Questions
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.
- impel
- dispel
- propel
- repel
Read the statements:
All women are entrepreneurs.
Some women are doctors.
Which of the following conclusions can be logically inferred from the above statements?
- All women are doctors.
- All doctors are entrepreneurs.
- All entrepreneurs are women.
- Some entrepreneurs are doctors.
Choose the most appropriate phrase from the options given below to complete the following sentence.
The aircraft ______ take of as soon as its flight plan was filed.
- is allowed to
- will be allowed to
- was allowed to
- has been allowed to
Find the odd one from the following group:
W, E, K, O
I, Q, W, A
F, N, T, X
N, V, B, D
- W, E, K, O
- I, Q, W, A
- F, N, T, X
- N, V, B, D
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 For T is
- a resident make with annual income Rs. 9 lakh
- a resident female with annual income Rs. 9 lakh
- a non-resident male with annual income Rs. 16 lakh
- a non-resident female with annual income Rs. 16 lakh
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?
- 2005
- 2004
- 2007
- 2006
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
- 1/4
- 1/3
- 1/2
- 2/3
$Lt_{x\rightarrow0}\frac{x-sinx}{1-cosx}$
is
- 0
- 1
- 3
- not defined
Given that the determinant of the matrix $\begin{bmatrix}
\ 1 & 3 & 0 \
\ 2 & 6 & 4 \
\ -1 & 0 & 2 \
\end{bmatrix}$ is - 12, the determinant of the matrix $\begin{bmatrix}
\ 2 & 6 & 0 \
\ 4 & 12 & 8 \
\ -2 & 0 & 4 \
\end{bmatrix}$ is
- - 96
- - 24
- 24
- 96
The matrix form of the linear system $\frac{dx}{dt}=3x-5y\hspace{0.2cm} and\frac {dy}{dt}=4x+8y$ is
- $\frac{d}{dt}\bigg(\begin{matrix} \ x \\ \ y \\ \end{matrix}\bigg) = \begin{bmatrix} \ 3 & -5 \\ \ 4 & 8 \\ \end{bmatrix}\bigg(\begin{matrix} \ x \\ \ y \\ \end{matrix}\bigg)$
- $\frac{d}{dt}\bigg(\begin{matrix} \ x \\ \ y \\ \end{matrix}\bigg) = \begin{bmatrix} \ 3 & 8 \\ \ 4 & -5 \\ \end{bmatrix}\bigg(\begin{matrix} \ x \\ \ y \\ \end{matrix}\bigg)$
- $\frac{d}{dt}\bigg(\begin{matrix} \ x \\ \ y \\ \end{matrix}\bigg) = \begin{bmatrix} \ 4 & -5 \\ \ 3 & 8 \\ \end{bmatrix}\bigg(\begin{matrix} \ x \\ \ y \\ \end{matrix}\bigg)$
- $\frac{d}{dt}\bigg(\begin{matrix} \ x \\ \ y \\ \end{matrix}\bigg) = \begin{bmatrix} \ 4 & 8 \\ \ 3 & -5 \\ \end{bmatrix}\bigg(\begin{matrix} \ x \\ \ y \\ \end{matrix}\bigg)$
Which one of the following describes the relationship among the three vectors, $\hat{i}+\hat{j}+\hat{k},2\hat{i}+3\hat{j}+\hat{k}\hspace{0.2cm}and\hspace{0.2cm} 5\hat{i}+6\hat{j}+4\hat{k}$?
- The vectors are mutually perpendicular.
- The vectors are linearly dependent.
- The vectors are linearly independent.
- The vectors are unit vectors.
