific heat at constant volume, $c_{v}=1000 J/kg.K$) at $1$ bar, and $300$ K is contained in a sealed rigid cylinder. During an adiabatic process, $100$ kJ of work is done on the system by a stirrer. The increase in entropy of the system is _______ $J/K$.
asked Feb 27, 2017 in Applications Arjun 24.6k points
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Consider steady flow of an incompressible fluid through two long and straight pipes of diameters $d_{1}$ and $d_{2}$ arranged in series. Both pipes are of equal length and the flow is turbulent in both pipes. The friction factor for turbulent flow though pipes is of the form, $f=K(Re)^{-n}$, where $K$ and ... $\left ( \dfrac{d_{2}}{d_{1}} \right )^{(5+n)}$
asked Feb 27, 2017 in Fluid Mechanics Arjun 24.6k points
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The velocity profile inside the boundary layer for flow over a flat plate is given as $\dfrac{u}{U_{\infty }}= \sin \left ( \dfrac{\Pi }{2}\dfrac{y}{\delta } \right )$, where $U_{\infty}$ is the free stream velocity and $\delta$ is the local boundary layer thickness. If $\delta^{*}$ is the local ... $\dfrac{2}{\Pi } \\$ $1-\dfrac{2}{\Pi } \\$ $1+\dfrac{2}{\Pi } \\$ $0$
asked Feb 27, 2017 in Fluid Mechanics Arjun 24.6k points
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