# Mechanical Engineering - GATE 2015 Paper Solution

#### SET - 1

Choose the appropriate word/phrase, out of the four options given below, to complete the following sentence.
Dhoni , as well as the other team members of Indian team, ________ present on the occasion.

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Choose the word most similar in meaning to the given word:
Awkward

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What is the adverb for the given word below?
Misogynous

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An electric bus has onboard instruments that report the total electricity consumed since the start of the trip as well as the total distance covered . During a single day of operation, the bus travels on stretches M,N,O and P, in that order. The cumulative distances travelled and the corresponding electricity consumption are shown in the Table below:

 Stretch Cumulative distance (km) Electricity used (kWh) M 20 12 N 45 25 O 75 45 P 100 57

The stretch where the electricity consumption per km is minimum is

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Ram and Ramesh appeared in an interview for two vacancies in the same department . The probability of Ram’s selection is 1/6 and that of Ramesh is 1/8. What is the probability that only one of them will be selected?

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In the following sentence certain parts are underlined and marked P,Q and R. One of the parts may contain certain error or may not be acceptable in standard written communication. Select the part containing an error. Choose D as your answer if there is no error.

 The student corrected all the errors that the instructor marked on the answer book. P Q R

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Given below are two statements followed by two conclusion. Assuming these statements to be true, decide which one logically follows.

Statements:
I. All film directors are playback singers.
II. All film directors are film stars.

Conclusions :
I.. All film directors are playback singers.
II. Some film stars are film directors.

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A tiger is 50 leaps of its own behind a deer. The tiger takes 5 leaps per minute to the deer’s 4. If the tiger and the deer cover 8 metres and 5 meter per leap respectively , what distance in metres will the tiger have to run before it catches the deer?

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If a2+b2+c2 = 1 , then ab+bc+ac lies in the interval.

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Lamenting the gradual sidelining of the arts in school curricula, a group of prominent artists wrote to the Chief Minister last year, asking him to allocate more funds to support arts education in schools. However, no such increase has been announced in this year’s Budget. The artists expressed their deep anguish at their request not being approved, but many of them remain optimistic about funding in the future.
Which of the statement(s) below is/are logically valid and can be inferred from the above statements?

(i) The artists expected funding for the arts to increase this year.
(ii) The Chief Minister was receptive to the idea of increasing funding for the arts.
(iii) The Chief Minister is a prominent artist.
(iv) Schools are giving less importance to arts education nowadays.

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If any two columns of a determinant $\mathrm{P}=\left|\begin{array}{ccc}4& 7& 8\\ 3& 1& 5\\ 9& 6& 2\end{array}\right|$ are interchanged, which one of the following statements regarding the value of the determinant is CORRECT?

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Among the four normal distributions with probability density functions as shown below, which one has the lowest variance?

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Simpson’s $\frac{1}{3}$ rule is used to integrate the function $f\left(x\right)=\frac{3}{5}{x}^{2}+\frac{9}{5}$ between x = 0 and x = 1 using the least number of equal sub – intervals. The value of the integral is ___________

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The value of $\lim_{x\rightarrow0}\frac{1-\cos\left(x^2\right)}{2x^4}\;$ is

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Given two complex numbers the argument of $\frac{{z}_{1}}{{z}_{2}}$ in degrees is

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Consider fully developed flow in a circular pipe with negligible entrance length effects. Assuming the mass flow rate , density and friction factor to be constant, if the length of the pipe is doubled and the diameter is halved, the head loss due to friction will increase by a factor of

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The Blasius equation related to boundary layer theory is a

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For flow of viscous fluid over a flat plate, if the fluid temperature is the same as the plate temperature, the thermal boundary layer is

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For an ideal gas with constant values of specific heats, for calculation of the specific enthalply,

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A carnot engine (CE-1) works between two temperature reservoirs A and B , where TA =900 K and TB = 500 K. A second Carnot engine (CE-2) works between temperature reservoirs B and C, where Tc = 300 K. In each cycle of CE-1 and CE-2 , all the heat rejected by CE-1 to reservoir B is used by CE-2 . For one cycle operation, if the net Q absorbed by CE-1 from reservoir A is 150 MJ, the net heat rejected to reservoir C by CE-2 (in MJ) is _________