1
GATE CSE 2025 Set 1
MCQ (Single Correct Answer)
+2
-0

Consider the following four variable Boolean function in sum-of-product form

$$F\left(b_3, b_2, b_1, b_0\right)=\Sigma(0,2,4,8,10,11,12)$$

where the value of the function is computed by considering $b_3 b_2 b_1 b_0$ as a 4-bit binary number, where $b_3$ denotes the most significant bit and $b_0$ denotes the least significant bit. Note that there are no don't care terms. Which ONE of the following options is the CORRECT minimized Boolean expression for $F$ ?

A
$\bar{b}_1 \bar{b}_0+\bar{b}_2 \bar{b}_0+b_1 \bar{b}_2 b_3$
B
$\bar{b}_1 \bar{b}_0+\bar{b}_2 \bar{b}_0$
C
$\bar{b}_2 \bar{b}_0+b_1 b_2 b_3$
D
$\bar{b}_0 \bar{b}_2+\bar{b}_3$
2
GATE CSE 2025 Set 1
Numerical
+2
-0

Consider the given sequential circuit designed using D-Flip-flops. The circuit is initialized with some value (initial state). The number of distinct states the circuit will go through before returning back to the initial state is _________ . (Answer in integer)

GATE CSE 2025 Set 1 Digital Logic - Sequential Circuits Question 2 English

Your input ____
3
GATE CSE 2025 Set 1
MCQ (Single Correct Answer)
+1
-0.33

$g(.)$ is a function from A to B, $f(.)$ is a function from B to C, and their composition defined as $f(g(.))$ is a mapping from A to C.

If $f(.)$ and $f(g(.))$ are onto (surjective) functions, which ONE of the following is TRUE about the function $g(.)$ ?

A
$g(.)$ must be an onto (surjective) function.
B
$g(.)$ must be a one-to-one (injective) function.
C
$g(.)$ must be a bijective function, that is, both one-to-one and onto.
D
$g(.)$ is not required to be a one-to-one or onto function.
4
GATE CSE 2025 Set 1
MCQ (More than One Correct Answer)
+1
-0

Consider the given system of linear equations for variables $x$ and $y$, where $k$ is a realvalued constant. Which of the following option(s) is/are CORRECT?

$$\begin{aligned} & x+k y=1 \\ & k x+y=-1 \end{aligned}$$

A
There is exactly one value of $k$ for which the above system of equations has no solution.
B
There exist an infinite number of values of $k$ for which the system of equations has no solution.
C
There exists exactly one value of $k$ for which the system of equations has exactly one solution.
D
There exists exactly one value of $k$ for which the system of equations has an infinite number of solutions.
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