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

Let \[ S=\{(2,5),\ (3,7),\ (4,-9),\ (-8,3)\}. \] Then:

Find constants a and b so that \(\lim_{x \to 0} \left( \frac{a}{2x} + \frac{a}{2} + b \right) = 1\)

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

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

Find constants a and b so that \(\lim_{x \to 0} \left( \frac{a}{2x} + \frac{a}{2} + b \right) = 1\)

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

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

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

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

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

Let $r$ be any real number and $(a_n) = \frac{1}{n^r}$ be sequence of real number, then}

Which of the following statement is true for sequence of real number

Let $(a_n) = (\frac{n+1}{n})$ and $(b_n) = (-1)^n$ be sequences of real number, 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: