GATE CSE 2014 SET-2


Q21.

The product of the non-zero eigenvalues of the matrix \begin{bmatrix} 1 & 0&0 & 0&1 \\ 0& 1& 1 & 1 & 0\\ 0& 1& 1& 1&0 \\ 0 & 1 & 1 & 1 & 0\\ 1&0 & 0&0 & 1 \end{bmatrix} is_______.
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Q22.

A non-zero polynomial f(x) of degree 3 has roots at x = 1,x = 2 and x = 3. Which one of the following must be TRUE?
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Q23.

If the matrix A is such that \begin{bmatrix} 2\\ -4\\ 7 \end{bmatrix}\begin{bmatrix} 1 &9 &5 \end{bmatrix} Then the determinant of A is equal to ________.
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Q24.

A computer has twenty physical page frames which contain pages numbered 101 through 120. Now a program accesses the pages numbered 1, 2, ..., 100 in that order, and repeats the access sequence THRICE. Which one of the following page replacement policies experiences the same number of page faults as the optimal page replacement policy for this program?
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Q25.

The number of distinct minimum spanning trees for the weighted graph below is
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Q26.

Consider the equation (123)_{5}=(x8)_{y} with x and y as unknown. The number of possible solutions is _____ .
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Q27.

The value of a float type variable is represented using the single-precision 32-bit floating point format of IEEE-754 standard that uses 1 bit for sign, 8 bits for biased exponent and 23 bits for mantissa. A float type variable x is assigned the decimal value of -14.25. The representation of x in hexadecimal notation is
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Q28.

An IP machine Q has a path to another IP machine H via three IP routers R1, R2, and R3. Q---R1---R2---R3---H H acts as an HTTP server, and Q connects to H via HTTP and downloads a file. Session layer encryption is used, with DES as the shared key encryption protocol. Consider the following four pieces of information: [I1] The URL of the file downloaded by Q [I2] The TCP port numbers at Q and H [I3] The IP addresses of Q and H [I4] The link layer addresses of Q and H Which of I1, I2, I3, and I4 can an intruder learn through sniffing at R2 alone?
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Q29.

Consider the grammar defined by the following production rules, with two operators * and + S \rightarrowT *P T \rightarrowU| T*U P \rightarrow Q +P |Q Q \rightarrow Id U \rightarrow Id Which one of the following is TRUE?
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Q30.

In the Newton-Raphson method, an initial guess of x_{0}=2 is made and the sequence x_{0},x_{1},x_{2}... is obtained for the function 0.75x^{3}-2x^{2}-2x+4=0 Consider the statements (I) x_{3}=0. (II) The method converges to a solution in a finite number of iterations. Which of the following is TRUE?
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