Gate Exam

X,Y and Z are closed intervals of unit length on the real line. The overlap of X and Y is half
a unit. The overlap of Y and Z is also half a unit. Let the overlap of X and Z be k units. Which
of the following is true?
(a) k must be 1
(b) k must be 0
(c) k can take any value between 0 and 1
(d) None of the above
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Gate Other Question

The determinant of the matrix
2 0 0 0
8 1 7 2.
2 0 2 0
9 0 6 1 Consider the following statements:
S1: The sum of two singular n x n matrices may be non-singular
S2: The sum of two n x n non-singular matrices may be singular.
Which of the following statements is correct?
(a) 51 and S2 are both true
(b) 51 is true, S2 is false
(c) 51 is false, S2 is true
(d) 51 and S2 are both false