Let M= [K,∑,Γ,Δ,s,F] be a push down automation, where
K = {s, f}, F = {f},∑ {a,b},Γ = {a} and
Which one of the following strings is not a member of L(M)?
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Solution
baaba is not a member of language accepted by given PDA.
Using a 4-bit 2’s complement arithmetic, which of the following additions will result in an overflow?
(i)1100 + 1100
(ii)0011 + 0111
(iii)1111 + 0111
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Solution
In case of (i), no sign change takes place so no overflow.In case of (ii), no sign change from (+ve) to (–ve) hence overflow.In case of (iii), one member is positive and other is negative,hence there is not chance of overflow.Hence correct answer is (b).
If f(1) = 2, f(2) = 4 and f(4) = 16, what is the value of f(3) using Lagrange’s Interpolation formula?
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Solution
If matrix X = \(\begin{bmatrix} a & 1 \\ -a^{2} + a – 1 & 1 – a \end{bmatrix}\) and X2– X+ I = O(I is the identity matrix and O is the zero matrix),
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Solution
Let p, q, r and s be four primitive statements.
Consider the following arguments:
P:[(¬pvq)^(r→s)^(pvr)]→(¬s→q)
Q:[(¬p^q)^(q→(p)-r)]→¬r
R:[(q^r)→p^(¬qvp)]→r
S:[p^(p→r)^(¬qv¬p)]→q
Which of the above arguments are valid?
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Solution
[(¬pvq)^(r→s)^(pvr)]→(¬s→q) and [^(p→r)^(pv-r)]→q are valid argument
In how many ways can we distribute 5 distinct balls, B1, B2,… B5 in 5 distinct cells, C1, C2, ….,C5 such that Ball Bi is not in cell Ci∀i= 1, 2, …, 5 and each cell contains exactly one ball?
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Solution
Number of distribution = 120 – 4 × 3 × 2 × 1= 120 – 24 = 96
Let H1, H2, H3,…be harmonic numbers. Then, for nεZ+
,\(\sum_{j=1}^{n}\) Hj can be expressed as
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Solution
Let H1, H2, H3 be harmonic numbers, then
\(\sum_{j=1}^{n}\) Hj = (n+1)H-n
Let X and Y be two exponentially distributed and independent random variables with mean α and β,respectively. If Z = min(X, Y), then the mean of Z is given by
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Solution
Let A be an n ×n matrix of the following form.
What is the value of the determinant of A?
We have four resources each creating 250 characters per second. If the interleaved unit is a character and 1 synchronization bit is added to each frame, fiind the duration of each character in each source and the data rate of the link.