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GATE20152GA9
$\log \tan 1^o + \log \tan 2^o +$ ..… $+ \log \tan 89^o$ is $1$ $1/\sqrt{2}$ $0$ $1$
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GATE20152GA8
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_____
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GATE20152GA7
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 sentence ... Houses looks so pretty with lighted lamps all around $2,5,3,4$ $5,2,4,3$ $3,5,4,2$ $4,5,2,3$
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GATE20152GA6
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.
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GATE20152GA5
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)
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GATE20152GA4
Find the missing sequence in letter series below: A, CD, DHI, ?, UVWXY LMN MNO MNOP NOPQ
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GATE20152GA1
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
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GATE2015314
If $P(X) = \displaystyle{\frac{1}{4}}$, $P(Y) = \displaystyle{\frac{1}{3}}$, and $P(X \cap Y) = \displaystyle{\frac{1}{12}}$, the value of $P(Y/X)$ is $\displaystyle{\frac{1}{4}}$ $\displaystyle{\frac{4}{25}}$ $\displaystyle{\frac{1}{3}}$ $\displaystyle{\frac{29}{50}}$
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GATE2015312
Saturated vapor is condensed to saturated liquid in a condenser. The heat capacity ratio is $C_r = \displaystyle{\frac{C_{min}}{C_{max}}}$. The effectiveness ($\varepsilon$) of the condenser is $\displaystyle{\frac{1exp[NTU(1+C_r)]}{1+C_r}}$ $\displaystyle{\frac{1exp[NTU(1C_r)]}{1C_rexp[NTU(1C_r)]}}$ $\displaystyle{\frac{NTU}{1+NTU}}$ $1exp(NTU)$
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GATE201534
In the figure, link $2$ rotates with constant angular velocity $\omega_2$. A slider link $3$ moves outwards with a constant relative velocity $V_{Q/P}$, where $Q$ is a point on slider $3$ and $P$ is a point on link $2$. The magnitude and direction of Coriolis component ... $\omega_2$ $\omega_2$ $V_{Q/P}$; direction of $V_{Q/P}$ rotated by $90^o$ opposite to the direction of $\omega_2$
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GATE2015328
Figure shows a single degree of freedom system. The system consists of a massless rigid bar OP hinged at O and a mass $m$ at end P. The natural frequency of vibration of the system is $f_n=\displaystyle{\frac{1}{2\pi }\sqrt{\frac{k}{4m}}}$ ... $f_n=\displaystyle{\frac{1}{2\pi }\sqrt{\frac{2k}{m}}}$
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GATE2015327
Figure shows a wheel rotating about $O_2$. Two points $A$ and $B$ located along the radius of wheel have speeds of $80$ $m/s$ and $140$ $m/s$ respectively. The distance between the points $A$ and $B$ is $300$ $mm$. The diameter of the wheel (in $mm$) is ________
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GATE2015325
An airstandard Diesel cycle consists of the following processes: $1$$2$: Air is compressed isentropically. $2$$3$: Heat is added at constant pressure. $3$$4$: Air expands isentropically to the original volume. $4$$1$: Heat is rejected at constant volume. If $\gamma$ ... $1\displaystyle{\frac{\gamma (T_4T_1)}{T_3T_2}}$ $1\displaystyle{\frac{T_4T_1}{(\gamma 1)(T_3T_2)}}$
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GATE2015319
Which of the following statements are TRUE for damped vibrations? P. For a system having critical damping, the value of damping ratio is unity and system does not undergo a vibratory motion. Q. Logarithmic decrement method is used to determine the amount of damping in a physical ... proportional to the square of relative velocity. P and Q only P and S only P, Q and R only Q and S only
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GATE2015316
The value of $\displaystyle{\lim_{x\rightarrow 0}\left(\frac{\sin x}{2\sin x+x\cos x}\right)}$ is ________
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GATE2015330
For ball bearings, the fatigue life $L$ measured in number of revolutions and the radial load $F$ are related by $FL^{1/3} = K$, where $K$ is a constant. It withstands a radial load of $2$ $kN$ for a life of $540$ million revolutions. The load (in $kN$) for a life of one million revolutions is ________
