1
GATE CSE 2025 Set 2
MCQ (More than One Correct Answer)
+2
-0

Which of the following Boolean algebraic equation(s) is/are CORRECT?

A
$\bar{A} B C+A \bar{B} \bar{C}+\bar{A} \bar{B} \bar{C}+A \bar{B} C+A B C=B C+\bar{B} \bar{C}+\bar{A} \bar{B}$
B
$A B+\bar{A} C+B C=A B+\bar{A} C$
C
$(A+C)(\bar{A}+B)=A B+\bar{A} C$
D
$\overline{(A+\bar{B}+\bar{D})(C+D)(\bar{A}+C+D)(A+B+\bar{D})}=\bar{A} D+\bar{C} \bar{D}$
2
GATE CSE 2025 Set 2
MCQ (Single Correct Answer)
+1
-0.33

If $A=\left(\begin{array}{cc}1 & 2 \\ 2 & -1\end{array}\right)$, then which ONE of the following is $A^8$ ?

A
$\left(\begin{array}{cc}25 & 0 \\ 0 & 25\end{array}\right)$
B
$\left(\begin{array}{cc}125 & 0 \\ 0 & 125\end{array}\right)$
C
$\left(\begin{array}{cc}625 & 0 \\ 0 & 625\end{array}\right)$
D
$\left(\begin{array}{cc}3125 & 0 \\ 0 & 3125\end{array}\right)$
3
GATE CSE 2025 Set 2
MCQ (Single Correct Answer)
+1
-0.33

The value of $x$ such that $x>1$, satisfying the equation $\int_1^x t \ln t d t=\frac{1}{4}$ is

A
$\sqrt{e}$
B
$e$
C
$e^2$
D
$e-1$
4
GATE CSE 2025 Set 2
MCQ (Single Correct Answer)
+1
-0.33

Let $L, M$, and $N$ be non-singular matrices of order 3 satisfying the equations $L^2=L^{-1}, M=L^8$ and $N=L^2$. Which ONE of the following is the value of the determinant of $(M-N)$ ?

A
0
B
1
C
2
D
3
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