Recent questions tagged gateme-2015-set2

$\log \tan 1^{\circ} + \log \tan 2^{\circ} + \dots + \log \tan 89^{\circ}$ is $1$ $1/\sqrt{2}$ $0$ $-1$
From a circular sheet of paper of radius $30$ $cm$, a sector of $10\%$ area is removed. If the remaining part is used to make a conical surface, then the ratio of radius and height of cone is_____
In the following question,the first and last sentence of the passage are in order and numbered $1$ and $6$. The rest of passage is split in $4$ parts and numbered as $2, 3, 4$ and $5$. These four parts are not arranged in proper order. Read the sentences and arrange them in a logical ... exchange sweets Houses looks so pretty with lighted lamps all around $2,5,3,4$ $5,2,4,3$ $3,5,4,2$ $4,5,2,3$
Ram and Shyam shared a secret and promised to each other that it would remain between them. Ram expressed himself in one of the following ways a given in the choices below. Identify the correct way as per standard English. It would remain between you and me. It would remain between I and you. It would remain between you and I. It would remain between me.
If $x>y>1$ Which of the following must be true? $\ln x>\ln y$ $e^x>e^y$ $y^x>x^y$ $\cos x>\cos y$ (i) and (ii) (i) and (iii) (iii) and (iv) (ii) and (iv)
Find the missing sequence in letter series below: A, CD, DHI, ?, UVWXY LMN MNO MNOP NOPQ
Choose the correct verb to fill in the blank below: Let us _____ introvert alternate atheist altruist
Choose the most suitable one word substitute for the following expression: Connotation of a road or way Pertinacious Viaticum Clandestine Ravenous
Ms.X will be in Bagdogra from $01/05/2014$ to $20/05/2014$ and from $22/05/2014$ to $31/05/2014$.On the morning of $21/5/2104$, she will reach Kochi via Mumbai. Which of the statement below is logically valid and can be inferred from the above sentence? Ms.X will be in ... only one day,only in May. Ms.X will be only in Kochi for one day,only in May. Only Ms.X will be in Kochi for one day in May.
Choose the most appropriate word from the options given below to complete the following sentence. If the athlete had wanted to come first in the race, he _________ several hours every day. should practice should have practiced practised should be practicing
A manufacturer has the following data regarding a product: Fixed cost per month = $Rs$. $50000$ Variable cost per unit = $Rs.$ $200$ Selling price per unit = $Rs$. $300$ Production capacity = $1500$ units per month If the production is carried out at $80\%$ of the rated capacity, then the monthly profit (in $Rs$.) is ____________
A project consists of $7$ activities. The network along with the time durations (in days) for various activities is shown in the figure. The minimum time (in days) for completion of the project is_________
A resistance-capacitance relaxation circuit is used in an electrical discharge machining process. The discharge voltage is $100$ $V$. At a spark cycle time of $25$ $μs$, the average power input required is $1$ $kW$. The capacitance (in $μF$) in the circuit is $2.5$ $5.0$ $7.5$ $10.0$
A single point cutting tool with $0^\circ$ rake angle is used in an orthogonal machining process. At a cutting speed of $180$ $m/min$, the thrust force is $490$ $N$. If the coefficient of friction between the tool and the chip is $0.7$, then the power consumption (in $kW$) for the machining operation is ________
