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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
Questions below followed by three quantities. Find the relationship between them. Quantity I: In a class with a certain number of students if a teacher weighing 78 kg is added, then average weight of class is increased by 2 kg. If one more teacher weighing 66 kg is added, then the average weight of the class increases by 3.5 kg over the original average. What is the original average weight (in kg) of the class? Quantity II: The average age of 16 students and their teacher's age is 16 years. If the teacher's age is excluded, the average reduces by 2. What is the teacher's age? Quantity III: Average weight of three friends A, B and C is 46 kg. Another person D joins the group and now the average is 45 kg. If another person E whose weight is 6 kg more than D, joins the group replacing A, then average weight of B, C, D and E becomes 47 kg. What is the weight of A (in kg)?
The average of eight batsmen J, K, L, M, N, O, R, and T is compared. The number of batsman having average less than L are same as the number of batsman having average more than M. Average of T is less than M and more than K. Average of L is less than K. Average of two batsman lies between the average of M and L. Average of O is less than N and K both. Which of the following can be the correct sequence of their averages?
In a company there are 252 engineers, in which the ratio of the number of electronics engineers and computer engineers is 2 ∶ 1. The ratio of the number of electronics engineers and computer engineers becomes 1 ∶ 1 after recruitment of some more computer engineers. The average age of all the engineers is now 22 years and the average age of the computer engineers is 2 years less than the average age of electronics engineers. (A) The average age (in years) of electronics engineers is 21 (B) The average age (in years) of computer engineers is 21 (C) The average age (in years) of electronics engineers is 23 (D) The average age (in years) of electronics engineers is 25 (E) The average age (in years) of computer engineers is 23 Choose the correct answer from the options given below: 
Which of the following statements are true with regards to the selection of a sample size? (i) The sample size (n) may be a fixed percentage of lot size (N). (ii) The sample size (n) may be kept constant irrespective of lot size (N). (iii) Sample size (n) can be selected at the personal whim of the inspector.
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.
Quantity I: The average age of a cricket team of 11 players is x years. After three years, four players leave the team and four new players join in place of them then the current average age becomes (x + 2) years. The current average age of the players who left the team was 18 years then find the average of the current age of the 4 new joiners? Quantity II: In a group of 6 students, the average age of the 5 youngest students is 12 years and the average age of the 5 oldest students is 15 years. What is the average age of all the students? (it is given that the age of them is in arithmetic progression)?
Questions below followed by three quantities. Find the relationship between them. Quantity I: Average age of 14 members of team is 25 years. While oldest member of the team is 26 years older than youngest member of the team. Out of remaining 12 members of team, average age of six members of team is 28 years and the remaining six members is 20 years. What is the age of oldest member of the team? Quantity II: Average age of Nitu, Rekha and Shyam is 17 years. Two new persons Divya and Raju joined them so that average age of all become 19 years. If Divya is 2 years older than Raju and Rekha is 2 years older and 1 year older than Shyam and Nitu respectively. What is sum of the average age of Nitu and Shyam together and average age of Divya and Rekha together? Quantity III: The average age of father, mother and their two sons is 27.5. Five years ago, the ratio of ages of father, mother and two sons (elder and younger) is 7 : 5 : 2 : 1. Find the sum of ages of two sons after 7 years.