List of practice Questions

The Bode magnitude plot of a first order stable system is constant with frequency. The asymptotic value of the high frequency phase, for the system, is -180°. This system has

The figure below shows the front and rear view of a disc, which is shaded with identical patterns. The disc is flipped once with respect to any one of the fixed axes 1-1, 2-2, or 3-3 chosen uniformly at random.
What is the probability that the disc DOES NOT retain the same front and rear views after the flipping operation?

Altruism is the human concern for the wellbeing of others. Altruism has been shown to be motivated more by social bonding, familiarity, and identification of belongingness to a group. The notion that altruism may be attributed to empathy or guilt has now been rejected.
Which one of the following is the CORRECT logical inference based on the information in the above passage?

There are two identical dice with a single letter on each of the faces. The following six letters: Q, R, S, T, U, and V, one on each of the faces. Any of the six outcomes are equally likely. The two dice are thrown once independently at random. What is the probability that the outcomes on the dice were composed only of any combination of the following possible outcomes: Q, U, and V?

The price of an item is 10% cheaper in an online store S compared to the price at another online store M. Store S charges ₹150 for delivery. There are no delivery charges for orders from store M. A person bought the item from the store S and saved ₹100.
What is the price of the item at the online store S (in ₹) if there are no other charges than what is described above?

The letters P, Q, R, S, T, and U are to be placed one per vertex on a regular convex hexagon, but not necessarily in the same order.
Consider the following statements:
The line segment joining R and S is longer than the line segment joining P and Q.
The line segment joining R and S is perpendicular to the line segment joining P and Q.
The line segment joining R and U is parallel to the line segment joining T and Q.
Based on the above statements, which one of the following options is CORRECT?

An ant is at the bottom-left corner of a grid (point P) as shown above. It aims to move to the top-right corner of the grid. The ant moves only along the lines marked in the grid such that the current distance to the top-right corner strictly decreases.
Which one of the following is part of a possible trajectory of the ant during the movement?

A damper with damping coefficient, \( c \), is attached to a mass of 5 kg and spring of stiffness 5 kN/m as shown in the figure. The system undergoes under-damped oscillations.
If the ratio of the 3rd amplitude to the 4th amplitude of oscillations is 1.5, the value of \( c \) is _________ Ns/m (rounded off to the nearest integer).

A uniform rigid prismatic bar of total mass \( m \) is suspended from a ceiling by two identical springs as shown in the figure.
Let \( \omega_1 \) and \( \omega_2 \) be the natural frequencies of mode I and mode II respectively (with \( \omega_1<\omega_2 \)).
The value of \( \omega_2/\omega_1 \) is _________ (rounded off to one decimal place).

An ideal ramjet is to operate with exhaust gases optimally expanded to ambient pressure at an altitude where temperature is 220 K. The exhaust speed at the nozzle exit is 1200 m/s at a temperature of 1100 K.
Given: \( \gamma = 1.4 \) at 220 K; \( R = 287 \, \text{J/(kg-K)} \) for air; \( \gamma = 1.33 \) at 1100 K; \( R = 287 \, \text{J/(kg-K)} \) for exhaust gases.
The cruise speed of this ramjet is _________ m/s (rounded off to nearest integer).

A multistage axial compressor takes in air at 1 atm, 300 K and compresses it to a minimum of 5 atm.
The mean blade speed is 245 m/s and work coefficient, \( \frac{\Delta c \, \theta}{U} \), is 0.55 for each stage.
For air, use \( C_p = 1005 \, \text{J/(kg-K)} \), \( R = 287 \, \text{J/(kg-K)} \), and \( \gamma = 1.4 \).
If the compression is isentropic, the number of stages required is _________ (rounded off to the next higher integer).

As you grow older, an injury to your ______ may take longer to _____

In a 500 m race, P and Q have speeds in the ratio of 3 : 4. Q starts the race when P has already covered 140 m. What is the distance between P and Q (in m) when P wins the race?

Three bells P, Q, and R are rung periodically in a school. P is rung every 20 minutes; Q is rung every 30 minutes and R is rung every 50 minutes.
If all the three bells are rung at 12:00 PM, when will the three bells ring together again the next time?

