GATE-CS-2017 (Set 2)

Question 61

Consider the following database table named top_scorer. Consider the following SQL query:

SELECT ta.player FROM top_scorer AS ta
WHERE ta.goals > ALL ( SELECT tb.goals
		       FROM top_scorer AS tb
		       WHERE tb.country = \'Spain\' )
      AND ta.goals > ANY (SELECT tc.goals
	       	        FROM top_scorer AS tc
		        WHERE tc.country = \'Germany\')

The number of tuples returned by the above SQL query is ____. Note: This questions appeared as Numerical Answer Type.

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Question 62

If a random variable X has a Poisson distribution with mean 5, then the expression E[(X + 2)²] equals _____.

Note: This question appeared as Numerical Answer Type.

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Question 63

Given f(w, x, y, z) = Σ_m(0,1,2,3,7,8,10) + Σ_d(5,6,11,15), where d represents the don\'t-care condition in Karnaugh maps. Which of the following is a minimum product-of-sums(POS) form of f(w,x,y,z)?

• f = (w\' + z\' )( x\' + z )
• f = (w\' + z ) ( x + z )
• f = ( w + z ) ( x \' + z )
• f = ( w + z\' ) ( x\' + z )

Question 64

Two transactions T₁ and T₂ are given as:

T1: r1(X)w1(X)r1(Y)w1(Y)

T2 : r2(Y)w2(Y)r2(Z)w2(Z)

where r_i(V) denotes a read operation by transaction T_i on a variable V and w_i(V) denotes a write operation by transaction T_i on a variable V. The total number of conflict serializable schedules that can be formed by T1 and T2 is ______ 

Note: This question appeared as Numerical Answer Type.

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Question 65

If the characteristic polynomial of a 3 × 3 matrix M over R (the set of real numbers) is λ³ - 4λ² + aλ + 30, where a ∈ R, and one eigen value of M is 2, then the largest among the absolute values of the eigenvalues of M is _______
Note: This question appeared as Numerical Answer Type.

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