List of top Questions asked in ICAR AIEEA (PG)- 2020

First four terms of the Taylor series of the function \(f(x) = x^3 + 2x^2 + x - 1\) at \(c = 3\) are:

The value of \(\lim_{x \to 0} \frac{\sqrt{1 + x} - \sqrt{1 - x}}{\sin x}\) is:

The value of \(\lim_{x \to \infty} \sqrt{\frac{3x - 5}{x - 2}}\) is:

For \(f(x) = [x^2 + 1]^{[x + 1]\), where \([x]\) denotes the greatest integer less than or equal to \(x\), which of the following is not true:}

For the function \(f(x) = x^3 - 3x\) on \([-1, 3]\), the points of maxima and minima are respectively:

A particle moving on the x-axis has position \(x(t) = 2t^3 + 3t^2 - 36t + 40\) feet after an elapsed time of t seconds. Its velocity after 3 seconds is:

If A is an n x n real matrix, then:

Which of the following statements is false?

If an n x n matrix A satisfies the equation \(A^2 - 2A + I = 0\), then:
1. \(A^3 = 3A - 2I, A^4 = 4A - 3I\)
2. \(A^3 = 2A - I, A^4 = 4A - 3I\)
3. \(A^3 = 2A^2 - 3I, A^4 = 3A^2 - 4I\)
4. \(A^3 = 4A - 3I, A^4 = 3A - 2I\)

If \(A = \begin{pmatrix} 2 & 3 1 & 2 \end{pmatrix}\), then \(A^{-1}\) is:

The center and radius of the circle \(r^2 = 4r \cos \theta\) are:

For the function \(f(x) = \begin{cases \frac{\sin x}{x} & x \neq 0 h & x = 0 \end{cases}\), the value of \(h\) for which the function is continuous at \(x = 0\) is:}

If \(A = \begin{pmatrix} 4 & -6 -8 & 12 \end{pmatrix}\), then a nontrivial solution of \(A x = 0\) is:

If \(A = \begin{pmatrix} 1 & 1 1 & 1 \end{pmatrix}\), then the entries of \(A^3\) are:

Which of the following statements is false for sets A, B and C?

Which of the following is true?

Which of the following is the most suitable extension teaching method for the problem of rat control in a rural village?
A. Campaign
B. Group Discussion
C. Group Meeting
D. Radio talk

The least upper bound (lub) and greatest lower bound (glb) of the set \( \{1 + ((-1)^n / n) ; n\in \mathbb{N\} \) are:}

If \(a, b, c\) are in G.P., then which of the following is true?

The value of \((\cos 15^\circ + i \sin 15^\circ)^6\) is:

The value of \(z = \frac{(-1 + i)^4{(\sqrt{3} + i)^{10}}\) is:}

Which one of the following techniques is used to generate innovative and creative ideas?

Given below are two statements:
Statement I: News is difficult to define because it has many variables.
Statement II: News must be factual, yet not all facts are news.
In the light of the above statements, choose the most appropriate answer from the options given below:

Which of the following is a communication technique where the farmer and farm families are not at home nor in their fields when the extension professional visits?

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