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

Which of the following is the experimental condition in case of binomial distribution?

Let \(X\) follows a binomial \((n, p)\) distribution, the skewness of the distribution will be zero if:

The coefficient of variation of Poisson distribution with mean 9 is:

Integrating factor for the differential equation \((x^2 + y^2 + x) \, dx + xy \, dy = 0\) is:

Number of first order equations in a system equivalent to the equation \(x''' + 3x'' + 2x' - 5x = \sin 2t\) is:

For the system \(x' = y; \, y' = -x\), the solution curve has the form:

The total differential \(df\) for the function \(f(x, y, z) = x^2 y^3 z^4\) is:

For the function \(f(x, y) = x^3 + x^2 y^2\), the values of \(f_x(-1, -1)\) and \(f_y(-1, -1)\) are respectively:

The equations of asymptotes for the hyperbola \(xy - 3x - 2y = 0\) are:

A solution to the difference equation \(u_{x+3} - 3u_{x+1} - 2u_x = 0\) is of the form:

A solution to the differential equation \(\left(y - x \frac{dy}{dx}\right) = a \left(y^2 + \frac{dy}{dx}\right)\) is:

Which of the following equations is exact?

Solution of the differential equation \(x \sin \frac{y}{x} \, dy = \left( y \sin \frac{y}{x} - x \right) dx\) is:

For the differential equation \(x^{\alpha} y^{\beta} (m y \, dx + n x \, dy) = 0\), the integrating factor, for any value of \(k\) is:

Equations of the circle circumscribing the triangle formed by the lines \(x + y = 6\), \(2x + y = 4\), \(x + 2y = 5\) is:

For the parabola \(4(y - 1)^2 = -7(x - 3)\), the coordinates of vertex, focus and length of the latus rectum are respectively:

If the angle between the lines joining the foci of an ellipse to an extremity of the minor axis is \(90^\circ\), and the major axis is \(2\sqrt{2}\), then the equation of ellipse and its eccentricity is:

The value of \(\int \frac{2x - 9}{\sqrt{x^2 - 9x + 1}} \, dx\) is:

The value of \(\int_{0}^{\frac{\pi}{2}} \sin^5 x \, dx\) is:

The value of \(\int_{0}^{1} \frac{x^2}{\sqrt{1 - x^2}} \, dx\) is:

For the sequence \((x_n)\), if \(x_1 > 1\) and \(x_{n+1} = 2 - \frac{1}{x_n}\), \(n \geq 1\), which of the following is true:

The value of \(\iint_R x^2 y^5 \, dx \, dy\), where R is the rectangle with vertices (1, 0), (1, 1), (2, 1) and (2, 0) is:

The value of \(\int_{0}^{4} \int_{0}^{4-x} x y \, dx \, dy\) is:

For a continuous function \(f(r, \theta)\) defined on a region D in \((r, \theta)\) plane, the area of the domain D is given by:

The value of the integral \(\int \frac{dx}{1 + e^x}\) is equal to: