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(#M40021674) GATE QUESTION MATHS Keep an EYE

Consider two well-formed formulas in prepositional logic
El: P - iP
E2: (Pi - iP)v(--iPiP)
Which of the following statements is correct?
(a) Fl is satisfiable, F2 is valid
(b) Fl unsatisfiable, F2 is satisfiable
(c) Fl is unsatisfiable, F2 is valid
(d) Fl and F2 are both satisfiable

Asked In Gate MAN (12 years ago)

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(#M40021673) GATE QUESTION MATHS Keep an EYE

Consider the following relations:
R1 (a,b) iff (a+b) is even over the set of integers
R2 (a,b) iff (a+b) is odd over the set of integers
R3 (a,b) iff a.b > 0 over the set of non-zero rational numbers
R4 (a,b) iff a + bi 2 over the set of natural numbers
Which of the following statements is correct?
(a) Ri and R2 are equivalence relations, R3 and R4 are not
(b) Ri and R3 are equivalence relations, R2 and R4 are not
(c) Ri and R4 are equivalence relations, R2 and R3 are not
(d) Ri, R2, R3 and R4 are all equivalence relations

Asked In Gate MAN (12 years ago)

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(#M40021672) GATE QUESTION MATHS Keep an EYE

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

Asked In Gate MAN (12 years ago)

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(#M40021671) GATE QUESTION MATHS Keep an EYE

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
Visit

Asked In Gate MAN (12 years ago)

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(#M40021670) GATE QUESTION MATHS Keep an EYE

The determinant of the matrix
2 0 0 0
8 1 7 2.
2 0 2 0
9 0 6 1

Asked In Gate MAN (12 years ago)

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(#M40021669) GATE QUESTION MATHS Keep an EYE

The minimum number of cards to be dealt from an arbitrarily shuffled deck of 52 cards to
guarantee that three cards are from some same suit is
(a) 3
(b) 8
(c) 9
(d) 12

Asked In Gate MAN (12 years ago)

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(#M40019996) GATE QUESTION series Keep an EYE

5,3,12,9,36,81,?

Asked In Gate milind (12 years ago)

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(#M40019953) GATE QUESTION BINOMIAL THEOREM Keep an EYE

The number of real negative terms in the binomial expansion of (1+ix)^(4n-2), n € N and x > 0 is?

Asked In Gate vignesh (12 years ago)

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(#M40019952) GATE QUESTION PERMUTATION AND COMBINATION Keep an EYE

If A and B are two independent events such that and P(A'∩B)=2/7 and P(A∩B')=1/5, then P(A) is

Asked In Gate vignesh (12 years ago)

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(#M40019951) GATE QUESTION PERMUTATION AND COMBINATION Keep an EYE

Let α, β and γ be the cube roots of p (p < 0). For any real numbers x, y and z, the value of (xα+yβ+zγ) ⁄(xβ+yγ+zα) is

Asked In Gate vignesh (12 years ago)

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