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GATE2015351
For the linear programming problem: Maximize $Z = 3X_1 + 2X_2$ Subject to $−2X_1 + 3X_2 ≤ 9$ $X_1 − 5 X_2 ≥ −20$ $X_1, X_2 ≥ 0$ The above problem has unbounded solution infeasible solution alternative optimum solution degenerate solution
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GATE2015347
The torque (in $N$$m$) exerted on the crank shaft of a two stroke engine can be described as $T = 10000 + 1000 \sin(2θ) − 1200 \cos(2θ)$, where $θ$ is the crank angle as measured from inner dead center position. Assuming the resisting torque to be constant, the power (in $kW$) developed by the engine at $100$ $rpm$ is ________
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GATE2015344
Laplace transform of the function $f(t)$ is given by $F(s)=L\begin{bmatrix} f(t) \end{bmatrix}=\int_{0}^{\infty }f(t)e^{st}dt$ . Laplace transform of the function shown below is given by $\displaystyle{\frac{1e^{2s}}{s}}$ $\displaystyle{\frac{1e^{s}}{2s}}$ $\displaystyle{\frac{22e^{s}}{s}}$ $\displaystyle{\frac{12e^{s}}{s}}$
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GATE2015342
For a given matrix $P=\begin{bmatrix} 4+3i & i\\ i & 43i \end{bmatrix}$, where $i=\sqrt{1}$, the inverse of matrix $P$ is $P=\displaystyle{\frac{1}{24}}\begin{bmatrix} 43i & i\\ i & 4+3i \end{bmatrix}$ ... $P=\displaystyle{\frac{1}{25}}\begin{bmatrix} 4+3i & i\\ i & 43i \end{bmatrix}$
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GATE2015354
A brick wall $\left(k=0.9\displaystyle{\frac{W}{m.k}}\right)$ of thickness $0.18$ $m$ separates the warm air in a room from the cold ambient air. On a particular winter day, the outside air temperature is $−5^oC$ and the room needs to be maintained at $27^oC$ ... resistance of the air inside the room, the heat loss, in $\displaystyle{\frac{W}{m^2}}$, is $88$ $110$ $128$ $160$
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GATE20153GA3
Choose the statement where underlined word is used correctly When the teacher eludes to different authors, he is being elusive. When the thief keeps eluding the police, he is being elusive. Matters that are difficult to understand, identify or remember are allusive. Mirages can be allusive, but a better way to express them is illusory.
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GATE20153GA2
Fill the blank with the correct idiom/phrase. That boy from the town was ______________________ in the sleepy village. dog out of heard sheep from the heap fish out of water bird from the flock
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GATE20153GA1
Choose the appropriate word/phrase, out of the four options given below, to complete the following sentence: Apparent lifelessness _________ dormant life. harbours leads to supports affects
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GATE20153GA10
A coin is tossed thrice. Let C be the event that head occurs in each of first two tosses. Let Y be the event that tails occurs in third toss. Let Z be the event that two tails occur in three tosses. Based on the above information, which one of the following statement is TRUE? X and Y are not independent Y and Z are dependent Y and Z are independent X and Z are independent
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GATE20153GA9
Right triangle $PQR$ is to be constructed in $xy$plane so that the right angle is at $P$ and line $PR$ is parallel to $x$axis.The $x$ and $y$ coordinates of $P$, $Q$ and $R$ are to be integers that satisfies the inequalities: $4\leq x\leq 5$ and $6\leq y\leq 16$. How many different triangles could be constructed with these properties? $110$ $1100$ $9900$ $10000$
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GATE20153GA8
In the given figure $Q$ is a right triangle, $PS:QS = 3:1$ $RT:QT = 5:2$ $PU:UR = 1:1$ If area of triangle $QTS$ is $20$ $cm^2$, then the area of triangle $PQR$ in $cm^2$ is_____
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GATE20153GA7
