# Mechanical Engineering - GATE 2014 Paper Solution

Question No. 1

#### SET - 1

Choose the most appropriate phrase from the options given below to complete the following sentence.

The aircraft_________ take off as soon as its flight plan was filed.

Question No. 2

All women are entrepreneurs.

Some women are doctors.

Which of the following conclusions can be logically inferred from the above statements?

Question No. 3

Choose the most appropriate word from the options given below to complete the following sentence.

Many ancient cultures attributed disease to supernatural causes. However, modern science has largely helped _________ such notions.

Question No. 4

The statistics of runs scored in a series by four batsmen are provided in the following table. Who is the most consistent batsman of these four?

 Batsman Average Standard deviation K 31.2 5.21 L 46.0 6.35 M 54.4 6.22 N 17.9 5.90

Question No. 5

What is the next number in the series?

12 35 81 173 357 ____

Question No. 6

Find the odd one from the following group:

W,E,K,O   I,Q,W,A    F,N,T,X    N,V,B,D

Question No. 7

For submitting tax returns, all resident males with annual income below Rs 10 lakh should fill up Form P and all resident females with income below Rs 8 lakh should fill up Form Q. All people with incomes above Rs 10 lakh should fill up Form R, except non residents with income above Rs 15 lakhs, who should fill up Form S. All others should fill Form T. An example of a person who should fill Form T is

Question No. 8

A train that is 280 metres long, travelling at a uniform speed, crosses a platform in 60 seconds and passes a man standing on the platform in 20 seconds. What is the length of the platform in metres?

Question No. 9

The exports and imports (in crores of Rs.) of a country from 2000 to 2007 are given in the following bar chart. If the trade deficit is defined as excess of imports over exports, in which year is the trade deficit 1/5th of the exports?

Question No. 10

You are given three coins: one has heads on both faces, the second has tails on both faces, and the third has a head on one face and a tail on the other. You choose a coin at random and toss it, and it comes up heads. The probability that the other face is tails is

Question No. 11

Given that the determinant of the matrix $\left[\begin{array}{ccc}1& 3& 0\\ 2& 6& 4\\ -1& 0& 2\end{array}\right]$ is -12, the determinant of the matrix $\left[\begin{array}{ccc}2& 6& 0\\ 4& 12& 8\\ -2& 0& 4\end{array}\right]$ is

Question No. 12

$\underset{x\to 0}{Lt}\frac{x-\mathrm{sin}x}{1-\mathrm{cos}x}$ is

Question No. 13

The argument of the complex number $\frac{1+i}{1-i}$ , where $i=\sqrt{-1},$,is

Question No. 14

The matrix form of the linear system $\frac{\mathrm{dx}}{\mathrm{dt}}=3x-5y$ and $\frac{\mathrm{dy}}{\mathrm{dt}}=4x+8y$ is

Question No. 15

Which one of the following describes the relationship among the three vectors,$\widehat i+\widehat j+\widehat k,2\widehat i+3\widehat j+\widehat k$ and $5\widehat i+6\widehat j+4\widehat k$ ?

Question No. 16

A circular rod of length ‘L’ and area of cross-section ‘A’ has a modulus of elasticity ‘E’ and coefficient of thermal expansion ‘α’. One end of the rod is fixed and other end is free. If the temperature of the rod is increased by ΔT, then

Question No. 17

A metallic  rod of 500 mm  length and 50mm diameter when subjected to a tensile force of 100KN at the ends,experinces an increse an its length by 0.5mm and a reduction in its diameter by 0.015mm.The poission's ratio of the road material is__________

Question No. 18

Critical damping is the

Question No. 19

A  circular object of radius r rolls without slipping on a horizontal level floor with center having velocity V. The velocity at the point of contact between the object and floor is