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BPharm students at NIILM University benefit from a well-rounded and student-friendly campus environment. The university provides separate hostels for boys and girls, equipped with 24/7 electricity, clean water, hot water during winters, and medical assistance. The academic setup includes smart classrooms, air-conditioned computer labs, and strong Wi-Fi connectivity. With recreational options like indoor-outdoor sports and a hygienic mess, students enjoy both academic focus and a healthy campus lifestyle.

Graduates of the NIILM University BPharm programme can explore a wide range of career opportunities across the pharmaceutical and healthcare sectors. Popular job roles include Pharmacist, Drug Inspector, Clinical Researcher, Medical Representative, and Medical Writer. The average salary ranges from INR 2.5 LPA to INR 5.8 LPA, depending on the profile. With its industry-aligned curriculum, NIILM University equips students with the skills needed for diverse pharmaceutical careers.

The aspirants of BBA in Healthcare at DPSRU must fulfil the course-specific eligibility requirements. Aspirants who are Class 12 or equivalent examination pass from a recognised board with a minimum of 55% aggregate can apply. The students must hold the relevant documents for verification purposes. Further, it must be noted that the mentioned aggregate is as per an unofficial source. Hence, is indicative.

DPSRU BBA fee is cumulative of different components, such as tuition fee, security deposit, etc. Students who get finalised have to pay the fee amount to lock their seats. The total tuition fee for the UG course is INR 1.8 lakh, hostel fee is INR 1.25 lakh, and one-time fee is INR 5,000. It must be noted that the mentioned fee amount is as per the official website/ sanctioning body. It is still subject to revision and hence, is indicative. 

59. We have, tan x= $\frac{-4}{3}$ , x in IInd quadrant.

Since, $\frac{\pi }{2}<x<\pi$

$\frac{\pi }{4}<\frac{x}{2}<\frac{\pi }{2}$

sin $\frac{x}{2}$ , cos $\frac{x}{2}$ , tan $\frac{x}{2}$ are all positive.

Now, sec²x = 1 + tan²x = 1 + ${\left(\frac{-4}{3}\right)}^2$ = 1 + $\frac{16}{9}$ = $\frac{9+16}{9}$ = $\frac{25}{9}$

secx = ±$\frac{5}{3}$

cosx = ±$\frac{3}{5}$ .

cosx = $\frac{-3}{5}$ as x is in IInd quadrant.

Now, 2 sin². = 1 cosx.    [cos 2x = 1 2 sin²x.]

2 sin² $\frac{x}{2}$ = 1 $\left(\frac{-3}{5}\right)$

2 sin² $\frac{x}{2}$ =  1 +$\frac{3}{5}$= $\frac{5+3}{5}$ = $\frac{8}{5}$ .

sin² $\frac{x}{2}$ = $\frac{8}{2\times 5}$ = $\frac{4}{5.}$

Seeing, the University of Toronto is a selective university. International students are required to meet certain admission requirements. One of the most important being the GPA. Minimum grade of 70% in grade 12 (English subject). 

An overall admission average of 75% is important to be considered at this university. 

58. L.H.S = sin 3x + sin 2x - sin x

= sin 3x - sin x + sin 2x.

= 2 cos $\frac{3x+x}{2}$ . sin $\frac{3x-x}{2}$ + sin 2x $\left[?sinA-sinB=2cos\frac{A+B}{2}sin\frac{A-B}{2}\right]$

= 2 cos $\frac{4x}{2}$ sin $\frac{2x}{2}$ + sin 2x.

= 2 cos 2x sin x + 2 sin xcosx        [ $?$ sin 2x = 2sin xcosx]

= 2 sin x [cos 2x + cosx]

= 2 sin x $\left[2cos\frac{2x+x}{2}cos\frac{2x-x}{2}\right]$ $\left[?cosA+cosB=2cos\frac{A+B}{2}cos\frac{A-B}{2}\right]$

= 2 sin x $\left[2.cos\frac{3x}{2}cos\frac{x}{2}\right]$

= 4 sin xcos $\frac{x}{2}$ . cos $\frac{3x}{2}$ = R.H.S.

