List of practice Questions

A centrifugal compressor is designed to operate with air. At the leading edge of the tip of the inducer, the blade angle is $45^\circ$, and the relative Mach number is 1.0. The stagnation temperature of the incoming air is 300 K. Consider $\gamma = 1.4$. Neglect pre-whirl and slip. The inducer tip speed is .............. m/s (rounded off to the nearest integer).

Consider the following Fanno flow problem: Flow enters a constant area duct at a temperature of 273 K and a Mach number 0.2 and eventually reaches sonic condition (Mach number = 1) due to friction. Assume $\gamma = 1.4$. The static temperature at the location where sonic condition is reached is ................. K (rounded off to 2 decimal places).

Consider an artificial satellite moving around the Moon in an elliptic orbit. The altitude of the satellite from the Moon's surface at the perigee is 25 km and at the apogee is 134 km. Assume the Moon to be spherical with a radius of 1737 km. The trajectory is considered with reference to a coordinate system fixed to the center of mass of the Moon. The ratio of the speed of the satellite at the perigee to that at the apogee is .......... (rounded off to 2 decimal places).

Consider the plane strain field given by \(\varepsilon_{xx} = 10\,x y^{2}, \; \varepsilon_{yy} = -5\,x^{2}y \text{ and } \gamma_{xy} = A \, x y (2x - y)\) where \(A\) is a constant and \(\gamma_{xy}\) is the engineering shear strain. The value of \(A\) for the strain field to be compatible is .................. (rounded off to 1 decimal place).

Two separate load cases act at a point. Case I: pure uniaxial tension of \(10\ \text{N/mm}^2\) along the \(x'\)-axis; Case II: pure uniaxial compression of \(10\ \text{N/mm}^2\) along the \(y'\)-axis. The axes \((x',y')\) are rotated by \(45^\circ\) with respect to the \((x,y)\) axes. Find the sum of the maximum and minimum principal stresses for the combined loading (rounded to 1 decimal place). \begin{center} \includegraphics[width=0.7\textwidth]{15.jpeg} \end{center}

Using thin airfoil theory, find the lift coefficient of a NACA 0012 airfoil at \(\alpha=5^\circ\) in uniform flow (rounded to 2 decimal places).

In the \(T\!-\!s\) diagram shown, several ideal–gas processes are sketched: \(aa'\), \(bb'\), \(cc'\), \(dd'\). Match each curve to the process it best represents. \begin{center} \includegraphics[width=0.7\textwidth]{04.jpeg} \end{center}

The following system of linear equations \[ 7x-3y+z=0,\quad 3x-y+z=0,\quad x-y-z=0 \] has:

The acceleration of a body travelling in a straight line is \(a=-C_1-C_2v^2\) where \(v\) is the velocity and \(C_1,C_2 > 0\). Starting with an initial positive velocity \(v_0\), the distance travelled before coming to rest for the first time is:

Let the foot of perpendicular from a point \( P(1,2,-1) \) to the straight line \( L : \frac{x}{1} = \frac{y}{0} = \frac{z}{-1} \) be \( N \). Let a line be drawn from \( P \) parallel to the plane \( x + y + 2z = 0 \) which meets \( L \) at point \( Q \). If \( \alpha \) is the acute angle between the lines \( PN \) and \( PQ \), then \( \cos \alpha \) is equal to:

With reference to the tree diagram for the sentence \emph{'John wants him to be a doctor', which of the following statements are CORRECT?}

A study on the use of the sounds in a language L was carried out in three geographical regions across both adult speakers and children below the age of 6 years. The palatal glide [j] and the retroflex lateral [l] are variants (allophones) of the standard sound [l], a retroflex glide. The table below describes usage of the three sounds across the three regions and the two populations. Which of the following conclusions are valid given the results of the study? \begin{center} \begin{tabular}{|c|cc|cc|cc|} \hline Sounds in L & \multicolumn{2}{c|}{Region 1} & \multicolumn{2}{c|}{Region 2} & \multicolumn{2}{c|}{Region 3}
& Adults & Children & Adults & Children & Adults & Children
\hline [j] & 1\% & 75\% & 28\% & 80\% & 25\% & 78\%
[l] & 11\% & 23\% & 45\% & 18\% & 74\% & 22\%
[l] & 88\% & 2\% & 27\% & 2\% & 1\% & 0\%
\hline \end{tabular} \end{center}

