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First we arrange 5 red cubes in a row and assume x? , x? , x? , x? , x? and x? number of blue cubes between them
Here, x? + x? + x? + x? + x? + x? = 11
and x? , x? , x? , x? ≥ 2
so x? + x? + x? + x? + x? + x? = 3
No. of solutions =? C? = 56

|adj (adj (A)| = |A|? ¹² = |A|?
|A| = | (14, 28, -14), (-14, 28), (25, -14, 14) |
= (14)² | (1, 2, -1), (-1, 2), (25/14, -1, 1) |
= (14)² (3–2 (–5)–1 (–1)
|A|? = (14)? => |A| = 14²

To apply for the BSc course offered at Karnataka State Open University, one must satisfy the preset admission criteria as specified by the university/ governing body. To be eligible for the BSc course offered at KSOU, one must meet the following conditions:

• Class 12 in the Science stream from any recognised board or
• Any other equivalent examinations in the Science stream

Y = A·B + B·C
(i) o to t? A = 0, B = 0, C = 1
(ii) Y = 0.0 + 0.1 = 0 + 1 = 1
(ii) t? to t? A = 1, B = 0, C = 1 Y = 1.0 + 0.1 = 0 + 1 = 1
(iii) t? to t? A = 0, B = 1, C = 0 Y = 0.1 + 0.1 = 0 + 1 = 1

Let e? = t then equation reduces to
t³ – 11t – 45/t + 81/t² = 0
=> 2t? – 22t³ + 81t – 45 = 0 . (i)
If roots of
e³? – 11e²? – 45e? + 81/2 = 0
=> α? + α? + α? = ln45 => p = 45

Candidates after getting admission at Annamalai University DDE can download the soft copy of study material from the university's website. The syllabus and self learning study materials for the programme is supplied during the time of admission. For the second, third and fourth semesters/ years, the self-learning study material is dispatched by CDOE via post on receipt of the tuition fee for respective years. Students should also have paid the fees in full for the
previous years to get the study material.

YBN University BSc admission can be granted based on the applicants performance in Class 12 or equivalent examination. Thus, the performance in Class 12 can be evaluated. The university may offer entrance-based admission as well in some of the specialisations. It can accept university/ state/ national-level entrance exams. Hence, scores of CUET may get accepted. Besides, it is crucial that the course aspirants meet the prescribed eligibility requirements. 

f (x) = 2e²? / (e²? +e? ) and f (1-x) = 2e²? / (e²? +e¹? )
∴ f (x) + f (1-x) = 1/2
i.e. f (x) + f (1-x) = 2
∴ f (1/100) + f (2/100) + . + f (99/100)
Σ? f (x/100) + f (1-x/100) + f (1/2)
= 49 x 2 + 1 = 99

| p | q | p^q | ¬ (p^q) | (¬ (p^q)vq | pvq | p? q | p? (pvq) |
|-|-|-|-|-|-|-|-|
| T | T | T | F | T | T | T | T |
| T | F | F | T | T | T | F | T |
| F | T | F | T | T | T | T | T |
| F | F | F | T | T | F | T | T |
Tautology, Tautology

sin? ¹ (√3/2) + cos? ¹ (-√3/2) + tan? ¹ (-1)
= π/3 + 5π/6 – π/4
= (4π+10π–3π)/12 = 11π/12

Annamalai University DDE provides exemption from payment of tuition fee, special fees and alumni fees to differently-abled students including those visually challenges residing in Tamil Nadu. Aspirants must submit Disability Certificate issued by the District Welfare Officer for the Differently Abled Citizens. However, they are required to pay other prescribes fees such as admission fee, registration fees, eligibility fee, postage, PCP fee, etc.

(cos (2π/7) + cos (4π/7) + cos (6π/7)/ (sin (3π/7)cos (π/7) = (2sin (π/7)cos (2π/7) + 2sin (π/7)cos (4π/7) + 2sin (π/7)cos (6π/7)/ (2sin (π/7)
= (sin (3π/7)-sin (π/7) + sin (5π/7)-sin (3π/7) + sin (π)-sin (5π/7)/ (2sin (π/7) = (-sin (π/7)/ (2sin (π/7) = -1/2

Given P (X=3) = 5P (X=4) and n=7
=>? C? p³q? = 5? C? p? q³
=> q = 5p and also p + q = 1
=> p = 1/6 and q = 5/6
Mean = 7/6 and variance = 35/36
Mean + Variance
= 7/6 + 35/36 = 77/36

V = ir
i = V/r
i = (1/r) [v is same for r? & r? ]
i? /i? = r? /r?
i? = (r? / (r? +r? )i?
i? /i? = r? / (r? +r? )