The limit $\rm p = \displaystyle\lim_{x \rightarrow \pi} \left( \frac{x^2 + α x + 2 \pi^2}{x - \pi + 2 \sin x} \right)$

Solution of ∇2T = 0 in a square domain (0 < x < 1 and 0 < y < 1) with boundary conditions: T(x, 0) = x; T(0

Given a function $\rm ϕ = \frac{1}{2} (x^2 + y^2 + z^2) $ in three-dimensional Cartesian space, the value of the su

The Fourier series expansion of x3 in the interval −1 ≤ x < 1 with periodic continuation has

If A = $\begin{bmatrix} 10 & 2k + 5 \\\ 3k - 3 & k + 5 \end{bmatrix} $ is a symmetric matrix, the valu

The value of the integral $\rm \oint \left( \frac{6z}{2z^4 - 3z^3 + 7 z^2 - 3z + 5} \right) dz$ evaluated over a count

The system of linear equations in real (x, y) given by $\rm \begin{pmatrix} \rm x & \rm y \end{pmatrix} \begin{bmat

Let a random variable X follow Poisson distribution such that Prob(X = 1) = Prob(X = 2). The value of Prob(X

Consider two vectors $\rm \vec a = 5 i + 7 j + 2 k $ $\rm \vec b = 3i - j + 6k$ Magnitude of the component of $\

The plane of the figure represents a horizontal plane. A thin rigid rod at rest is pivoted without friction about a

A structure, along with the loads applied on it, is shown in the figure. Self-weight of all the members is negligible an

Two rigid massless rods PR and RQ are joined at frictionless pin-joint R and are resting on ground at P and Q, respectiv

A cylindrical disc of mass m = 1 kg and radius r = 0.15 m was spinning at 𝜔 = 5 rad/s when it was placed on a flat

A tiny temperature probe is fully immersed in a flowing fluid and is moving with zero relative velocity with respect to

In the following two-dimensional momentum equation for natural convection over a surface immersed in a quiescent fluid a

The figure shows a purely convergent nozzle with a steady, inviscid compressible flow of an ideal gas with constant ther

A solid spherical bead of lead (uniform density = 11000 kg/m3) of diameter d = 0.1 mm sinks with a constant velocity V i

Consider steady, one-dimensional compressible flow of a gas in a pipe of diameter 1 m. At one location in the pipe, the

A steady two-dimensional flow field is specified by the stream function ψ = kx3y, where x and y are in meter

A flat plate made of cast iron is exposed to a solar flux of 600 W/m2 at an ambient temperature of 25 °C. Assume that th

Consider a rod of uniform thermal conductivity whose one end (x = 0) is insulated and the other end (x = L) is exposed t

Consider a solid slab (thermal conductivity, k = 10 W∙m-1∙K-1) with thickness 0.2 m and of infinite extent in the other

During open-heart surgery, a patient’s blood is cooled down to 25 °C from 37 °C using a concentric tube counter-flow hea

In a linear programming problem, if a resource is not fully utilized, the shadow price of that resource is

Which one of the following is NOT a form of inventory?

Activities A to K are required to complete a project. The time estimates and the immediate predecessors of these activit

An assignment problem is solved to minimize the total processing time of four jobs (1, 2, 3 and 4) on four different mac

The product structure diagram shows the number of different components required at each level to produce one unit of the

A square threaded screw is used to lift a load W by applying a force F. Efficiency of square threaded screw is expressed

A CNC worktable is driven in a linear direction by a lead screw connected directly to a stepper motor. The pitch of the

The type of fit between a mating shaft of diameter $25.0^{\begin{matrix} +0.010 \\\ -0.010 \end{matrix}}$ mm a

Which of the following methods can improve the fatigue strength of a circular mild steel (MS) shaft?

A bracket is attached to a vertical column by means of two identical rivets U and V separated by a distance of 2a = 100

Which of the following heat treatment processes is/are used for surface hardening of steels?

Which of the following additive manufacturing technique(s) can use a wire as a feedstock material?

Electrochemical machining operations are performed with tungsten as the tool, and copper and aluminum as two differ

Under orthogonal cutting condition, a turning operation is carried out on a metallic workpiece at a cutting speed of 4 m

A 1 mm thick cylindrical tube, 100 mm in diameter, is orthogonally turned such that the entire wall thickness of the tub

A 4 mm thick aluminum sheet of width w = 100 mm is rolled in a two-roll mill of roll diameter 200 mm each. The workpiece

Two mild steel plates of similar thickness, in butt-joint configuration, are welded by gas tungsten arc welding pro

A uniform light slender beam AB of section modulus EI is pinned by a frictionless joint A to the ground and supported by

Assuming the material considered in each statement is homogeneous, isotropic, linear elastic, and the deformations are i

An L-shaped elastic member ABC with slender arms AB and BC of uniform crosssection is clamped at end A and connecte

A thin-walled cylindrical pressure vessel has mean wall thickness of t and nominal radius of r. The Poisson’s ratio of t

The figure shows a schematic of a simple Watt governor mechanism with the spindle O1O2 rotating at an angular velocity&n

A rigid uniform annular disc is pivoted on a knife edge A in a uniform gravitational field as shown, such that it can ex

A planar four-bar linkage mechanism with 3 revolute kinematic pairs and 1 prismatic kinematic pair is shown in the figur

Consider a forced single degree-of-freedom system governed by $\rm \ddot x(t) + 2 ζ ω_n \dot x (t) + ω_n^2 x(t) = ω

A schematic of an epicyclic gear train is shown in the figure. The sun (gear 1) and planet (gear 2) are external, a

The Clausius inequality holds good for

A polytropic process is carried out from an initial pressure of 110 kPa and volume of 5 m3 to a final volume of 2.5 m3.

In Fe-Fe3C phase diagram, the eutectoid composition is 0.8 weight % of carbon at 725 ºC. The maximum solubility of carbo

Consider a one-dimensional steady heat conduction process through a solid slab of thickness 0.1 m. The higher temperatur

In a steam power plant based on Rankine cycle, steam is initially expanded in a high-pressure turbine. The steam is then

An engine running on an air standard Otto cycle has a displacement volume 250 cm3 and a clearance volume 35.7 cm3. The p

After playing _________ hours of tennis, I am feeling _________ tired to walk back.

The average of the monthly salaries of M, N and S is ₹ 4000. The average of the monthly salaries of N, S and P is ₹ 5000

A person travelled 80 km in 6 hours. If the person travelled the first part with a uniform speed of 10 kmph and the rema

Four girls P, Q, R and S are studying languages in a University. P is learning French and Dutch. Q is learning Chinese a

A block with a trapezoidal cross-section is placed over a block with rectangular cross section as shown above. Which o

Humans are naturally compassionate and honest. In a study using strategically placed wallets that appear “lost”, it was

A rhombus is formed by joining the midpoints of the sides of a unit square. What is the diameter of the largest circle

An equilateral triangle, a square and a circle have equal areas. What is the ratio of the perimeters of the equilateral

Given below are three conclusions drawn based on the following three statements. Statement 1 : All teachers are profess

In a 12-hour clock that runs correctly, how many times do the second, minute, and hour hands of the clock coincide, in a