Linear Algebra

July 29, 2015 by Arjun Suresh 5 Comments

Materials for GATE preparation in Linear Algebra

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GATE Overflow
Aptitude Overflow

Answered: GATE2004-89

1. Recursive languages are closed under concatenation. 2. Recursive languages are closed under quotient with regular language. Let's assume L3 = {#}. ------> regular because finite. Hence recursive. L4= L1.L3 = {wi# : wi belongs to L1) L4 is recursive. (1) L5= {#}.L1 ----> recursive (1) S1: given L1 is recursive Therefore L2=L4.L1 is also recursive. (1) Hence S1 is true. S2: given L2 is recursive Therefore L1= L2/L5 is also recursive. (2) S2 is true as well. ANSWER: (a) [...]

Answered: GATE2015-3-42

We can't compare both functions. No doubt option D [...]

Answered: Avg. disk access time.

Time taken for one full rotation = 60/6000 sec = 1/100 sec = 0.01 sec = 10 msec Average rotational delay = ½ x Time taken for one full rotation = ½ x 10 msec = 5 msec Transfer time = (512bytes / 40 kb) sec … [...]

Answered: Andrew S. Tanenbaum Edition 5th Exercise 6 Question 37 (Page No. 609)

Total Time= 270000 + 730000 = 1000000 T1 = 270000 T2= 730000 Average = T1+T2/Total Time = (270,000*0 + 730,000*1 msec)/1,000,000 = 730 micro Seconds [...]

Answered: TIFR2020-A-1

5 balls we have. 2 balls can be drawn in 10 ways Ball1, Ball2 Ball1, Ball3 Ball1, Ball4 Ball1, Ball5 Ball2, Ball3 Ball2, Ball4 Ball2, Ball5 Ball3, Ball4 Ball3, Ball5 Ball4, Ball5 Let x be the larger number on the balls drawn x P(x) 1 0 2 1 3 2 4 3 5 4 We have to calculate $\sum_{1}^{5} x P(x)$ $1(0) + 2(\frac{1}{10})+ 3(\frac{2}{10})+ 4(\frac{3}{10})+ 5(\frac{4}{10}) = 4$ [...]

Answered: Cormen Edition 3 Exercise 10.2 Question 5 (Page No. 240)

all dictionary operations INSERT, SEARCH and DELETION will be done in O(n) time. [...]

Answered: NIELIT 2017 DEC Scientific Assistant A - Section A: 6

All of the girls agree that the first three numbers are 995. Three of them agree that the fourth number is 9. Three agree that the fifth number is 2. Three agree that the sixth number is 6; three others agree that the seventh number is also 6. "Option A" is the best choice because it is made up of the numbers that most of the girls agree they saw. [...]

Answered: NIELIT 2016 MAR Scientist D: 8

Correct Answer: (D) Explanation: This game introduces the idea of reciprocal causation. For example, the constraint that says “If A, then B, and if B, then A” should be transcribed in one of the following two ways, based on the configurations of the other variables in the diagram: You will run into reciprocal causation in the final constraint of this logic game. Here are the final diagrams that you should create: Notice how the reciprocal causation constraints are diagrammed. Be aware of the implications of these constraints. For instance, if $B$ is not sent (diagram B), then $A$ cannot… [...]

Answered: NIELIT 2016 MAR Scientist D: 7

Answered: NIELIT 2016 MAR Scientist D: 6

Correct Answer: (A) Explanation: This game introduces the idea of reciprocal causation. For example, the constraint that says “If $A$, then $B$, and if $B$, then $A$” should be transcribed in one of the following two ways, based on the configurations of the other variables in the diagram: You will run into reciprocal causation in the final constraint of this logic game. Here are the final diagrams that you should create: Notice how the reciprocal causation constraints are diagrammed. Be aware of the implications of these constraints. For instance, if $B$ is not sent (diagram B), then $A$ cannot be sent… [...]

Answered: NIELIT 2016 MAR Scientist D: 33

The answer is (C). three [...]

Answered: NIELIT 2016 MAR Scientist D: 32

The answer is (B). $K$ and $L$ [...]

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