# Mechanical Engineering - GATE 2016 Paper Solution

#### SET - 1

Which of the following is CORRECT with respect to grammar and usage?

Mount Everest is ____________.

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The policeman asked the victim of a theft, “What did you _______ ?"

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Despite the new medicine’s ______________ in treating diabetes, it is not ______________widely.

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In a huge pile of apples and oranges, both ripe and unripe mixed together, 15% are unripe fruits. Of the unripe fruits, 45% are apples. Of the ripe ones, 66% are oranges. If the pile contains a total of 5692000 fruits, how many of them are apples?

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Michael lives 10 km away from where I live. Ahmed lives 5 km away and Susan lives 7 km away from where I live. Arun is farther away than Ahmed but closer than Susan from where I live. From the information provided here, what is one possible distance (in km) at which I live from Arun’s place?

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A person moving through a tuberculosis prone zone has a 50% probability of becoming infected. However, only 30% of infected people develop the disease. What percentage of people moving through a tuberculosis prone zone remains infected but does not show symptoms of disease?

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In a world filled with uncertainty, he was glad to have many good friends. He had always assisted them in times of need and was confident that they would reciprocate. However, the events of the last week proved him wrong.

Which of the following inference(s) is/are logically valid and can be inferred from the above passage?

(i) His friends were always asking him to help them.
(ii) He felt that when in need of help, his friends would let him down.
(iii)He was sure that his friends would help him when in need.
(iv) His friends did not help him last week.

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Leela is older than her cousin Pavithra. Pavithra’s brother Shiva is older than Leela. When Pavithra and Shiva are visiting Leela, all three like to play chess. Pavithra wins more often than Leela does.

Which one of the following statements must be TRUE based on the above?

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If $\frac12q^{-a}=\frac1r\;$ and $r^{-b}=\frac1s$ and $S^{-C}=\frac1q$ the value of $abc$ is .

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P, Q, R and S are working on a project. Q can finish the task in 25 days, working alone for 12 hours a day. R can finish the task in 50 days, working alone for 12 hours per day. Q worked 12 hours a day but took sick leave in the beginning for two days. R worked 18 hours a day on all days.What is the ratio of work done by Q and R after 7 days from the start of the project?

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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

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If $f(t)$ is a function defined for all $t\geq0$, its Laplace transform $f(s)$ is defined as

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$f(z)=u(x,y)+iv(x,y)$ is an analytic function of complex variable $z=x+\;i\;y$ where $i\sqrt{-1}$. If $u(x,y)=2\;xy$, then $v(x,y)$ may be expressed as

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Consider a Poisson distribution for the tossing of a biased coin. The mean for this distribution is $\mu$. The standard deviation for this distribution is given by

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Solve the equation $x=10 cos(x)$ using the Newton-Raphson 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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A rigid ball of weight 100 N is suspended with the help of a string. The ball is pulled by a horizontal force $F$ such that the string makes an angle of $30^\circ$ with the vertical. The magnitude of force $F$ (in N) is __________

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A point mass M is released from rest and slides down a spherical bowl (of radius R) from a height H as shown in the figure below. The surface of the bowl is smooth (no friction). The velocity of the mass at the bottom of the bowl is

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The cross sections of two hollow bars made of the same material are concentric circles as shown in the figure. It is given that r3 > r1 and r4 > r2 , and that the areas of the cross-sections are the same. $J_1$ and $J_2$ are the torsional rigidities of the bars on the left and right, respectively. The ratio $J_2/J_1$ is

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A cantilever beam having square cross-section of side $\alpha$ is subjected to an end load. If $\alpha$ is increased by 19%, the tip deflection decreases approximately by

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A car is moving on a curved horizontal road of radius 100 m with a speed of 20 m/s. The rotating masses of the engine have an angular speed of 100 rad/s in clockwise direction when viewed from the front of the car. The combined moment of inertia of the rotating masses is 10 kg-$\mathrm m^2$. The magnitude of the gyroscopic moment (in N-m) is __________