List of top Statistical Science Questions asked in ICAR AIEEA (PG)

Vertical and horizontal asymptotes of the curve \(y = \frac{3x + 5}{7 - x}\) are respectively:

The infinite series \(3 + \frac{1}{6}x - \frac{1}{216}x^2 - \frac{1}{3888}x^3 + \cdots\) represents the Maclaurin series for the function:

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 \(\lim_{x \to 0^+} \left(\frac{1}{x} - \frac{1}{\sin x}\right)\) is:

For the sequence \(s_n = \frac{b^n}{n^2}\), which of the following is true?

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

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:

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:

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

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. \(A^3 = 4A - 3I, A^4 = 3A - 2I\)

Which of the following statements is false?

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

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

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

Which of the following is true?

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

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

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