Deductive and Inductive Reasoning - Logic - General Aptitude (GA) Previous Year Questions

1

2012 · General Aptitude (GA) · Logic · Deductive and Inductive Reasoning

Computer Science & Information Technology (CS) 2012

Q.1 Consider the following logical inferences.
I₁: If it rains then the cricket match will not be played.
The cricket match was played.
Inference: There was no rain.
I₂: If it rains then the cricket match will not be played.
It did not rain.
Inference: The cricket match was played.
Which of the following is TRUE?

A

Both I₁ and I₂ are correct inferences

B

I₁ is correct but I₂ is not a correct inference

C

I₁ is not correct but I₂ is a correct inference

D

Both I₁ and I₂ are not correct inferences

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2

2012 · General Aptitude (GA) · Logic · Deductive and Inductive Reasoning

Computer Science & Information Technology (CS) 2012

Q.4 Assuming P ≠ NP, which of the following is TRUE?

A

NP-complete = NP

B

NP-complete ∩ P = ∅

C

NP-hard = NP

D

P = NP-complete

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3

2012 · General Aptitude (GA) · Logic · Deductive and Inductive Reasoning

Computer Science & Information Technology (CS) 2012

Q.6 The truth table

X	Y	f(X,Y)
0	0	0
0	1	0
1	0	1
1	1	1

represents the Boolean function

A

X

B

X + Y

C

X ⊕ Y

D

Y

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4

2012 · General Aptitude (GA) · Logic · Deductive and Inductive Reasoning

Computer Science & Information Technology (CS) 2012

Q.12 What is the complement of the language accepted by the NFA shown below?
Assume Σ = {a} and ε is the empty string.

A

∅

B

{ε}

C

a*

D

{a, ε}

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5

2012 · General Aptitude (GA) · Logic · Deductive and Inductive Reasoning

Computer Science & Information Technology (CS) 2012

Q.13 What is the correct translation of the following statement into mathematical logic?
“Some real numbers are rational”

A

∃x (real(x) ∨ rational(x))

B

∀x (real(x) → rational(x))

C

∃x (real(x) ∧ rational(x))

D

∃x (rational(x) → real(x))

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6

2012 · General Aptitude (GA) · Logic · Deductive and Inductive Reasoning

Computer Science & Information Technology (CS) 2012

Which of the following problems are decidable?
1) Does a given program ever produce an output?
2) If \(L\) is a context-free language, then, is \(\bar{L}\) also context-free?
3) If \(L\) is a regular language, then, is \(\bar{L}\) also regular?
4) If \(L\) is a recursive language, then, is \(\bar{L}\) also recursive?

A

1, 2, 3, 4

B

1, 2

C

2, 3, 4

D

3, 4

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7

2012 · General Aptitude (GA) · Logic · Deductive and Inductive Reasoning

Computer Science & Information Technology (CS) 2012

Consider the following transactions with data items P and Q initialized to zero:
\(T_1\): read (P); read (Q); if P = 0 then Q := Q + 1; write (Q).
\(T_2\): read (Q); read (P); if Q = 0 then P := P + 1; write (P).
Any non-serial interleaving of \(T_1\) and \(T_2\) for concurrent execution leads to

A

A serializable schedule

B

A schedule that is not conflict serializable

C

A conflict serializable schedule

D

a schedule for which a precedence graph cannot be drawn

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8

2012 · General Aptitude (GA) · Logic · Deductive and Inductive Reasoning

Computer Science & Information Technology (CS) 2012

What is the minimal form of the Karnaugh map shown below? Assume that X denotes a don't care term.

