**Q.1-Q.5 Carry one mark each.**

Q.1- The fishermen, **_** the flood victims owed their lives, were rewarded by the government.

(A) whom

(B) to which

(C) to whom

(D) that

Ans: (C) to whom

Q.2- Some students were not involved in the strike.

If the above statement is true, which of the following conclusions is/are logically necessary?

- some who were involved in the strike were students.
- No students was involved in the strike.
- At least one student was involved in the strike.
- Some who were not involved in the strike were students.

(A) 1 and 2

(B) 3

(C) 4

(D) 2 and 3

Ans: (C) 4

Q.3- The radius as well as the height of a circular cone increases by 10%. The percentage increase in its volume is *__*.

(A) 17.1

(B) 21.0

(C) 33.1

(D) 72.8

Ans:(C) 33.1

Q.4- Five numbers 10, 7, 5, 4 and 2 are to be arranged in a sequence from left to right following the directions given below:

- No two odd or even numbers are next to each other.
- The second number from the left is exactly half of the left-most number.
- The middle number is exactly twice the right-most number.

which is the second number from the right?

(A) 2

(B) 4

(C) 7

(D) 10

Ans:(C) 7

Q.5- Until Iran came along, India had never been *__* in kabaddi.

(A) defeated

(B) defeating

(C) defeat

(D) defeatist

Ans:(A) defeated

**Q.6- Q.10 carry two marks each.**

Q.6- Since the last one year, after a 125 basis point reduction in repo rate by the Reserve Bank of India, banking institutions have been making a demand to reduce interest rates on small savings. Finally, the government announced yesterday a reduction in interest rates on small saving schemes to bring them on par with fixed deposit interest rates.

Which one of the following statements can be inferred from the given passage?

(A) Whenever the Reserve Bank of India reduces the repo rate, the interest rates on small saving schemes are also reduced.

(B) Interest rates on small saving schemes are always maintained on par with fixed deposit interest rates.

(C) The government sometimes takes into consideration the demands of banking institutions before reducing the interest rates on small saving schemes.

(D) A reduction in interest rates on small saving schemes follow only after a reduction in repo rate by the Reserve Bank of India.

Ans: (C) The government sometimes takes into consideration the demands of banking institutions before reducing the interest rates on small saving schemes.

Q.7- In a country of 1400 millions population, 70% own mobile phones. Among the mobile phone owners, only 294 million access the Internet. Among these Internet users, only half buy goods from e-commerce portals. What is the percentage of these buyers in the country?

(A) 10.50

(B) 14.70

(C) 15.00

(D) 50.00

Ans: (A) 10.50

Q.8- The nomenclature of Hindustani music has changed over the centuries. Since the medieval period dhrupad styles were identified as *baanis*. Terms like *gayaki* and *baaj* were used to refer to vocal and instrumental styles, respectively. With the institutionalization of music education the term gharana became acceptable. Gharana originally referred to hereditary musicians from a particular lineage, including disciples and grand disciples.

Which one of the following pairings is NOT correct?

(A) *dhrupad, baani*

(B) *gayaki, vocal*

(C) *baaj*, institution

(D) *gharana, lineage*

Ans: (C) *baaj*, institution

Q.9- Two trains started at 7 AM from the same point. The first train travelled north at a speed of 80km/h and the second train travelled south at a speed of 100km/h. The time at which they were 540 km apart is *__* AM.

(A) 9

(B) 10

(C) 11

(D) 11.30

Ans: (B) 10

Q.10- ” I read somewhere that in ancient times the prestige of a kingdom depended upon the number of taxes that it was able to levy on its people. It was very much like the prestige of a head-hunter in his own community.”

Based on the paragraph above, the prestige of a head-hunter depended upon **_**

(A) the prestige of the kingdom

(B) the prestige of the heads

(C) the number of taxes he could levy

(D) the number of heads he could gather

Ans: (D) the number of heads he could gather

Q.1- Q.25 carry one mark each.