Consider a thin symmetric airfoil at a 2 degree angle of attack in a uniform flow at 50 m/s. The pitching moment coefficient about its leading edge is _________ (rounded off to three decimal places).

A convergent-divergent nozzle with adiabatic walls is designed for an exit Mach number of 2.3. It is discharging air to atmosphere under the conditions indicated in the figure.
Flow through the nozzle is inviscid, the characteristic gas constant for air is 287 J/(kg-K), and \( \gamma = 1.4 \).
When the reservoir pressure is 25 bar (absolute), and temperature is 300 K, Prandtl-Meyer expansion waves appear at the nozzle exit as shown.
The minimum percentage change in the reservoir pressure required to eliminate the wave system at the nozzle exit under steady state is _________ %.

A conventional airplane of mass 5000 kg is doing a level turn of radius 1000 m at a constant speed of 100 m/s at sea level.
Taking the acceleration due to gravity as 10 m/s\(^2\), the bank angle of the airplane is _________ degrees.

Given: The tip deflection and tip slope for a tip-loaded cantilever of length \( L \) are: \[ \delta = \frac{NL^3}{3EI} \quad \text{and} \quad \theta = \frac{NL^2}{2EI}, \] where \( N \) is the tip force and \( EI \) is the flexural rigidity.
A cantilever \( PQ \) of rectangular cross-section is subjected to transverse load, \( F \), at its mid-point. Two cases are considered as shown in the figure. In Case I, the end \( Q \) is free and in Case II, \( Q \) is simply supported.
The ratio of the magnitude of the maximum bending stress at \( P \) in Case I to that in Case II is _________ (rounded off to one decimal place).

A simply supported Aluminium column of length 1 m and rectangular cross-section \( w \times t \) with \( t \leq w \), is subjected to axial compressive loading.
Young’s modulus is 70 GPa. Yield stress under uniaxial compression is 120 MPa.
The value of \( t \) at which the failure load for yielding and buckling coincide is _________ mm.

A 0.5 m long thin-walled circular shaft of radius 2 cm is to be designed for an axial load of 7.4 kN and a torque of 148 Nm applied at its tip, as shown in the figure.
The allowable stress under uniaxial tension is 100 MPa.
Using the maximum principal stress criterion, the minimum thickness, \( t \), of the shaft so that it does not fail is _________ mm (rounded off to the nearest integer).

A 10 kN axial load is applied eccentrically on a rod of square cross-section (1 cm $\times$ 1 cm) as shown in the figure.
The strains measured by the two strain gages attached to the top and bottom surfaces at a distance of 0.5 m from the tip are \( \varepsilon_1 = 0.0016 \) and \( \varepsilon_2 = 0.0004 \), respectively.
The eccentricity in loading, \( e \), is _________ mm.

For a thin-walled I section, the width of the two flanges as well as the web height are the same, i.e., \( 2b = 20 \, \text{mm} \). Thickness is 0.6 mm.
The second moment of area about a horizontal axis passing through the centroid is _________ mm\(^4\).

Consider a high Earth-orbiting satellite of angular momentum per unit mass \(\vec{h}\) and eccentricity \(e\). The mass of the Earth is \(M\) and \(G\) is the universal gravitational constant. The distance between the satellite’s center of mass and the Earth’s center of mass is \(r\), the true anomaly is \(\theta\), and the phase angle is zero. Which of the following statements is/are true?

A rocket operates at an absolute chamber pressure of 20 bar to produce thrust \(F_1\). The hot exhaust is optimally expanded to 1 bar (absolute pressure) using a convergent-divergent nozzle with exit to throat area ratio \(\left(\frac{A_e}{A_t}\right)\) of 3.5 and thrust coefficient, \(C_{F,1} = 1.42\). The same rocket when operated at an absolute chamber pressure of 50 bar produces thrust \(F_2\) and the thrust coefficient is \(C_{F,2}\). Which of the following statement(s) is/are correct?

The vector field \( \vec{v} = x^3 \hat{i} + y^3 \hat{j} + z^3 \hat{k} \) is a vector field where \( \hat{i}, \hat{j}, \hat{k} \) are the base vectors of a Cartesian coordinate system.
Using the Gauss divergence theorem, the value of the outward flux of the vector field over the surface of a sphere of unit radius centered at the origin is _________ (rounded off to one decimal place).