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Four  matrices  M1, M2, M3 and M4 of dimensions p×q, q×r, r×s and s×t respectively can be multiplied in several ways with different number of total scalar multiplications. For example when multiplied as [(M1 × M2) × (M3 × M4)] the total number of scalar multiplications is  pqr + rst + prt. When multiplied as [((M1 × M2)× M3)) × M4], the total number of scalar multiplications is pqr + prs + pst. If p = 10, q = 100, r = 20, s = 5 and t = 80, then the minimum number of scalar multiplications needed is:
The curl of curl of a vector is given by,
The curl of a curl of a vector gives a
The length of a rectangular field F is 3 km greater than the side of a square field M , and the width of field F is 3 km less then the side of field M. If the area of field M is m2 square km, what is the area of field F?
The perimeter of a rectangular field is fourth times of the perimeter of a square field. The ratio of the length of the rectangular field to the side of the square field is 6:1 and the diagonal of the square is 5√2 cm. Then, the area of the square field is what percentage of the area of the rectangular field?
The divergence of a vector is a scalar, while the curl of a vector is another
The gradient of a scalar field V is a vector that represents both magnitude and the direction of the maximum space rate of increase of V.
Consider the following statements concerning railways: 1. A level stretch equal to the maximum train length is to be provided between the gradient reaches where a rising gradient is followed by a falling gradient. 2. Vertical curves in railway tracks are not set out as parabolas. 3. Diamond crossings can be laid on curves also. 4. Curves should be avoided at the top level segment of bridges. Which of the above statements are correct?
Curl is defined as the angular velocity at every point of the vector field. State True/False.
Given below are certain facts about distance and displacement. Choose the option which gives the correct information about the two. A. It is a scalar quantity. B. It is a vector quantity. C. It can be zero. D. It cannot be zero. E. The quantity that is scalar is either equal or greater in magnitude than the quantity that is vector.