Given below are two statements followed by two conclusions. Assuming these statements to be true, decide which one logically follows: Statements: No manager is a leader. All leaders are executives. Conclusions: No manager is an executive. No executive ... . Only conclusion I follows Only conclusion II follows Neither conclusion I nor II follows Both conclusion I and II follows
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GATE20153GA6
Select the option in place of underlined parts of sentence. Increased productivity necessary reflects greater efforts made by the employees. Increase in productivity necessary Increase productivity is necessary Increase in productivity necessarily No improvement required
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GATE20153GA5
Five teams have to compete in a league, with every team playing every other team exactly once, before going to the next round. How many matches will have to held to complete the league round of matches? $20$ $10$ $8$ $5$
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GATE201615
Solve the equation $x=10\cos(x)$ using the NewtonRaphson method. The initial guess is $x=\pi /4$. The value of the predicted root after the first iteration, up to second decimal, is ________
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GATE201613
$f(z)=u(x,y)+iv(x,y)$ is an analytic function of complex variable $z=x+iy$ where $i=\sqrt{1}$. If $u(x,y)$=$2xy$ , then $v(x,y)$ may be expressed as $x^2 + y^2 + $ constant $x^2 – y^2 +$ constant $x^2 + y^2 +$ constant $(x^2 + y^2) +$ constant
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GATE201611
The solution to the system of equations $\begin{bmatrix} 2 & 5\\4 &3 \end{bmatrix}\begin{bmatrix} x\\y \end{bmatrix}=\begin{bmatrix} 2\\ 30 \end{bmatrix}$ is $6,2$ $6,2$ $6,2$ $6,2$
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GATE2016119
The INCORRECT statement about regeneration in vapor power cycle is that it increases the irreversibility by adding the liquid with higher energy content to the steam generator heat is exchanged between the expanding fluid in the turbine and the compressed ... the principle is similar to the principle of Stirling gas cycle it is practically implemented by providing feed water heaters
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GATE2016118
Consider two hydraulic turbines having identical specific speed and effective head at the inlet. If the speed ratio $\displaystyle{\left(\frac{N_1}{N_2}\right)}$ of the two turbines is $2$, then the respective power ratio $\displaystyle{\left(\frac{P_1}{P_2}\right)}$ is _____________
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GATE2016117
Propane ($C_3H_8$) is burned in an oxygen atmosphere with $10$% deficit oxygen with respect to the stoichiometric requirement. Assuming no hydrocarbons in the products, the volume percentage of $CO$ in the products is __________.
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GATE2016113
The instantaneous streamwise velocity of a turbulent flow is given as follows: $u(x,y,z,t)=\overline{u}(x,y,z)+{u}'(x,y,z,t)$ The timeaverage of the fluctuating velocity ${u}'(x,y,z,t)$ is $\displaystyle{\frac{u'}{2}}$ $\displaystyle{\frac{\overline{u}}{2}}$ zero $\displaystyle{\frac{\overline{u}}{2}}$
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GATE2016112
The spring constant of a helical compression spring DOES NOT depend on coil diameter material strength number of active turns wire diameter
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GATE201618
The cross sections of two hollow bars made of the same material are concentric circles as shown in the figure. It is given that $r_3$ > $r_1$ and $r_4$ > $r_2$, and that the areas of the crosssections are the same. $J_1$ and $J_2$ are the torsional rigidities of ... right, respectively. The ratio $\displaystyle{\frac{J_2}{J_1}}$ is $>1$ $<0.5$ $=1$ between $0.5$ and $1$
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GATE2016131
A twomember truss $PQR$ is supporting a load $W$. The axial forces in members $PQ$ and $QR$ are respectively $2W$ tensile and $\sqrt{3}W$ compressive $\sqrt{3}W$ tensile and $2W$ compressive $\sqrt{3}W$ compressive and $2W$ tensile $2W$ compressive and $\sqrt{3}W$ tensile
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