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

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 :

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

The necessary condition of a convergent sequence is :

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 :

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

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

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

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

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

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

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

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

Patience is a must to solve all the problems of our life.

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

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

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

Assume that farmers didn't have a contract with a company and he got Rs. 43 per kg for both of the products for the time period of 2011 to 2017. The farmer will have _________ compared to existing system.

At the time of the sale, the machine tools suffer further taxation.

Liberal education makes a man cultural.

He has given up the habit to read books.

He was nostalgic with his childhood.

The ratio of Undergraduate and post graduate pursuing students from state B to Undergraduate and post graduate pursuing students from state A is ?