57. L.H.S. = $\frac{(sin7x+sin5x)+(sin9x+sin3x)}{(cos7x+cos5x)+(cos9x+cos3x)}.$

Using sin A + sin B = 2 sin $\frac{A+B}{2}$ cos $\frac{A-B}{2}$

cos A + cos B = 2 cos $\frac{A+B}{2}$ cos $\frac{A-B}{2}.$

56. L.H.S = sin x + sin 3x + sin 5x + sin 7x.

= (sin x + sin 7x) + (sin 3x + sin 5x)

Using,

sin A + sin B = 2 sin $\frac{A+B}{2}$ cos $\frac{A-B}{2}.$

L.H.S. = 2. Sin $\frac{x+7x}{2}$ cos $\frac{x-7x}{2}$ + 2 sin $\frac{3x+5x}{2}$ cos $\frac{3x-5x}{2}$

= 2 sin $\frac{8x}{2}$ cos $\left(-\frac{6x}{2}\right)$ + 2 sin $\frac{8x}{2}$ cos $\left(-\frac{2x}{2}\right)$

= 2 sin 4x cos 3x + 2 sin 4x cosx.[ $?$ cos (-x) = cosx]

= 2 sin 4x[cos 3x + cosx]

Using cos A + cos B = 2 cos $\frac{\mathrm{A\; +}B}{2}$ cos $\frac{A-B}{2}.$

So, L.H.S. = 2 sin 4x $\left[2·cos\frac{3x+x}{2}cos\frac{3x-x}{2}\right].$

= 2 sin 4x $\left[2·cos\frac{4x}{2}·cos\frac{2x}{2}\right]$

= 4 sin 4x. cos 2x cosx = R.H.S.

Before applying to NIILM University BPharm programme, students should review the curriculum, total tuition fees, eligibility criteria, faculty expertise, and placement assistance. It's also important to compare the programme with other universities in terms of value, infrastructure, and recognition. Checking official updates and student reviews can help make a more informed decision.

55. L.H.S = (cos x-cos y)² + (sin x- sin y)²

= ${\left[-2sin\frac{x+y}{2}sin\frac{x-y}{2}\right]}^2+{\left[2cos\frac{x+y}{2}sin\frac{x-y}{2}\right]}^2$

= 4 sin² $\left(\frac{x+y}{2}\right)$ sin² $\left(\frac{x-y}{2}\right)$ + 4 cos² $\left(\frac{x+y}{2}\right)$ sin² $\left(\frac{x-y}{2}\right)$

= 4 sin² $\left(\frac{x-y}{2}\right)$ $\left[si{n}^2\left(\frac{x+y}{2}\right)+co{s}^2\left(\frac{x+y}{2}\right)\right]$

= 4 $si{n}^2\left(\frac{x-y}{2}\right)$ . [ $?$ sin²∅ + cos²∅= 1]

= R.H.S.

The primary eligibility requirement to get admission into the BArch course at Jindal School of Arts and Architecture is that candidates must complete their Class 12 with PCM/ Diploma with Mathematics. Moreover, candidates must have secured a minimum aggregate of 50%. Additionally, for the selection process, the university accepts the scores of NATA.  

Admission to Somaiya School of Civilisation is entrance based. Candidates are required to appear for SVUET in order to get the chance of securing a seat at the Somaiya School of Civilisation courses. Candidates can choose from the BA and MA programmes for admission based on their eligibility criteria. 
Candidates are required to clear the SVUET cutoff set by the institute for admission into the available courses. 

NIILM University offers the BPharm programme at a tuition fee of INR 2,72,000, which is competitively priced when compared to other institutes in Haryana. For instance, Sushant University charges INR 6 Lakh, while Gurugram University has a similar fee of INR 2.7 Lakh, making NIILM an affordable option for many students.