The following data from Sinhala contains TWO pairs of sentences, 1 and 2. Each member of the pair is marked A and B and they differ in specific ways from each other. Identify the changes that are observed across each pair. \begin{center} \begin{tabular}{|c|l|l|} \hline 1. & A: \textit{lamea kataawa ahanəwa} & B: \textit{lameəṭə kataawa əhenəwa}
& child story hear & child story hear
& (The) child listens (actively) to the story. & (The) child hears the story (despite himself).
\hline 2. & A: \textit{malli nitərəmə aɳdənəwa} & B: \textit{malliṭə nitərəmə aɳdənəwa}
& brother always cries & brother always cries
& Brother always cries. & Brother always bursts into tears (despite himself).
\hline \end{tabular} \end{center}

Consider the underlined NPs in the following three sentences: i. \underline{John} broke the window ii. \underline{The window} broke iii. \underline{The stone} broke the window Choose the correct values for the grammatical roles (X\textsubscript{1-3}) and for the semantic roles (Y\textsubscript{1-3}) of these NPs from the options given below.

Consider the following sentence: \textit{King Puru of the Pauravas, the lion, fought Alexander the emperor in the battlefield of Jhelum (Hydaspes).} Identify all the CORRECT lexico-semantic relations that appear in the given sentence from the options provided.

Match each of the word formation processes given in Column X with an example that is given in Column Y and select the correctly matched sequence. Column X \quad\quad\quad\quad\quad Column Y
P. calque \quad\quad\quad\quad\quad\quad\quad\quad\quad i. braille
Q. eponym \quad\quad\quad\quad\quad\quad\quad\quad ii. instagram
R. blend \quad\quad\quad\quad\quad\quad\quad\quad\quad iii. karaoke
S. coinage \quad\quad\quad\quad\quad\quad\quad\quad\quad iv. worldview
T. borrowing \quad\quad\quad\quad\quad\quad\quad v. google

Two sentences are given below: I. I was in Boston last winter, and I found it really cold \underline{there}.
II. \underline{Here}, have some tea!
Pick the CORRECT option with respect to the underlined adverbs.

Which of the following observations can be accounted for by B.F. Skinner's theory of language development?

Many English words at one time had meanings that were quite different from their current ones. Match each of the semantic changes in Column X to an example given in Column Y and select the appropriate sequence. Note: The older meanings of the words of Column Y are provided in the corresponding row in Column Z. \begin{tabular}{|c|c|c|} \hline Column X & Column Y & Column Z
\hline P. narrowing & i. silly & 'happy, prosperous'
Q. broadening & ii. pretty & 'tricky, sly, cunning'
R. amelioration & iii. bead & 'prayer'
S. pejoration & iv. aunt & 'father's sister'
\hline \end{tabular}

Choose from the options given, the word(s) that give rise to (or trigger) \textbf{presuppositions when reading the following lines: } \begin{quote} A Jewish physicist, Robert Oppenheimer, directed the development of a new kind of bomb in a project called Trinity. He regretted the building of the bomb because of the cost to mankind. After the war, he was suspected of having communist sympathies and he quickly lost popular support. \end{quote}

One, a sign language user with Broca's aphasia has difficulty producing signs. But the same signer has no difficulty in drawing pictures or picking up an object. Two, a hearing person becomes paralysed in an accident and loses all motor ability, but is able to speak fluently. What conclusions can we draw from these two cases about how language is represented in the brain?

Consider the following sentence: The historian will put the paintings in his house on the wall in the museum. Which interpretation is NOT possible among the following?

Match the numbered parts of the vocal tract (in the diagram given below) with the correct label from those given in the box and choose the appropriate option. \includegraphics[width=0.5\linewidth]{3.png}
Labels: a. Labial cavity
b. Pharyngeal cavity
c. Alveolar ridge
d. Laryngeal cavity

Consider the predicate calculus expression, \(\forall x\, P(x) \rightarrow \exists x\, P(x)\). Which of the following English sentences with respect to a club called Sunshine is/are equivalent to this predicate calculus expression?