List of top Questions asked in ICAR AIEEA (PG)

The process of evaluating a definite integral from a set of tabulated values of the integrand is called:

If $\Delta$ and $\nabla$ be the first forward difference and first backward difference operator respectively, then the expression $(1+\Delta)(1-\nabla)$ is equivalent to :

A toy manufacturer produces an inexpensive doll (flopsy) and an expensive doll (mopsy) in units of x hundreds and y hundreds respectively. Suppose it is possible to produce the doll in such a way that y = \(\frac{82-10x}{10-x}\) , 0 \(\le\) x \(\le\) 8 and that the company receives twice as much for selling a mopsy doll as for selling a flopsy doll. The level of production for both flopsy and mopsy dolls for which the total revenue derived from selling these dolls is maximized is given by :

The area under the curve y = cos x on $\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$ is given by :

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

If $z = f(x, y)$ and $x = e^u + e^{-v$ and $y = e^{-u} - e^v$, then :}

Let \(\mathbb{R}^n = V\) is a vector space over the field of real numbers, then which of the following is a subspace ?

The vertical asymptote for \(f(x) = \frac{3x+5{7-x}\) is given by :}

The necessary condition of a convergent sequence is :

The series \(\sum_{n=1}^{\infty} \frac{1}{n}\) is :

Let \(z_1\) and \(z_2\) be two complex numbers, then the dot product of \(z_1\) and \(z_2\) is :

If \(\lim_{x \to -a} \frac{x^9 + a^9}{x + a} = 9\), then the possible values of a are given by :

The value of \(\frac{5+5i}{3-4i} + \frac{20}{4+3i}\) is given by :

Let B = \(\begin{bmatrix} 5 & -9 & 6 0 & 2 & 3 0 & 0 & 7 \end{bmatrix}\) , then its reduced echelon form is :

Let A = \(\begin{bmatrix} 1 & 2 & 0 & -1 2 & 6 & -3 & -3 3 & 10 & -6 & -5 \end{bmatrix}\) , then rank of matrix A is :

Let A and B be two invertible matrices, then which of the following is true ?

The eccentricity of the parabola is :

Let \(x^2 = -\frac{25}{2}y\) be the equation of a parabola, then the equation of its directrix is given by :

Let \(W_1\) and \(W_2\) are two subspaces of a vector space V over the field F, then :

Let A and B be two matrices and \(\gamma\) be any scalar, then :

The sum of \(\frac{1}{1 \times 2} + \frac{1}{2 \times 3} + \frac{1}{3 \times 4} + \dots + \frac{1}{9 \times 10}\) is :

Let A and B be two non-empty sets, then \((A \cup B)^c\) is equal to :

Polar form of the complex number \(z = -4 + i4\sqrt{3}\) is :

Let \(z_1\) and \(z_2\) be two complex numbers, then :

Let ($\text{a}_\text{n}$) and ($\text{b}_\text{n}$) are two convergent sequences of real numbers, then which of the following is always true ?