During a TIG welding process, the arc current and arc voltage were $50$ $A$ and $60$ $V$, respectively, when the welding speed was $150$ $mm/min$. In another process, the TIG welding is carried out at a welding speed of $120$ $mm/min$ at the same arc voltage and heat input ... so that weld quality remains the same. The welding current (in $A$) for this process is $40.00$ $44.72$ $55.90$ $62.25$
The flow stress (in $MPa$) of a material is given by $\sigma =500\varepsilon ^{0.1}$, where $ε$ is true strain. The Young’s modulus of elasticity of the material is $200$ $GPa$. A block of thickness $100$ $mm$ made of this material is compressed to $95$ $mm$ thickness and then the load is removed. The final dimension of the block (in $mm$) is _________
In a two-stage wire drawing operation, the fractional reduction (ratio of change in cross-sectional area to initial cross-sectional area) in the first stage is $0.4$. The fractional reduction in the second stage is $0.3$. The overall fractional reduction is $0.24$ $0.58$ $0.60$ $1.00$
A cube and a sphere made of cast iron (each of volume $1000$ $cm^3$) were cast under identical conditions. The time taken for solidifying the cube was $4$ $s$. The solidification time (in $s$) for the sphere is __________
In a Rankine cycle, the enthalpies at turbine entry and outlet are $3159$ $kJ/kg$ and $2187$ $kJ/kg$, respectively. If the specific pump work is $2$ $kJ/kg$, the specific steam consumption (in $kg/kW$-$h$) of the cycle based on net output is _______________
For the same values of peak pressure, peak temperature and heat rejection, the correct order of efficiencies for Otto, Dual and Diesel cycles is $\eta _{\text{Otto}}> \eta _{\text{Dual}}> \eta _{\text{Diesel}}$ $\eta _{\text{Diesel}}> \eta _{\text{Dual}}> \eta _{\text{Otto}}$ ... $\eta _{\text{Diesel}}> \eta _{\text{Otto}}> \eta _{\text{Dual}}$
One kg of air ($R=287 \: J/kg – K$) undergoes an irreversible process between equilibrium state $1(20^{\circ}C$, $0.9 \: m^3$) and equilibrium state $2 ( 20^{\circ} C$, $0.6\: m^3$). The change in entropy $s_2 – s_1$ (in $J/kg – K$) is _______
Work is done on an adiabatic system due to which its velocity changes from $10$ $m/s$ to $20$ $m/s$, elevation increases by $20$ $m$ and temperature increases by $1$ $K$. The mass of the system is $10$ $kg$, $C_v$ = $100$ $J/(kg.K)$ and gravitational ... $kJ$) on the system is _______
A cylindrical uranium fuel rod of radius $5 \: mm$ in a nuclear reactor is generating heat at the rate of $4 \times 107 \: W/m^3$. The rod is cooled by a liquid (convective heat transfer coefficient $1000 \: W/m^2-K$) at $25^{\circ}C$. At steady state, the surface temperature (in $K$) of the rod is $308$ $398$ $418$ $448$
A balanced counterflow heat exchanger has a surface area of $20$ $m^2$ and overall heat transfer coefficient of $20$ $W$/$m^2$-$K$. Air ($C_p$=$1000$ $J$/$kg$-$K$) entering at $0.4$ $kg/s$ and $280$ $K$ is to be preheated by the air leaving the system at $0.4$ $kg/s$ and $300$ $K$. The outlet temperature (in $K$) of the preheated air is $290$ $300$ $320$ $350$
For a fully developed laminar flow of water (dynamic viscosity $0.001$ $P_{a-s}$) through a pipe of radius $5$ $cm$, the axial pressure gradient is −$10$ $Pa/m$. The magnitude of axial velocity (in $m/s$) at a radial location of $0.2$ $cm$ is _______
The head loss for a laminar incompressible flow through a horizontal circular pipe is $h_1$. Pipe length and fluid remaining the same, if the average flow velocity doubles and the pipe diameter reduces to half its previous value, the head loss is $h_2$. The ratio $h_2$/$h_1$ is $1$ $4$ $8$ $16$
