List of top Questions asked in ICAR AIEEA (PG)

Which of the following statements is correct?

For testing goodness of fit, suppose the observed frequencies for two classes are 28 and 12. It is expected that these occur in the ratio 3:1. The value of Chi-square statistic for testing this is:

In a random sample of 100 voters in an area, 59 voters were in favour of a candidate A. The value of the test statistic for testing \(H_0: P = 0.5\) against \(H_0: P \neq 0.5\) is:

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:

Which of the following is a central difference operator?

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:

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: