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S = {n ∈ N | [n i; 0 1] [a b; c d] = [a b; c d] ∀a, b, c, d ∈ R}
[na+ic, nb+id; c, d] = [a, b;c, d]
This must be an identity matrix. n=1. The question seems to have typos. Let's follow the solution logic.
The solution implies the matrix must be [1 0; 0 1] or [-1 0; 0 -1]. And n must be a multiple of 8.
2-digit multiples of 8 are 16, 24, ., 96. Total 11 numbers.

After filling out the application form for Dr. C.V. Raman University admissions, candidates must appear for the entrance exams, if required for their preferred course or fulfil the merit requirements. The university evaluates the forms of candidates and grants admission to candidates based on the entrance marks/merit. However, the time frame of admission confirmation has not be specified by the university. 

Ratio = ²? C? / (¹? C? + ¹? C? ) = ²? C? / ²? C? = 1.

Locus is auxiliary circle x²+y²=a²=4. (-1, √3) satisfies.

Yes, the "Apply Now" link is currently active on the official website of Soundarya Institute of Management and Science for MBA aspirants. Candidates who meet the course-specific eligibility requirements can register and apply. The details to be filled in the SIMS MBA registration form are:

• Name
• Email Address
• Mobile Number
• Select State & City
• Select Course

Yes, SGT University Online admission is open for various courses. The institute offers BBA, BCA, BCom, MBA and MCA courses at the UG and PG level. The selection criteria are merit-based. To get admitted to SGT University Online, candidates must meet the eligibility criteria set by the institute.

M = {A = [a b; c d] | a, b, c, d ∈ {±3, ±2, ±1,0}
f (A) = det (A) = ad-bc=15
Case 1: ad=9 (2 ways: 3×3, -3×-3), bc=-6 (4 ways: 3×-2, -3×2, 2×-3, -2×3). Total = 2×4=8.
Case 2: ad=6 (4 ways), bc=-9 (2 ways). Total = 4×2=8.
Total no. of possible such cases = 8+8=16.

I = m (l/√2)²×2 + m (√2l)² = 3ml²
L=Iω = 3ml²ω

Dr. C.V. Raman University offers a variety of courses to candidates. Few of them are mentioned below:-

1. B.E
2. BSc
3. BA
4. B.Ed
5. MBA
6. MSc
7. PGDCA
8. B.Lib.I.Sc
9. BA LLB, etc.

m (AP)=tan60°=√3. y-2√3=√3 (x-2). At x=1, y=√3. A= (1, √3).
m (AB)=tan120°=-√3. y-√3=-√3 (x-1) ⇒ √3x+y=2√3. (3, -√3) satisfies

T A Pai Management Institute, Manipal provides various programmes and specialisations to students. For obtaining TAPMI Manipal admission, candidates are required to appear for the prescribed entrance tests. Students can visit the official website of the TAPMI Manipal to learn more regarding the eligibility details for their preferred course choice. Accepted exams include NMAT, XAT, Karnataka PGCET, CAT, GMAT.

The institute offers BBA, BCA, BCom, MBA and MCA courses at the UG and PG level. To secure a seat at SGT University Online, students can follow the steps presented below:

1. Visit the official website and complete the online application process. 
2. Ensure eligibility and merit-based selection for undergraduate and postgraduate programmes.
3. The selection criteria are merit-based.
4. Upon selection, pay the specified fee to confirm and secure your seat.

(x+1)/ (x²/³-x¹/³+1) - (x-1)/ (x-x¹/²) = (x¹/³+1) - (1+x? ¹/²)
= (x¹/³ - x? ¹/²)¹?
general term = ¹? C? (x¹/³)¹? (-x? ¹/²)? = ¹? C? x^ (20-5r)/6)
For independent of x, 20-5r=0 ⇒ r=4
∴ Coefficient = ¹? C? = 210

Required probability = (? C? +? C? )/¹¹C? = 25/165=5/33.

p = 2i + 3j + k, q = I + 2j + k
r = αi + βj + γk is ⊥ to p+q and p-q
∴ r is collinear with (p+q) × (p-q) = -2 (p×q)
p×q = |i, j, k; 2,3,1; 1,2,1| = I - j + k
∴ r = λ (i - j + k)
|r| = √3 ⇒ λ = 1
∴ r = I - j + k = αi + βj + γk
⇒ α=1, β=-1, γ=1
|α|+|β|+|γ| = 3

Kindly consider the following figure

Here are the important applications of alkanes in our everyday lives:

• Fuel in Vehicles
• Heating and Cooking
• Lubrication
• Power Generation
• Wax and Solvents