The total emissive power of a surface is $500 \: W/ m^2$ at a temperature $T_1$ and $1200 \: W/m^2$ at a temperature $T_2$, where the temperatures are in Kelvin. Assuming the emissivity of the surface to be constant, the ratio of the temperatures $\dfrac{T_1}{T_2}$ is $0.308$ $0.416$ $0.803$ $0.874$
A hollow shaft ($d_o$ = $2d_i$ where $d_o$ and $d_i$ are the outer and inner diameters respectively) needs to transmit $20$ $kW$ power at $3000$ $RPM$. If the maximum permissible shear stress is $30$ $MPa$, do is $11.29$ $mm$ $22.58$ $mm$ $33.87$ $mm$ $45.16$ $mm$
The values of function $f(x)$ at $5$ discrete points are given below: $\begin{array}{|l|l|l|l|l|l|} \hline x & 0& 0.1 & 0.2 & 0.3 & 0.4 \\ \hline f(x) & 0 & 10 & 40& 90 & 160 \\ \hline \end{array}$ Using Trapezoidal rule with step size of $0.1$, the value of $\int_{0}^{0.4}f(x)dx$ is __________
Consider the following differential equation: $\dfrac{dy}{dt}=-5y$; initial condition: $y=2$ at $t=0$. The value of $y$ at $t=3$ is $-5e^{-10}$ $2e^{-10}$ $2e^{-15}$ $-15e^{2}$
The surface integral $\displaystyle{} \int \int_{s}^{ }\dfrac{1}{\pi }(9xi-3yj)\cdot nds$ over the sphere given by $x^2+y^2+z^2=9$ is
The chance of a student passing an exam is $20 \%$. The chance of a student passing the exam and getting above $90 \%$ marks in it is $5 \%$. GIVEN that a student passes the examination, the probability that the student gets above $90 \%$ marks is $\dfrac{1}{18} \\$ $\dfrac{1}{4} \\$ $\dfrac{2}{9} \\$ $\dfrac{5}{18}$
A hollow shaft of $1 \: m$ length is designed to transmit a power of $30\: kW$ at $700 \text{rpm}$. The maximum permissible angle of twist in the shaft is $1^{\circ}$. The inner diameter of the shaft is $0.7$ times the outer diameter. The modulus of rigidity is $80 \: GPa$. The outside diameter (in $mm$) of the shaft is__________
A single-degree-freedom spring-mass system is subjected to a sinusoidal force of $10$ $N$ amplitude and frequency $ω$ along the axis of the spring. The stiffness of the spring is $150$ $N/m$, damping factor is $0.2$ and the undamped natural frequency is $10ω$. At steady state, the amplitude of vibration (in $m$) is approximately $0.05$ $0.07$ $0.70$ $0.90$
In a certain slider-crank mechanism, lengths of crank and connecting rod are equal. If the crank rotates with a uniform angular speed of $14$ $rad/s$ and the crank length is $300$ $mm$, the maximum acceleration of the slider (in $m$/$s^2$) is ___________
In a plane stress condition, the components of stress at a point are $\sigma_x =20$ $MPa$, $\sigma _y=80$ $MPa$ and $\tau_ {xy}$=$40$ $MPa$ The maximum shear stress (in $MPa$) at the point is $20$ $25$ $50$ $100$
A cantilever beam with square cross-section of $6 \: mm$ side is subjected to a load of $2 \: kN$ normal to the top surface as shown in the figure. The Young’s modulus of elasticity of the material of the beam is $210 \: GPa$. The magnitude of slope (in radian) at $Q$ ($20 \: mm$ from the fixed end) is ________
For the truss shown in the figure, the magnitude of the force (in $kN$) in the member SR is $10$ $14.14$ $20$ $28.28$
A cantilever beam OP is connected to another beam PQ with a pin joint as shown in the figure. A load of $10$ $kN$ is applied at the mid-point of PQ. The magnitude of bending moment (in $kN$-$m$) at fixed end O is $2.5$ $5$ $10$ $25$
The initial velocity of an object is $40$ $m/s$. The acceleration a of the object is given by the following expression: $a=-0.1v$ where $v$ is the instantaneous velocity of the object. The velocity of the object after $3$ seconds will be _______