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 |
- K
- L
- M
- N
Critical damping is the
- largest amount of damping for which no oscillation occurs in free vibration
- smallest amount of damping for which no oscillation occurs in free vibration
- largest amount of damping for which the motion is simple harmonic in free vibration
- smallest amount of damping for which the motion is simple harmonic in free vibration
The argument of the complex number $\frac{1+i}{1-i}$, where i = $\sqrt{-1}$, is
- – $\pi$
- $-\frac{\pi}{2}$
- $\frac{\pi}{2}$
- $\pi$
A circular object of radius r rolls without slipping on a horizontal level floor with the centre having velocity V. The velocity at the point of contact between the object and the floor is
- zero
- V in the direction of motion
- V opposite to the direction of motion
- V vertically upward from the floor
For the given statements:
I. Mating spur gear teeth is an example of higher pair
II. A revolute joint is an example of lower pair
Indicate the correct answer.
- Both I and II are false
- I is true and II is false
- I is false and II is true
- Both I and II are true
A rigid link PQ is 2 m long and oriented at 20o to the horizontal as shown in the figure. The magnitude and direction of velocity VQ, and the direction of velocity VP are given. The magnitude of VP (in m/s) at this instant is
- 2.14
- 1.89
- 1.21
- 0.96
Biot number signifies the ratio of
- convective resistance in the fluid to conductive resistance in the solid
- conductive resistance in the solid to convective resistance in the fluid
- inertia force to viscous force in the fluid
- buoyancy force to viscous force in the fluid
The maximum theoretical work obtainable, when a system interacts to equilibrium with a reference environment, is called
- Entropy
- Enthalpy
- Exergy
- Rothalpy
For a completely submerged body with centre of gravity ‘G’ and centre of buoyancy ‘B’, the condition of stability will be
- G is located below B
- G is located above B
- G and B are coincident
- independent of the locations of G and B
Which one of the following is a CFC refrigerant?
- R744
- R290
- R502
- R718
In a power plant, water (density = 1000 kg/m3) is pumped from 80 kPa to 3 MPa. The pump has an isentropic efficiency of 0.85. Assuming that the temperature of the water remains the same, the specific work (in kJ/kg) supplied to the pump is
- 0.34
- 2.48
- 2.92
- 3.43
The jobs arrive at a facility, for service, in a random manner. The probability distribution of number of arrivals of jobs in a fixed time interval is
- Normal
- Poisson
- Erlang
- Beta
Which one of the following instruments is widely used to check and calibrate geometric features of machine tools during their assembly?
- Ultrasonic probe
- Coordinate Measuring Machine (CMM)
- Laser interferometer
- Vernier calipers
The major difficulty during welding of aluminium is due to its
- high tendency of oxidation
- high thermal conductivity
- low melting point
- low density
The process of reheating the martensitic steel to reduce its brittleness without any significant loss in its hardness is
- normalising
- annealing
- quenching
- tempering
For machining a rectangular island represented by coordinates P(0, 0), Q(100, 0), R(100, 50) and S(0, 50) on a casting using CNC milling machine, an end mill with a diameter of 16 mm is used. The trajectory of the cutter centre to machine the island PQRS is
- (- 8, - 8), (108, - 8), (108, 58), (- 8, 58), (- 8, - 8)
- (8, 8), (94, 8), (94, 44), (8, 44), (8, 8)
- (- 8, 8), (94, 8), (94, 44), (8, 44), (- 8, 8)
- (0, 0), (100, 0), (100, 50), (50, 0), (0, 0)
A circular rod of length ‘L’ and area of cross-section ‘A’ has a modulus of elasticity ‘E’ and coefficient of thermal expansion ‘$\alpha$’. One end of the rod is fixed and other end is free. If the temperature of the rod is increased by $\triangle$T, then
- stress developed in the rod is E$\alpha$ $\triangle$T and strain developed in the rod is $\alpha$ $\triangle$T
- both stress and strain developed in the rod are zero
- stress developed in the rod is zero and strain developed in the rod is $\alpha$$\triangle$T
- stress developed in the rod is E$\alpha$ $\triangle$T and strain developed in the rod is zero
Consider a two-dimensional laminar flow over a long cylinder as shown in the figure below.