Q.1- The maximum value of the function *f*(*x*) = *xe ^{-x}*(where x is real) is

(A) 1/e

(B) 2/e^{2}

(C) (e^{-1/2})/2

(D) ∞

Ans: (A) 1/e

Q.2- Vector \overrightarrow b is obtained by rotating \overrightarrow{a\;\;}=\widehat{l\;}+\;\widehat J by 90^{0} about \widehat K, where \widehat I\;,\;\widehat J and \widehat K are unit vectors along the x, y and z axes, respectively. \widehat b is given by

(A) \widehat I\;-\;\widehat J

(B) -\widehat I\;+\;\widehat J

(C) \widehat I\;+\;\widehat J

(D) -\widehat I\;-\;\widehat J

Ans: (B) -\widehat I\;+\;\widehat J

Q.3- A scalar function is given by* f (x, y*) = *x*^{2} + *y*^{2}. Take \widehat I and \widehat J as unit vectors along the* x* and *y* axes, respectively. At (*x, y*) = (3, 4), the direction along which f increases the fastest is

(A) \frac15\left(4\widehat I\;-3\widehat J\right)

(B) \frac15\left(3\widehat I\;-4\widehat J\right)

(C) \frac15\left(3\widehat I\;+4\widehat J\right)

(D) \frac15\left(4\widehat I\;+3\widehat J\right)

Ans: (C) \frac15\left(3\widehat I\;+4\widehat J\right)

Q.4- The dimensions of kinematic viscosity of a fluid (where L is length, T is time) are

(A)* LT*^{-1}

(B) *L*^{2}*T*^{-1}

(C) *LT*^{-2}

(D) *L*^{-2}*T*

Ans: (B) *L*^{2}*T*^{-1}

Q.5- Φ (x, y) represents the velocity potential of a two-dimensional flow with velocity field \overrightarrow{V\;}=u(x,\;y)\;\widehat I\;+\;v(x,\;y)\;\widehat J, where \widehat{I\;} and \widehat J are unit vectors along the x and y axes, respectively. Which of the following is **necessarily** true?

(A) \nabla^2\phi=0

(B) \nabla\times\overrightarrow V=0

(C) \nabla\cdot\overrightarrow V=0

(D) u=-\partial\phi/\partial y,\;v=\partial\phi/\partial x

Ans: (B) \nabla\times\overrightarrow V=0

Q.6- For a quasi-one-dimensional supersonic flow through a diverging duct, which of the following is true in the direction of the flow?

(A) Both the Mach number and the static temperature increase.

(B) The Mach number increases and the static temperature decreases.

(C) The Mach number decreases and the static temperature increases.

(D) Both the Mach number and the static temperature decrease.

Ans: (B) The Mach number increases and the static temperature decreases.

Q.7- For a NACA2415 airfoil of chord length c, which of the following is true?

(A) Maximum camber is located at 0.2*c* from the leading edge.

(B) Maximum thickness is located at 0.15*c* from the leading edge.

(C) Maximum camber is 0.02*c*.

(D) Maximum thickness is o.o5*c*.

Ans: (C) Maximum camber is 0.02*c*.

Q.8- When a propeller airplane in ground-roll during take-off experiences headwind, which of the following statements is FALSE?

(A) The drag on the airplane increases.

(B) The thrust from the propellers decreases.

(C) The wing lift increases.

(D) The ground-roll distance increases.

Ans: (D) The ground-roll distance increases.

Q9- Which of the following graphs represents the response of a dynamically unstable airplane?

Ans:

Ans:

Q.10- The propulsive efficiency of a ramjet engine is lower than that of a low bypass turbofan engine operating under the same conditions and producing the same thrust, primarily because the ramjet engine

(A) has larger kinetic energy lost in the exhaust jet.

(B) has lower thrust power.

(C) is not self-starting.

(D) has higher thrust to weight ratio.

Ans: (A) has larger kinetic energy lost in the exhaust jet.

