NIMCET Boolean algebra Previous Year Question Paper and Solution with PDF

Consider the following minterm for F:F(P, Q, R, S) = Σ0, 2, 5, 7, 8, 10, 13, 15. The minterms 2, 7, 8, and 13 are don't care terms. The minimal sum of products form for F is

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NIMCET Previous Year PYQNIMCET NIMCET 2023 PYQ

Solution

Qus : 7NIMCET PYQ

Cosider the following Boolean Expression for F:

$F(P,Q,R,S)=PQ+\overline{P}QR+\overline{P}Q\overline{R}S$ .

The minimum sum of products form of F is

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NIMCET Previous Year PYQNIMCET NIMCET 2023 PYQ

Solution

Qus : 8NIMCET PYQ

The number of minterms in a $n$ variable truth tableis

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NIMCET Previous Year PYQNIMCET NIMCET 2023 PYQ

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Qus : 9NIMCET PYQ

Let $\oplus$ and $\odot$ denote the Exclusive - OR and Exclusive-NOR operations respectively. Which of the following is not correct?

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NIMCET Previous Year PYQNIMCET NIMCET 2023 PYQ

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Qus : 10NIMCET PYQ

The reduced form of the Boolean function $F=xyz+xyz^{\prime}^{}+x^{\prime}yz+xy^{\prime}z$ is

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NIMCET Previous Year PYQNIMCET NIMCET 2023 PYQ

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Qus : 11NIMCET PYQ

How many Boolean expressions can be be formed with 3 Boolean variables?

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NIMCET Previous Year PYQNIMCET NIMCET 2019 PYQ

Solution

Qus : 12NIMCET PYQ

The minimum number of NAND gates required for implementing the Boolean expression $AB+A\, \overline{B}C+A\, \overline{B}\, \overline{C}$

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Solution

$AB+A\, \overline{B}C+A\, \overline{B}\, \overline{C}$

=$AB+AB'C+AB'C'$

=$AB+AB'(C+C')$

=$AB+AB'$

=$A(B+B')$

Qus : 13NIMCET PYQ

Which of the following is equivalent to the Boolean expression:

$(X+Y).(X+\overline{Y}).(\overline{X}+Y)$

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NIMCET Previous Year PYQNIMCET NIMCET 2022 PYQ

Solution

$(X+Y).(X+\overline{Y}).(\overline{X}+Y)$

=$(X+Y)(X+Y')(X'+Y)$

=$(XX+XY+YX+YY')(X'+Y)$

=$(X+XY)(X'+Y)$

=$X(1+Y)(X'+Y)$

=$X(X'+Y)$

=$XX'+XY$

=$XY$

Qus : 14NIMCET PYQ

Write the simplified form of the Boolean expression

(A+C)(AD+AD')+AC+C

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NIMCET Previous Year PYQNIMCET NIMCET 2022 PYQ

Solution

(A+C)(AD+AD')+AC+C

=(A+C)A(D+D')+C(A+1)

=(A+C)+C

=A+C

Qus : 15NIMCET PYQ

The Boolean expression AB+ AB' + A'C + AC is unaffected by the value of the Boolean variable

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NIMCET Previous Year PYQNIMCET NIMCET 2022 PYQ

Solution

$\begin{array}{ll}{A(B+\overline{B})+C(A+\overline{A})} \\ {A+C}\, \end{array}$

Qus : 16NIMCET PYQ

If a signal passing through a gate is inhibited by sending a low into one of the inputs, and the output is HIGH, the gate is a(n):

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NIMCET Previous Year PYQNIMCET NIMCET 2022 PYQ

Solution

Output is high if any of the input is low. The truth table for NAND gate is:

A	B	Output
0	0	0
0	1	1
1	0	1
1	1	1

Table representing NAND Gate.

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