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.

Read the statements:

All women are entrepreneurs. Some women are doctors.

Which of the following conclusions can be logically inferred from the above statements?

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.

Find the odd one from the following group:

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

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 1/5^th of the exports?

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

^{$Lt_{x\rightarrow0}\frac{x-sinx}{1-cosx}$}

is

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

The matrix form of the linear system ^{$\frac{dx}{dt}=3x-5y\hspace{0.2cm} and\frac {dy}{dt}=4x+8y$} is

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 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?

Critical damping is the

The argument of the complex number ^{$\frac{1+i}{1-i}$}, where i = ^$\sqrt{-1}$, is

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

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.

A rigid link PQ is 2 m long and oriented at 20^o to the horizontal as shown in the figure. The magnitude and direction of velocity V_Q, and the direction of velocity V_P are given. The magnitude of V_P (in m/s) at this instant is

Biot number signifies the ratio of

The maximum theoretical work obtainable, when a system interacts to equilibrium with a reference environment, is called

For a completely submerged body with centre of gravity ‘G’ and centre of buoyancy ‘B’, the condition of stability will be

Which one of the following is a CFC refrigerant?

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

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

Which one of the following instruments is widely used to check and calibrate geometric features of machine tools during their assembly?

The major difficulty during welding of aluminium is due to its

The process of reheating the martensitic steel to reduce its brittleness without any significant loss in its hardness is

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

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

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 T_s. The local heat transfer coefficient is minimum at point

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

In solid-state welding, the contamination layers between the surfaces to be welded are removed by

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

In the following table, x is a discrete random variable and p(x) is the probability density. The standard deviation of x is

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

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

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

In exponential smoothening method, which one of the following is true?

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

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. T_W 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

For the given assembly: 25 H7/g8, match Group A with Group B: