1. The minor Mij of an n x n matrix is the determinant of (n - 1) x (n - 1) matrix formed by deleting the ith row and j the column of n x n matrix.



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MCQ-> Study the following information carefully and answer the questions given below: Eight persons — E, F, G, H, W, X, Y and Z — are sitting in two parallel rows containing four persons each. E. F, G and H are sitting in row-1 facing north and W. X, Y and Z are sitting in row-2 facing south (but not necessarily in the same order.) Thus, each person sitting in row – 1 faces another person sitting in row – 2, Each of the two rows consists of one Doctor, one Engineer, one Pilot and one Scientist (but not necessarily in the same order). • The Doctor of row-1 sits second to the right of H. X faces one of the immediate neighbours of H. Only one person sits between the X and the Scientist. • The one who faces the Scientist of row – 2 is an immediate neighbour of E. Only one person sits between E and the Pilot. • W sits second to the right of Z. Y does not face G. The Scientist of row-1 faces the Engineer of row – 2. • G faces one of the immediate neighbours of the Doctor of row-2. The Doctor of row-2 does not sit at any of the extreme ends of the line. Z is not a Doctor.Which of the following represents the people sitting at extreme ends of both the lines?
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MCQ-> Based on the information answer the questions which follow.An agent has to send a secret message to CBI office in Delhi. He needs to compile his message using following 12 code words- Scare, Logical, Mouse, Beauty, Helping, Roses, Cats, Doctor, Arguments. Crude. Ferry and Mineral. The agent compiles the coded message and delivers it to CBI office in form of a $$4\times3$$ matrix. Each coded word has been allocated a position in the matrix ($$1\times2$$ position represents row 1 and column 2). The clues to compile the secret message are: i. The words in $$2\times1$$ and $$3\times1$$ have the same number of letters. ii. Roses is to the immediate left of Beauty and Mineral is immediately above Roses. iii. The word in $$4\times3$$ is shorter than the word in $$1\times2$$. iv. Ferry is separated from Helping horizontally by only one word Logical. v. Arguments is at position $$2\times3$$ in the matrix and the word immediately below it has odd number of letters.vi. Crude and Doctor are in the same horizontal row and Crude is to the right of Doctor. vii. Cats is not in the same row or column as Mouse.The product of the position of a coded word is 8. Identify the word.
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