Choose the most appropriate word from the options given below to complete the following sentence.

Communication and interpersonal skills are _________ important in their own ways.

Choose the most appropriate pair of words from the options given below to complete the following sentence.

She could not ______ the thought of ______ the election to her bitter rival.

Find the odd one in the following group:

Q, W, Z, B B, H, K, M W, C, G, J M, S, V, X

Which of the options given below best completes the following sentence?

She will feel much better if she _________.

A regular die has six sides with numbers 1 to 6 marked on its sides. If a very large number of throws show the following frequencies of occurrence:

1 " 0.167; 2 " 0.167; 3 " 0.152; 4 " 0.166; 5 " 0.168; 6 " 0.180. We call this die

Lights of four colors (red, blue, green, yellow) are hung on a ladder. On every step of the ladder there are two lights. If one of the lights is red, the other light on that step will always be blue. If one of the lights on a step is green, the other light on that step will always be yellow. Which of the following statements is not necessarily correct?

The total exports and revenues from the exports of a country are given in the two charts shown below. The pie chart for exports shows the quantity of each item exported as a percentage of the total quantity of exports. The pie chart for the revenues shows the percentage of the total revenue generated through export of each item. The total quantity of exports of all the items is 500 thousand tones and the total revenues are 250 crore rupees. Which item among the following has generated the maximum revenue per kg?

It takes 30 minutes to empty a half-full tank by draining it at a constant rate. It is decided to simultaneously pump water into the half-full tank while draining it.

What is the rate at which water has to be pumped in so that it gets fully filled in 10 minutes?

^{$Lt_{x \rightarrow0} \bigg( \frac{e^{2x} - 1}{sin(4x)} \bigg)$} is equal to

A box contains 25 parts of which 10 are defective. Two parts are being drawn simultaneously in a random manner from the box. The probability of both the parts being good is

A steel cube, with all faces free to deform, has Young’s modulus, E, Poisson’s ratio, ^_v, and coefficient of thermal expansion, ^_$\alpha$. The pressure (hydrostatic stress) developed within the cube, when it is subjected to a uniform increase in temperature, ^{$\triangle T$}, is given by

A 4-bar mechanism will all revolute pairs has link lengths l_f = 20 mm, l_in = 40 mm, l_co = 50 mm and l_out = 60 mm. The suffixes ‘f ’, ‘in’, ‘co’ and ‘out’ denote the fixed link, the input link, the coupler and output link respectively. Which one of the following statements is true about the input and output links?

For laminar forced convection over a flat plate, if the free stream velocity increases by a factor of 2, the average heat transfer coefficient

In vibration isolation, which one of the following statements is NOT correct regarding Transmissibility (T)?

A thin plate of uniform thickness is subject to pressure as shown in the figure below:

Under the assumption of plane stress, which one of the following is correct?

For an incompressible flow field, ^$\bar{V}$, which one of the following conditions must be satisfied?

If there are m sources and n destinations in a transportation matrix, the total number of basic variables in a basic feasible solution is

The thermal efficiency of an air-standard Brayton cycle in terms of pressure ratio rp and ^_y(= c_p/c_v) is given by

A robot arm PQ with end coordinated P(0, 0) and Q(2, 5) rotates counter clockwise about P in the XY plane by 90c. The new coordinate pair of the end point Q is

In a heat exchanger, it is observed that ^{_{$\triangle T_1 = \triangle T_2$}}, where ^{_{$\triangle T_1$}} is the temperature difference between the two single phase fluid streams at one end and ^{_{$\triangle T_2$}} is the temperature difference at the other end. This heat exchanger is

An analytic function of a complex variable z = x + iy is expressed as F(z) = u(x, y) + iv(x, y), where i = ^$\sqrt{-1}$. If u(x, y) = 2xy, then v(x, y) must be

The following four unconventional machining processes are available in a shop floor. The most appropriate one to drill a hole of square cross section of 6 mm ^_x 6 mm and 25 mm deep is

Match the Machine Tools (Group A) with the probable Operations (Group B):

For the three bolt system shown in the figure, the bolt material has shear yield strength of 200 MPa. For a factor of safety of 2, the minimum metric specification required for the bolt is

The flatness of a machine bed can be measured using

A cantilever beam of length, L, with uniform cross-section and flexural rigidity, EI, is loaded uniformly by a vertical load, w per unit length. The maximum vertical deflection of the beam is given by

The flexural rigidity (EI) of a cantilever beam is assumed to be constant over the length of the beam shown in figure. If a load P and bending moment PL/2 are applied at the free end of the beam then the value of the slope at the free end is

A component can be produced by any of the four processes I, II, III and IV. The fixed cost and the variable cost for each of the processes are listed below. The most economical process for producing a batch of 100 pieces is

What is the natural frequency of the spring mass system shown below? The contact between the block and the inclined plane is frictionless. The mass of the block is denoted by m and the spring constants are denoted by k₁ and k₂ as shown below.

With respect to metal working, match Group A with Group B:

A hole of 20 mm diameter is to be drilled in a steel block of 40 mm thickness. The drilling is performed at rotational speed of 400 rpm and feed rate of 0.1 mm/rev.

The required approach and over run of the drill together is equal to the radius of drill. The drilling time (in minute) is

A rectangular hole of size 100 mm ^_x 50 mm is to be made on a 5 mm thick sheet of steel having ultimate tensile strength and shear strength of 500 MPa and 300 MPa, respectively. The hole is made by punching process. Neglecting the effect of clearance, the punching force (in kN) is

For the CNC part programming, match Group A with Group B:

Curl of vector ^{$\bar{F} = x^2 z^2 \hat{i} - 2xy^2z \hat{j} + 2y^2z^3 \hat{k}$}

Consider the two states of stress as shown in configurations I and II in the figure below. From the standpoint of distortion energy (von-Mises) criterion, which one of the following statements is true?

The general solution of the differential equation ^{$\frac{dy}{dx}$} = cos(x + y), with c as a constant, is

The relationship between true strain (^$\in_T$) and engineering strain (^$\in_E$) in a uniaxial tension test is given as

One of the eigen vectors of the matrix ^{$\begin{bmatrix} \ -5 & 2 \ \ -9 & 6 \ \end{bmatrix}$} is