List of top Questions asked in AP ECET BSc Mathematics

If \[ \overline{F}=(2x^{2}-3z)\mathbf{i}-2xy\mathbf{j}-4x\mathbf{k}, \] then \[ \int_{V}\nabla\cdot\overline{F}\,dV=\_ \] where \(V\) is the closed region bounded by \[ x=0,\quad y=0,\quad z=0,\quad \text{and}\quad x+2y+z=4. \] 

My grandmother and I were good friends. My parents left me with her when they went to live in the city, and we were constantly together. She used to wake me up in the morning and get me ready for school. She said her morning prayer in a monotonous singsong while she bathed and dressed me, in the hope that I would listen and get to know it by heart; I listened because I loved her voice but never bothered to learn it. Then she would fetch my wooden slate, which she had already washed. After a breakfast of a thick, stale chapati with a little butter and sugar spread on it, we went to school. She carried several stale chapatis with her for the village dogs.

Read the following information to answer the question:
I). A, B, C, D, E and F are sitting in a circle facing centre.
II). A is between B and E.
III). C is between D and F.
IV). E is to the immediate right of D.

In a code, the \(r^{\text{th}}\) letter is shifted to the \((27-2r)^{\text{th}}\) letter for \(r = 1, 2, \ldots, 13\). The fourteenth letter is shifted to the \(26^{\text{th}}\) letter, and for \(r = 15, 16, \ldots, 26\), the \(r^{\text{th}}\) letter is shifted to the \((2r-28)^{\text{th}}\) letter. For decoding, the inverse process of the above is followed. Using this coding and decoding, answer the question:

Directions: The number in each question below is to be codified in the following code:

An automobile company manufactures vehicles as given in the following Pie-chart. Answer the question after studying the Pie-chart.