List of top Questions asked in ICAR AIEEA (PG)- 2023

The value of \(\int_{0}^{6} f(x)\,dx\), if \(f(x)=\begin{cases}x^2, & x < 2 \\ 3x-2, & x \ge 2\end{cases}\), is given by:

If the function \(f(x,y)\) has mixed second order partial derivatives \(f_{xy}\) and \(f_{yx}\) that are continuous in an open disk containing \((x_0,y_0)\), then:

Let f be a function such that f and all its derivatives exist in an open interval I containing c, then the Taylor’s series of f at x = c is given by :

If $\Delta$ and $\nabla$ be the first forward difference and first backward difference operator respectively, then the expression $(1+\Delta)(1-\nabla)$ is equivalent to :

The formula to solve simple non-linear equation f(x) = 0 by Newton’s Raphson Method is given by :

The process of evaluating a definite integral from a set of tabulated values of the integrand is called:

If \(A\) is any real number and \(r\) is a positive rational number, then the value of \(\lim_{x\to +\infty}\frac{A}{x^r}\) is:

The solution of the differential equation \(\frac{d^2x}{dt^2}+6\frac{dx}{dt}+9x=0\) is given by:

Suppose the function f is continuous at the point P(c, f(c)). Then, the graph of f has a vertical tangent at P if :

If \(z=f(x,y)\), \(x=e^u+e^{-v}\), and \(y=e^{-u}-e^v\), then:

The value of \(\iint_R y^2x\,dy\,dx\) over the rectangle \(R=\{(x,y):-3\le x\le 2,\;0\le y\le 1\}\) is given by:

The solution of the differential equation \(xy^{\prime\prime}+y^{\prime}=4x\) is given by:

The value of \(\int \cos^{-1}(2x)\,dx\) is given by:

The solution of the differential equation $\cos(x+y)dx + [3y^2 + 2y + \cos(x+y)]dy = 0$ is given by :

The area under the curve y = cos x on $\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$ is given by :

Given below are two statements, one is labelled as Assertion (A) and other one labelled as Reason (R).
Assertion (A) : A good measure of dispersion needs to be least affected by change in the sampling.
Reason (R) : Standard deviation is the best measure of dispersion.
In light of the above statements, choose the most appropriate answer from the options given below:

The average variable cost is the result of ____________.

One dimensional flow is :

Given below are two statements :
Statement (I) : The commercial unit of energy is 1 kWh.
Statement (II) : 1 kWh = \(2.6 \times 10^6\) J
In light of the above statements, choose the most appropriate answer from the options given below.

If \(\theta=t^n e^{-\frac{r^2}{4t}}\), then the value of \(n\) that will make \(\frac{1}{r^2}\frac{\partial}{\partial r}\left(r^2\frac{\partial \theta}{\partial r}\right)=\frac{\partial \theta}{\partial t}\) is given by:

In actual machines ____________.

If \(2x^3 + 3x^2 + 5x + 6 = 0\) has roots \(\alpha\), \(\beta\), \(\gamma\) then, find \(\alpha + \beta + \gamma\)

The current flowing through the armature of a d.c. shunt machine at maximum efficiency is given by :

Which of the followings statements are true about the cut-throat and Parshall flumes.
(A) The cut-throat flume is similar to the Parshall flume, but has no throat section, only converging and diverging sections
(B) It gives nearly as accurate measurements as Parshall flume in free flow condition for smaller throat widths
(C) Angles of convergence and divergence of cut-throat flume changes with size of the flume
(D) Because it is easier to construct and install, the cut-throat flume is often preferred to the Parshall flume
Choose the correct answer from the options given below: