Lecturer Mathematics Past Paper 03-06-2023 by SPSC

Q11: If Hessian Matric H is zero at any point, then the point is called?

Parabolic

Elliptic

Hyperbolic

None of these

Q12: As u = (2, -2, 3) and v = (1, -3, 4), then ||-2u + 2v|| is ______?

2√3

√2

√3

None of these

Calculation: First, compute -2u + 2v:−2u=(−4,4,−6)−2u=(−4,4,−6)2v=(2,−6,8)2v=(2,−6,8)−2u+2v=(−4+2,4−6,−6+8)=(−2,−2,2)−2u+2v=(−4+2,4−6,−6+8)=(−2,−2,2)

Explanation

Calculation: First, compute -2u + 2v:
- $- 2 u = (- 4, 4, - 6)$
- $2 v = (2, - 6, 8)$
- $- 2 u + 2 v = (- 4 + 2, 4 - 6, - 6 + 8) = (- 2, - 2, 2)$
Norm Calculation: The norm (magnitude) of $- 2 u + 2 v$ is:
$∣ ∣ - 2 u + 2 v ∣ ∣ = \sqrt{(- 2)^{2} + (- 2)^{2} + 2^{2}} = \sqrt{4 + 4 + 4} = \sqrt{12} = 2 \sqrt{3}$

Answer:

Q13: Y = 5x and dx/dt = 2 the day/dt will be _____?

12

11

10

None of these

Q14: Average rate of change of function f(x)=x ^3 +1 over the interval [2,3] will be?

21

20

19

None of these

Q15: Choose the correct spelling: Invairunment, Environmen, Enwironment, Environment

Invairunment

Environmen

Enwironment

Environment

Q16: If every element of a group G is its own inverse then G is called?

Cyclic

Abelian

Finite

None of these

Explanation

If every element of a group $G$ is its own inverse, then $g^2 = e$ for all $g in G$ , meaning all elements are of order 2.

Such a group is Abelian because the group operation commutes: $(gh)^2 = e$ implies $g$ and $h$ must commute.

Q17: An experiment consists of throwing a die and the drawing a letter at random from the English alphabet. Then total number of points in sample space will be?

18

144

156

None of these

Q18: From the data 3.4, 2.5, 4.8, 2.9, 3.6, 2.8, 3.3, 5.6, 3.7, 2.8, 4.4, 4.0, 5.2, 3.0, 4.8, the sample median will be?

2.9

3.7

3.6

None of these

Arrange Data in Ascending Order:2.5,2.8,2.8,2.9,3.0,3.3,3.4,3.6,3.7,4.0,4.4,4.8,4.8,5.2,5.62.5,2.8,2.8,2.9,3.0,3.3,3.4,3.6,3.7,4.0,4.4,4.8,4.8,5.2,5.6

Explanation

Arrange Data in Ascending Order:
$2.5, 2.8, 2.8, 2.9, 3.0, 3.3, 3.4, 3.6, 3.7, 4.0, 4.4, 4.8, 4.8, 5.2, 5.6$
Find Median:
- There are 15 data points (odd number), so the median is the 8th value in the ordered list.
- The 8th value is 3.6.

Q19: Choose the correct spelling: Eliminete, Eliminate, Eleminate, Elementate

Eliminete

Eliminate

Eleminate

Elementate

Q20: Let S be a set. An order on S is a relation denoted by?

≥

≤

≠

None of these