1
GATE ME 2024
MCQ (Single Correct Answer)
+1
-0.33

Consider the system of linear equations

x + 2y + z = 5

2x + ay + 4z = 12

2x + 4y + 6z = b

The values of a and b such that there exists a non-trivial null space and the system admits infinite solutions are

A

a = 8, b = 14

B

a = 4, b = 12

C

a = 8, b = 12

D

a = 4, b = 14

2
GATE ME 2023
Numerical
+1
-0

A linear transformation maps a point (π‘₯, 𝑦) in the plane to the point (π‘₯Μ‚, 𝑦̂) according to the rule

π‘₯Μ‚ = 3𝑦, 𝑦̂ = 2π‘₯.

Then, the disc π‘₯2 + 𝑦2 ≀ 1 gets transformed to a region with an area equal to _________ . (Rounded off to two decimals)

Use Ο€ = 3.14. 

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3
GATE ME 2022 Set 1
MCQ (Single Correct Answer)
+1
-0.33
If A = $\begin{bmatrix} 10 & 2k + 5 \\\ 3k - 3 & k + 5 \end{bmatrix} $ is a symmetric matrix, the value of k is _______.
A
8
B
5
C
-0.4
D
$\frac{1 + \sqrt{1561}}{12}$
4
GATE ME 2017 Set 2
Numerical
+1
-0
The determinant of a $$2 \times 2$$ matrix is $$50.$$ If one eigenvalue of the matrix is $$10,$$ the other eigenvalue is __________.
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