GATE CSE 2017 SET-2

Q31.

Consider the following tables T1 and T2. In table T1, P is the primary key and Q is the foreign key referencing R in table T2 with ondelete cascade and on-update cascade. In table T2, R is the primary key and S is the foreign key referencing P in table T1 on-delete set NULL and on-update cascade. In order to delete record (3,8) from table T1, the number of additional records that need to be deleted from table T1 is _____.
GateOverflow

Q32.

If the characteristics polynomial of 3x3 matrix M over R ( the set of real numbers) is \lambda ^{3}-4\lambda ^{2}+a\lambda +30,a\in R, and one eigenvalue of M is 2, then the largest among the absolute values of the eigenvalues of M is ________.
GateOverflow

Q33.

Let P=\begin{bmatrix} 1 & 1&-1 \\ 2&-3 & 4\\ 3 &-2 & 3 \end{bmatrix} and Q=\begin{bmatrix} -1 & -2&-1 \\ 6 & 12& 6\\ 5&10 & 5 \end{bmatrix} be two matrices. Then the rank of P +Q is _____________.
GateOverflow

Q34.

Consider a quadratic equation x^{2} -13x +36 = 0 with coefficients in a base b. The solutions of this equation in the same base b are x = 5 and x = 6. Then b = ___________.
GateOverflow

Q35.

Consider the C program fragment below which is meant to divide x by y using repeated subtractions. The variables x, y, q and r are all unsigned int. while (r >= y) { r = r - y; q = q +1; } Which of the following conditions on the variables x, y, q and r before the execution of the fragment will ensure that the loop terminates in a state satisfying the condition x==(y*q+r)?
GateOverflow

Q36.

Consider the set X={a, b,c,d,e} under the partial ordering R={(a,a),(a,b),(a,c),(a,d),(a,e),(b,b),(b,c),(b,e),(c,c),(c,e),(d,d),(d,e),(e,e)}. The Hasse diagram of the partial order (X, R) is shown below. The minimum number of ordered pairs that need to be added to R to make (X, R) a lattice is _____.
GateOverflow

Q37.

Match the following according to input (from the left column) to the complier phase (in the right column) that processes it.
GateOverflow

Q38.

The minimum possible number of states of a deterministic automaton that accepts the regular language L=\{w_{1}aw_{2}|w_{1},w_{2}\in \{a,b\}^{*},|w_{1}|=2,|w_{2}|\geq 3\} is ____
GateOverflow

Q39.

Let \delta denote that transition function and \hat{\delta} denote the extended transition function of the \epsilon- NFA whose transition table is given below: Then \hat{\delta}(q_{2},aba) is ____
GateOverflow

Q40.

The representation of the value of a 16-bit unsigned integer X in hexadecimal number system is BCA9. The representation of the value of X in octal number system is
GateOverflow