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GATE2017155
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, ... one of the following options is correct? Only $i$. Only $ii$. Both $i$ and $ii$. Neither $i$ nor $ii$
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GATE2017154
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, ... play better than James. Steve was known to play better than Mark. James and Steve were good friends. James played better than steve.
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GATE2017153
Let $S_{1}$ be the plane figure consisting of the points $(x, y)$ given by the inequalities $x  1 \leq 2$ and $y+2 \leq 3$. Let $S_{2}$ be the plane figure given by the inequalities $xy \geq 2, y \geq 1$, and $x \leq 3$. Let $S$ be the union of $S_{1}$ and $S_{2}$. The area of $S$ is. $26$ $28$ $32$ $34$
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GATE2017152
What is the sum of the missing digits in the subtraction problem below? 5 _ _ _ _ 48 _ 89 _______ 1111 $8$ $10$ $11$ Cannot be determined.
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GATE2017151
"Here, throughout the early $1820$s, Stuart continued to fight is losing battle to allow his sepoys to wear their castemarks and their own choice of facial hair on parade, being again reprimanded by the commanderinchief. His retort that 'A ... sepoys to wear castemarks. The commanderincheif was exempt from the Europeans prejudice that dictated how the sepoys were to dress.
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GATE2017150
$P$, $Q$ 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.
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GATE2017149
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 $Rs. 20,000$ $Rs. 30,000$ $Rs. 32,300$ $Rs. 40,000$
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GATE2017148
A rightangled 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? $\frac{5\pi}{12}$ $\frac{5\pi}{24}$ $\frac{24\pi}{5}$ $\frac{10\pi}{13}$
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GATE2017147
As the two speakers become increasingly agitated, the debate became _________. lukewarm poetic forgiving heated
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GATE2017146
He was one of my best _______ and I felt his loss ________. friend, keenly friends, keen friend, keener friends, keenly
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GATE2017145
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.
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GATE2017144
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
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GATE2017143
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.
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GATE2017142
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. Job Processing Time (days) P 15 Q 9 R 22 S 12
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GATE2017141
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 ________.
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GATE2017140
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 $5$ $6.67$ $10$ $20$
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GATE2017139
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: N60 G01 X 30 Y 55 Z5 F50 N70 G02 X 50 Y 35 R 20 N80 G01 Z 5 The coordinates of the centre of the circular arc are: $(30, 55)$ $(50, 55)$ $(50, 35)$ $(30, 35)$
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GATE2017138
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.
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GATE2017137
For an inline slidercrank 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
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GATE2017132
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 deformed length of the elongated diagonal, up to three decimal places is _______ units.
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GATE2017136
A thin uniform rigid bar of Length $L$ and mass $M$ is hinged at point $O$, located at a distance of $\frac{L}{3}$ 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 $m=\frac{M}{4}$ is fixed at ... of the system is $\sqrt{\frac{5k}{M}}$ $\sqrt{\frac{5k}{2M}}$ $\sqrt{\frac{3k}{2M}}$ $\sqrt{\frac{3k}{M}}$
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GATE2017135
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 ________.
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GATE2017134
A horizontal bar, fixed at one end $(x=0)$, has a length of $1$ m, and crosssectional 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
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GATE2017133
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 _________ $N/mm^{2}$.
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GATE2017131
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 ... velocity of the centre of disk $B$ is $\sqrt{\frac{3}{4}}$ $\sqrt{\frac{3}{2}}$ $1$ $\sqrt{2}$
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GATE2017130
A point mass of $100$ kg is dropped onto a massless elastic bar (crosssectional 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
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GATE2017129
An initially stressfree massless elastic beam of length $L$ and circular crosssection 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 ... , the temperature rise required to cause the beam to buckle is proportional to $d$ $d^{2}$ $d^{3}$ $d^{4}$
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GATE2017128
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 ______ $^{\circ} C$.
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GATE2017127
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 ... $2$ to the surrounding environment is _______ kW.
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GATE2017126
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 _______.
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GATE2017125
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 $30^{\circ}$ ... saturation pressure of water at $30^{\circ} C$ is $4246$ Pa, the mass of water vapour per kg of dry air is _________ grams.
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GATE2017112
Match the processes with their characteristics: Process Characteristics P: Electrical Discharge Machining 1: No residual stress Q: Ultrasonic Machining 2: Machining of electrically conductive materials R: Chemical Machining 3: Machining of glass S: Ion Beam Machining 4: Nanomachining $P2, Q3, R1, S4$ $P3, Q2, R1, S4$ $P3, Q2, R4, S1$ $P2, Q4, R3, S1$
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GATE2017124
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 ________ $K$
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GATE2017123
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 _______ $J/K$.
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GATE2017122
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 $2$ $1$ $2\sqrt{5}$ $0$
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GATE2017121
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 ... $\left ( \frac{d_{2}}{d_{1}} \right )^{(5+n)}$
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GATE2017120
The velocity profile inside the boundary layer for flow over a flat plate is given as $\frac{u}{U_{\infty }}= \sin \left ( \frac{\Pi }{2}\frac{y}{\delta } \right )$, where $U_{\infty}$ is the free stream velocity and $\delta$ is the local boundary layer thickness. If $\delta^{*}$ is the ... of $\frac{\delta ^{*}}{\delta }$ is $\frac{2}{\Pi }$ $1\frac{2}{\Pi }$ $1+\frac{2}{\Pi }$ $0$
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GATE2017119
$P(0, 3), Q (0.5, 4)$ 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 $0$ $0.25$ $0.5$ $1$
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GATE2017118
A parametric curve defined by $x= \cos \left ( \frac{\Pi u}{2} \right ), y= \sin \left ( \frac{\Pi u}{2} \right )$ in the range $0 \leq u \leq 1$ is rotated about the $X$axis by 360 degrees. Area of the surface generated is $\frac{\Pi }{2}$ $\pi$ $2 \pi$ $4 \pi$
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GATE2017117
For the vector $\vec{V}=2yz\hat{i}+3xz \hat{j}+4xy \hat{k}$, the value of $\bigtriangledown$. $(\bigtriangledown \times \vec{V})$ is ________.
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