1
GATE ME 2022 Set 2
MCQ (Single Correct Answer)
+1
-0.33
A polynomial ψ(s) = ansn + an-1sn-1 + ......+ a1s + a0 of degree n > 3 with constant real coefficients an, an-1, ... a0 has triple roots at s = -σ. Which one of the following conditions must be satisfied?
A
ψ(s) = 0 at all the three values of s satisfying s3 + σ3 = 0
B
ψ(s) = 0, $\frac{d\psi(s)}{ds}=0$ and $\frac{d^2\psi(s)}{ds^2}=0$ at s = -σ
C
ψ(s) = 0, $\frac{d^2\psi(s)}{ds^2}=0$ and $\frac{d^4\psi(s)}{ds^4}=0$ at s = -σ
D
ψ(s) = 0, $\frac{d^3\psi(s)}{ds^3}=0$  at s = -σ
2
GATE ME 2022 Set 2
MCQ (Single Correct Answer)
+2
-0.66

For the exact differential equation,

$\frac{du}{dx}=\frac{-xu^2}{2+x^2u}$

which one of the following is the solution?

A
u2 + 2x2 = constant
B
xu2 + u = constant
C
$\frac{1}{2}x^2u^2+2u$ =  constant
D
$\frac{1}{2}ux^2+2u$  = constant
3
GATE ME 2022 Set 2
MCQ (More than One Correct Answer)
+2
-0
A is a 3 × 5 real matrix of rank 2. For the set of homogeneous equations Ax = 0, where 0 is a zero vector and x is a vector of unknown variables, which of the following is/are true?
A
The given set of equations will have a unique solution.
B
The given set of equations will be satisfied by a zero vector of appropriate size.
C
The given set of equations will have infinitely many solutions.
D
The given set of equations will have many but a finite number of solutions.
4
GATE ME 2022 Set 2
Numerical
+2
-0
If the sum and product of eigenvalues of a 2 × 2 real matrix $\begin{bmatrix}3&p\\\ p&q\end{bmatrix} $ are 4 and -1 respectively, then |p| is _______ (in integer).
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