# Recent questions tagged gateme-2017-set1

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.
"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.
$P$, $Q$ 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.
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.
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. $26$ $28$ $32$ $34$
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 $ii$
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 $Rs. 20,000$ $Rs. 30,000$ $Rs. 32,300$ $Rs. 40,000$
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? $\dfrac{5\pi}{12} \\$ $\dfrac{5\pi}{24} \\$ $\dfrac{24\pi}{5} \\$ $\dfrac{10\pi}{13}$
As the two speakers become increasingly agitated, the debate became _________. lukewarm poetic forgiving heated
He was one of my best _______ and I felt his loss ________. friend, keenly friends, keen friend, keener friends, keenly
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.
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 _________ $m/s$
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.
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. $\begin{array}{|l|l|} \hline \text{Job} & \text{Processing Time (days)} \\ \hline P & 15 \\ \hline Q & 9 \\ \hline R & 22 \\ \hline S & 12 \\ \hline \end{array}$
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 ________.
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 $5$ $6.67$ $10$ $20$
Circular arc on a part profile is being machined on a vertical CNC milling machine. CNC part program using metric units with absolute dimensions is listed below: ... $(30, 55)$ $(50, 55)$ $(50, 35)$ $(30, 35)$
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.
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
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 $\sqrt{\dfrac{3}{4}} \\$ $\sqrt{\dfrac{3}{2}} \\$ $1 \\$ $\sqrt{2}$
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 $\sqrt{\dfrac{5k}{M}} \\$ $\sqrt{\dfrac{5k}{2M}} \\$ $\sqrt{\dfrac{3k}{2M}} \\$ $\sqrt{\dfrac{3k}{M}}$
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 ________.
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
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 _________ $N/mm^{2}$.
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.
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
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 $d$ $d^{2}$ $d^{3}$ $d^{4}$
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 ______ $^{\circ} C$.
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.
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 _______.
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.
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 $2$ $1$ $2\sqrt{5}$ $0$
$P(0, 3), Q (0.5, 4)$ 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 $0$ $0.25$ $0.5$ $1$
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 $\dfrac{\Pi }{2} \\$ $\pi \\$ $2 \pi \\$ $4 \pi$
For the vector $\vec{V}=2yz\hat{i}+3xz \hat{j}+4xy \hat{k}$, the value of $\bigtriangledown$. $(\bigtriangledown \times \vec{V})$ is ________.
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.
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 ________ $K$
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 _______ $J/K$.
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 ... $\left ( \dfrac{d_{2}}{d_{1}} \right )^{(5+n)}$
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 ... $\dfrac{2}{\Pi } \\$ $1-\dfrac{2}{\Pi } \\$ $1+\dfrac{2}{\Pi } \\$ $0$