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In a village 50% of the villagers produce rice, 40% of the villagers produce apples and 50% of the villagers produce vegetables, 20% of the villagers produce rice and apples both, 25% of the villagers produce apples and vegetables both, 20% of the villagers produce rice and vegetables both and 10% of the villagers produce all three. Find the percentage of villagers who do not produce anything.
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
If two non-zero vectors are added together, and the resultant vector is zero, what must be true of the two vectors?
As in the determination of the various unknown forces in the free body diagram involves the use of vectors. So one of the vector law is commutative law and it is valid for the cross product of two vectors. (Commutative law: PxQ = QxP; for two vectors P and Q)
Which of the following statements are true/false?
1. A minimum rate of wages for the time spent by employees for the production of output is minimum time rate.
2. Minimum piece rate is the rate based on the quantity of the output employees have produced.
3. The guaranteed time rate is a minimum rate of remuneration to apply in the case of employees employed on piece work for the purpose of securing to such employees a minimum rate of wages on a time work basis.
4. A minimum rate of remuneration to apply in the case of employees employed on piece work for the purpose of securing to such employees a minimum rate of wages on a time work basis is overtime rate.
A suit, a trouser, and a shirt are to be stitched from a cloth. The cloth required for the suit is the average of cloth required for trousers and shirt. The length of the cloth for suit is 1.5 times the cloth required for the shirt. The length of cloth required for shirt is 5 times the even prime number. Which of the following is/are correct? A. Cloth required for trousers is 20 m B. Average length of cloth required for all the dresses = Cloth required for suit C. Initially, the cloth was 45 m D. Cloth required for shirt is 15 m
The vectors which start from the same initial point are called collinear vectors.
It is given that X1, X2, ... XM are M non-zero, orthogonal vectors. The dimension of the vector space spanned by the 2M vectors X1, X2 ... XM, -X1, -X2 ... -XM is
In a village there are 300 people. They produce different crops, out of all people 190 people produce paddy, 160 people produce wheat and 100 people produce both paddy and wheat. Find the number of people who neither produce paddy nor wheat. 
There are 12 points in a plane of which 5 are collinear. Barring these five points no three are collinear. The number of quadrilaterals one can form using these points is