GATE ME 2022 Set 2 | GATE ME Year Wise Previous Years Questions

GATE ME 2022 Set 2

MCQ (Single Correct Answer)

-0.33

A polynomial ψ(s) = a_nsⁿ + a_n-1s^n-1 + ......+ a₁s + a₀ of degree n > 3 with constant real coefficients a_n, a_n-1, ... a₀ has triple roots at s = -σ. Which one of the following conditions must be satisfied?

ψ(s) = 0 at all the three values of s satisfying s³ + σ³ = 0

ψ(s) = 0, $\frac{d\psi(s)}{ds}=0$ and $\frac{d^2\psi(s)}{ds^2}=0$ at s = -σ

ψ(s) = 0, $\frac{d^2\psi(s)}{ds^2}=0$ and $\frac{d^4\psi(s)}{ds^4}=0$ at s = -σ

ψ(s) = 0, $\frac{d^3\psi(s)}{ds^3}=0$ at s = -σ

GATE ME 2022 Set 2

MCQ (Single Correct Answer)

-0.66

For the exact differential equation,

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

which one of the following is the solution?

u² + 2x² = constant

xu² + u = constant

$\frac{1}{2}x^2u^2+2u$ = constant

$\frac{1}{2}ux^2+2u$ = constant

GATE ME 2022 Set 2

MCQ (More than One Correct Answer)

-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?

The given set of equations will have a unique solution.

The given set of equations will be satisfied by a zero vector of appropriate size.

The given set of equations will have infinitely many solutions.

The given set of equations will have many but a finite number of solutions.

GATE ME 2022 Set 2

Numerical

-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).

Your input ____

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