Questions
Directions: Carry One Mark Each.
If a2 + b2 + c2 = 1, then ab + bc + ac lies in the interval
- $\bigg[1, \frac{2}{3} \bigg]$
- $\bigg[\frac{-1}{2} , 1\bigg]$
- $\bigg[-1, \frac{1}{2} \bigg]$
- [2, –4]
Directions: Carry One Mark Each.
Ram and Ramesh appeared in an interview for two vacancies in the same department. The probability of Ram’s selection is $\frac{1}{6}$ and that of Ramesh's selection is $\frac{1}{8}$. What is the probability that only one of them will be selected?
- $\frac{47}{48}$
- $\frac{1}{4}$
- $\frac{13}{48}$
- $\frac{35}{48}$
Directions: Carry Two Marks Each.
Given below are two statements followed by two conclusions. Assuming these statements to be true, decide which conclusion(s) logically follow(s).
Statements:
All film stars are playback singers.
All film directors are film stars.
Conclusions:
I. All film directors are playback singers.
II. Some film stars are film directors.
- Only conclusion I follows
- Only conclusion II follows
- Neither conclusion I nor II follows
- Both conclusions I and II follow
Directions: Carry One Mark Each.
An electric bus has on-board 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 distance 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|
Which of the following is the stretch where the electricity consumption per km is the minimum?
- M
- N
- O
- P
The function of interpolator in a CNC machine controller is to
- control spindle speed
- coordinate feed rates of axes
- control tool rapid approach speed
- perform miscellaneous (M) functions (tool change, coolant control, etc.)
If any two columns of a determinant P = $\begin{vmatrix}
\ 4 & 7 & 8 \
\ 3 & 1 & 5 \
\ 9 & 6 & 2 \
\end{vmatrix}$are interchanged, which of the following statements regarding the value of the determinant is correct?
- The absolute value remains unchanged, but the sign will change.
- Both the absolute value and the sign will change.
- The absolute value will change, but the sign will not change.
- Both the absolute value and the sign will remain unchanged.
For an ideal gas with constant values of specific heats and calculation of specific enthalpy,
- it is sufficient to know only the temperature
- both temperature and pressure are required to be known
- both temperature and volume are required to be known
- both temperature and mass are required to be known
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
- 4
- 6
- 32
- 64
Which of the following types of stress-strain relationships best describes the behaviour of brittle materials, such as ceramics and thermosetting plastics? ($\sigma$ = stress and $\epsilon$ = strain)
Holes of diameter 25.0$+0.040\\
+0.020$mm are assembled interchangeably with the pins of diameter 25.0$+0.005\\
-0.008$mm. The minimum clearance in the assembly will be
- 0.048 mm
- 0.015 mm
- 0.005 mm
- 0.008 mm
The value of $lim_{x \rightarrow0}\frac{1-cos(x^2)}{2x^4}$ is
- 0
- $\frac{1}{2}$
- $\frac{1}{4}$
- undefined
Among the four normal distributions with probability density functions as shown below, which one has the lowest variance?
- I
- II
- III
- IV
The Blasius equation related to boundary layer theory is a
- third-order linear partial differential equation
- third-order nonlinear partial differential equation
- second-order nonlinear ordinary differential equation
- third-order nonlinear ordinary differential equation
Which of the following is the most conservative fatigue failure criterion?
- Soderberg
- Modified Goodman
- ASME elliptic
- Gerber
Consider a slider crank mechanism with non-zero masses and inertia. A constant torque T is applied on the crank, as shown in the figure. Which of the following plots best resembles variation of crank angle, $\theta$ versus time?
For the flow of viscous fluid over a flat plate, if the fluid temperature is the same as the plate temperature, the thermal boundary layer is
- thinner than the velocity boundary layer
- thicker than the velocity boundary layer
- of the same thickness as the velocity boundary layer
- not formed at all
In a linear arc welding process, the heat input per unit length is inversely proportional to
- welding current
- welding voltage
- welding speed
- duty cycle of the power source
A 10 mm diameter electrical conductor is covered by an insulation of 2 mm thickness. The conductivity of the insulation is 0.08 W/m-K and the convection coefficient at the insulation surface is 10 W/m2-K. Addition of further insulation of the same material will
- increase heat loss continuously
- decrease heat loss continuously
- increase heat loss to a maximum and then decrease heat loss
- decrease heat loss to a minimum and then increase