The free stream velocity is $U\omega$ and the free stream temperature $T\omega$ is lower than the cylinder surface temperature Ts. The local heat transfer coefficient is minimum at point
- 1
- 2
- 3
- 4
The main cutting force acting on a tool during the turning (orthogonal cutting) operation of a metal is 400 N. The turning was performed using 2 mm depth of cut and 0.1 mm/rev feed rate. The specific cutting pressure (in N/mm2) is
- 1000
- 2000
- 3000
- 4000
In solid-state welding, the contamination layers between the surfaces to be welded are removed by
- alcohol
- plastic deformation
- water jet
- sand blasting
The integral $\oint\limits_x(ydx-xdy)$ is evaluated along the circle x2 + y2 = $\frac{1}{4}$ traversed in counter clockwise direction. The integral is equal to
- 0
- $-\frac{\pi}{4}$
- $-\frac{\pi}{2}$
- $\frac{\pi}{4}$
In the following table, x is a discrete random variable and p(x) is the probability density. The standard deviation of x is
| x | 1 | 2 | 3 |
| p(x) | 0.3 | 0.6 | 0.1 |
- 0.18
- 0.36
- 0.54
- 0.6
A block R of mass 100 kg is placed on a block S of mass 150 kg as shown in the figure. Block R is tied to the wall by a massless and inextensible string PQ. If the coefficient of static friction for all surfaces is 0.4, the minimum force F (in kN) needed to move the block S is
- 0.69
- 0.88
- 0.98
- 1.37
A rigid uniform rod AB of length L and mass m is hinged at C such that AC = L/3, CB = 2L/3. Ends A and B are supported by springs of spring constant k. The natural frequency of the system is given by
- $\sqrt\frac{k}{2m}$
- $\sqrt\frac{k}{m}$
- $\sqrt\frac{2k}{m}$
- $\sqrt\frac{5k}{m}$
A reversible heat engine receives 2 kJ of heat from a reservoir at 1000 K and a certain amount of heat from a reservoir at 800 K. It rejects 1 kJ of heat to a reservoir at 400 K. The net work output (in kJ) of the cycle is
- 0.8
- 1.0
- 1.4
- 2.0
In exponential smoothening method, which one of the following is true?
- 0 $\leq$ $\alpha$ $\leq$ 1 and high value of $\alpha$ is used for stable demand
- 0 $\leq$ $\alpha$ $\leq$ 1 and high value of $\alpha$ is used for unstable demand
- $\alpha$ $\geq$ 1 and high value of $\alpha$ is used for stable demand
- $\alpha$ $\leq$ 0 and high value of $\alpha$ is used for unstable demand
Jobs arrive at a facility at an average rate of 5 in an 8 hour shift. The arrival of the jobs follows Poisson distribution. The average service time of a job on the facility is 40 minutes. The service time follows exponential distribution. Idle time (in hours) at the facility per shift will be
- $\frac{5}{7}$
- $\frac{14}{3}$
- $\frac{7}{5}$
- $\frac{10}{3}$
The non-dimensional fluid temperature profile near the surface of a convectively cooled flat plate is given by $\frac{T_w-T}{T_w-T_w}$ = $a+b\frac{y}{L}+c\bigg(\frac{y}{L}\bigg)^2$, where y is measured perpendicular to the plate, L is the plate length, and a, b and c are arbitrary constants. TW and $T_\omega$ are wall and ambient temperatures, respectively. If the thermal conductivity of the fluid is k and the wall heat flux is q², the Nusselt number $Nu=\frac{q''}{T_w-T_\infty}\frac{L}{K}$ is equal to
- a
- b
- 2c
- (b + 2c)
For the given assembly: 25 H7/g8, match Group A with Group B:
| Group A | Group B | ||
| P. | H | I. | Shaft type |
| Q. | ITS | II. | Hole type |
| R. | IT7 | III. | Hole tolerance grade |
| S. | g | IV. | Shaft tolerance grade |
- P - I, Q - III, R - IV, S - II
- P - I, Q - IV, R - III, S - II
- P - II, Q - III, R - IV, S - I
- P - II, Q - IV, R - III, S - I