A four-variable Boolean function is realized using
4 $$ \times $$ 1
multiplexers as shown in the
figure.
The minimized expression for F(U, V, W, X)
is
A
$$\left( {UV + \overline U \overline V } \right)\overline W $$
B
$$\left( {UV + \overline U \overline V } \right)\left( {\overline W \overline X + \overline W X} \right)$$
C
$$\left( {U\overline V + \overline U V} \right)\overline W $$
D
$$\left( {U\overline V + \overline U V} \right)\left( {\overline W \overline X + \overline W X} \right)$$
2
GATE ECE 2018
MCQ (Single Correct Answer)
+1
-0.33
A function F(A, B, C) defined by three Boolean variables A, B and C when expressed as sum
of products is given by
F = $$\overline A .\overline B .\overline C + \overline A .B.\overline C + A.\overline B .\overline C $$
where, $$\overline A $$, $$\overline B $$, and $$\overline C $$ are the complements of the respective variables. The product of sums
(POS) form of the function F is
A
F = (A + B + C)(A + $$\overline B $$ + C)($$\overline A $$ + B + C)
B
F = ($$\overline A $$ + $$\overline B $$ + $$\overline C $$)($$\overline A $$ + B + $$\overline C $$)(A + $$\overline B $$ + $$\overline C $$)
C
F = (A + B + $$\overline C $$)(A + $$\overline B $$ + $$\overline C $$)($$\overline A $$ + B + $$\overline C $$)($$\overline A $$ + $$\overline B $$ + C)($$\overline A $$ + $$\overline B $$ + $$\overline C $$)
D
F = ($$\overline A $$ + $$\overline B $$ + C)($$\overline A $$ + B + C)(A + $$\overline B $$ + C)(A + B + $$\overline C $$)(A + B + C)
3
GATE ECE 2018
MCQ (Single Correct Answer)
+1
-0.33
Let
M
be a real
4 $$ \times $$ 4
matrix. Consider the following statements :
S1:
M
has
4
linearly independent eigenvectors.
S2:
M
has
4
distinct eigenvalues.
S3:
M
is non-singular (invertible).
Which one among the following is TRUE?
A
S1 implies S2
B
S2 implies S1
C
S1 implies S3
D
S3 implies S2
4
GATE ECE 2018
Numerical
+1
-0
Consider matrix $$A = \left[ {\matrix{
k & {2k} \cr
{{k^2} - k} & {{k^2}} \cr
} } \right]$$ and
