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.

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

Q36.

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

Q37.

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

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