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Consider a system described by ẋ = Ax + Bu y = Cx + Du The system is completely output controllable if and only if Where: x = State vector (n-vector) u = Control vector (r-vector) y = Output vector (m-vector) A = n × n matrix B = n × r matrix C = m × n matrix D = m × r matrix
P, Q and R invested in a business for 2.5 years, such that P’s initial investment was 60% more than Q’s initial investment, while R’s initial investment was 25% less than P’s initial investment. After 10 months, each of them invested 25% of their initial investment. What part of the total profit will P received after 2.5 years?
Anika and Anushree always used to spend their time by playing coin games after their school hours. Once they decided to play a game of coins in which one player has to guess the number of coins by closing her eyes with the help of clues given by other player. During Anika’s turn, she closed Anushree’s eyes and put some coins on table. She then gave her clue by saying that one fourth of coins are showing their heads but if I turn over two coins then in that case, one third of them will show heads. So, Anushree can you guess how many number of coins I initially placed on the table?
Consider the following three statements about link state and distance vector routing protocols, for a large network with 500 network nodes and 4000 links. [S1] The computational overhead in link state protocols is higher than in distance vector protocols. [S2] A distance vector protocol (with split horizon) avoids persistent routing loops, but not a link state protocol. [S3] After a topology change, a link state protocol will converge faster than a distance vector protocol. Which one of the following is correct about S1, S2, and S3?
In rolling, there is the involvement of the vector math. So for rolling which of the following is correct? (For A representing the vector representation of the axis of rotation, r the radius vector and F the force vector)
The Burgers vector b is the vector which defines the magnitude and direction of slip. For a pure edge dislocation, the Burgers vector is perpendicular to the dislocation line, while for a pure screw dislocation, the Burgers vector is parallel to the dislocation line.
The extremum (minimum or maximum) point of a function f(x) is to be determined by solving $$\frac{{{\text{df}}\left( {\text{x}} \right)}}{{{\text{dx}}}} = 0$$   using the Newton-Raphson method. Let f(x) = x3 - 6x and x0 = 1 be the initial guess of x. The value of x after two iterations (x2) is
In the initial step of EM algorithm, the 20-residue-long binding motif patterns in each sequence are aligned as an initial guess of the motif.
When the MP of an article is increased by 25%, and the article is sold at a 40% discount on new MP, the profit becomes 3 times of the initial profit. The initial MP of the article is 60% above its CP. If the initial MP of the article is Rs. 2400, find the initial profit percent on that article?
Anil and Ruhi started a business with an initial investment of 5 : 8. After four months Anil doubled his investment and Ruhi reduced to 60% of initial investment and Sujeet joined them with the sum of Ruhi’s initial and Anil’s current investment. After another 8 months they distributed the profit in which Sujeet receives 18,000 then find the initial investment of Ruhi?