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All posts related to Gate

Silvester
Shared from GATE Mock Test - 3 (Chemical Engg.) on Jun 26, 2019 4:14 PM

Directions: Choose the grammatically incorrect sentence from the given options.

 
He is of Asian origin.
They belonged to Africa.
She is an European.
They migrated from India to Australia.
Please type your answer before submitting.
Silvester

Kdfjhkjfghjkfghfjghdfjk

Bhanu Pratap Singh Rathore
Shared from GATE-2018 (CS) on Jun 26, 2019 4:08 PM

Consider the first-order logic sentence


Where is a quantifier-free first-order logic formula using only predicate
symbols and possibly equality, but no function symbols. Suppose has a model with a universe
containing 7 elements.

Which one of the following statements is necessarily true?

 
There exists at least one model of with universe of size less than or equal to 3.
There exists no model of with universe of size less than or equal to 3.
There exists no model of with universe of size greater than 7.
Every model of has a universe of size equal to 7.
Please type your answer before submitting.
Bhanu Pratap Singh Rathore

Let's interpret the problem this way : ∀ are always True and ∃ are always False for empty sets. So there exists at least one model with universe of size 3 (or less than). Therefore, option (A) is necessarily TRUE.

Bhanu Pratap Singh Rathore
Shared from GATE-2018 (CS) on Jun 25, 2019 6:08 PM

Let N be the set of natural number

Consider the following sets
P: Set of Rational numbers (positive and negative)
Q: Set of functions from {0, 1} to N
R: Set of functions from N to {0, 1}
S: Set of finite subset of N.

Which of the sets above are countable?

 
Q and S only
P and S only
P and R only
P, Q and S only
Please type your answer before submitting.
Bhanu Pratap Singh Rathore

If a set S is countable, then P(S) i.e 2^S is uncountable.

Bhanu Pratap Singh Rathore
Shared from GATE-2018 (CS) on Jun 25, 2019 4:33 PM

Consider the relations r(A, B) and s (B, C), where s.B is a primary key and r.B is a foreign key referencing s. B. Consider the query
Q : r

Let LOJ denote the natural left outer-join operation. Assume that r and s contain no null values. Which one of the following queries is NOT equivalent to Q?

 
(r s)
(rLOJs)
rLOJ
(r)LOJs
Please type your answer before submitting.
Bhanu Pratap Singh Rathore

There is some mistake in question. Consider the relations r(A, B) and s(B, C), where s.B is a primary key and r.B is a foreign key referencing s.B. Consider the query Q: r⋈(σB<5(s)) Let LOJ denote the natural left outer-join operation. Assume that r and s contain no null values. Which one of the following is NOT equivalent to Q? (A) σB<5(r ⋈ s) (B) σB<5(r LOJ s) (C) r LOJ (σB<5(s)) (D) σB<5(r)LOJ s

Abhishek
Shared from Network Theory on May 04, 2019 12:23 PM

A 100Ω 1 W resistor and a 800Ω. 2 W resistors are connected in series. The maximum DC voltage that can be applied continuously to the series circuit without exceeding the power limit of any of the resistors is

 
45 V
50 V
60 V
90 V
Please type your answer before submitting.
Abhishek

If voltage is 90v then power dissipated in 800 ohm resistor is 8w which is exceeding it's limit of 2w. please explain.