Q.11- While flying at Mach 2.0,11 km altitude and producing the same thrust, what is the correct order from the lowest thrust specific fuel consumption (*tsfc*) to the highest* tsfc*?

(A) Turbofan, Ramjet, Turbojet

(B) Turbofan, Turbojet, Ramjet

(C) Ramjet, Turbojet, Turbofan

(D) Turbojet, Turbofan, Ramjet

Ans: (B) Turbofan, Turbojet, Ramjet

Q.12- For a single stage subsonic compressor, which of the following statements about the highest possible compressor pressure ratio (CPR) is correct?

(A) CPR of an axial compressor > CPR of centrifugal compressor.

(B) CPR of an axial compressor < CPR of centrifugal compressor.

(C) CPR of an axial compressor = CPR of centrifugal compressor.

(D) CPR of any value can be attained with either an axial or a centrifugal compressor.

Ans: (B) CPR of an axial compressor < CPR of centrifugal compressor.

Q.13- For a beam subjected to a transverse shear load through its shear center,

(A) the twist per unit length is zero.

(B) the shear stress is uniform throughout the cross-section.

(C) the bending stresses in the cross section are zero.

(D) the shear strain is zero at the shear center.

Ans: (A) the twist per unit length is zero.

Q.14- A function *f* (*x*) is defined by f\left(x\right)=\frac12\left(x+\left|x\right|\right). The value of

\int_{-1}^1f\left(x\right)\;dx is **_** (round off to 1 decimal place).

Ans: 0.5 to 0.5

Q.15- The value of the following limit is____ (round off to 2 decimal places).

\lim_{\theta\rightarrow0}\frac{\theta-\sin\;\theta}{\theta^3}Ans: 0.16 to 0.17

Q.16- The simulate the aerodynamic forces on a cylinder of 1 m diameter due to a uniform air flow of 1 m/s at standard temperature and pressure (STP), low-speed wind tunnel experiments at STP are conducted on a 0.1 m diameter cylinder. The free stream air speed in the wind tunnel experiments should be *__* m/s (*round off to the* *nearest integer*).

Ans: 10 to 10

Q.17- The power-off glide range for an airplane with a maximum Lift to Drag ratio of 18, when the glide starts at an altitude of 4 km, is *__* km (round off to the nearest integer).

Ans: 72 to 72

Q.18- For an airplane flying in a vertical plane, the angle of attack is 3^{0}, the horizontal and vertical components of velocity in wind axis are 300 km/h and 15.72 km/h, respectively. The pitch attitude of the airplane is *_* degrees (round off to 2 decimal places).

Ans: 5.98 to 6.00

Q.19- An airplane is in steady level flight with a true air speed of 50 m/s. The ambient air density and ambient pressure at the flight altitude are 0.91 kg/m^{3} and 7 × 10^{4} N/m^{2}, respectively. At sea level, air density is 1.225 kg/m^{3} and ambient pressure is 1.01 × 10^{5} N/m^{2}. The equivalent or indicated air speed of the airplane is *__* m/s (*round* *off to 2 decimal places*).

Ans: 43.05 to 43.15

Q.20- For the complete combustion of 1 mole of ethanol (C_{2}H_{5}OH), the required number of moles of oxygen is *_*.

Ans: 3 to 3

Q.21- One kg of daitomic gas is heated and its temperature increases from 100 K to 600 K. The energy added at constant pressure during this process is 500 kJ. The specific heat at constant volume for the gas is *__* kJ/kgK. (round off to 2 decimal places).

Ans: 0.70 to 0.72

Q.22- The number of independent elastic constants for a homogeneous isotropic linear elastic material is *_*.

Ans: 2 to 2

Q.23- A thin plate with Young’s modulus 210 GPa and Poisson’s ratio 0.3 is loaded as shown in the figure. The change in length along the y-direction is *__* mm (round off to 1 decimal place).

Ans: 0.2 to 0.2

Q.24- For the state of stress shown in the figure, the normal stress, σn, on a plane inclined at 45 degrees to the x-axis is *_* MPa (round off to the nearest integer).

Ans: 247 to 255

Q.25- In the spring-mass system, shown in the figure, mass m = 3 kg and the spring stifness k = 20 kN/m. The natural frequency of the system is *__* Hz (round off to the nearest integer).

Ans: 16 to 16

**Q.26- Q.55 carry two marks each.**

Q.26- The following system of equations

2x – y – z =0,

-x + 2y – z = 0,

-x – y + 2z = 0

(A) has no solution.

(B) has a unique solution.

(C) has three solutions.

(D) has an infinite number of solutions.

Ans: (D) has an infinite number of solutions.

Q. 27- A supersonic flow in a constant area duct at Mach number M1 encounters a ramp of angle Θ_{1} (see Figure 1). The resulting oblique shock with angle β_{1} is then reflected from the top wall. For the reflected shock, the turn angle is Θ_{2} and the shock angle is β_{2}.

Use the weak shock solution from the Θ-β-M plot shown in Figure 2 to choose the correct option from the following.

(A) β_{1} > β_{2}

(B) β_{1} < β_{2}

(C) Θ_{1} > Θ_{2}

(D) Θ_{1} < Θ_{2}

Ans: (B) β_{1} < β_{2}

Q.28- Which of the following statements about adverse yaw of an airplane is/are correct?

P. It is caused by flow separation resulting from large rudder deflection.

Q. It is caused by dissimilar drag forces acting on the two halves of the wing resulting from aileron deflections of same magnitude.

R. It can be eliminated by ensuring that the upward deflection of one aileron is greater than the downward deflection of the opposite aileron.

(A) P only

(B) Q only

(C) P and R

(D) Q and R

Ans: (D) Q and R

Q.29- In a turbojet engine, the compressor outlet temperature increases with decreasing efficiency of the compressor. If the turbine inlet temperature remains constant, with decreasing efficiency of the compressor, the thrust specific fuel consumption of the engine

(A) decreases, as the heat input is lower.

(B) remains unchanged.

(C) increases, as the compressor needs more work input from the turbine.

(D) decreases, as the thrust produced is higher.

Ans: (C) increases, as the compressor needs more work input from the turbine.

Q.30- For a 1 m long simply supported beam with a concentrated vertical load of 200 N and a concentraed bending moment of 100 Nm at the center as shown in the figure, the correct bending moment diagram is:

Ans:

Q.31- For real x, the number of points of intersection between the curves *y* = *x* and *y* = cos *x* is *__*.

Ans: 1 to 1

Q.32- One of the eigenvalues of the following matrix is 1.

\begin{pmatrix}x&2\-1&3\end{pmatrix}The other eigenvalue is *__*.

Ans: 2 to 2

Q.33- The curve *y* = *f*(*x*) is such that its slope is equal to *y*^{2} for all real *x*. If the curve passes through (1, -1), the value of* y* at *x* = -2 is *__* (*round off to 1 decimal place*).

Ans: 0.5 to 0.5

Q.34- The inviscid, incompressible flow field resulting from a uniform flow past a circular cylinder of radius R centered at the origin is given by:

u_r=U\left(1-\frac{R^2}{r^2}\right)\cos\;\theta u_\theta=-U\left(1+\frac{R^2}{r^2}\right)\sin\;\thetawhere u_{r} and u_{Θ} are the radial and azimuthal velocity components in polar coordinates, (r,Θ), as shown in the figure. U is the free stream speed. Ignore the effects of gravity. The azimuthal location (in the first quadrant) on the cylinder at which the pressure coefficient is zero is *__* degrees (*round off to the nearest integer*).

Ans: 30 to 30

Q.35- A cylindrical container of radius R = 50 cm is filled with water up to a height h* _{o}*. Upon rotating the cylindrical about its central axis at a constant angular speed, the free surface takes a parabolic shape (see figure), and is displaceds by h1 = 10 cm at r = R. The magnitude of the downward displacement h2 of the free surface at r = 0 is

(*round off to the nearest integer*).

