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for reflexive (x, x)
x³ - 3x²x + 3x³ = 0
. reflexive
For symmetric
(x, y)? R
x³ - 3x²y - xy² + 3y³ = 0
? (x - 3y) (x² - y²) = 0
For (y, x)
(y - 3x) (y² - x²) = 0
? (3x - y) (x² - y²) = 0
Not symmetric

The Nagaland Board of School Education released the NBSE HSLC routine 2026 on December 1, 2025. Based on the released date, the board will hold the Nagaland Board 10th exams from February 13 to February 26, 2026. As the official dates are out, we have updated the same here. Stay connected for the latest update on the same.

Yes, the University of Portsmouth actively encourages its students to gain hands-on work experience. The internships at the university are advertised in the Autumn, and students can even partake in Summer internships. Moreover, these work experience opportunities are personalized as per one's major and specializations, making the students more skilled in their respective fields through practical experience. Some of the schemes include the Business and Management mentoring scheme for MBA/BBA students, and the Accounting and Finance Mentoring Scheme for accounting and finance students. 

$\left|\widehat{A}+\widehat{B}\right|=\sqrt[]{A^2+B^2+2ABcos\theta }$

$=\sqrt[]{1+1+2cos\theta }$

$=\sqrt[]{2\left(1+cos\theta \right)}$

= $\sqrt[]{2\times 2co{s}^2\raisebox{1ex}{$\theta $}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$

$\left|\widehat{A}+\widehat{B}\right|=2cos\raisebox{1ex}{$\theta $}\!\left/ \!\raisebox{-1ex}{$2$}\right.$  -(1)

$\left|\widehat{A}-\widehat{B}\right|=\sqrt[]{A^2+B^2-2ABcos\theta }$

$=\sqrt[]{1+1-2cos\theta }$

$=2sin\raisebox{1ex}{$\theta $}\!\left/ \!\raisebox{-1ex}{$2$}\right.$  -(2)

(2) $÷$ $$ (1)

$\frac{\left|\widehat{A}-\widehat{B}\right|}{\left|\widehat{A}+\widehat{B}\right|}=\frac{2sin\raisebox{1ex}{$\theta $}\!\left/ \!\raisebox{-1ex}{$2$}\right.}{2cos\raisebox{1ex}{$\theta $}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$

$\Rightarrow \left|\widehat{A}-\widehat{B}\right|=\left|\widehat{A}+\widehat{B}\right|tan\raisebox{1ex}{$\theta $}\!\left/ \!\raisebox{-1ex}{$2$}\right.$

NTR University of Health Sciences is affiliated with more than 80 colleges that offer BSc courses, and the total number of seats offered for the courses is around 5,123, from, two of the affiliated colleges offer the highest number of seats in the BSc course. Check out the name of the affiliated college with the number of offered seats in the table below:

⇒3αβ−2αβ=−1
⇒2αβ=4⇒αβ=2 . (i)
b.c=10
⇒−3α−2β−α=10
⇒4α+2β=−10
⇒2α+β=−5 . (ii)
From (i) and (ii)
α=−1/2, α=−2
β=−4, β=−1
a=i−2j−k
b=3i−2j+2k
c=2i−2j+k
a. (b×c)=9

Portsmouth University is considered on of the top universities of the UK and has housed several notable personalities. Some of the notable alumni of the University of Portsmouth include Ben Fogle (Broadcaster), Grayson Perry (Artist), Timothy Nigel Peake (Retired Astronaut), Simon Armitage (Poet/Novelist), Lauren Steadman (Swimmer), Martin Whitmarsh (Businessman), Saeid Zibakalam (Activist), Ron Davies (Politician), Andrea Byrne (Journalist), Rizwan Khan (Broadcaster), Laycon (Rapper/Singer), and John Akomfrah (Artsit/Screenwriter).

e? dy = e? /α dx
⇒−e? =e? /α+c
y (ln2)=ln2 and y (0)=−ln2
⇒−2=−1/α+c
⇒c=−2−1/α
⇒e? = 1/α e? −2−1/α
⇒−e? ² = 1/α e? ²−2−1/α
⇒2? ¹=3/α
⇒α=2

The future perfect tense follows a simple structure. To form a sentence using the future perfect tense, we use will + have + past participle of the verb. Look at the following example to understand the rule of future perfect tense better:

• He will have driven 10 miles by 2 PM.
• Sharon will have slept for three hours by the time we reach the beach.
• You will have baked the cupcake by dinner time.

Equation of the ellipse
(x−3)²/a² + (y+4)²/b² = 1
a=2
ae=1⇒e=1/2
⇒b²=3
Equation of tangent
y+4=m (x−3)±√4m²+3
⇒mx−y=4+3m±√4m²+3
⇒3m±√4m²+3=0
⇒9m²=4m²+3
⇒5m²=3

A² = [1 2 3; 0 1 2; 0 1]
A³=A².A= [1 3 6; 0 1 3; 0 1]
A²? = [1 20 1+2+3.20; 0 1 20; 0 1] = [1 20 210; 0 1 20; 0 1]
M= [20 210 520; 0 20 210; 0 20]
M (a? )=T? =n (n+1)/2
S? = 1/2 [ n (n+1) (2n+1)/6 + n (n+1)/2 ]
⇒S? =1540
⇒M=2020

The future perfect tense is used when expressing an action or event that will have been completed at a specific future time. The event or action being talked about in the future perfect tense has a specified deadline. 

Example:

• I will have completed this task by tomorrow.

∫? ^ (π/2) sin³x e? sin²? dx
=∫? ^ (π/2) (1−cos²x)sinx e? (¹? cos²? )dx
=2∫? ^ (π/2) (1−cos²x)sinx e? (¹? cos²? )dx
Let cos²x=t⇒sin2xdx=−dt
=−2∫? (1−t)e? (¹? ) dt/ (−2cosx)
=1/e ∫? e? dt −∫? te? dt
=1/e [e? ]? − [te? −e? ]?
=2e−3∫? ¹ √t e? dt
⇒α=2, β=3
α+β=5

A= {1,2,3,4,5.100}
B= {4,7,10,13,16,19.}
C= {2,4,6,8,10.}
B−C= {7,13,19, .97}
A∩ (B−C)= {7,13,19, .97}
sum of elements=832

The University of Portsmouth placement rate stands at 85.5% as of 2025, and 98% of graduates are employed or continuing their education, as per official sources. Moreover, as per the HESA graduate outcome survey, in 2023, 68% of the PG students and 58% of UG students were employed full-time. The University of Portsmouth average salary stands at INR 35.9L, and the graduates of Portsmouth can potentially get employed by top recruiters such as Warner Brothers Film Studios, BBC, Royal Navy, and Portsmouth City Council.

Business and Management Studies courses at the Dubai campus are not separately accredited by professional bodies. The Birla Institute of Technology and Science, Dubai, is accredited as a whole by international professional bodies. The university is licensed and accredited by KHDA, Government of Dubai. BITS Pilani, Dubai Campus is rated 5 stars by KHDA in partnership with QS in 2019. Dubai campus offers only those courses that are authorized by the University Grants Commission (UGC), India.