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

Evaluate the integral \(I = \int_0^1 \frac{1}{1+x} dx\) by using Simpson's one-third rule with \(h = 0.5\)

If \(z = 3x^2y - x \sin xy\), then:

If \(z = 3x^2 y - x\sin(xy)\), then

Evaluate \(\lim_{x \to +\infty} \frac{x}{\sqrt{x^2 + 1000}}\)

In hyperbola, the length of the transverse axis is the distance between:

Let \(Z_1 = -2 + 2i\) and \(Z_2 = 3i\), then:

The center of the circle \(4x^2 + 4y^2 - 8x + 12y - 25 = 0\) is:

Let \(x + iy = (2 - i)^2 + \left(\frac{7-4i}{2-i}\right) - 8\), the values of \(x\) and \(y\) are:

The length of the latus rectum of \(x^2 = -9y\) is equal to:

Let \(Z_1\) and \(Z_2\) be two complex numbers, then:

Which of the following statement is true?

Let \(\sum_{n=1}^\infty a_n\) be series of real number, then:

Let \(A = \begin{bmatrix} 2 & 1 & 4 3 & 2 & 5 0 & -1 & 1 \end{bmatrix}\) be a matrix, then the rank of \(A\) is:

Let \(A\) be an \(n \times n\) matrix of real number such that \(A^2 = A\), then the Eigen values \(A\) are:

The solution of the system of equations
\[ x_1 - 3x_2 + 4x_3 = 3 \]
\[ 2x_1 - 5x_2 + 7x_3 = 6 \]
\[ 3x_1 - 8x_2 + 11x_3 = 11 \]
is given by:

Let \(A\) be a \(5 \times 5\) skew-symmetric matrix, then the determinant of \(A\) is:

Let $\sum_{n=1}^\infty a_n$ is absolutely convergent series, then}

Let \(a, b \in \mathbb{R}\) and \(0 \le a < b\), then:

Let \(c\) be any real number and \(1 < c\), then:

Let $\sum_{n=1}^\infty \frac{1}{n^2}$ and $\sum_{n=1}^\infty \frac{1}{n^{\frac{1}{2}}}$ be series, then}

The series $\sum_{n=1}^\infty (-1)^n \frac{1}{n^2}$ is}

$\lim_{n\to\infty} (1 + \frac{1}{n})^{2n}$ is equal to}

Let $(a_n)$ and $(b_n)$ be sequences of real number. Let $(\frac{a_n}{b_n})$ and $(a_n b_n)$ are convergent, then

Which of the following scores are not considered while calculating the SP scores?

Which of the following does not constitute an online resource for aligning sequence pairs?