1
GATE CE 2023 Set 2
MCQ (Single Correct Answer)
+2
-0.67

The solution of the differential equation

$\rm \frac{d^3y}{dx^3}-5.5\frac{d^2y}{dx^2}+9.5\frac{dy}{dx}-5y=0$

is expressed as 𝑦 = 𝐢1𝑒2.5π‘₯ + 𝐢2𝑒𝛼π‘₯ + 𝐢3𝑒𝛽π‘₯ , where 𝐢1, 𝐢2, 𝐢3, 𝛼, and 𝛽 are constants, with Ξ± and Ξ² being distinct and not equal to 2.5. Which of the following options is correct for the values of 𝛼 and 𝛽?

A
1 and 2
B
βˆ’1 and βˆ’2
C
2 and 3
D
βˆ’2 and βˆ’3
2
GATE CE 2023 Set 2
MCQ (Single Correct Answer)
+2
-0.67
Two vectors [2 1 0 3]𝑇 and [1 0 1 2]𝑇 belong to the null space of a 4 Γ— 4 matrix of rank 2. Which one of the following vectors also belongs to the null space?
A
[1 1 βˆ’1 1]T
B
[2 0 1 2]T
C
[0 βˆ’2 1 βˆ’1]T
D
[3 1 1 2]T
3
GATE CE 2023 Set 2
MCQ (Single Correct Answer)
+2
-0.67

Cholesky decomposition is carried out on the following square matrix [𝐴]. 

$\rm [A]=\begin{bmatrix}8&-5\\\ -5&a_{22}\end{bmatrix}$

Let 𝑙ij and π‘Žij be the (i, j)th elements of matrices [𝐿] and [𝐴], respectively. If the element 𝑙22 of the decomposed lower triangular matrix [𝐿] is 1.968, what is the value (rounded off to the nearest integer) of the element π‘Ž22?

A
5
B
7
C
9
D
11
4
GATE CE 2023 Set 2
MCQ (Single Correct Answer)
+1
-0.33
In the context of Municipal Solid Waste Management, β€˜Haul’ in β€˜Hauled Container System operated in conventional mode’ includes the _________.
A
time spent by the transport truck at the disposal site
B
time spent by the transport truck in traveling between a pickup point and the disposal site with a loaded container
C
time spent by the transport truck in picking up a loaded container at a pickup point
D
time spent by the transport truck in driving from the depot to the first pickup point
EXAM MAP