List of top Questions asked in ICAR AIEEA (PG)- 2023

The value of $\int_0^{\pi/2} \sin^2 \frac{x}{2} \cos^2 \frac{x}{2} \, dx$ is given by}

The solution of the differential equation $x \frac{dy}{dx} + y = x^3 y^6$ is given by}

The value of $\int x \tan^{-1}x \, dx$ is given by}

Using chain rule, the derivative of $\omega = x^2 y - y^2$ with respect to t along the path $x = \sin t$ and $y = e^t$ at $t = 0$ is given by

The value of \(\lim_{x \to 1^-} \frac{x-1}{|x^2-1|}\) is given by

Roots of the equation \(x^3 - 23x^2 + 142x - 120 = 0\) are

The horizontal asymptote for \(y = \frac{-8}{x^2-4}\) is given by

If \(x = a\sin^3 t\) and \(y = b\cos^3 t\), then the value of \(\frac{d^2y}{dx^2}\) is given by

If $u = \sin^{-1}\left( \frac{x+2y+3z}{x^8+y^8+z^8} \right)$, then the value of $x\frac{\partial u}{\partial x} + y\frac{\partial u}{\partial y} + z\frac{\partial u}{\partial z}$ is given by}

Let \(Z_1 = r_1(\cos \theta_1 + i\sin \theta_1)\) and \(Z_2 = r_2(\cos \theta_2 + i\sin \theta_2)\) be two complex numbers, then value of \(Z_1Z_2\) is

Let \(3x + 2iy - ix + 5y = 7 + 5i\), then values of \(x\) and \(y\) respectively are given by

If \(\cos \theta = \frac{e^{i\theta} + e^{-i\theta}}{2}\) and \(\sin \theta = \frac{e^{i\theta} - e^{-i\theta}}{2i}\), then \(\cos \theta - i\sin \theta\) is equal to

If A and B be orthogonal matrices of same size, then

From point Q which is outside the circle, the length of the tangent to the circle is 24 cm and the distance of Q from the centre is 25 cm, then the radius of the circle is given by

The sum and product of the roots of the polynomial \(x^2 - 2x - 8\) are respectively

\(\lim_{n\to\infty} \frac{1+2+3+\dots+n}{n^2}\) is

The equation of conic section whose vertices are \((0, \pm 8)\) and asymptotes are \(y = \pm \frac{4}{3}x\) is given by

The series \(\sum_{n=1}^\infty a_n = \sum_{n=1}^\infty \frac{1}{n^2}\) and \(\sum_{n=1}^\infty b_n = \sum_{n=1}^\infty \frac{1}{n^3}\) are

For what value of \(p\), the series \(\sum_{n=1}^\infty \frac{1}{n^p}\) is convergent

The value of \(i^i\), (\(i^2 = -1\)) is

Let $V$ and $W$ be vector spaces and $T: V \to W$ be linear transformation, then

Let $A_{m \times n}$ be any matrix and Rank ($A$) = 0, then matrix $A$ is}

Which of the following statement is always true for a square matrix

The inverse of a matrix $A = \begin{bmatrix} 0 & 2 & 4 \\ 2 & 4 & 2 \\ 3 & 3 & 1 \end{bmatrix}$ is}

Let \((a_n) = r^n\), where \(r\) be any real number, then