List of top Questions asked in ICAR AIEEA (PG)

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

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

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

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

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

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

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

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

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

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

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

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

Let \((a_n) = (-1)^n\) and \((b_n) = -2^n\) be sequences of real numbers, then

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

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

The determinant of a matrix $A = \begin{bmatrix} 0 & 0 & 0 & 0 & 0 & 1 \\ 0 & 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 & 0 \\ 1 & 0 & 0 & 0 & 0 & 0 \end{bmatrix}$ is}

Which of the following invention gave birth to the much cheaper microcomputers?

Let $T: \mathbb{R}^2(\mathbb{R}) \to \mathbb{R}^2(\mathbb{R})$ be a linear transformation such that $T$ is a rotation at angle of $90^\circ$ in clockwise direction in $\mathbb{R}^2$, then}

Let $A$ be an $n \times n$ matrix of real numbers such that $A^2 = I$, then the eigen values of $A$ are

Which of the following statement is always true

Let $A$ be a $5 \times 5$ skew-symmetric matrix of real numbers, then which of the following is true

Which of the following language does the computer understand?

Which of the following is not a characteristic of a computer?

A wireless technology built-in electronic gadgets used for exchanging data over short distances is?

Which of the following is invalid statement in FORTRAN