List of top Questions asked in ICAR AIEEA (PG)- 2024

The formula to solve simple nonlinear equation \(f(x) = 0\) by Newton's Raphson Method is given by

The value of \(\int_0^\infty x^7 e^{-x^2} dx\) is

Find the interval in which the graph of the function given by \(f(x) = x^4 - 4x^3 + 10\) is concave up.

The line \(y = L\) is a horizontal asymptote of the graph of the function \(f\) if

The point at which the tangent to the curve \(y = x^3 - 3x^2 - 9x + 7\) is parallel to the x-axis is

Find the value of \(\int_{-1}^2 |x| dx\)

The formula to solve simple nonlinear equation \(f(x) = 0\) by Newton's Raphson Method is given by

If the interval of differencing being unity and \(\Delta\) be the forward difference operator, then the value of \(\Delta\left(\frac{x^2}{x^2}\right)\) is given by

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

Evaluate the integral \(I = \int_0^1 \frac{1}{1+x} dx\) by using Simpson's one-third rule with \(h = 0.5\)

Evaluate \(\lim_{x \to +\infty} \frac{x}{\sqrt{x^2 + 1000}}\)

If \(z = 3x^2y - x \sin xy\), then:

If \(z = 3x^2 y - x\sin(xy)\), then

Let \(x + iy = (2 - i)^2 + \left(\frac{7-4i}{2-i}\right) - 8\), the values of \(x\) and \(y\) are:

Let \(Z_1 = -2 + 2i\) and \(Z_2 = 3i\), then:

The center of the circle \(4x^2 + 4y^2 - 8x + 12y - 25 = 0\) is:

In hyperbola, the length of the transverse axis is the distance between:

The length of the latus rectum of \(x^2 = -9y\) is equal to:

Let \(Z_1\) and \(Z_2\) be two complex numbers, then:

Which of the following statement is true?

Let \(A\) be an \(n \times n\) matrix of real number such that \(A^2 = A\), then the Eigen values \(A\) are:

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

Let \(A = \begin{bmatrix} 2 & 1 & 4 3 & 2 & 5 0 & -1 & 1 \end{bmatrix}\) be a matrix, then the rank of \(A\) is:

The solution of the system of equations
\[ x_1 - 3x_2 + 4x_3 = 3 \]
\[ 2x_1 - 5x_2 + 7x_3 = 6 \]
\[ 3x_1 - 8x_2 + 11x_3 = 11 \]
is given by: