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Which of the following is an adverb?

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If a² + b² + c² = 1, then ab + bc + ac lies in the interval

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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?

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In the following sentence, certain parts are underlined and marked P, Q and R. One of the parts may contain certain error or may not be acceptable in standard written communication. Select the part containing an error. Choose (4) as your answer if there is no error.

The student corrected ^{$\frac{\text{all the errors}}{P}$} that ^{$\frac{\text{the instructor marked}}{Q}$} on the ^{$\frac{\text{answer book}}{R}$}.

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Lamenting the gradual sidelining of arts in school curricula, a group of prominent artists wrote to the Chief Minister last year, asking him to allocate more funds to support arts education in schools. However, no such increase has been announced in this year’s budget. The artists expressed their deep anguish at their request not being approved, but many of them remain optimistic about funds coming in the future.

Which of the following statements are logically valid and can be inferred from the above statements?

I. The artists expected funding for arts to increase this year. II. The Chief Minister was receptive to the idea of increasing funding for arts. III. The Chief Minister is a prominent artist. IV. Schools are giving less importance to arts education nowadays.

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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.

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Choose the appropriate word/phrase out of the four options given below to complete the following sentence.

Dhoni, as well as the other team members of the Indian team, _________ present on the occasion.

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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?

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Choose the word which is most similar in meaning to the given word.

Awkward

The function of interpolator in a CNC machine controller is to

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?

For an ideal gas with constant values of specific heats and calculation of specific enthalpy,

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

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

The value of ^{$lim_{x \rightarrow0}\frac{1-cos(x^2)}{2x^4}$} is

Among the four normal distributions with probability density functions as shown below, which one has the lowest variance?

The Blasius equation related to boundary layer theory is a

Which of the following is the most conservative fatigue failure criterion?

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

In a linear arc welding process, the heat input per unit length is inversely proportional to

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

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

Match the following:

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

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

Match the following:

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

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

Fine the solution of ^{$\frac{d^2y}{dx^2}$} = y, which passes through the origin and the point (In 2, ^{$\frac{3}{4}$}).

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

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 U_m being the mean velocity of flow. The value of T_m is

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.

The critical path (CP) in the network is

For the truss shown in the figure, the magnitude of the force in member PR and the support reaction at R respectively are

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?

The probability of obtaining at least two ‘‘six’’ in throwing a fair dice 4 times is

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