A

\(b\bar{d}\)

B

\(b\bar{d} + b\bar{c}\)

C

\(b\bar{d} + a\bar{b} c\bar{d}\)

D

\(b\bar{d} + b\bar{c} + c\bar{d}\)

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9

2012 · General Aptitude (GA) · Logic · Deductive and Inductive Reasoning

Computer Science & Information Technology (CS) 2012

Fetch_And_Add(X,i) is an atomic Read-Modify-Write instruction that reads the value of memory location X, increments it by the value i, and returns the old value of X. It is used in the pseudocode shown below to implement a busy-wait lock. L is an unsigned integer shared variable initialized to 0. The value of 0 corresponds to lock being available, while any non-zero value corresponds to the lock being not available.
AcquireLock(L){    while (Fetch_And_Add(L,1))      L = 1; } ReleaseLock(L){    L = 0; }
This implementation

A

fails as L can overflow

B

fails as L can take on a non-zero value when the lock is actually available

C

works correctly but may starve some processes

D

works correctly without starvation

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10

2012 · General Aptitude (GA) · Logic · Deductive and Inductive Reasoning

Computer Science & Information Technology (CS) 2012

Consider the program given below, in a block-structured pseudo-language with lexical scoping and nesting of procedures permitted.

Program main;
Var ...

Procedure A1;
Var ...
Call A2;
End A1

Procedure A2;
Var ...

Procedure A21;
Var ...
Call A1;
End A21;

Call A21;
End A2

Call A1;
End main.

Consider the calling chain: Main → A1 → A2 → A21 → A1
The correct set of activation records along with their access links is given by

A

Diagram A: Main with access link to A1, A1 with access link to A2, A2 with access link to A21, A21 with access link to A1; frame pointer points to A1.

B

Diagram B: Main with access link to A1, A1 with access link to A2, A2 with access link to A21, A21 with access link to A1; frame pointer points to A1.

C

Diagram C: Main with access link to A1, A1 with access link to A2, A2 with access link to A21, A21 with no access link; frame pointer points to A1.

D

Diagram D: Main with access link to A1, A1 with access link to A2, A2 with access link to A21, A21 with access link to A1; frame pointer points to A1.

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11

2012 · General Aptitude (GA) · Logic · Deductive and Inductive Reasoning

Computer Science & Information Technology (CS) 2012

Suppose R1(A, B) and R2(C, D) are two relation schemas. Let r1 and r2 be the corresponding relation instances. B is a foreign key that refers to C in r2. If data in r1 and r2 satisfy referential integrity constraints, which of the following is ALWAYS TRUE?

A

Π_B(r1) - Π_C(r2) = ∅

B

Π_C(r2) - Π_B(r1) = ∅

C

Π_B(r1) = Π_C(r2)

D

Π_B(r1) - Π_C(r2) ≠ ∅

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12

2012 · General Aptitude (GA) · Logic · Deductive and Inductive Reasoning

Computer Science & Information Technology (CS) 2012

Consider the set of strings on {0,1} in which, every substring of 3 symbols has at most two zeros. For example, 001110 and 011001 are in the language, but 100010 is not. All strings of length less than 3 are also in the language. A partially completed DFA that accepts this language is shown below.
The missing arcs in the DFA are

A

Table A

B

Table B

C

Table C

D

Table D

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13

2012 · General Aptitude (GA) · Logic · Deductive and Inductive Reasoning

Computer Science & Information Technology (CS) 2012

How many tuples does the result of the following SQL query contain?
SELECT A.Id
FROM A
WHERE A.Age > ALL (SELECT B.Age
FROM B
WHERE B.Name = ‘Arun’)

