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

The coefficient of variation of Poisson distribution with mean 9 is

A random variable X is normally distributed with zero mean and unit variance. The variance of $X^2$ is

If all frequencies of classes are same, the value of chi-square ($\chi^2$) is:

For any discrete distribution, what is the value of $\beta_2$?

If \(\Gamma(n)=\int_{0}^{\infty} e^{-x}x^{n-1}\,dx,\; n > 0\), then the value of \(\int_{0}^{\pi/2}\sin^{n}x\,dx\) is given by:

The value of \(\lim_{x \to +\infty}\sqrt[3]{\frac{3x+5}{6x-8}}\) is given by:

If f is continuous on an open interval containing a value $x_0$, and if f changes the direction of its concavity at the point ($x_0, f(x_0)$), then f has :

The value of \(\int_{0}^{6} f(x)\,dx\), if \(f(x)=\begin{cases}x^2, & x < 2 \\ 3x-2, & x \ge 2\end{cases}\), is given by:

Let f be a function such that f and all its derivatives exist in an open interval I containing c, then the Taylor’s series of f at x = c is given by :

The process of evaluating a definite integral from a set of tabulated values of the integrand is called:

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:

Suppose the function f is continuous at the point P(c, f(c)). Then, the graph of f has a vertical tangent at P if :

The value of \(\int \cos^{-1}(2x)\,dx\) is given by:

If \(2x^3 + 3x^2 + 5x + 6 = 0\) has roots \(\alpha\), \(\beta\), \(\gamma\) then, find \(\alpha + \beta + \gamma\)

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

The value of \(\int \cos^{-1}(2x)\,dx\) is given by:

The value of \(\iint_{R} y^2x\,dy\,dx\) over the rectangle \(R=\{(x,y):-3\le x\le 2,\;0\le y\le 1\}\) is given by:

The value of \(\lim_{x \to +\infty} \sqrt[3]{\frac{3x+5}{6x-8}}\) is given by:

If \(\Gamma(n)=\int_{0}^{\infty} e^{-x}x^{n-1}\,dx,\; n > 0\), then the value of \(\int_{0}^{\pi/2}\sin^{n}x\,dx\) is given by:

The value of \(\int_{0}^{6} f(x)\,dx\), if \(f(x)=\begin{cases}x^2, & x < 2 \\ 3x-2, & x \ge 2\end{cases}\), is given by:

Let f be a function such that f and all its derivatives exist in an open interval I containing c, then the Taylor’s series of f at x = c is given by :

Suppose the function f is continuous at the point P(c, f(c)). Then, the graph of f has a vertical tangent at P if :

If the function f(x, y) has mixed second order partial derivatives $f_{xy$ and $f_{yx}$ that are continuous in an open disk containing ($x_0, y_0$), then :}

Suppose f is continuous on [a, b] and differentiable on (a, b). If f(a) = f(b), then there exists at least one number c between a and b such that $f'(c) = 0$ is the statement of

If f is continuous on an open interval containing a value $x_0$, and if f changes the direction of its concavity at the point ($x_0, f(x_0)$), then f has :