If two complex numbers Z1 = 5 + (5$\sqrt{3}$) i and $z_2=\frac{2}{\sqrt{3}}+2i$, the argument of $\frac{z_1}{z_2}$ in degrees is
- 0
- 30
- 60
- 90
Match the following:
| Product | Process | |
| P | Rails | (1) Blow molding |
| Q | Engine crankshaft | (2) Extrusion |
| R | Aluminium channels | (3) Forging |
| S | PET water bottles | (4) Rolling |
- P - 4, Q - 3, R - 1, S - 2
- P - 4, Q - 3, R - 2, S - 1
- P - 2, Q - 4, R - 3, S - 1
- P - 3, Q - 4, R - 2, S – 1
The solidification time of a casting is proportional to $\Big(\frac{V}{A}\Big)^{2}$ , where V is the volume of the casting and A is the total casting surface area losing heat. Two cubes of the same material and size are cast using sand casting process. The top face of one of the cubes is completely insulated. The ratio of the solidification time for the cube with top face insulated to that of the other cube is
- $\frac{25}{36}$
- $\frac{36}{25}$
- 1
- $\frac{6}{5}$
Considering a massless rigid rod and small oscillations. The natural frequency (in rad/s) of vibration of the system, as shown in the figure, is
- $\sqrt{\frac{400}{1}}$
- $\sqrt{\frac{400}{2}}$
- $\sqrt{\frac{400}{3}}$
- $\sqrt{\frac{400}{4}}$
Match the following:
| Equation | Physical interpretation |
| (P) $\triangledown \times \bar{V}$ = 0 | (I) Incompressible continuity equation |
| (Q) $\triangledown. \bar{V}$ = 0 | (II) Steady flow |
| (R) $\frac{D\bar{v}}{Dt}=0$ | (III) Irrotational flow |
| (S) $\frac{a\bar{V}}{at}=0$ | (IV) Zero acceleration of fluid particle |
- P - IV, Q - I, R - II, S - III
- P - IV, Q - III, R - I, S - II
- P - III, Q - I, R - IV, S - II
- P - III, Q - I, R - II, S - IV
A triangular facet in a CAD model has vertices P1(0, 0, 0); P2(1, 1, 0); and P3(1, 1, 1). The area of the facet is
- 0.500
- 0.707
- 1.414
- 1.732
In the assembly shown below, the part dimensions are:
L1 = $22.0^{\pm 0.01}$ mm and L2 = L3 = $10.0^{\pm 0.005}$ mm
Assuming the normal distribution of part dimensions, the dimension L4 (in mm) for assembly condition would be
- $2.0^{\pm o.008}$
- $2.0^{\pm o.012}$
- $2.0^{\pm o.016}$
- $2.0^{\pm o.020}$
Fine the solution of $\frac{d^2y}{dx^2}$ = y, which passes through the origin and the point (In 2, $\frac{3}{4}$).
- $y=\frac{1}{2}e^x+e^{-x}$
- $y=\frac{1}{2}(e^x-e^{-x})$
- $y=\frac{1}{2}(e^x-e^{-x})$
- $y=\frac{1}{2}e^x+e^{-x}$
A mobile phone has a small motor with an eccentric mass used for vibrator mode. The location of the eccentric mass on motor with respect to the center of gravity (CG) of the mobile and the rest of the dimensions of the mobile phone are shown. The mobile is kept on a flat horizontal surface.
In addition, eccentric mass = 2 grams, eccentricty = 2.19 mm, mass of the mobile = 90 grams and g = 9.81 m/s2.
Uniform speed (in RPM) of the motor for which the mobile will get just lifted off the ground at the end Q is approximately
- 3000
- 3500
- 4000
- 4500
For flow through a pipe of radius R, the velocity and temperature distributions are as follow:
u(r, x) = C1 and T(r, x) C2 $\bigg[1-(\frac{r}{R})^3\bigg]$, where C1 and C2 are constants.
The bulk mean temperature is given by $T_m = \frac{2}{u_mR^2} \int\limits_0^R u(r, x)T (r, x) r dr$, with Um being the mean velocity of flow.
The value of Tm is
- $\frac{0.5C_2}{U_m}$
- 0.5 C2
- 0.6C2
- $\frac{0.6C_2}{U_m}$
Following data refers to the activities of a project, where node 1 refers to the start and node 5 refers to the end of the project.
| Activity | Duration (days) |
| 1-2 | 2 |
| 2-3 | 1 |
| 4-3 | 3 |
| 1-4 | 3 |
| 2-5 | 3 |
| 3-5 | 2 |
| 4-5 | 4 |
The critical path (CP) in the network is
- 1 – 2 – 3 – 5
- 1 – 4 – 3 – 5
- 1 – 2 – 3 – 4 – 5
- 1 – 4 – 5
For the truss shown in the figure, the magnitude of the force in member PR and the support reaction at R respectively are
- 122.47 kN and 50 kN
- 70.71 kN and 100 kN
- 70.71 kN and 50 kN
- 81.65 kN and 100 kN
A pinion with radius r1 and inertia l1 is driving a gear with radius r2 and inertia I2. Torque $\tau$1 is applied on pinion. The following are free body diagrams of pinion and gear showing important forces (F1 and F2) of interaction. Which of the following holds true?
- F1 $ \neq$F2; ; F2 = 
- F1 = F2; ; F2 =
- F1 = F2; ; F2 =
- F1 $ \neq$F2; ; F2 = 
The probability of obtaining at least two ‘‘six’’ in throwing a fair dice 4 times is
- $\frac{425}{432}$
- $\frac{19}{144}$
- $\frac{13}{144}$
- $\frac{125}{432}$
A machine element is subjected to the following bi-axial state of stress:
$\sigma_y=20$ MPa; $\tau_{xy}=40$ MPa
If the shear strength of the material is 100 MPa, the factor of safety as per Tresca’s maximum shear stress theory is
- 1.0
- 2.0
- 2.5
- 3.3