A

4

B

3

C

0

D

1

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14

2012 · General Aptitude (GA) · Logic · Deductive and Inductive Reasoning

Computer Science & Information Technology (CS) 2012

The FIRST and FOLLOW sets for the non-terminals A and B are

A

FIRST(A) = {a, b, ε} = FIRST(B)
FOLLOW(A) = {a, b}
FOLLOW(B) = {a, b, $}

B

FIRST(A) = {a, b, $}
FIRST(B) = {a, b, ε}
FOLLOW(A) = {a, b}
FOLLOW(B) = {$}

C

FIRST(A) = {a, b, ε} = FIRST(B)
FOLLOW(A) = {a, b}
FOLLOW(B) = ∅

D

FIRST(A) = {a, b} = FIRST(B)
FOLLOW(A) = {a, b}
FOLLOW(B) = {a, b}

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15

2012 · General Aptitude (GA) · Logic · Deductive and Inductive Reasoning

Computer Science & Information Technology (CS) 2012

The appropriate entries for E1, E2, and E3 are

A

E1: S → aAbB, A → S
E2: S → bAaB, B → S
E3: B → S

B

E1: S → aAbB, S → ε
E2: S → bAaB, S → ε
E3: S → ε

C

E1: S → aAbB, S → ε
E2: S → bAaB, S → ε
E3: B → S

D

E1: A → S, S → ε
E2: B → S, S → ε
E3: B → S

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16

2014 · General Aptitude (GA) · Logic · Deductive and Inductive Reasoning

Computer Science & Information Technology (CS) 2014 [Session 1]

Consider the following Boolean expression for F: \( F(P, Q, R, S) = PQ + \bar{P}QR + \bar{P}Q\bar{R}S \) The minimal sum-of-products form of F is

A

PQ + QR + QS

B

P + Q + R + S

C

P + Q + R + S

D

PR + \bar{P}R + S

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17

2014 · General Aptitude (GA) · Logic · Deductive and Inductive Reasoning

Computer Science & Information Technology (CS) 2014 [Session 3]

Consider the following minterm expression for \( F \): \( F(P,Q,R,S) = \sum 0,2,5,7,8,10,13,15 \). The minterms 2, 7, 8 and 13 are 'do not care' terms. The minimal sum-of-products form for \( F \) is

A

\(Q\bar{S} + \bar{Q}S \)

B

\(\bar{Q}\bar{S} + QS \)

C

\(Q\bar{R}\bar{S} + \bar{Q}\bar{R}S + QRS + \bar{Q}R\bar{S} \)

D

\(\bar{Q}\bar{R}\bar{S} + \bar{Q}RS + Q\bar{R}S + QR\bar{S} \)

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18

2014 · General Aptitude (GA) · Logic · Deductive and Inductive Reasoning

Computer Science & Information Technology (CS) 2014 [Session 3]

Consider the following combinational function block involving four Boolean variables \( x \), \( y \), \( a \), \( b \) where \( x \), \( a \), \( b \) are inputs and \( y \) is the output. f (x, y, a, b) { if (x is 1) y = a; else y = b; } Which one of the following digital logic blocks is the most suitable for implementing this function?

A

Full adder

B

Priority encoder

C

Multiplexor

D

Flip-flop

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19

2014 · General Aptitude (GA) · Logic · Deductive and Inductive Reasoning

Computer Science & Information Technology (CS) 2014 [Session 3]

Let \( A \) be a square matrix of size \( n \times n \). Consider the following pseudocode. What is the expected output? C = 100; for i = 1 to n do for j = 1 to n do { Temp = A[i][j] + C; A[i][j] = A[j][i]; A[j][i] = Temp - C; } for i = 1 to n do for j = 1 to n do output (A[i][j]);

A

The matrix \(A \) itself

B

Transpose of the matrix \(A \)

C

Adding 100 to the upper diagonal elements and subtracting 100 from lower diagonal elements of \(A \)

D

None of the above

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20

2015 · General Aptitude (GA) · Logic · Deductive and Inductive Reasoning

Computer Science & Information Technology (CS) 2015 [Session 1]

The given statement is followed by some courses of action. Assuming the statement to be true, decide the correct option.
Statement:
There has been a significant drop in the water level in the lakes supplying water to the city.
Course of action:
(I) The water supply authority should impose a partial cut in supply to tackle the situation.
(II) The government should appeal to all the residents through mass media for minimal use of water.
(III) The government should ban the water supply in lower areas.

A

Statements I and II follow.

B

Statements I and III follow.

C

Statements II and III follow.

D

All statements follow.

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