1
GATE ME 2022 Set 1
MCQ (Single Correct Answer)
+2
-0.66

The value of the integral

$\rm \oint \left( \frac{6z}{2z^4 - 3z^3 + 7 z^2 - 3z + 5} \right) dz$

evaluated over a counter-clockwise circular contour in the complex plane enclosing only the pole z = i, where 𝑖 is the imaginary unit, is

A
(-1 + i) π
B
(1 + i) π
C
2(1 - i) π
D
(2 + i) π
2
GATE ME 2022 Set 1
MCQ (More than One Correct Answer)
+2
-0

The system of linear equations in real (x, y) given by

$\rm \begin{pmatrix} \rm x & \rm y \end{pmatrix} \begin{bmatrix} 2 & 5- 2 α \\\ α & 1 \end{bmatrix} = \rm \begin{pmatrix} \rm 0 & \rm 0 \end{pmatrix} $

involves a real parameter α and has infinitely many non-trivial solutions for special value(s) of α. Which one or more among the following options is/are non-trivial solution(s) of (x, y) for such special value(s) of α ?

A
x = 2, y = −2
B
x = −1, y = 4
C
x = 1, y = 1
D
x = 4, y = −2
3
GATE ME 2022 Set 1
Numerical
+2
-0

Let a random variable X follow Poisson distribution such that

Prob(X = 1) = Prob(X = 2).

The value of Prob(X = 3) is __________ (round off to 2 decimal places).

Your input ____
4
GATE ME 2022 Set 1
Numerical
+2
-0

Consider two vectors

$\rm \vec a = 5 i + 7 j + 2 k $

$\rm \vec b = 3i - j + 6k$

Magnitude of the component of $\vec a$ orthogonal to $\vec b$ in the plane containing the vectors $\vec a$ and $\vec{\bar b}$ is ______ (round off to 2 decimal places).

Your input ____
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