Ans: 10 to 10

Q.36- A two-dimensional, incompressible fluid flow is described by the stream function ψ = xy^{3} m^{2}/s on the Cartesian x-y plane. If the density and dynamic viscosity of the fluid are 1 kg/m^{3} and 0.1 kg/m-s, respectively, the magnitude of the pressure gradient in the x direction at x = 1 m and y = 1 m is **_** N/m3 (*round off to 1 decimal place*).

Ans: 3.5 to 3.7 OR 2.3 to 2.5

Q.37- The static pressure ratio across a stationary normal shock is given by

\frac{p_2}{p_1}=1+\frac{2\gamma}{\gamma+1}\left(M_1^2-1\right),

where *M*_{1} is the upstream Mach number. For a stationary normal shock in air (γ = 1.4, R = 287 J/kg-K) with upstream flow conditions given by: speed 800 m/s, static temperature 300 K and static pressure 1 atm, the static pressure downstream of the shock is *__* atm. (*round off to 2 decimal places*).

Ans: 5.95 to 6.10

Q.38- For a symmetric airfoil at an angle of attack of 10^{o}, assuming thin airfoil theory, the magnitude of the pitching moment coefficient about the leading edge is *__* (*round off to 2 decimal places*).

Ans: 0.24 to 0.30

Q.39- The span-wise distribution of circulation over a finite wing of span b = 10 m is

\Gamma\left(y\right)=\Gamma_0\sqrt{1-\left(\frac{2y}b\right)^2}If Γ0 = 20 *m*^{2}/*s* and the free stream density and speed are 1.2 kg/m^{3} and 100 m/s, respectively, the total lift is *__* kN (*round off to 2* *decimal places*).

Ans: 18.00 to 19.20

Q.40- The airplane shown in figure starts executing a symmetric pull-up maneuver from steady level attitude with a constant nose-up pitch acceleration of 20 deg/s^{2}. The vertical load factor measured at this instant at the center of gravity (CG) is 2. Given that acceleration due to gravity is 9.81 m/s^{2}, the vertical load factor measured at point P on the nose of the airplane, which is 2 m ahead of the CG, is *_* (*round off to 2 decimal places*).

Ans: 2.06 to 2.08

Q.41- Consider an airplane with a weight of 8000 N, wing area of 16 m^{2}, wing zero-lift drag coefficient of 0.02, Oswald’s efficiency factor of 0.8, and wing aspect ratio of 6, in steady level flight with wing lift coefficient of 0.375. Considering the same flight speed and ambient density, the ratio of the induced drag coefficient during steady level flight to that during a 30^{0} climb is *__* (*round off to 2 decimal* *places*).

Ans: 1.32 to 1.35

Q.42- The product of earth’s mass (*M*) and the universal gravitational constant (G) is GM = 3.986 × 10 14 m^{3}/s^{2}. The radius of earth is 6371 km. The minimum increment in the velocity to be imparted to a spacecraft flying in a circular orbit around the earth at an altitude of 4000 km to make it exit earth’s gravitational field is *__* km/s (*round off to 2 decimal places*).

Ans: 2.54 to 2.62

Q.43- A propeller driven airplane has a gross take-off weight of 4905 N with a wing area of 6.84 m2. Assume that the wings are operating at the maximum C_{L}^{3/2}/C_{D }of 13, The propeller efficiency is 0.9 and the specific fuel consumption of the engine is 0.76 kg/kW-hr. Given that the density of air at sea level is 1.225 kg/m^{3} and the acceleration due to gravity is 9.81 m/s^{2}, the weight of the fuel required for an endurance of 18 hours at sea level is ____N (*round off the nearest integer*).

