1
GATE EE 2025
MCQ (Single Correct Answer)
+1
-0.33

Consider the set $S$ of points $(x, y) \in R^2$ which minimize the real valued function

$$ f(x, y)=(x+y-1)^2+(x+y)^2 $$

Which of the following statements is true about the set $S$ ?

A
The number of elements in the set $S$ is finite and more than one.
B
The numebr of elements in the set $S$ is infinite.
C
The set $S$ is empty.
D
The number of elements in the set $S$ is exactly one.
2
GATE EE 2025
MCQ (Single Correct Answer)
+1
-0.33
Let $v_1$ and $v_2$ be the two eigen vectors corresponding to distinct eigen values of a $3 \times 3$ real symmetric matrix. Which one of the following statements is true?
A
$v_1^T v_2 \neq 0$
B
$v_1^T v_2=0$
C
$v_1+v_2=0$
D
$v_1-v_2=0$
3
GATE EE 2025
MCQ (Single Correct Answer)
+1
-0.33

Let $A=\left[\begin{array}{ccc}1 & 1 & 1 \\ -1 & -1 & -1 \\ 0 & 1 & -1\end{array}\right]$ and $b=\left[\begin{array}{c}1 / 3 \\ -1 / 3 \\ 0\end{array}\right]$, then the system of linear equations $A x=b$ has

A
a unique solution
B
infinitely many solutions
C
a finite number of solutions
D
no solution
4
GATE EE 2025
MCQ (Single Correct Answer)
+1
-0.33

Let $P=\left[\begin{array}{ccc}2 & 1 & 0 \\ -1 & 0 & 0 \\ 0 & 0 & 1\end{array}\right]$ and let $I$ be the identity matrix. Then $P^2$ is equal to

A
$2 P-I$
B
$P$
C
$I$
D
$P+I$
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