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

Let $A_{m \times n}$ be any matrix and Rank ($A$) = 0, then matrix $A$ is}

Which of the following statement is always true for a square matrix

Let \((a_n) = (-1)^n\) and \((b_n) = -2^n\) be sequences of real numbers, then

Let \((a_n) = r^n\), where \(r\) be any real number, then

Let $A$ be an $n \times n$ matrix of real numbers such that $A^2 = I$, then the eigen values of $A$ are

Let $A$ be a $5 \times 5$ skew-symmetric matrix of real numbers, then which of the following is true

Which of the following statement is always true

The determinant of a matrix $A = \begin{bmatrix} 0 & 0 & 0 & 0 & 0 & 1 \\ 0 & 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 & 0 \\ 1 & 0 & 0 & 0 & 0 & 0 \end{bmatrix}$ is}

Let $T: \mathbb{R}^2(\mathbb{R}) \to \mathbb{R}^2(\mathbb{R})$ be a linear transformation such that $T$ is a rotation at angle of $90^\circ$ in clockwise direction in $\mathbb{R}^2$, then}

Let \((a_n)=n^2\) and \((b_n)=1+\frac{1}{n^2}\) be sequences of real numbers, then:

Let \(a_n=\frac{1}{n^2}\) be a sequence of real numbers. Then the sequence is:

Let \(\sum_{n=1}^{\infty}a_n\) be any series of real numbers, then which of the following statement is true?

Let \(a\) and \(b\) be two real numbers with \(a,b > 0\) and \(a < b\). Then which of the following is true?

Let ($\text{a}_\text{n}$) and ($\text{b}_\text{n}$) are two convergent sequences of real numbers, then which of the following is always true ?

Let x and y be two real numbers, then which of the following is always true ?

Which of the following is the sequence alignment tool ?

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:

Let \(\sum_{n=1}^{\infty}a_n\) be any series of real numbers. Then, which of the following statement is true?

Let \(\sum_{n=1}^{\infty}(-1)^na_n=\sum_{n=1}^{\infty}(-1)^n\dfrac{1}{\sqrt{n}}\) be a series, then:

The series \(\sum_{n=1}^{\infty} \frac{1}{n}\) is :

The necessary condition of a convergent sequence is :

The sum of \(\frac{1}{1 \times 2} + \frac{1}{2 \times 3} + \frac{1}{3 \times 4} + \dots + \frac{1}{9 \times 10}\) is :

Let A and B be two non-empty sets, then \((A \cup B)^c\) is equal to :

Let ($\text{a}_\text{n}$) and ($\text{b}_\text{n}$) are two convergent sequences of real numbers, then which of the following is always true ?

Let x and y be two real numbers, then which of the following is always true ?