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Yes, they can be used for a singular person, and this usage is both grammatically correct and widely accepted in Modern English. Known as singular 'they', it is commonly used when the gender of a person is unknown, irrelevant, or when referring to someone who identifies as non-binary.

Singular 'they' has been used by well-known authors like Shakespeare and Jan Austen in their works. It helps avoid awkward or gendered language and has become a practical choice in both spoken and written English.

Example: Someone left their phone on the table.

Yes, you can get direct admission at Apollo Institute of Nursing via the management quota. The institute offers BSc in Nursing in full-time mode through the Akhil Gujarat Self-Financed Nursing Colleges Management Association. Interested students can visit the official website of the institute to learn all about the admission critreia and process including the admission chances. Alternatively, students can also connect with the admission counsellors of the institute to learn more.

$L_1:4x+3y+2=0$  

$L_2:3x-4y-11=0$               

Since circle C touches the line L2 at Q intersection point L1 and L2 is (1, -2)

P lies of L₁

$\therefore P\left(x,-\frac{1}{3}\left(2+4x\right)\right)$               

Now,

PQ = 5 ? (x – 1)² + ${\left(\frac{4x+2}{3}-2\right)}^2=25$  

$\Rightarrow x=4,-2$                     

$?$ The circle lies below the axis

y = -6

p (4, -6)

Now distance of P from 5x – 12 y + 51 = 0

$=\left|\frac{20+72+51}{13}\right|=\frac{143}{13}=11$                

$x^2-3x+p=0$

$\alpha ,\beta ,\gamma ,\delta$ in G.P.

$\alpha +\alpha r=3$

$x^2-6x+q=0$

$\alpha r^2+\alpha r^3=6$

$\left(2\right)÷\left(1\right)\Rightarrow r^2=2$

So,  $\frac{2q+p}{2q-p}=\frac{2r^5+r}{2r^5-r}=\frac{2r^4+1}{2r^4-1}=\frac{9}{7}$

Ranking comes from many things like infrastructure, student-faculty ratio, lab facilities, research, scholarships and student feedback. If these are all good then ranking goes up . Students can check these points before picking Uka Tarsadia BTech seat.

The course duration for the UG Diploma programmes at Skyward College of Aviation and Hotel Management are as follows: 

Diploma in Hotel Management: One year

Diploma in Airport Ground service, Hotel Management, Travel and Tourism: One year

Candidates are required to pay the course fee and secure their seats once they get the final admission offer. 

Hi, yes you can definitely pursue BSc in Biotechnology without any entrance exam as most of the colleges accept students on merit basis. You can also pursue BSc in Biotechnology by appearing for entrance exams like TS EAMCET, CUET, SAT India, etc.

There are approximately 60 best B Pharma university in the Delhi NCR region. Some of them are mentioned below along with their tuition fees:

Disclaimer: This information is sourced from official website.

Personal pronouns and possessive adjectives are closely related, but they serve different grammatical roles in a sentence. Possessive pronouns replace a noun, for example: This book is mine, whereas possessive adjectives comes before a noun, example: This is my book.

$\left(1-x^2\right)dy=\left(xy+\left(x^3+2\right)\sqrt[]{1-x^2}\right)dx$

$\therefore \frac{dy}{dx}-\frac{x}{1-x^2}y=\frac{x^3+3}{\sqrt[]{1-x^2}}$

$\therefore l.F.=e^{{\displaystyle \int \frac{X}{1-x^2}dx}}=\sqrt[]{1-x^2}$

$\therefore y\left(x\right)=\frac{x^4+12x}{4\sqrt[]{1-x^2}}$

$\therefore {\displaystyle \underset{\frac{-1}{2}}{\overset{\frac{1}{2}}{\int }}\sqrt[]{1-x^2}y\left(x\right)dx={\displaystyle \underset{\frac{-1}{2}}{\overset{\frac{1}{2}}{\int }}\left(\frac{x^4+12x}{4}\right)}dx}$

$\therefore k=\frac{1}{320}$

$\therefore k^{-1}=320$

Yes ranking matter because it tells how well college maintain study quality, labs, teachers and placements. Many recruiters also see from where you did BTech, so good ranking helps you stand out when you apply for job.

Uka Tarsadia BTech ranking 2025 is mostly good as university got NAAC B+ grade. It means they doing decent job in academics, labs and overall campus. But students should check the latest NIRF or other rankings too for fresh information every year.

TAPMI Manipal offers admission to various courses such as MBA and BBA on the basis of merit and valid entrance scores. The Institute provides admission to MBA on the basis of various accepted entrance exams such as CAT/ XAT/ GMAT/ NMAT and other equivalent exams along with group discussion and personal interview. Apart from this, candidates must secure a minimum aggregate of 50% in graduation.

Area of shaded region

$={\displaystyle {\int }_{-\left(\frac{1}{2}\right)}^0\frac{3}{2}\left({\left(1-x^{\frac{2}{3}}\right)}^{\frac{3}{2}}+x\right)dx+{\displaystyle {\int }_0^1{\left(1-x^{\frac{2}{3}}\right)}^{\frac{3}{2}}dx}}$

$x=si{n}^3\theta$

$\therefore dx=3si{n}^2\theta cos\theta d\theta$

$={\displaystyle {\int }_{-\frac{\pi }{4}}^{\frac{\pi }{2}}3si{n}^2\theta co{s}^4\theta d\theta +\left(0-\frac{1}{16}\right)}$

$=\frac{9\pi }{64}+\frac{1}{16}-\frac{1}{16}=\frac{36\pi }{256}=A$

$\therefore \frac{256A}{\pi }=36$

The UG Diploma specialisations offered by Skyward College of Aviation and Hotel Management are as follows: 

$?y\left(x\right)={\left(x^x\right)}^x$

$\therefore y=x^{x^2}$

$\therefore \frac{dy}{dx}=x^2.x^{x^2-1}-x^{x^2}\mathcal{l}nx.2x$

$\therefore \frac{dx}{dy}=\frac{1}{x^{x^2+1}\left(1+2lnx\right)}$ ….(i)

$\frac{d^{2}x}{dx}=\frac{d}{dx}\left({\left(x^{x^2+1}\left(1+2lnx\right)\right)}^{-1}\right).\frac{dx}{dy}$

$\begin{array}{l}{\left(\frac{d^{2}x}{d{y}^2}\right)}_{x=1}=-4\\ {\left(\frac{d^{2}x}{d{y}^2}\right)}_{x=1}+20=16\end{array}$

 $f\left(x\right)=\left[1+x\right]+\frac{{\alpha }^{2\left|x\right|}+\left\{x\right\}+\left[x\right]-1}{2\left[x\right]+\left\{x\right\}}$

$li{m}_{x\to 0}-f\left(x\right)=\alpha -\frac{4}{3}$

$\Rightarrow li{m}_{h\to 0}1-1+\frac{{\alpha }^{-h-1}-1-1}{-h-1}=\alpha -\frac{4}{3}$

$\therefore \frac{{\alpha }^{-1}-2}{-1}\alpha -\frac{4}{3}$

32 - 10 + 3 = 0

$\therefore \alpha =3or1/3$

$?\alpha$ in integer, hence = 3