Ans:1440 to 1490

Q.44- The design of an airplane is modified to increase the vertical tail area by 20% and decrease the moment arm from the aerodynamic centre of the vertical tail to the airplane centre of gravity by 20%. Assuming all other factors remain unchanged, the ratio of the modified to the original directional static stability ( C_{Nβ} due to tail fin) is *__* (*round off to 2 decimal places*).

Ans: 0.96 to 0.96

Q.45- For a rocket engine, the velocity ratio r is V_{ a}/V _{e}, where V _{a} is the vehicle velocity and V _{e} is the exit velocity of the exhaust gases. Assume the flow to be optimally expanded through the nozzle. For* r* = 2, if F is the thrust produced and m is the mass flow rate of exhaust gases, then,* F*/(*mVe*) is *__*.

Ans: 1 to 1

Q.46- The specific impulse of a rocket engine is 3000 Ns/kg. The mass of the rocket at burnout is 1000 kg. The propellant consumed in the process is 720 kg. Assume all factors contributing to velocity loss to be negligible. The change in vehicle velocity *Δu* is ____km/s (*round off to 2 decimal places*).

Ans: 1.60 to 1.65

Q.47- The combustion products of a gas turbine engine can be assumed to be a calorically perfect gas with ϒ = 1.2. The pressure ratio across the turbine stage is 0.14. The measured turbine inlet and exit stagnation temperatures are 1200 K and 900 K, respectively. The total-to-total turbine efficiency is *__*% (*round off to the nearest integer*).

Ans: 88 to 90

Q48- The figure shows the velocity triangles for an axial compressor stage. The specific work input to the compressor stage is ___kJ/kg (*round off to 2 decimal places*).

Ans: 2.50 to 2.60

Q.49- As shown in the figure, a rigid slab CD of weight W (distributed uniformly along its length) is hung from a ceiling using three cables of identical length and cross- sectional area. The central cable is made of steel (Young’s modulus = 3E) and the other two cables are made of aluminum (Young’s modulus = E). The percentage of the total weight taken by the central cable is *__*% (*round off to the integer*).

Ans: 60 to 60

Q.50- All the bars in the given truss are elastic with Young’s modulus 200 GPa, and have identical cross-sections with moment of inertia 0.1 cm4. The lowest value of the load P at which the truss fails due to bucking is *_* kN (*round off to the nearest integer*).

Ans: 550 to 570

Q.51- A solid circular shaft is designed to transmit a torque* T* with a factor of safety of 2. It is proposed to replace to the solid shaft by a hollow shaft of the same material and identical outer radius. If inner radius is half the outer radius, the factor of safety for the hollow shaft is *__* (*round off to 1 decimal place*).

Ans: 1.8 to 1.9

Q. 52- In the structure shown in the figure, bars AB and BC are made of identical material and have circular cross-sections of 10 mm radii. The yield stress of the material under uniaxial tension is 280 MPa. Using the von Mises yield criterion, the maximum load along the z-direction (perpendicular to the plane of paper) that can be applied at C, such that AB does not yield is ____N (*round off to the nearest integer).*

Ans: 310 to 320

Q.53- A thin-walled tube, with the cross-section shown in the figure, is subjected to a torque of T = 1 kN-m. The walls have uniform thickness t = 1 mm and shear modulus G = 26 GPa. Assume that the curved portion is semi-circular. The shear stress in the wall is *__* MPa (*round off to 1 decimal place*).

Ans: 17.0 to 17.5

Q.54- For a damped spring-mass system, mass *m* = 10 kg, stiffness *k* = 103 N/m, and damping coefficient* c* = 20 kg/s. The ratio of the amplitude of oscillation of the first cycle to that of the fifth cycle is *__* (*round off to 1 decimal place*).

Ans: 12.3 to 12.6

Q.55- For the system of springs and masses shown below, *k* = 1250 N/m and *m* = 10 kg. The highest natural frequency, *ω*, of the system is *__* radians/s (*round off to the nearest integer*).

Ans: 25 to 25

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